
412 Mass. 545 (1992)
591 N.E.2d 165
COMMERCIAL UNION INSURANCE COMPANY & others[1]
vs.
BOSTON EDISON COMPANY.
Supreme Judicial Court of Massachusetts, Suffolk.
January 8, 1992.
April 27, 1992.
Present: LIACOS, C.J., ABRAMS, LYNCH, O'CONNOR, & GREANEY, JJ.
Francis H. Fox (Robert A. Miley with him) for the plaintiffs.
George E. Richardson for the defendant.
ABRAMS, J.
The plaintiffs, former coowners of the building at One Beacon Street in Boston (building), brought an action for breach of contract and restitution for money paid by mutual mistake against the Boston Edison Company (Edison), claiming that Edison had overcharged them for steam usage at the building between January, 1974, and January 10, 1979. Edison, alleging that the overcharge was the result of the plaintiffs' improper installation of the steam metering system in the building, and that the plaintiffs had refused to accept Edison's reasonable settlement offer for the overcharge, asserted a counterclaim for violation of G.L.c. 93A (1990 ed.). The judge dismissed Edison's counterclaim before trial for failure to state a claim on which relief could be granted, and denied Edison's motion for leave to file an amended counterclaim. At trial, the judge directed a verdict for the plaintiffs on liability on their restitution claim, and the jury awarded damages of $650,000 on that claim. The jury found for Edison on the plaintiffs' contract claim. The judge entered final judgment on the plaintiffs' jury verdict in the amount of $1,590,371. We allowed Edison's application for direct review. On appeal, Edison claims errors based on the admission in evidence of a computer simulation and expert opinions based on the simulation. Edison also challenges *547 the amount of damages and the rate of interest applied to the judgment. The plaintiffs, in their cross-appeal, argue that the judge erred in not directing a verdict or granting judgment notwithstanding the verdict for them on their contract claim. We affirm.
Facts. Under the terms of an agreement between Edison and the plaintiffs, Edison supplied and the plaintiffs purchased steam for the air conditioning, cooking, and space and water heating systems in the building.
Due to a problem with the metering system of which the parties were unaware, the meter overregistered the amount of steam being used. The problem came to light when the building manager, having taken several unsuccessful steps to reduce the steam bills by conserving steam usage in the building, finally shut down the steam system entirely, only to discover that the low-range steam meter nevertheless continued to register steam flow at eighteen percent. The problem was traced to the meter having been defectively installed when the building was built. During the time that the faulty metering system was in place, Edison had charged the plaintiffs $3,756,531.30 for steam used.
Edison does not dispute that it overcharged the plaintiffs during the relevant time period; rather, it disputes the amount of the overcharge. Prior to the litigation, Edison reviewed numerous steam usage charts for the relevant period and, applying a "correction formula" recommended by the meter manufacturer, concluded that the meter was off by four percent, rather than the eighteen percent recorded by the building manager and asserted by the plaintiffs. Edison nevertheless decided to split the difference between its and the plaintiffs' estimated percentage of error. Basing its overcharge calculations on a system error of eleven percent, Edison offered $93,764.86 to the plaintiffs. Edison took the position that this figure constituted an estimate in lieu of an accurate reading, which the plaintiffs were bound to accept *548 under the terms of the agreement.[2] The plaintiffs rejected Edison's calculations as premised on the erroneous assumption that the percentage of error had remained constant throughout the five-year period.
The plaintiffs relied on a computer simulation to make their own calculations of actual steam usage. The computer program, called TRACE (Trane Air Conditioning Economics), consists of scientific formulae and algorithms[3] concerning heat transfer, building materials, operating characteristics of various heating and air handling equipment, and weather history, among other things. To generate a simulation, the computer program uses data specifying a particular building's construction materials, operating patterns, architectural details, latitude, longitude, outside air flow, and heating, ventilating and air conditioning equipment, among other things.
Evidentiary issues regarding TRACE. Edison moved in limine to exclude the TRACE evidence on the grounds that the data and equations used in the simulation were neither accurate nor complete, and that the program had not achieved general acceptance by the community of scientists involved. The judge, defining the relevant scientific community as heating, ventilating and air conditioning (HVAC) and building design professionals, determined that this group had accepted TRACE as scientifically reliable. At trial, following a voir dire of the plaintiffs' expert, the judge further found that the program data and equations were accurate and complete, and ruled admissible the TRACE evidence and related expert testimony.
*549 Edison claims error in the admission of the TRACE evidence. First, Edison argues that the results of the TRACE simulation are inadmissible hearsay, and the judge therefore erred in admitting them in evidence. We disagree.
The function of computer programs like TRACE "is to perform rapidly and accurately an extensive series of computations not readily accomplished without use of a computer." Schaeffer v. General Motors Corp., 372 Mass. 171, 177 (1977). We permit experts to base their testimony on calculations performed by hand, cf., e.g., Anthony's Pier Four, Inc. v. HBC Assocs., 411 Mass. 451, 478 (1992); Kroeger v. Stop & Shop Cos., 13 Mass. App. Ct. 310, 323 (1982). There is no reason to prevent them from performing the same calculations, with far greater rapidity and accuracy, on a computer. Therefore, as we indicated in Schaeffer, supra at 177-178, we treat computer-generated models or simulations like other scientific tests, and condition admissibility on a sufficient showing that: (1) the computer is functioning properly; (2) the input and underlying equations are sufficiently complete and accurate (and disclosed to the opposing party, so that they may challenge them); and (3) the program is generally accepted by the appropriate community of scientists. See Commonwealth v. Fatalo, 346 Mass. 266, 269 (1963).
Edison urges us to reject the computer simulation evidence. We decline to do so. We note that we are not the first jurisdiction to recognize that computer models or simulations may be used to assist the fact finder. Generally courts have permitted computer models in cases not easily susceptible of other forms of proof. See, e.g., Seattle Master Builders Ass'n v. Pacific Northwest Elec. Power & Conservation Planning Council, 786 F.2d 1359, 1370 (9th Cir.1986), cert. denied, 479 U.S. 1059 (1987) (allowing use of computer simulations of value of energy conservation methods based on principles derived from American Society of Heating, Refrigerating and Air Conditioning Engineers "Handbook of Fundamentals" to determine energy conservation value); Perma Research & Dev. Co. v. Singer Co., 542 F.2d 111, *550 115 (2d Cir.), cert. denied, 429 U.S. 987 (1976) (results of computer simulation used to form basis of expert testimony regarding feasibility of perfection of automobile anti-skid device); United States v. Dioguardi, 428 F.2d 1033, 1037 (2d Cir.), cert. denied, 400 U.S. 825 (1970) (computer analysis employed to determine when defendant would have exhausted his inventory, had he not concealed assets); Pearl Brewing Co. v. Joseph Schlitz Brewing Co., 415 F. Supp. 1122, 1134 (S.D. Tex. 1976) (computer simulation used to test varying market conditions in price-fixing case); United States v. United Technologies Corp., 1977-2 Trade Cas. (CCH) par. 61,647 (1977) (econometric model used in antitrust case); In re Sugar Indus. Antitrust Litig., 73 F.R.D. 322, 353 (E.D. Pa. 1976) (expert could rely on statistical model to formulate his opinion as to class damages in complex antitrust case); Messex v. Louisiana Dep't of Highways, 302 So.2d 40, 44 (La. Ct. App. 1974) (computer simulation of automobile accident used to assist court in determining whether defendant had reasonable opportunity to avoid accident). There is no reason to exclude computer simulations provided the computer simulation meets the appropriate standards of admissibility.
Edison next argues that the judge erred in determining that the TRACE program, at least as employed to estimate past steam heat consumption rather than predict future consumption, has been generally accepted by the relevant community of scientists. There was no error.
In determining whether TRACE is generally accepted by the relevant community of scientists, we make our "own determination without regard to the conclusions of the trial or motion judge." Commonwealth v. Curnin, 409 Mass. 218, 223 (1991). In so doing, we "may properly consider not only the evidence in the record but also the reasoning and conclusions of other courts and the writings of experts." Id.
The plaintiffs offered evidence showing that TRACE has been used by engineers and HVAC design professionals to model energy consumption in over 40,000 buildings. The most common applications for TRACE include comparing *551 the energy efficiency of alternative heating and cooling systems, and predicting a building's energy consumption. Where TRACE is used for the latter purpose, the predictions are quite accurate. California requires a computer analysis of building energy consumption before a new building permit is issued for a multi-story building. The California Energy Commission has approved TRACE for this purpose, pursuant to Cal. Code Regs. tit. 20, § 1409 (1990). TRACE also is used to recreate past energy consumption in buildings. There is no reason for disturbing the judge's conclusion simply because, in this case, TRACE was used to calculate past, rather than future or hypothetical, energy consumption  that is, because the TRACE input consisted of historical rather than hypothetical facts about the building's operations and weather conditions.[4]
Edison further argues that HVAC engineers are not the relevant community of scientists for purposes of determining whether TRACE has been generally accepted. We have said that "the requirement of the Frye v. United States, 293 F.2d 1013 (D.C. Cir.1923)] rule of general acceptability is satisfied, in our opinion, if the principle is generally accepted by those who would be expected to be familiar with its use." Commonwealth v. Lykus, 367 Mass. 191, 203 (1975). The evidence showed that approximately eighty percent of TRACE users are HVAC engineers. Edison proposes that the relevant community of scientists is "the community involved in the field of fluid flow measurement or custody *552 transfer fluids." Edison's argument amounts to the following: those who use meters to measure energy consumption, rather than those who use computer simulations, should pass on the validity of the computer simulation. We reject this argument.
Edison also argues that the evidence was insufficient to support the judge's conclusion that the data and equations used in the TRACE program were accurate and complete, because the judge did not have access to the thousands of pages of coding of the TRACE program. This argument is without merit. As discussed supra at 549, the judge is required to determine (1) the completeness and accuracy of the data and underlying equations; and (2) whether the program is generally accepted by the appropriate community of scientists. Edison's argument confounds these two requirements. Because "[t]hose most qualified [to assess the general validity of a scientific method such as a computer simulation] are not judges, but rather are scientists with special knowledge who are most familiar with the method or theory in question." Commonwealth v. Mendes, 406 Mass. 201, 205 (1989), the judge is required to determine only whether TRACE is generally accepted by the appropriate community of scientists. The judge need not determine whether all the complex, underlying coding is complete and accurate.
In Schaeffer v. General Motors Corp., 372 Mass. 171, 178 (1977), we held that the judge must "conduct a hearing in the absence of the jury on the question whether the tests conducted and results ascribed thereto meet the prescribed standards for the admissibility of such evidence." In ruling on the admissibility of the TRACE program, the judge received and reviewed, among other things, the depositions (and attached exhibits) of three people involved in performing the simulation; three affidavits submitted by the plaintiffs' experts; seven affidavits submitted by Edison's experts (including responsive affidavits); articles regarding TRACE and computer evidence generally; the section of the California state administrative code which approves the use of TRACE; and numerous memoranda of law. Furthermore, as noted above, the judge conducted a three-hour voir dire of the plaintiffs' chief *553 TRACE experts. Edison maintains that the Schaeffer hearing requirement was not fulfilled in this case because not all the witnesses were called to testify in person. We decline to hold that in all cases only a voir dire hearing of all the relevant witnesses can satisfy the Schaeffer hearing requirement.
Another requirement set out in Schaeffer is that the judge must "put into the record, by dictation, for the transcript or otherwise, the findings of fact made by him as the basis for the admission or exclusion of the evidence in question." Schaeffer, supra at 178. Edison argues that the judge did not comply with this second Schaeffer requirement. We reject this argument, too. In this case, the judge issued seven pages of findings regarding the general acceptance of TRACE, and read into the record her findings that the input used was accurate.
Edison argues that the opinion of one of the plaintiffs' experts as to the amount of steam used in the building during the relevant time period was inadmissible because it was based on facts or data not independently admissible. Cf. Department of Youth Servs. v. A Juvenile, 398 Mass. 516, 527-532 (1986). Given our conclusion that the TRACE results are admissible, this claim fails.
Edison further argues that it was denied a fair opportunity to prepare effective cross-examination of the plaintiffs' expert witnesses because it was not furnished with the actual coding of the TRACE program (i.e., how the algorithms described in the manuals were written and arranged into computer language). As a result, it claims, the TRACE results and expert opinions should not have been admitted. The judge found and ruled that the TRACE program itself is proprietary and confidential.[5] Edison suggests that it was entitled to the information, *554 even if it were proprietary. Cf. Perma Research & Dev. v. Singer Co., 542 F.2d 111, 115 (2d Cir.1976) (no abuse of discretion where judge refused to order disclosure of proprietary program). We need not reach this issue, however, because the judge was justified in rejecting Edison's request for the underlying coding on the basis that it was not made in a timely manner. Edison did not ask for the coding until it filed a third request for production of documents. At the time of the third request, one scheduled trial date already had come and gone. There was no error in the judge's ruling that disclosure was not required.
Edison's motion to amend damages award. The jury determined that Edison did not breach its contract with the plaintiffs in connection with providing steam service to the buildings. Edison argues that the contract provision that "when meters fail to register or are determined to be in error, [Edison] may estimate the quantity and rate of taking [of steam]," creates an obligation on the plaintiffs' part to accept Edison's "estimate" as long as it is "reasonable." Therefore, because (1) the jury found that Edison did not breach the contract and (2) Edison's estimate was reasonable, argues Edison, the judge accordingly must reduce the damage award to correspond to Edison's estimate ($93,764.86). The contract language cited by Edison in support of its argument, on its face, simply provides Edison a method for billing a customer when the meter on which the bill is based is found to be either not functioning or inaccurate. Nowhere does the contract state that the customer has no right to challenge the estimated bill. The judge was correct in refusing to reduce the damage award. In the alternative, Edison asks that the judgment be reversed and the action remanded for a new trial by reason of what it characterizes as "the jury's inconsistent findings in its special *555 verdict." Because the findings were not inconsistent, we similarly reject this request.
Rate of interest on the damage award. The $1,590,371 judgment entered on the plaintiffs' jury verdict included interest at the rate of twelve percent per annum, calculated from the dates of the plaintiffs' overpayments. Edison claims that the judge incorrectly determined both the rate of interest applicable to the plaintiffs' damage award and the date from which the interest should have been awarded. The interest rate should have been calculated at the rate of six percent per annum pursuant to G.L.c. 107, § 3 (1990 ed.), according to Edison; alternatively, Edison argues that interest should have been calculated at the rate of eight percent per annum pursuant to a tolling agreement entered into by the parties prior to the commencement of the action.[6] Moreover, the interest on the damage award should have been calculated as of April 1, 1980, pursuant to the tolling agreement, asserts Edison.[7]
*556 General Laws c. 231, § 6C (1990 ed.), is applicable to all actions "based on contractual obligations."[8] Actions for money paid by mistake sound in contract, see Mechanics Nat'l Bank v. Worcester County Trust Co., 341 Mass. 465, 473 (1960); Flower v. Suburban Land Co., 332 Mass. 30, 31, 33 (1954); Flavin v. Morrissey, 327 Mass. 217 (1951). Therefore, the judge did not err in awarding the plaintiffs interest at the rate of twelve percent per annum in conformity with G.L.c. 231, § 6C. Nor did the judge err in calculating interest from the date of the overpayments. Cf. Broomfield v. Kosow, 349 Mass. 749, 759 (1965); National Shawmut Bank v. Fidelity Mut. Life Ins. Co., 318 Mass. 142, 152 (1945); Montgomery Door & Sash Co. v. Atlantic Lumber Co., 206 Mass. 144, 157 (1910).
Edison's reliance on the tolling agreement in support of its arguments regarding interest on the award is misplaced. The tolling agreement unambiguously provides that the plaintiffs reserve all rights with respect to interest; in forebearing to bring suit on April 1, 1980, they would not lose their right to receive interest from at least that date and at the statutory rate then in effect.
Edison's counterclaim. Edison claims that the judge improperly dismissed its (amended) counterclaim and denied its motion for leave to serve a second amended counterclaim. There was no error. The substance of Edison's counterclaims is that the plaintiffs attempted to "extort from Edison" an "unreasonable, exorbitant and unjustifiable" rebate for Edison's overcharges, in violation of G.L.c. 93A. The plaintiffs' demand for reimbursement of money Edison itself acknowledges was paid by mistake does not give rise to c. 93A liability. Cf. Whitinsville Plaza, Inc. v. Kotseas, 378 Mass. *557 85, 103 (1979) (bringing suit to enforce anticompetitive deed restrictions does not give rise to c. 93A liability); Levings v. Forbes & Wallace, Inc., 8 Mass. App. Ct. 498, 504 (1979) (refusal to pay a bill because one disputes the amount does not give rise to c. 93A liability).
The plaintiffs' motion for a directed verdict. At the close of the evidence, the plaintiffs moved for a directed verdict. The judge granted the motion as to the money paid by mistake count, but denied it as to the breach of contract count. The contract count was thereupon submitted to the jury, which rendered a verdict for Edison. The plaintiffs moved for judgment notwithstanding the verdict. This motion was denied. The plaintiffs argue that the judge improperly denied their motions for a directed verdict and judgment notwithstanding the verdict on the breach of contract count.
The plaintiffs assert that Edison's unintentional overcharges constitute a breach of contract because, argue the plaintiffs, the contract unambiguously requires the plaintiffs to pay only for steam actually used. However, several of the contract provisions seem to indicate that the plaintiffs are required to pay for metered steam usage. For example, the contract states that the plaintiffs shall pay Edison "[a fixed amount] per M pounds of steam per month for [X] hours use of the billing demand.... The ... demand will be determined each month (in M pounds of steam per hour) by instruments installed by [Edison]." Paragraph three of the terms and conditions states that "[t]he customer shall be responsible for all charges for steam furnished under the agreement...." The judge did not err in determining that the contract was ambiguous on this point, and so properly determined that the question was one for the jury. See Edmonds v. United States, 642 F.2d 877, 881 (1st Cir.1981) (where contract contains ambiguities a question of fact for jury is presented), citing Trafton v. Custeau, 338 Mass. 305, 307-308; Gillentine v. McKneand, 426 F.2d 717, 721 (1st Cir.1979).
Judgment affirmed.
NOTES
[1]  American Employers' Insurance Co., The Employers' Fire Insurance Co., and the Northern Assurance Co. of America.
[2]  The first paragraph of the agreement states: "Such meters as may be required to determine the quantity and rate of taking of steam delivered shall be supplied by [Edison] and installed by the Customer upon the Customer's premises at a point or points most convenient for [Edison's] service; provided, however, that where metering is impractical, or when meters fail to register or are determined to be in error, the Company may estimate the quantity and rate of taking."
[3]  An algorithm is "a process, or set of rules, usually one expressed in algebraic notation, now used especially in computing, machine translation and linguistics." 1 Oxford English Dictionary 59 (Supp. 1972).
[4]  The plaintiffs modified the basic TRACE program. Edison also argues that, even if the TRACE program has achieved general acceptance by a community of scientists, there is no evidence that the particular, specially modified version of the program used in this litigation has achieved general acceptance. This argument is without merit. The judge found that the modifications were designed to increase the accuracy of the simulation: "[A]djustments were made [to the TRACE program] until a close match with ... actual consumption figures [for a year in which the meter was working properly] was achieved." Furthermore, the judge found that TRACE is "reliable and accurate [in predicting building energy consumption] within plus or minus 10% of actual consumption"; the plaintiffs also added ten percent to the steam consumption calculated by TRACE.
[5]  The equations and procedures on which the program is based, however, are set forth in the publicly available standard reference handbook of the American Society of Heating, Refrigerating and Air Conditioning Engineers, Inc. (ASHRAE). Edison had nine manuals on TRACE, setting forth in detail the input needed by the TRACE program and the mathematical equations and algorithms which form the basis of the program. The equations in the program are standard ASHRAE algorithms and physical laws of heat transfer. In addition, Edison had the opportunity to review all the input used in the TRACE simulation for this litigation, and one of Edison's own experts created energy simulation computer programs similar to TRACE, relying on the same type of algorithms.
[6]  The tolling agreement provides in pertinent part: "2. Each party to this Agreement further agrees with the other party, in consideration of their mutual promises, that the period of time from January 1, 1980 to April 1, 1980 or the termination of the effectiveness of this Paragraph 2 by notice as described below, whichever first occurs, will not be put forward or relied upon in any way by that party in computing the running of time under any applicable statute of limitations or for purposes of laches, estoppel or like defenses in defense against any claim, under any applicable principle of law, arising out of or relating in any way to steam consumption in the Building or any matters relating to or affecting the same, which may at any time hereafter be asserted against either party by the other party."

Subsequently the parties amended the agreement as follows:
"2. Without in any way waiving or limiting [the plaintiffs'] previous demands for the payment of interest, Edison agrees in any event to pay [the plaintiffs] interest at the rate of eight per cent (8%) per annum on any and all amounts finally paid by Edison to [the plaintiffs] in connection with said alleged overcharges for steam, whether by way of settlement, judgment awarded in a lawsuit or otherwise, in each case from April 1, 1980 to the date of payment."
[7]  Alternatively, Edison argues that the plaintiffs should receive interest on the damage award only for the period between when the plaintiffs demanded reimbursement for the overcharge and when they rejected Edison's $93,764.86 offer. This argument is premised on Edison's interpretation of the contract provision regarding estimates when the meter fails or is in error, an interpretation which we reject. See supra at 554. Accordingly, we reject this claim.
[8]  General Laws c. 231, § 6C (1990 ed.), provides, in pertinent part: "In all actions based on contractual obligations, upon a verdict, finding or order for judgment for pecuniary damages, interest shall be added ... to the amount of damages, at the contract rate, if established, or at the rate of twelve per cent per annum from the date of the breach or demand...."
