Details

Time bar (total: 2.3s)

analyze224.0ms (9.7%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
15.6%84.3%0.1%6
37.5%62.4%0.1%7
46.8%53.1%0.1%8
57.8%39.8%2.4%9
64.6%30.4%5%10
71.8%20.3%7.9%11
74.1%16.2%9.7%12
77.4%10.7%12%13
78.6%8.4%13%14
Compiler

Compiled 22 to 18 computations (18.2% saved)

sample24.0ms (1%)

Algorithm
1×intervals
Results
14.0ms256×body128valid
0.0ms7×body128invalid
Compiler

Compiled 43 to 37 computations (14% saved)

simplify143.0ms (6.2%)

Algorithm
1×egg-herbie
Rules
615×div-sub_binary64_424
608×times-frac_binary64_425
503×associate-/l*_binary64_364
352×associate-/l/_binary64_366
276×distribute-rgt-in_binary64_369
241×unsub-neg_binary64_413 associate-/r*_binary64_363
231×distribute-lft-in_binary64_368
226×associate-/r/_binary64_365
205×associate-*l/_binary64_362
163×associate-*r/_binary64_361
151×cancel-sign-sub-inv_binary64_385
148×*-commutative_binary64_350
131×neg-sub0_binary64_414
128×neg-mul-1_binary64_415
116×associate-*l*_binary64_360
110×sub-neg_binary64_412
108×associate-*r*_binary64_359
72×distribute-rgt-neg-out_binary64_379
68×distribute-lft-neg-out_binary64_378
35×distribute-frac-neg_binary64_382
32×associate-+r+_binary64_351
26×associate-+l+_binary64_352
25×distribute-rgt-neg-in_binary64_377
24×*-rgt-identity_binary64_409 *-lft-identity_binary64_408 distribute-lft-neg-in_binary64_376
22×mul0-rgt_binary64_402
21×mul0-lft_binary64_401
20×div0_binary64_400
19×distribute-neg-frac_binary64_383
18×distribute-rgt-out_binary64_372
16×/-rgt-identity_binary64_410
12×sub0-neg_binary64_406 associate-+l-_binary64_354 +-commutative_binary64_349
9×distribute-neg-in_binary64_380 associate-+r-_binary64_353
8×mul-1-neg_binary64_411 associate--r+_binary64_355
6×+-rgt-identity_binary64_404
4×distribute-lft-out_binary64_370
3×--rgt-identity_binary64_405 distribute-rgt-out--_binary64_373
2×remove-double-neg_binary64_407 difference-of-squares_binary64_388
1×1-exp_binary64_463 +-lft-identity_binary64_403 distribute-lft-out--_binary64_371 count-2_binary64_367
0×not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64_682 erf-erfc_binary64_681 erf-odd_binary64_680 if-if-and-not_binary64_679 if-if-and_binary64_678 if-if-or-not_binary64_677 if-if-or_binary64_676 if-not_binary64_675 if-same_binary64_674 if-false_binary64_673 if-true_binary64_672 not-gte_binary64_671 not-lte_binary64_670 not-gt_binary64_669 not-lt_binary64_668 gte-same_binary64_667 lte-same_binary64_666 gt-same_binary64_665 lt-same_binary64_664 sinh---cosh_binary64_611 sinh-+-cosh_binary64_610 sinh-cosh_binary64_609 tanh-def-c_binary64_608 tanh-def-b_binary64_607 tanh-def-a_binary64_606 cosh-def_binary64_605 sinh-def_binary64_604 tan-neg_binary64_551 cos-neg_binary64_550 sin-neg_binary64_549 tan-0_binary64_548 cos-0_binary64_547 sin-0_binary64_546 hang-m-tan_binary64_545 hang-p-tan_binary64_544 hang-m0-tan_binary64_543 hang-p0-tan_binary64_542 hang-0m-tan_binary64_541 hang-0p-tan_binary64_540 tan-+PI/2_binary64_539 tan-+PI_binary64_538 tan-PI_binary64_537 tan-PI/3_binary64_536 tan-PI/4_binary64_535 tan-PI/6_binary64_534 cos-+PI/2_binary64_533 cos-+PI_binary64_532 cos-PI_binary64_531 cos-PI/2_binary64_530 cos-PI/3_binary64_529 cos-PI/4_binary64_528 cos-PI/6_binary64_527 sin-+PI/2_binary64_526 sin-+PI_binary64_525 sin-PI_binary64_524 sin-PI/2_binary64_523 sin-PI/3_binary64_522 sin-PI/4_binary64_521 sin-PI/6_binary64_520 sub-1-sin_binary64_519 sub-1-cos_binary64_518 -1-add-sin_binary64_517 -1-add-cos_binary64_516 1-sub-sin_binary64_515 1-sub-cos_binary64_514 cos-sin-sum_binary64_513 log-E_binary64_509 log-pow_binary64_508 log-rec_binary64_507 log-div_binary64_506 log-prod_binary64_505 pow-base-0_binary64_503 unpow1/3_binary64_486 unpow3_binary64_485 unpow2_binary64_484 unpow1/2_binary64_483 pow-plus_binary64_482 exp-to-pow_binary64_481 pow-base-1_binary64_479 unpow0_binary64_478 unpow1_binary64_477 unpow-1_binary64_476 exp-lft-cube_binary64_475 exp-lft-sqr_binary64_474 exp-cbrt_binary64_473 exp-sqrt_binary64_472 exp-prod_binary64_471 div-exp_binary64_470 rec-exp_binary64_469 prod-exp_binary64_468 exp-diff_binary64_467 exp-neg_binary64_466 exp-sum_binary64_465 e-exp-1_binary64_464 exp-1-e_binary64_462 exp-0_binary64_461 rem-log-exp_binary64_460 rem-exp-log_binary64_459 cube-unmult_binary64_456 cube-mult_binary64_449 cube-div_binary64_448 cube-prod_binary64_447 cube-neg_binary64_446 rem-3cbrt-rft_binary64_445 rem-3cbrt-lft_binary64_444 rem-cbrt-cube_binary64_443 rem-cube-cbrt_binary64_442 sqr-abs_binary64_434 sqr-neg_binary64_433 rem-sqrt-square_binary64_432 rem-square-sqrt_binary64_431 *-inverses_binary64_399 +-inverses_binary64_398 lft-mult-inverse_binary64_397 rgt-mult-inverse_binary64_396 remove-double-div_binary64_395 pow-sqr_binary64_392 sqr-pow_binary64_391 difference-of-sqr--1_binary64_390 difference-of-sqr-1_binary64_389 unswap-sqr_binary64_387 swap-sqr_binary64_386 cancel-sign-sub_binary64_384 distribute-neg-out_binary64_381 distribute-rgt1-in_binary64_375 distribute-lft1-in_binary64_374 associate--r-_binary64_358 associate--l-_binary64_357 associate--l+_binary64_356
Counts
1 → 5
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01632
13629
29329
334429
4116429
5321829

prune18.0ms (0.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New145
Fresh011
Picked000
Done000
Total156
Error
0.1b
Counts
6 → 5
Compiler

Compiled 194 to 134 computations (30.9% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (/.f64 1 a) (/.f64 -1 b))
0.2b
(/.f64 (/.f64 (+.f64 (/.f64 1 a) (/.f64 -1 b)) (-.f64 b a)) (+.f64 b a))
0.2b
(*.f64 (/.f64 PI.f64 2) (/.f64 (/.f64 (+.f64 (/.f64 1 a) (/.f64 -1 b)) (-.f64 b a)) (+.f64 b a)))
0.2b
(/.f64 (+.f64 (/.f64 1 a) (/.f64 -1 b)) (-.f64 b a))

rewrite1.2s (49.6%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
838×*-un-lft-identity_binary64_419
710×times-frac_binary64_425
349×add-sqr-sqrt_binary64_441
229×distribute-lft-out_binary64_370
206×add-cube-cbrt_binary64_454
150×associate-*r*_binary64_359
65×div-inv_binary64_416
61×difference-of-squares_binary64_388 distribute-lft-out--_binary64_371
42×associate-/l*_binary64_364
32×add-exp-log_binary64_457 add-cbrt-cube_binary64_455
24×associate-/r/_binary64_365
13×div-exp_binary64_470 cbrt-undiv_binary64_453 associate-*l*_binary64_360
10×flip3--_binary64_423 flip--_binary64_394
9×associate-/r*_binary64_363
6×pow1_binary64_480 add-log-exp_binary64_458 prod-exp_binary64_468 cbrt-unprod_binary64_452 unswap-sqr_binary64_387
4×associate-/l/_binary64_366 flip3-+_binary64_422 flip-+_binary64_393
2×frac-2neg_binary64_430 clear-num_binary64_418 frac-add_binary64_427
1×pow-prod-down_binary64_490 frac-times_binary64_429 associate-*l/_binary64_362 associate-*r/_binary64_361 *-commutative_binary64_350 sum-log_binary64_510 +-commutative_binary64_349
Counts
4 → 467
Calls

4 calls:

83.0ms
(*.f64 (/.f64 PI.f64 2) (/.f64 (/.f64 (+.f64 (/.f64 1 a) (/.f64 -1 b)) (-.f64 b a)) (+.f64 b a)))
33.0ms
(/.f64 (/.f64 (+.f64 (/.f64 1 a) (/.f64 -1 b)) (-.f64 b a)) (+.f64 b a))
20.0ms
(/.f64 (+.f64 (/.f64 1 a) (/.f64 -1 b)) (-.f64 b a))
14.0ms
(+.f64 (/.f64 1 a) (/.f64 -1 b))
Compiler

Compiled 16006 to 8285 computations (48.2% saved)

series413.0ms (17.8%)

Error
0.1b
Counts
4 → 48
Calls

4 calls:

116.0ms
(*.f64 (/.f64 PI.f64 2) (/.f64 (/.f64 (+.f64 (/.f64 1 a) (/.f64 -1 b)) (-.f64 b a)) (+.f64 b a)))
101.0ms
(/.f64 (+.f64 (/.f64 1 a) (/.f64 -1 b)) (-.f64 b a))
91.0ms
(/.f64 (/.f64 (+.f64 (/.f64 1 a) (/.f64 -1 b)) (-.f64 b a)) (+.f64 b a))
64.0ms
(+.f64 (/.f64 1 a) (/.f64 -1 b))
Compiler

Compiled 2064 to 1597 computations (22.6% saved)

simplify334.0ms (14.4%)

Algorithm
1×egg-herbie
Rules
429×associate-*r/_binary64_361
387×distribute-rgt-in_binary64_369
374×associate-*l/_binary64_362
306×associate-/l/_binary64_366
285×associate-/l*_binary64_364
257×*-commutative_binary64_350
203×associate-/r*_binary64_363
200×associate-*l*_binary64_360
184×associate-*r*_binary64_359
113×times-frac_binary64_425
104×*-rgt-identity_binary64_409
85×*-lft-identity_binary64_408
80×sub-neg_binary64_412
77×cancel-sign-sub-inv_binary64_385
73×distribute-lft-in_binary64_368
52×distribute-neg-frac_binary64_383
49×log-div_binary64_506
48×sqr-pow_binary64_391
42×distribute-rgt-neg-in_binary64_377
39×distribute-lft-neg-out_binary64_378 +-commutative_binary64_349
38×neg-mul-1_binary64_415 /-rgt-identity_binary64_410 distribute-lft-neg-in_binary64_376 associate-/r/_binary64_365
37×neg-sub0_binary64_414
30×div-sub_binary64_424 distribute-rgt-neg-out_binary64_379
28×cube-div_binary64_448
25×log-prod_binary64_505
16×exp-prod_binary64_471 pow-sqr_binary64_392
14×cube-prod_binary64_447 swap-sqr_binary64_386 distribute-neg-in_binary64_380
13×distribute-rgt-out_binary64_372
10×distribute-rgt-out--_binary64_373
9×cube-unmult_binary64_456
8×difference-of-squares_binary64_388 associate-+l-_binary64_354
7×associate-+r-_binary64_353 associate-+l+_binary64_352
6×unpow3_binary64_485 pow-plus_binary64_482 cube-mult_binary64_449 unswap-sqr_binary64_387 associate-+r+_binary64_351
5×distribute-lft-out--_binary64_371 associate--l+_binary64_356
4×unsub-neg_binary64_413 distribute-frac-neg_binary64_382 associate--r+_binary64_355
3×exp-sqrt_binary64_472 mul-1-neg_binary64_411 remove-double-neg_binary64_407 remove-double-div_binary64_395 distribute-lft-out_binary64_370 associate--r-_binary64_358
2×unpow2_binary64_484 pow-base-1_binary64_479 unpow1_binary64_477 *-inverses_binary64_399
1×log-rec_binary64_507 prod-exp_binary64_468 1-exp_binary64_463 exp-1-e_binary64_462 div0_binary64_400 distribute-neg-out_binary64_381 associate--l-_binary64_357
0×not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64_682 erf-erfc_binary64_681 erf-odd_binary64_680 if-if-and-not_binary64_679 if-if-and_binary64_678 if-if-or-not_binary64_677 if-if-or_binary64_676 if-not_binary64_675 if-same_binary64_674 if-false_binary64_673 if-true_binary64_672 not-gte_binary64_671 not-lte_binary64_670 not-gt_binary64_669 not-lt_binary64_668 gte-same_binary64_667 lte-same_binary64_666 gt-same_binary64_665 lt-same_binary64_664 sinh---cosh_binary64_611 sinh-+-cosh_binary64_610 sinh-cosh_binary64_609 tanh-def-c_binary64_608 tanh-def-b_binary64_607 tanh-def-a_binary64_606 cosh-def_binary64_605 sinh-def_binary64_604 tan-neg_binary64_551 cos-neg_binary64_550 sin-neg_binary64_549 tan-0_binary64_548 cos-0_binary64_547 sin-0_binary64_546 hang-m-tan_binary64_545 hang-p-tan_binary64_544 hang-m0-tan_binary64_543 hang-p0-tan_binary64_542 hang-0m-tan_binary64_541 hang-0p-tan_binary64_540 tan-+PI/2_binary64_539 tan-+PI_binary64_538 tan-PI_binary64_537 tan-PI/3_binary64_536 tan-PI/4_binary64_535 tan-PI/6_binary64_534 cos-+PI/2_binary64_533 cos-+PI_binary64_532 cos-PI_binary64_531 cos-PI/2_binary64_530 cos-PI/3_binary64_529 cos-PI/4_binary64_528 cos-PI/6_binary64_527 sin-+PI/2_binary64_526 sin-+PI_binary64_525 sin-PI_binary64_524 sin-PI/2_binary64_523 sin-PI/3_binary64_522 sin-PI/4_binary64_521 sin-PI/6_binary64_520 sub-1-sin_binary64_519 sub-1-cos_binary64_518 -1-add-sin_binary64_517 -1-add-cos_binary64_516 1-sub-sin_binary64_515 1-sub-cos_binary64_514 cos-sin-sum_binary64_513 log-E_binary64_509 log-pow_binary64_508 pow-base-0_binary64_503 unpow1/3_binary64_486 unpow1/2_binary64_483 exp-to-pow_binary64_481 unpow0_binary64_478 unpow-1_binary64_476 exp-lft-cube_binary64_475 exp-lft-sqr_binary64_474 exp-cbrt_binary64_473 div-exp_binary64_470 rec-exp_binary64_469 exp-diff_binary64_467 exp-neg_binary64_466 exp-sum_binary64_465 e-exp-1_binary64_464 exp-0_binary64_461 rem-log-exp_binary64_460 rem-exp-log_binary64_459 cube-neg_binary64_446 rem-3cbrt-rft_binary64_445 rem-3cbrt-lft_binary64_444 rem-cbrt-cube_binary64_443 rem-cube-cbrt_binary64_442 sqr-abs_binary64_434 sqr-neg_binary64_433 rem-sqrt-square_binary64_432 rem-square-sqrt_binary64_431 sub0-neg_binary64_406 --rgt-identity_binary64_405 +-rgt-identity_binary64_404 +-lft-identity_binary64_403 mul0-rgt_binary64_402 mul0-lft_binary64_401 +-inverses_binary64_398 lft-mult-inverse_binary64_397 rgt-mult-inverse_binary64_396 difference-of-sqr--1_binary64_390 difference-of-sqr-1_binary64_389 cancel-sign-sub_binary64_384 distribute-rgt1-in_binary64_375 distribute-lft1-in_binary64_374 count-2_binary64_367
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
043316468
1117915663
2401515624

end0.0ms (0%)

Profiling

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