Details

Time bar (total: 49.7s)

analyze1.3s (2.6%)

Algorithm
search
egg-herbie
Rules
872×unswap-sqr_binary64_387
470×distribute-rgt-in_binary64_369
438×distribute-lft-in_binary64_368
368×*-commutative_binary64_350
320×associate-*l*_binary64_360
272×unsub-neg_binary64_413
236×associate-*r*_binary64_359
186×difference-of-squares_binary64_388 distribute-rgt-neg-in_binary64_377
170×associate-/l/_binary64_366
162×cancel-sign-sub-inv_binary64_385
158×distribute-lft-neg-in_binary64_376
122×neg-sub0_binary64_414 associate-/r/_binary64_365
114×neg-mul-1_binary64_415
92×sub-neg_binary64_412 sqr-pow_binary64_391
88×associate-+r+_binary64_351
72×associate-/l*_binary64_364
62×associate-+l+_binary64_352
60×distribute-lft-neg-out_binary64_378
56×pow-sqr_binary64_392
54×associate-/r*_binary64_363
50×associate-*r/_binary64_361
42×mul0-rgt_binary64_402 mul0-lft_binary64_401
40×distribute-rgt-neg-out_binary64_379
38×associate-*l/_binary64_362
34×+-commutative_binary64_349
24×pow-plus_binary64_482
22×associate-+l-_binary64_354
20×distribute-neg-in_binary64_380 associate--r+_binary64_355
18×+-lft-identity_binary64_403
16×cube-unmult_binary64_456 cube-prod_binary64_447 remove-double-neg_binary64_407
14×associate-+r-_binary64_353
12×sub0-neg_binary64_406 +-rgt-identity_binary64_404
*-lft-identity_binary64_408
unpow3_binary64_485 unpow2_binary64_484 cube-mult_binary64_449 --rgt-identity_binary64_405 distribute-rgt-out_binary64_372 distribute-lft-out_binary64_370
associate--r-_binary64_358 associate--l+_binary64_356
1-exp_binary64_463
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 unpow1/2_binary64_483 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-div_binary64_448 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 times-frac_binary64_425 div-sub_binary64_424 mul-1-neg_binary64_411 /-rgt-identity_binary64_410 *-rgt-identity_binary64_409 div0_binary64_400 *-inverses_binary64_399 +-inverses_binary64_398 lft-mult-inverse_binary64_397 rgt-mult-inverse_binary64_396 remove-double-div_binary64_395 difference-of-sqr--1_binary64_390 difference-of-sqr-1_binary64_389 swap-sqr_binary64_386 cancel-sign-sub_binary64_384 distribute-neg-frac_binary64_383 distribute-frac-neg_binary64_382 distribute-neg-out_binary64_381 distribute-rgt1-in_binary64_375 distribute-lft1-in_binary64_374 distribute-rgt-out--_binary64_373 distribute-lft-out--_binary64_371 count-2_binary64_367 associate--l-_binary64_357
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01438
13338
27238
317938
443538
5140538
6350838
7524238
022
122
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
25%62.4%12.6%5
25%56.2%18.8%6
28.1%50%22%7
28.1%46.8%25.1%8
29.7%41.4%29%9
29.7%39.4%30.9%10
31.1%35.8%33.1%11
31.1%34.4%34.5%12
31.5%32.9%35.6%13
31.5%32.1%36.4%14
Compiler

Compiled 14 to 12 computations (14.3% saved)

sample209.0ms (0.4%)

Algorithm
intervals
Results
53.0ms98×body1024valid
44.0ms53×body1024nan
32.0ms50×body2048valid
14.0ms38×body512valid
13.0ms29×body512nan
13.0ms66×body128overflowed
5.0ms55×body128valid
3.0ms15×body256valid
3.0msbody1024invalid
3.0ms11×body256nan
2.0msbody512invalid
1.0msbody256invalid
1.0ms20×body128nan
1.0msbody128invalid
Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify50.0ms (0.1%)

Algorithm
egg-herbie
Rules
673×distribute-rgt-neg-in_binary64_377
436×unswap-sqr_binary64_387
309×*-commutative_binary64_350
248×sub-neg_binary64_412
235×distribute-rgt-in_binary64_369 associate-/l/_binary64_366
234×unsub-neg_binary64_413
228×associate-/r/_binary64_365
219×distribute-lft-in_binary64_368
205×distribute-lft-neg-out_binary64_378
204×distribute-lft-neg-in_binary64_376
196×distribute-rgt-neg-out_binary64_379
181×neg-sub0_binary64_414
177×neg-mul-1_binary64_415
176×cancel-sign-sub_binary64_384
166×cancel-sign-sub-inv_binary64_385
160×associate-*l*_binary64_360
118×associate-*r*_binary64_359
93×difference-of-squares_binary64_388
86×distribute-neg-out_binary64_381 +-commutative_binary64_349
83×distribute-neg-in_binary64_380
73×associate-/l*_binary64_364
72×sqr-pow_binary64_391
70×associate--r+_binary64_355
69×associate-*r/_binary64_361
66×associate-+l-_binary64_354
64×associate-/r*_binary64_363
52×sub0-neg_binary64_406 associate-*l/_binary64_362
44×associate-+r+_binary64_351
42×associate--l+_binary64_356
40×pow-sqr_binary64_392 associate-+r-_binary64_353
31×associate-+l+_binary64_352
26×cube-prod_binary64_447
23×swap-sqr_binary64_386
22×remove-double-neg_binary64_407 --rgt-identity_binary64_405 mul0-rgt_binary64_402 mul0-lft_binary64_401
20×pow-plus_binary64_482 +-lft-identity_binary64_403
16×+-rgt-identity_binary64_404
13×cube-unmult_binary64_456
distribute-rgt-out_binary64_372
*-lft-identity_binary64_408
unpow3_binary64_485 unpow2_binary64_484 cube-mult_binary64_449 distribute-lft-out_binary64_370 associate--r-_binary64_358
unpow1_binary64_477
1-exp_binary64_463 *-rgt-identity_binary64_409 distribute-rgt-out--_binary64_373 associate--l-_binary64_357
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 unpow1/2_binary64_483 exp-to-pow_binary64_481 pow-base-1_binary64_479 unpow0_binary64_478 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-div_binary64_448 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 times-frac_binary64_425 div-sub_binary64_424 mul-1-neg_binary64_411 /-rgt-identity_binary64_410 div0_binary64_400 *-inverses_binary64_399 +-inverses_binary64_398 lft-mult-inverse_binary64_397 rgt-mult-inverse_binary64_396 remove-double-div_binary64_395 difference-of-sqr--1_binary64_390 difference-of-sqr-1_binary64_389 distribute-neg-frac_binary64_383 distribute-frac-neg_binary64_382 distribute-rgt1-in_binary64_375 distribute-lft1-in_binary64_374 distribute-lft-out--_binary64_371 count-2_binary64_367
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0919
12019
24019
39619
422819
572319
6179819
7329019
8483119

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
35.3b
Counts
1 → 1
Compiler

Compiled 13 to 11 computations (15.4% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b
(pow.f64 (+.f64 x 1) (/.f64 1 n))
0.0b
(pow.f64 x (/.f64 1 n))
2.1b
(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite157.0ms (0.3%)

Algorithm
rewrite-expression-head
Error
35.2b
Rules
33×add-sqr-sqrt_binary64_441
30×*-un-lft-identity_binary64_419
26×pow-unpow_binary64_496
21×add-cube-cbrt_binary64_454
20×unpow-prod-down_binary64_498
18×times-frac_binary64_425
difference-of-squares_binary64_388 sqr-pow_binary64_391
cancel-sign-sub-inv_binary64_385
add-log-exp_binary64_458 pow1_binary64_480 add-exp-log_binary64_457
add-cbrt-cube_binary64_455 distribute-lft-out--_binary64_371
distribute-lft-out_binary64_370 div-inv_binary64_416 pow-pow_binary64_491 pow-to-exp_binary64_488 pow-exp_binary64_487
diff-log_binary64_511 flip3--_binary64_423 sub-neg_binary64_412 flip--_binary64_394
Counts
3 → 85
Calls

3 calls:

11.0ms
(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
9.0ms
(pow.f64 (+.f64 x 1) (/.f64 1 n))
4.0ms
(pow.f64 x (/.f64 1 n))
Compiler

Compiled 1914 to 1374 computations (28.2% saved)

series743.0ms (1.5%)

Error
0.6b
Counts
3 → 42
Calls

3 calls:

401.0ms
(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
164.0ms
(pow.f64 x (/.f64 1 n))
100.0ms
(pow.f64 (+.f64 x 1) (/.f64 1 n))
Compiler

Compiled 2919 to 2245 computations (23.1% saved)

simplify155.0ms (0.3%)

Algorithm
egg-herbie
Rules
872×times-frac_binary64_425
278×cancel-sign-sub-inv_binary64_385
208×sub-neg_binary64_412
151×sqr-pow_binary64_391
129×+-commutative_binary64_349
124×unswap-sqr_binary64_387
116×distribute-rgt-in_binary64_369
102×exp-prod_binary64_471
92×associate-/r*_binary64_363
80×associate-+l+_binary64_352
78×associate-*r*_binary64_359 associate-+r+_binary64_351
77×distribute-neg-in_binary64_380 distribute-rgt-neg-in_binary64_377
74×associate--l+_binary64_356 *-commutative_binary64_350
71×log-pow_binary64_508
67×distribute-lft-neg-in_binary64_376
62×pow-sqr_binary64_392
57×neg-mul-1_binary64_415 neg-sub0_binary64_414
55×associate-/l*_binary64_364
54×associate-*l*_binary64_360
50×associate--r+_binary64_355
44×exp-sum_binary64_465 distribute-neg-frac_binary64_383
43×log-prod_binary64_505
41×unsub-neg_binary64_413
38×associate-*r/_binary64_361
34×associate-*l/_binary64_362
27×swap-sqr_binary64_386 distribute-rgt-out_binary64_372
24×unpow3_binary64_485 cube-prod_binary64_447
22×difference-of-squares_binary64_388
21×distribute-lft-neg-out_binary64_378
19×associate-/l/_binary64_366
13×exp-diff_binary64_467 cube-unmult_binary64_456 distribute-rgt-out--_binary64_373
12×pow-plus_binary64_482
11×associate-+r-_binary64_353
10×exp-to-pow_binary64_481 cube-mult_binary64_449
distribute-rgt-neg-out_binary64_379 distribute-lft-out_binary64_370
div-sub_binary64_424
log-div_binary64_506
rem-sqrt-square_binary64_432
unpow1/2_binary64_483 unpow1_binary64_477 prod-exp_binary64_468 mul-1-neg_binary64_411 *-rgt-identity_binary64_409
unpow2_binary64_484 pow-base-1_binary64_479 *-lft-identity_binary64_408 +-rgt-identity_binary64_404 distribute-lft-in_binary64_368
log-rec_binary64_507 exp-neg_binary64_466 /-rgt-identity_binary64_410 distribute-rgt1-in_binary64_375 associate-/r/_binary64_365
div-exp_binary64_470 remove-double-neg_binary64_407 distribute-frac-neg_binary64_382 distribute-lft-out--_binary64_371
1-exp_binary64_463 rem-3cbrt-lft_binary64_444 rem-square-sqrt_binary64_431 +-inverses_binary64_398 associate--r-_binary64_358
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 pow-base-0_binary64_503 unpow1/3_binary64_486 unpow0_binary64_478 unpow-1_binary64_476 exp-lft-cube_binary64_475 exp-lft-sqr_binary64_474 exp-cbrt_binary64_473 exp-sqrt_binary64_472 rec-exp_binary64_469 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-div_binary64_448 cube-neg_binary64_446 rem-3cbrt-rft_binary64_445 rem-cbrt-cube_binary64_443 rem-cube-cbrt_binary64_442 sqr-abs_binary64_434 sqr-neg_binary64_433 sub0-neg_binary64_406 --rgt-identity_binary64_405 +-lft-identity_binary64_403 mul0-rgt_binary64_402 mul0-lft_binary64_401 div0_binary64_400 *-inverses_binary64_399 lft-mult-inverse_binary64_397 rgt-mult-inverse_binary64_396 remove-double-div_binary64_395 difference-of-sqr--1_binary64_390 difference-of-sqr-1_binary64_389 cancel-sign-sub_binary64_384 distribute-neg-out_binary64_381 distribute-lft1-in_binary64_374 count-2_binary64_367 associate--l-_binary64_357 associate-+l-_binary64_354
Counts
127 → 103
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02743317
17263174
222212873
347482861
449842861
549882861

prune166.0ms (0.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New967103
Fresh000
Picked101
Done000
Total977104
Error
0.5b
Counts
104 → 7
Compiler

Compiled 2759 to 1854 computations (32.8% saved)

localize40.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.3b
(log.f64 (+.f64 1 x))
5.4b
(+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 1 x)) n) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))))
7.2b
(+.f64 (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)))
10.8b
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (*.f64 n n))) (+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 1 x)) n) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (*.f64 n n))) (+.f64 (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))

rewrite1.5s (2.9%)

Algorithm
rewrite-expression-head
Error
0.4b
Rules
91×add-log-exp_binary64_458
52×sum-log_binary64_510
36×frac-add_binary64_427
29×flip3-+_binary64_422 flip-+_binary64_393
24×frac-sub_binary64_428
20×associate-*r/_binary64_361
16×diff-log_binary64_511
15×*-un-lft-identity_binary64_419
add-sqr-sqrt_binary64_441
add-cube-cbrt_binary64_454 log-div_binary64_506 associate-+r-_binary64_353
pow1_binary64_480 add-exp-log_binary64_457
add-cbrt-cube_binary64_455 cancel-sign-sub-inv_binary64_385 div-sub_binary64_424 associate-+l-_binary64_354 log-prod_binary64_505
distribute-lft-out_binary64_370
distribute-lft-out--_binary64_371 associate--l-_binary64_357 +-commutative_binary64_349
flip3--_binary64_423 sub-neg_binary64_412 flip--_binary64_394 difference-of-squares_binary64_388 associate--l+_binary64_356 associate--r+_binary64_355 associate-+r+_binary64_351 log-pow_binary64_508 rem-log-exp_binary64_460
Counts
4 → 102
Calls

4 calls:

62.0ms
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (*.f64 n n))) (+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 1 x)) n) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (*.f64 n n))) (+.f64 (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))
17.0ms
(+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 1 x)) n) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))))
11.0ms
(+.f64 (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)))
4.0ms
(log.f64 (+.f64 1 x))
Compiler

Compiled 18230 to 11939 computations (34.5% saved)

series4.3s (8.6%)

Error
0.2b
Counts
4 → 50
Calls

4 calls:

1.8s
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (*.f64 n n))) (+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 1 x)) n) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (*.f64 n n))) (+.f64 (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))
1.2s
(+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 1 x)) n) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))))
991.0ms
(+.f64 (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)))
44.0ms
(log.f64 (+.f64 1 x))
Compiler

Compiled 10326 to 7721 computations (25.2% saved)

simplify342.0ms (0.7%)

Algorithm
egg-herbie
Rules
686×distribute-rgt-in_binary64_369
288×times-frac_binary64_425
203×*-commutative_binary64_350
177×cancel-sign-sub-inv_binary64_385
175×sub-neg_binary64_412
167×+-commutative_binary64_349
130×distribute-neg-in_binary64_380
116×distribute-rgt-neg-in_binary64_377
109×associate-+r+_binary64_351
84×neg-sub0_binary64_414
83×neg-mul-1_binary64_415
80×sqr-pow_binary64_391
79×distribute-lft-neg-in_binary64_376
59×associate-*r/_binary64_361
54×distribute-lft-in_binary64_368
48×associate-*r*_binary64_359
47×associate-*l*_binary64_360
40×distribute-lft-neg-out_binary64_378
37×associate-/r*_binary64_363
30×unswap-sqr_binary64_387
26×associate--r+_binary64_355
25×unpow3_binary64_485 cube-mult_binary64_449
22×associate--l+_binary64_356
21×div-sub_binary64_424
20×distribute-rgt-out_binary64_372
17×cube-prod_binary64_447
16×swap-sqr_binary64_386
14×distribute-frac-neg_binary64_382
12×exp-prod_binary64_471
10×unpow2_binary64_484 prod-exp_binary64_468 cube-div_binary64_448 associate-/l*_binary64_364
difference-of-squares_binary64_388 distribute-neg-frac_binary64_383 distribute-rgt-out--_binary64_373
unpow1_binary64_477 distribute-rgt-neg-out_binary64_379
exp-sum_binary64_465 associate-+r-_binary64_353
div-exp_binary64_470
mul-1-neg_binary64_411
log-prod_binary64_505 pow-sqr_binary64_392 distribute-lft-out_binary64_370
log-div_binary64_506 unsub-neg_binary64_413 associate-*l/_binary64_362 associate-+l-_binary64_354
log-rec_binary64_507 exp-diff_binary64_467 1-exp_binary64_463 rem-exp-log_binary64_459 cube-unmult_binary64_456 cube-neg_binary64_446 rem-3cbrt-lft_binary64_444 sqr-neg_binary64_433 rem-square-sqrt_binary64_431 *-lft-identity_binary64_408 remove-double-neg_binary64_407 distribute-rgt1-in_binary64_375 distribute-lft-out--_binary64_371 associate-+l+_binary64_352
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 pow-plus_binary64_482 exp-to-pow_binary64_481 pow-base-1_binary64_479 unpow0_binary64_478 unpow-1_binary64_476 exp-lft-cube_binary64_475 exp-lft-sqr_binary64_474 exp-cbrt_binary64_473 exp-sqrt_binary64_472 rec-exp_binary64_469 exp-neg_binary64_466 e-exp-1_binary64_464 exp-1-e_binary64_462 exp-0_binary64_461 rem-log-exp_binary64_460 rem-3cbrt-rft_binary64_445 rem-cbrt-cube_binary64_443 rem-cube-cbrt_binary64_442 sqr-abs_binary64_434 rem-sqrt-square_binary64_432 /-rgt-identity_binary64_410 *-rgt-identity_binary64_409 sub0-neg_binary64_406 --rgt-identity_binary64_405 +-rgt-identity_binary64_404 +-lft-identity_binary64_403 mul0-rgt_binary64_402 mul0-lft_binary64_401 div0_binary64_400 *-inverses_binary64_399 +-inverses_binary64_398 lft-mult-inverse_binary64_397 rgt-mult-inverse_binary64_396 remove-double-div_binary64_395 difference-of-sqr--1_binary64_390 difference-of-sqr-1_binary64_389 cancel-sign-sub_binary64_384 distribute-neg-out_binary64_381 distribute-lft1-in_binary64_374 count-2_binary64_367 associate-/l/_binary64_366 associate-/r/_binary64_365 associate--r-_binary64_358 associate--l-_binary64_357
Counts
152 → 134
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
068224637
1241022262
2524422262

prune1.4s (2.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1286134
Fresh066
Picked101
Done000
Total12912141
Error
0.2b
Counts
141 → 12
Compiler

Compiled 19032 to 12558 computations (34% saved)

localize61.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.2b
(+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (*.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))
10.8b
(-.f64 (+.f64 (*.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (/.f64 (log.f64 (+.f64 x 1)) n)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (*.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))))
10.8b
(-.f64 (+.f64 (*.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (/.f64 (log.f64 (+.f64 x 1)) n)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (*.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))))
10.8b
(-.f64 (+.f64 (*.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (/.f64 (log.f64 (+.f64 x 1)) n)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (*.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))))

rewrite4.5s (9.1%)

Algorithm
rewrite-expression-head
Error
0.2b
Rules
249×add-log-exp_binary64_458
147×sum-log_binary64_510
48×diff-log_binary64_511
28×flip3-+_binary64_422 flip-+_binary64_393 *-un-lft-identity_binary64_419
24×frac-sub_binary64_428
18×associate-+r-_binary64_353
13×add-sqr-sqrt_binary64_441
12×frac-add_binary64_427 cancel-sign-sub-inv_binary64_385
add-cube-cbrt_binary64_454
distribute-lft-out_binary64_370 distribute-lft-out--_binary64_371 log-div_binary64_506 div-sub_binary64_424 associate--l-_binary64_357
pow1_binary64_480 add-exp-log_binary64_457 add-cbrt-cube_binary64_455
flip3--_binary64_423 sub-neg_binary64_412 flip--_binary64_394 difference-of-squares_binary64_388 associate--l+_binary64_356 associate--r+_binary64_355
associate-+r+_binary64_351 +-commutative_binary64_349
Counts
4 → 148
Calls

4 calls:

68.0ms
(-.f64 (+.f64 (*.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (/.f64 (log.f64 (+.f64 x 1)) n)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (*.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))))
63.0ms
(-.f64 (+.f64 (*.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (/.f64 (log.f64 (+.f64 x 1)) n)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (*.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))))
60.0ms
(-.f64 (+.f64 (*.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (/.f64 (log.f64 (+.f64 x 1)) n)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (*.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))))
17.0ms
(+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (*.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))
Compiler

Compiled 44019 to 29557 computations (32.9% saved)

series8.3s (16.7%)

Error
0.2b
Counts
4 → 73
Calls

4 calls:

1.9s
(-.f64 (+.f64 (*.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (/.f64 (log.f64 (+.f64 x 1)) n)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (*.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))))
1.9s
(-.f64 (+.f64 (*.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (/.f64 (log.f64 (+.f64 x 1)) n)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (*.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))))
1.8s
(-.f64 (+.f64 (*.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (/.f64 (log.f64 (+.f64 x 1)) n)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (*.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))))
1.4s
(+.f64 (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (*.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))
Compiler

Compiled 35670 to 25558 computations (28.3% saved)

simplify638.0ms (1.3%)

Algorithm
egg-herbie
Rules
317×distribute-rgt-in_binary64_369
310×associate-/r*_binary64_363
301×distribute-lft-in_binary64_368
286×times-frac_binary64_425
171×associate-/l*_binary64_364
131×*-commutative_binary64_350
127×associate-*r/_binary64_361
118×+-commutative_binary64_349
113×sub-neg_binary64_412
106×associate-*l/_binary64_362
84×cancel-sign-sub-inv_binary64_385
81×associate-+r+_binary64_351
76×distribute-neg-in_binary64_380
70×sqr-pow_binary64_391
60×exp-prod_binary64_471 div-exp_binary64_470
47×neg-mul-1_binary64_415 neg-sub0_binary64_414
43×distribute-rgt-neg-in_binary64_377
25×distribute-lft-neg-in_binary64_376
19×unpow3_binary64_485 div-sub_binary64_424 associate--r+_binary64_355
18×cube-mult_binary64_449 distribute-lft-neg-out_binary64_378
17×associate--l+_binary64_356
16×unswap-sqr_binary64_387 associate-*r*_binary64_359
14×distribute-frac-neg_binary64_382 distribute-rgt-out_binary64_372
11×unpow1/2_binary64_483
10×prod-exp_binary64_468
unpow2_binary64_484 unpow1_binary64_477
cube-prod_binary64_447
swap-sqr_binary64_386 distribute-rgt-neg-out_binary64_379 associate-/l/_binary64_366 associate-/r/_binary64_365
exp-sum_binary64_465 difference-of-squares_binary64_388
associate-*l*_binary64_360
log-div_binary64_506 log-prod_binary64_505 distribute-rgt-out--_binary64_373 associate-+r-_binary64_353
mul-1-neg_binary64_411 distribute-neg-frac_binary64_383
cube-div_binary64_448 unsub-neg_binary64_413 *-rgt-identity_binary64_409 distribute-rgt1-in_binary64_375
log-pow_binary64_508 log-rec_binary64_507 exp-diff_binary64_467 1-exp_binary64_463 cube-unmult_binary64_456 cube-neg_binary64_446 rem-3cbrt-lft_binary64_444 sqr-neg_binary64_433 rem-square-sqrt_binary64_431 pow-sqr_binary64_392 distribute-lft-out--_binary64_371 associate-+l+_binary64_352
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 pow-base-0_binary64_503 unpow1/3_binary64_486 pow-plus_binary64_482 exp-to-pow_binary64_481 pow-base-1_binary64_479 unpow0_binary64_478 unpow-1_binary64_476 exp-lft-cube_binary64_475 exp-lft-sqr_binary64_474 exp-cbrt_binary64_473 exp-sqrt_binary64_472 rec-exp_binary64_469 exp-neg_binary64_466 e-exp-1_binary64_464 exp-1-e_binary64_462 exp-0_binary64_461 rem-log-exp_binary64_460 rem-exp-log_binary64_459 rem-3cbrt-rft_binary64_445 rem-cbrt-cube_binary64_443 rem-cube-cbrt_binary64_442 sqr-abs_binary64_434 rem-sqrt-square_binary64_432 /-rgt-identity_binary64_410 *-lft-identity_binary64_408 remove-double-neg_binary64_407 sub0-neg_binary64_406 --rgt-identity_binary64_405 +-rgt-identity_binary64_404 +-lft-identity_binary64_403 mul0-rgt_binary64_402 mul0-lft_binary64_401 div0_binary64_400 *-inverses_binary64_399 +-inverses_binary64_398 lft-mult-inverse_binary64_397 rgt-mult-inverse_binary64_396 remove-double-div_binary64_395 difference-of-sqr--1_binary64_390 difference-of-sqr-1_binary64_389 cancel-sign-sub_binary64_384 distribute-neg-out_binary64_381 distribute-lft1-in_binary64_374 distribute-lft-out_binary64_370 count-2_binary64_367 associate--r-_binary64_358 associate--l-_binary64_357 associate-+l-_binary64_354
Counts
221 → 205
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
048935309
1156733684
2486833684
3492233684

prune6.1s (12.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New2041205
Fresh01111
Picked101
Done000
Total20512217
Error
0.2b
Counts
217 → 12
Compiler

Compiled 54914 to 36642 computations (33.3% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.4b
(+.f64 (-.f64 (+.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (*.f64 n n))) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))) (/.f64 (-.f64 (log.f64 (+.f64 1 x)) (log.f64 x)) n)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))) (*.f64 (/.f64 (pow.f64 (log.f64 x) 2) (*.f64 n n)) -1/2))
3.9b
(-.f64 (log.f64 (+.f64 1 x)) (log.f64 x))
5.5b
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (*.f64 n n))) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3)))
8.1b
(-.f64 (+.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (*.f64 n n))) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))) (/.f64 (-.f64 (log.f64 (+.f64 1 x)) (log.f64 x)) n)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)))

rewrite574.0ms (1.2%)

Algorithm
rewrite-expression-head
Error
0.2b
Rules
29×add-log-exp_binary64_458
16×associate-*r/_binary64_361 frac-add_binary64_427
13×cube-div_binary64_448 *-un-lft-identity_binary64_419
11×sum-log_binary64_510
10×frac-sub_binary64_428
pow1_binary64_480 add-sqr-sqrt_binary64_441
diff-log_binary64_511 add-cube-cbrt_binary64_454 flip3-+_binary64_422 flip-+_binary64_393 log-prod_binary64_505 associate-*l/_binary64_362
cancel-sign-sub-inv_binary64_385 associate--l+_binary64_356
log-pow_binary64_508
add-exp-log_binary64_457 add-cbrt-cube_binary64_455 distribute-lft-out--_binary64_371
flip3--_binary64_423 sub-neg_binary64_412 flip--_binary64_394 associate--l-_binary64_357 associate--r+_binary64_355 associate-+l+_binary64_352
+-commutative_binary64_349 log-div_binary64_506
div-sub_binary64_424 associate-+r-_binary64_353 difference-of-squares_binary64_388 distribute-lft-out_binary64_370 associate-+l-_binary64_354
Counts
4 → 87
Calls

4 calls:

32.0ms
(+.f64 (-.f64 (+.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (*.f64 n n))) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))) (/.f64 (-.f64 (log.f64 (+.f64 1 x)) (log.f64 x)) n)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))) (*.f64 (/.f64 (pow.f64 (log.f64 x) 2) (*.f64 n n)) -1/2))
29.0ms
(-.f64 (+.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (*.f64 n n))) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))) (/.f64 (-.f64 (log.f64 (+.f64 1 x)) (log.f64 x)) n)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)))
14.0ms
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (*.f64 n n))) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3)))
8.0ms
(-.f64 (log.f64 (+.f64 1 x)) (log.f64 x))
Compiler

Compiled 8204 to 5507 computations (32.9% saved)

series4.4s (8.8%)

Error
0.2b
Counts
4 → 59
Calls

4 calls:

1.9s
(+.f64 (-.f64 (+.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (*.f64 n n))) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))) (/.f64 (-.f64 (log.f64 (+.f64 1 x)) (log.f64 x)) n)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))) (*.f64 (/.f64 (pow.f64 (log.f64 x) 2) (*.f64 n n)) -1/2))
1.5s
(-.f64 (+.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (*.f64 n n))) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))) (/.f64 (-.f64 (log.f64 (+.f64 1 x)) (log.f64 x)) n)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)))
690.0ms
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (*.f64 n n))) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3)))
109.0ms
(-.f64 (log.f64 (+.f64 1 x)) (log.f64 x))
Compiler

Compiled 7980 to 6050 computations (24.2% saved)

simplify181.0ms (0.4%)

Algorithm
egg-herbie
Rules
388×associate-*r*_binary64_359
366×associate-*l*_binary64_360
221×associate-/r*_binary64_363
209×times-frac_binary64_425
147×sub-neg_binary64_412
132×distribute-rgt-in_binary64_369
130×*-commutative_binary64_350
129×associate-/l*_binary64_364
122×associate-*r/_binary64_361
120×+-commutative_binary64_349
118×distribute-lft-in_binary64_368
117×cancel-sign-sub-inv_binary64_385
99×associate-*l/_binary64_362
77×distribute-rgt-neg-in_binary64_377
63×neg-sub0_binary64_414
62×distribute-lft-neg-in_binary64_376
61×neg-mul-1_binary64_415 associate-+r+_binary64_351
60×sqr-pow_binary64_391
51×distribute-neg-in_binary64_380
29×div-sub_binary64_424
28×associate--l+_binary64_356
23×unpow3_binary64_485
22×cube-mult_binary64_449 associate--r+_binary64_355
20×distribute-neg-frac_binary64_383
18×cube-prod_binary64_447 distribute-lft-neg-out_binary64_378
14×cube-div_binary64_448 swap-sqr_binary64_386 distribute-rgt-out_binary64_372
13×unswap-sqr_binary64_387
12×distribute-frac-neg_binary64_382
distribute-lft-out_binary64_370
unpow2_binary64_484 exp-prod_binary64_471 distribute-rgt-out--_binary64_373
unpow1_binary64_477 difference-of-squares_binary64_388 distribute-rgt-neg-out_binary64_379
prod-exp_binary64_468 exp-sum_binary64_465
exp-diff_binary64_467 mul-1-neg_binary64_411 associate-/r/_binary64_365 associate-+r-_binary64_353
log-prod_binary64_505 unsub-neg_binary64_413
log-div_binary64_506 div-exp_binary64_470 rem-exp-log_binary64_459 pow-sqr_binary64_392 associate-/l/_binary64_366 associate-+l-_binary64_354 associate-+l+_binary64_352
log-rec_binary64_507 pow-plus_binary64_482 1-exp_binary64_463 cube-unmult_binary64_456 cube-neg_binary64_446 rem-3cbrt-lft_binary64_444 sqr-neg_binary64_433 rem-square-sqrt_binary64_431 *-lft-identity_binary64_408 distribute-rgt1-in_binary64_375 distribute-lft-out--_binary64_371 count-2_binary64_367 associate--l-_binary64_357
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 pow-base-1_binary64_479 unpow0_binary64_478 unpow-1_binary64_476 exp-lft-cube_binary64_475 exp-lft-sqr_binary64_474 exp-cbrt_binary64_473 exp-sqrt_binary64_472 rec-exp_binary64_469 exp-neg_binary64_466 e-exp-1_binary64_464 exp-1-e_binary64_462 exp-0_binary64_461 rem-log-exp_binary64_460 rem-3cbrt-rft_binary64_445 rem-cbrt-cube_binary64_443 rem-cube-cbrt_binary64_442 sqr-abs_binary64_434 rem-sqrt-square_binary64_432 /-rgt-identity_binary64_410 *-rgt-identity_binary64_409 remove-double-neg_binary64_407 sub0-neg_binary64_406 --rgt-identity_binary64_405 +-rgt-identity_binary64_404 +-lft-identity_binary64_403 mul0-rgt_binary64_402 mul0-lft_binary64_401 div0_binary64_400 *-inverses_binary64_399 +-inverses_binary64_398 lft-mult-inverse_binary64_397 rgt-mult-inverse_binary64_396 remove-double-div_binary64_395 difference-of-sqr--1_binary64_390 difference-of-sqr-1_binary64_389 cancel-sign-sub_binary64_384 distribute-neg-out_binary64_381 distribute-lft1-in_binary64_374 associate--r-_binary64_358
Counts
146 → 128
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
049811317
1153910849
2503610849

prune675.0ms (1.4%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New1226128
Fresh3811
Picked011
Done000
Total12515140
Error
0.1b
Counts
140 → 15
Compiler

Compiled 9928 to 6411 computations (35.4% saved)

regimes2.4s (4.8%)

Accuracy

Total 7.0b remaining (96.5%)

Threshold costs 0b (0%)

Compiler

Compiled 28304 to 20384 computations (28% saved)

bsearch73.0ms (0.1%)

Steps
ItersRangePoint
8
9.43389880548063
7478.467015072123
113.7828166612893
Compiler

Compiled 1 to 2 computations (-100% saved)

simplify12.0ms (0%)

Algorithm
egg-herbie
Rules
18×+-commutative_binary64_349
17×*-commutative_binary64_350
13×sub-neg_binary64_412
12×neg-mul-1_binary64_415 neg-sub0_binary64_414
unsub-neg_binary64_413 distribute-neg-in_binary64_380 distribute-rgt-neg-in_binary64_377 distribute-lft-neg-in_binary64_376
distribute-neg-frac_binary64_383
1-exp_binary64_463
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 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 tan-0_binary64_548 cos-0_binary64_547 sin-0_binary64_546 unpow1_binary64_477 e-exp-1_binary64_464 exp-1-e_binary64_462 exp-0_binary64_461 sqr-abs_binary64_434 sqr-neg_binary64_433 mul-1-neg_binary64_411 /-rgt-identity_binary64_410 *-rgt-identity_binary64_409 *-lft-identity_binary64_408 remove-double-neg_binary64_407 sub0-neg_binary64_406 --rgt-identity_binary64_405 +-rgt-identity_binary64_404 +-lft-identity_binary64_403 cancel-sign-sub-inv_binary64_385 cancel-sign-sub_binary64_384 distribute-frac-neg_binary64_382 distribute-neg-out_binary64_381 distribute-rgt-neg-out_binary64_379 distribute-lft-neg-out_binary64_378
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
040110
154110
262110
376110
4101110
5121110
6136110
7144110
8146110
9145110

end0.0ms (0%)

sample11.5s (23.1%)

Algorithm
intervals
Results
1.6s2693×body1024valid
1.2s1711×body2048valid
1.1s1379×body1024nan
518.0ms2624×body128overflowed
483.0ms1233×body512valid
360.0ms727×body512nan
178.0ms1801×body128valid
176.0ms180×body1024invalid
133.0ms562×body256valid
115.0ms221×body512invalid
91.0ms371×body256nan
50.0ms740×body128nan
39.0ms135×body256invalid
35.0ms260×body128invalid
8.0msbody2048nan
Compiler

Compiled 7007 to 5036 computations (28.1% saved)

Profiling

Loading profile data...