### Table 1: Effect of removing useless variables

"... In PAGE 7: ... EXPERIMENTS AND DISCUSSION We have incorporated the analysis techniques for the elim- ination of useless stack and program variables as described in the paper in a cost analyzer for JBC programs. Table1 shows the effect of eliminating redundant stack and irrelevant local variables on a series of benchmarks for which our system can infer automatically CESs. We in- clude classical recursive programs such as Factorial, Hanoi, Fibonacci, MergeSort or QuickSort.... ..."

### Table 1: Efiect of removing useless variables

"... In PAGE 7: ... EXPERIMENTS AND DISCUSSION We have incorporated the analysis techniques for the elim- ination of useless stack and program variables as described in the paper in a cost analyzer for JBC programs. Table1 shows the efiect of eliminating redundant stack and irrelevant local variables on a series of benchmarks for which our system can infer automatically CESs. We in- clude classical recursive programs such as Factorial, Hanoi, Fibonacci, MergeSort or QuickSort.... ..."

### Table 1. Benchmarks

2000

"... In PAGE 3: ... 3 Results and Conclusions A variety of types of transformations in the vpo compiler have been validated using our approach, including algebraic simpli cation of expressions, basic block reordering, branch chaining, common subexpression elimination, constant fold- ing, constant propagation, unreachable code elimination, dead store elimination, evaluation order determination, lling delay slots, induction variable removal, instruction selection, jump minimization, register allocation, strength reduction, and useless jump elimination. Table1 shows some test programs that we have compiled while validating code-improving transformations. The third column indicates the number of im- proving transformations that were applied during the compilation of each pro- gram.... ..."

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### Table 1. Benchmarks

"... In PAGE 3: ... 3 Results and Conclusions A variety of types of transformations in the vpo compiler have been validated using our approach, including algebraic simpli cation of expressions, basic block reordering, branch chaining, common subexpression elimination, constant fold- ing, constant propagation, unreachable code elimination, dead store elimination, evaluation order determination, lling delay slots, induction variable removal, instruction selection, jump minimization, register allocation, strength reduction, and useless jump elimination. Table1 shows some test programs that we have compiled while validating code-improving transformations. The third column indicates the number of im- proving transformations that were applied during the compilation of each pro- gram.... ..."

### Table 3 shows the Sobol indices estimates using Monte-Carlo methods. For the

"... In PAGE 22: ... Thus, it seems that spline terms are useless for this variable which can be correctly explained by a linear model. Table3 shows the results for the Sobol indices estimation using Monte-Carlo meth-... In PAGE 24: ... It would be interesting for the physicists to know the interaction influence between the pellet radius and the irradiation power, but this information is not accessible for the moment in our analysis. [ Table3 about here.] 5 CONCLUSION This paper has proposed a solution to resolve the problem of uncertainty and sensi- tivity studies on stochastic computer models, posed ten years ago by Kleijnen [15].... In PAGE 35: ...Table3 : Sobol sensitivity indices (with standard deviations) from joint models fitted on the outputs of the METEOR code. Model indicates that values are deduced from the joint model formulas.... ..."

### Table 2. Elimination lemmas

2004

"... In PAGE 3: ... Note that the de- pendency graph of the constructions must be cycle free. To eliminate a point from the goal we need to apply one of the elimination lem- mas shown on Table2 on page 5. This table can be read as follows: To eliminate a point Y , choose the line corresponding to the way Y has been constructed, and apply the formula given in the column corresponding to the geometric quantity in which Y is used.... In PAGE 4: ... We rst translate the goal (A0B0 k AB) into its equivalent using the signed area: SA0B0A = SA0B0B Then we eliminate compound points from the goal starting by the last point in the order of their construction. The geometric quantities containing an oc- currence of B0 are SA0B0B and SA0B0A, B0 has been constructed using the rst construction on Table2 with = 1 2: SA0B0A = SAA0B0 = 1 2SAA0A + 1 2SAA0C = 1 2SAA0C and SA0B0B = SBA0B0 = 1 2SBA0A + 1 2SBA0C The new goal is SAA0C = SBA0A + SBA0C Now we eliminate A0 using: SCAA0 = 1 2SCAB + 1 2SCAC = 1 2SCAB SABA0 = 1 2SABB + 1 2SABC = 1... In PAGE 11: ... This tactic (called eliminate_all) rst searches the con- text for a point which is not used to build another point (a leaf in the dependency graph). Then for each occurrence of the point in the goal, it applies the right lemma from Table2 by nding in the context how the point has been constructed and which geometric quantity it appears in. Finally it removes the hypotheses stating how the point has been constructed from the context.... In PAGE 12: ...this classical reasoning step. As noted before, the elimination lemmas given in Table2 on page 5, do eliminate an occurrence of a point Y only if Y appears only one time in the geometric quantity (A,B,C and D must be di erent from Y ). If Y appears twice in S, this is not a problem because then the geometric quantity is zero, and so already eliminated by the simpli cation phase.... ..."

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### Table 5. Factorization of the eliminant

1998

"... In PAGE 28: ...his happens in Conjecture 1.1, Theorem 2.3, Theorem 3.9(i) and (iv), and in other cases. Table5 lists the degrees of the factors in the case of Conjecture 1.1.... ..."

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### Table 5. Factorization of the eliminant

1998

"... In PAGE 26: ...he integers. This happens in Conjecture 1.1, Theorem 2.3, Theorem 3.9(i) and (iv), and in other cases. Table5 lists the degrees of the factors in the case of Conjecture 1.1.... ..."

Cited by 10