Details

Time bar (total: 21.1s)

analyze1.1s (5.1%)

Algorithm
search
egg-herbie
Rules
70×*-commutative_binary64_350
57×associate-/l*_binary64_364
30×associate-/r/_binary64_365
26×distribute-rgt-out_binary64_372
24×associate-*r/_binary64_361
18×associate-*r*_binary64_359
16×associate-*l/_binary64_362
12×associate-/l/_binary64_366 associate-*l*_binary64_360
+-commutative_binary64_349
distribute-rgt-in_binary64_369
distribute-lft-out_binary64_370
associate-/r*_binary64_363
swap-a1-a2
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 1-exp_binary64_463 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 times-frac_binary64_425 div-sub_binary64_424 neg-mul-1_binary64_415 neg-sub0_binary64_414 unsub-neg_binary64_413 sub-neg_binary64_412 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 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 pow-sqr_binary64_392 sqr-pow_binary64_391 difference-of-sqr--1_binary64_390 difference-of-sqr-1_binary64_389 difference-of-squares_binary64_388 unswap-sqr_binary64_387 swap-sqr_binary64_386 cancel-sign-sub-inv_binary64_385 cancel-sign-sub_binary64_384 distribute-neg-frac_binary64_383 distribute-frac-neg_binary64_382 distribute-neg-out_binary64_381 distribute-neg-in_binary64_380 distribute-rgt-neg-out_binary64_379 distribute-lft-neg-out_binary64_378 distribute-rgt-neg-in_binary64_377 distribute-lft-neg-in_binary64_376 distribute-rgt1-in_binary64_375 distribute-lft1-in_binary64_374 distribute-rgt-out--_binary64_373 distribute-lft-out--_binary64_371 distribute-lft-in_binary64_368 count-2_binary64_367 associate--r-_binary64_358 associate--l-_binary64_357 associate--l+_binary64_356 associate--r+_binary64_355 associate-+l-_binary64_354 associate-+r-_binary64_353 associate-+l+_binary64_352 associate-+r+_binary64_351
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02580
16580
212080
317480
422880
525880
628580
727980
827980
033
133
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
25%74.9%0.1%6
25%74.9%0.1%7
25%74.9%0.1%8
25%74.9%0.1%9
25%64%11.1%10
31.2%54.6%14.2%11
39%44.1%16.9%12
39%41.5%19.5%13
42.9%37%20.1%14
Symmetry

(sort a1 a2)

Compiler

Compiled 20 to 16 computations (20% saved)

sample89.0ms (0.4%)

Algorithm
intervals
Results
17.0ms59×body1024valid
16.0ms56×body1024invalid
11.0ms150×body128valid
6.0ms30×body512valid
5.0ms25×body512invalid
2.0ms16×body256valid
2.0ms20×body128invalid
1.0ms10×body256invalid
0.0msbody2048valid
Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify17.0ms (0.1%)

Algorithm
egg-herbie
Rules
23×*-commutative_binary64_350
20×associate-/l*_binary64_364
11×associate-/r/_binary64_365
distribute-rgt-out_binary64_372 associate-*r/_binary64_361
associate-*r*_binary64_359
associate-*l/_binary64_362
associate-/l/_binary64_366 associate-*l*_binary64_360
+-commutative_binary64_349
distribute-rgt-in_binary64_369 associate-/r*_binary64_363
distribute-lft-out_binary64_370
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 1-exp_binary64_463 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 times-frac_binary64_425 div-sub_binary64_424 neg-mul-1_binary64_415 neg-sub0_binary64_414 unsub-neg_binary64_413 sub-neg_binary64_412 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 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 pow-sqr_binary64_392 sqr-pow_binary64_391 difference-of-sqr--1_binary64_390 difference-of-sqr-1_binary64_389 difference-of-squares_binary64_388 unswap-sqr_binary64_387 swap-sqr_binary64_386 cancel-sign-sub-inv_binary64_385 cancel-sign-sub_binary64_384 distribute-neg-frac_binary64_383 distribute-frac-neg_binary64_382 distribute-neg-out_binary64_381 distribute-neg-in_binary64_380 distribute-rgt-neg-out_binary64_379 distribute-lft-neg-out_binary64_378 distribute-rgt-neg-in_binary64_377 distribute-lft-neg-in_binary64_376 distribute-rgt1-in_binary64_375 distribute-lft1-in_binary64_374 distribute-rgt-out--_binary64_373 distribute-lft-out--_binary64_371 distribute-lft-in_binary64_368 count-2_binary64_367 associate--r-_binary64_358 associate--l-_binary64_357 associate--l+_binary64_356 associate--r+_binary64_355 associate-+l-_binary64_354 associate-+r-_binary64_353 associate-+l+_binary64_352 associate-+r+_binary64_351
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01320
12620
24620
36620
48520
59720
610820
710620
810620

prune5.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.4b
Counts
2 → 2
Compiler

Compiled 45 to 37 computations (17.8% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(cos.f64 th)
0.0b
(+.f64 (*.f64 a1 a1) (*.f64 a2 a2))
0.2b
(*.f64 (cos.f64 th) (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
0.4b
(/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2))

rewrite184.0ms (0.9%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
41×add-sqr-sqrt_binary64_441
38×times-frac_binary64_425
33×add-cube-cbrt_binary64_454 *-un-lft-identity_binary64_419
22×sqrt-prod_binary64_435 associate-*r*_binary64_359
11×add-exp-log_binary64_457 add-cbrt-cube_binary64_455
pow1_binary64_480 add-log-exp_binary64_458 associate-/r*_binary64_363
associate-/l*_binary64_364 unswap-sqr_binary64_387 associate-*l*_binary64_360
div-exp_binary64_470 cbrt-undiv_binary64_453 div-inv_binary64_416 flip3-+_binary64_422 associate-/l/_binary64_366 flip-+_binary64_393 prod-exp_binary64_468 cbrt-unprod_binary64_452
frac-2neg_binary64_430 clear-num_binary64_418 pow-prod-down_binary64_490 associate-*r/_binary64_361 *-commutative_binary64_350 sum-log_binary64_510 +-commutative_binary64_349
Counts
4 → 101
Calls

4 calls:

14.0ms
(*.f64 (cos.f64 th) (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
7.0ms
(/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2))
4.0ms
(+.f64 (*.f64 a1 a1) (*.f64 a2 a2))
1.0ms
(cos.f64 th)
Compiler

Compiled 2482 to 900 computations (63.7% saved)

series1.1s (5.4%)

Error
0.4b
Counts
4 → 48
Calls

4 calls:

618.0ms
(*.f64 (cos.f64 th) (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
298.0ms
(/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2))
140.0ms
(+.f64 (*.f64 a1 a1) (*.f64 a2 a2))
21.0ms
(cos.f64 th)
Compiler

Compiled 1922 to 1655 computations (13.9% saved)

simplify152.0ms (0.7%)

Algorithm
egg-herbie
Rules
410×sub-neg_binary64_412
348×associate-/l*_binary64_364
269×associate-*l/_binary64_362
258×associate-*r/_binary64_361
181×associate--l+_binary64_356
156×associate-+l+_binary64_352
155×distribute-rgt-in_binary64_369
144×associate--r+_binary64_355
136×cancel-sign-sub-inv_binary64_385
133×distribute-lft-in_binary64_368
131×associate-/r*_binary64_363
121×associate-*l*_binary64_360
119×associate-*r*_binary64_359
117×associate-/r/_binary64_365
109×associate-/l/_binary64_366
102×associate-+r+_binary64_351
98×times-frac_binary64_425
92×unswap-sqr_binary64_387
85×unsub-neg_binary64_413
84×*-commutative_binary64_350
65×neg-mul-1_binary64_415 neg-sub0_binary64_414
47×+-commutative_binary64_349
45×distribute-rgt-neg-in_binary64_377
38×associate-+l-_binary64_354
37×distribute-lft-neg-in_binary64_376
36×sqr-pow_binary64_391
31×log-div_binary64_506 associate-+r-_binary64_353
28×distribute-neg-in_binary64_380
26×cube-prod_binary64_447 *-rgt-identity_binary64_409
24×unpow3_binary64_485 exp-prod_binary64_471
23×div-sub_binary64_424
22×*-lft-identity_binary64_408
21×log-prod_binary64_505
18×cube-mult_binary64_449 cube-div_binary64_448
17×distribute-rgt-out_binary64_372
15×distribute-neg-frac_binary64_383
11×distribute-lft-neg-out_binary64_378
10×pow-plus_binary64_482 cube-unmult_binary64_456
/-rgt-identity_binary64_410 distribute-rgt-out--_binary64_373 distribute-lft-out_binary64_370
log-rec_binary64_507 pow-sqr_binary64_392 difference-of-squares_binary64_388
swap-sqr_binary64_386 associate--l-_binary64_357
unpow1/2_binary64_483 rem-sqrt-square_binary64_432
unpow2_binary64_484 unpow1_binary64_477 distribute-rgt-neg-out_binary64_379
distribute-lft-out--_binary64_371
prod-exp_binary64_468 exp-sum_binary64_465 1-exp_binary64_463 exp-1-e_binary64_462 rem-square-sqrt_binary64_431
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 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 div-exp_binary64_470 rec-exp_binary64_469 exp-diff_binary64_467 exp-neg_binary64_466 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 mul-1-neg_binary64_411 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-frac-neg_binary64_382 distribute-neg-out_binary64_381 distribute-rgt1-in_binary64_375 distribute-lft1-in_binary64_374 count-2_binary64_367 associate--r-_binary64_358
Counts
149 → 130
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01843451
14733196
215643100
344373100
449633100
549673100

prune177.0ms (0.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1237130
Fresh011
Picked101
Done000
Total1248132
Error
0.0b
Counts
132 → 8
Compiler

Compiled 2852 to 1170 computations (59% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(/.f64 (sqrt.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
0.3b
(*.f64 (*.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (sqrt.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
6.2b
(sqrt.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))
6.2b
(sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))

rewrite549.0ms (2.6%)

Algorithm
rewrite-expression-head
Error
0b
Rules
108×times-frac_binary64_425
102×sqrt-prod_binary64_435
86×add-sqr-sqrt_binary64_441
84×add-cube-cbrt_binary64_454 *-un-lft-identity_binary64_419
78×cbrt-prod_binary64_450
58×associate-*r*_binary64_359
38×add-exp-log_binary64_457
29×add-cbrt-cube_binary64_455
16×prod-exp_binary64_468 cbrt-unprod_binary64_452
11×pow1_binary64_480
div-exp_binary64_470 cbrt-undiv_binary64_453 associate-/r*_binary64_363
sqrt-div_binary64_436 associate-/l*_binary64_364
add-log-exp_binary64_458
flip3-+_binary64_422 flip-+_binary64_393 pow-prod-down_binary64_490 associate-*r/_binary64_361
pow1/2_binary64_499 sqrt-pow1_binary64_437 rem-sqrt-square_binary64_432 div-inv_binary64_416 associate-/l/_binary64_366
frac-times_binary64_429 associate-*l/_binary64_362 associate-*l*_binary64_360 *-commutative_binary64_350 frac-2neg_binary64_430 clear-num_binary64_418
Counts
4 → 201
Calls

4 calls:

31.0ms
(*.f64 (*.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (sqrt.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
12.0ms
(/.f64 (sqrt.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
4.0ms
(sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
4.0ms
(sqrt.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))
Compiler

Compiled 9640 to 4180 computations (56.6% saved)

series1.1s (5.3%)

Error
0.0b
Counts
4 → 42
Calls

4 calls:

637.0ms
(*.f64 (*.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (sqrt.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
244.0ms
(/.f64 (sqrt.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
86.0ms
(sqrt.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))
80.0ms
(sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
Compiler

Compiled 3145 to 2549 computations (19% saved)

simplify307.0ms (1.5%)

Algorithm
egg-herbie
Rules
404×associate-/r/_binary64_365
332×associate-*l*_binary64_360
284×associate-*r*_binary64_359
219×cancel-sign-sub-inv_binary64_385
206×associate-*r/_binary64_361
196×*-commutative_binary64_350
192×associate-*l/_binary64_362
181×associate-/l*_binary64_364
118×sub-neg_binary64_412
116×times-frac_binary64_425
111×unswap-sqr_binary64_387 distribute-rgt-in_binary64_369
102×log-prod_binary64_505
85×distribute-rgt-neg-in_binary64_377
84×distribute-lft-in_binary64_368 associate-/r*_binary64_363
69×distribute-lft-neg-in_binary64_376
67×associate-/l/_binary64_366
65×log-div_binary64_506 cube-div_binary64_448
55×+-commutative_binary64_349
50×exp-prod_binary64_471
47×*-rgt-identity_binary64_409
43×sqr-pow_binary64_391
37×*-lft-identity_binary64_408
36×neg-sub0_binary64_414
34×unpow3_binary64_485 distribute-neg-frac_binary64_383
32×neg-mul-1_binary64_415
31×associate-+l+_binary64_352
29×swap-sqr_binary64_386 distribute-neg-in_binary64_380
27×cube-mult_binary64_449 associate--l+_binary64_356
26×cube-prod_binary64_447 distribute-rgt-out_binary64_372
25×associate--r+_binary64_355
22×associate-+r+_binary64_351
17×distribute-rgt-out--_binary64_373
16×unsub-neg_binary64_413 distribute-lft-neg-out_binary64_378 distribute-lft-out_binary64_370
14×cube-unmult_binary64_456
13×associate-+r-_binary64_353
12×difference-of-squares_binary64_388
11×/-rgt-identity_binary64_410
10×pow-plus_binary64_482
associate-+l-_binary64_354
unpow1/2_binary64_483 rem-sqrt-square_binary64_432 mul-1-neg_binary64_411 pow-sqr_binary64_392
unpow2_binary64_484 unpow1_binary64_477 rem-square-sqrt_binary64_431 distribute-lft-out--_binary64_371
log-pow_binary64_508 +-rgt-identity_binary64_404 distribute-rgt-neg-out_binary64_379
unpow1/3_binary64_486 1-exp_binary64_463 exp-1-e_binary64_462 rem-3cbrt-lft_binary64_444 count-2_binary64_367
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-rec_binary64_507 pow-base-0_binary64_503 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 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-0_binary64_461 rem-log-exp_binary64_460 rem-exp-log_binary64_459 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 div-sub_binary64_424 remove-double-neg_binary64_407 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 +-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-frac-neg_binary64_382 distribute-neg-out_binary64_381 distribute-rgt1-in_binary64_375 distribute-lft1-in_binary64_374 associate--r-_binary64_358 associate--l-_binary64_357
Counts
243 → 216
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03139900
17717998
231307890
347917890
450007890
549607890

prune409.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2151216
Fresh077
Picked011
Done000
Total2159224
Error
0b
Counts
224 → 9
Compiler

Compiled 8441 to 3885 computations (54% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
0.3b
(*.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
6.2b
(sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
6.2b
(sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))

rewrite650.0ms (3.1%)

Algorithm
rewrite-expression-head
Error
0b
Rules
149×add-sqr-sqrt_binary64_441
146×times-frac_binary64_425
127×sqrt-prod_binary64_435
90×cbrt-prod_binary64_450
87×add-cube-cbrt_binary64_454 *-un-lft-identity_binary64_419
58×associate-*r*_binary64_359
27×add-exp-log_binary64_457
21×unswap-sqr_binary64_387
19×add-cbrt-cube_binary64_455
10×associate-*l*_binary64_360
associate-/r*_binary64_363
pow1_binary64_480 div-exp_binary64_470 prod-exp_binary64_468 cbrt-unprod_binary64_452 cbrt-undiv_binary64_453
sqrt-div_binary64_436 associate-/l*_binary64_364
add-log-exp_binary64_458
flip3-+_binary64_422 flip-+_binary64_393 div-inv_binary64_416
pow1/2_binary64_499 sqrt-pow1_binary64_437 rem-sqrt-square_binary64_432 associate-/l/_binary64_366
pow-prod-down_binary64_490 frac-times_binary64_429 associate-*l/_binary64_362 associate-*r/_binary64_361 *-commutative_binary64_350 frac-2neg_binary64_430 clear-num_binary64_418
Counts
4 → 226
Calls

4 calls:

39.0ms
(*.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
9.0ms
(/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
4.0ms
(sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
4.0ms
(sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
Compiler

Compiled 11015 to 4717 computations (57.2% saved)

series778.0ms (3.7%)

Error
0b
Counts
4 → 36
Calls

4 calls:

319.0ms
(*.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
234.0ms
(/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
88.0ms
(sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
81.0ms
(sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
Compiler

Compiled 2603 to 2101 computations (19.3% saved)

simplify384.0ms (1.8%)

Algorithm
egg-herbie
Rules
601×times-frac_binary64_425
327×associate-/r*_binary64_363
251×unswap-sqr_binary64_387
211×associate-*r/_binary64_361
205×associate-*l/_binary64_362
190×associate-/r/_binary64_365
168×sub-neg_binary64_412
154×associate-*l*_binary64_360
149×associate-/l*_binary64_364
141×*-commutative_binary64_350
135×associate-*r*_binary64_359
95×associate-/l/_binary64_366
90×cancel-sign-sub-inv_binary64_385
73×sqr-pow_binary64_391
67×log-div_binary64_506
65×distribute-rgt-in_binary64_369
64×cube-prod_binary64_447
61×neg-sub0_binary64_414
59×distribute-rgt-neg-in_binary64_377
57×log-prod_binary64_505 cube-div_binary64_448 neg-mul-1_binary64_415
56×distribute-lft-in_binary64_368
50×distribute-lft-neg-in_binary64_376
44×difference-of-squares_binary64_388
43×exp-prod_binary64_471 *-rgt-identity_binary64_409 associate-+l-_binary64_354
37×+-commutative_binary64_349
35×*-lft-identity_binary64_408
33×associate-+r-_binary64_353
28×unpow3_binary64_485
26×associate-+l+_binary64_352
23×/-rgt-identity_binary64_410
22×unsub-neg_binary64_413
21×+-rgt-identity_binary64_404 associate-+r+_binary64_351
20×pow-plus_binary64_482 swap-sqr_binary64_386
17×cube-mult_binary64_449 associate--r+_binary64_355
14×cube-unmult_binary64_456
12×sub0-neg_binary64_406 distribute-rgt-out--_binary64_373
11×pow-sqr_binary64_392
10×distribute-neg-frac_binary64_383 distribute-neg-in_binary64_380 associate--l+_binary64_356
log-rec_binary64_507
distribute-lft-neg-out_binary64_378 distribute-rgt-out_binary64_372
rem-sqrt-square_binary64_432 associate--r-_binary64_358 associate--l-_binary64_357
unpow1/2_binary64_483
div-sub_binary64_424
log-pow_binary64_508 mul-1-neg_binary64_411
unpow2_binary64_484 rem-square-sqrt_binary64_431
unpow1_binary64_477 remove-double-neg_binary64_407 +-lft-identity_binary64_403 distribute-lft-out--_binary64_371 count-2_binary64_367
unpow1/3_binary64_486 1-exp_binary64_463 exp-1-e_binary64_462 rem-3cbrt-lft_binary64_444 --rgt-identity_binary64_405 remove-double-div_binary64_395 distribute-rgt-neg-out_binary64_379 distribute-lft-out_binary64_370
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 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 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-0_binary64_461 rem-log-exp_binary64_460 rem-exp-log_binary64_459 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 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 difference-of-sqr--1_binary64_390 difference-of-sqr-1_binary64_389 cancel-sign-sub_binary64_384 distribute-frac-neg_binary64_382 distribute-neg-out_binary64_381 distribute-rgt1-in_binary64_375 distribute-lft1-in_binary64_374
Counts
262 → 193
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
023810322
16129400
221908956
341038736
449188360
549658360
649328360

prune362.0ms (1.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1921193
Fresh257
Picked011
Done011
Total1948202
Error
0b
Counts
202 → 8
Compiler

Compiled 7326 to 3406 computations (53.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (*.f64 a2 a2) (*.f64 a1 a1))
0.2b
(*.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
0.2b
(/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2)))
0.3b
(/.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

rewrite2.3s (10.9%)

Algorithm
rewrite-expression-head
Error
0b
Rules
1137×sqrt-prod_binary64_435
1119×times-frac_binary64_425
625×add-sqr-sqrt_binary64_441
578×add-cube-cbrt_binary64_454 *-un-lft-identity_binary64_419
283×associate-*r*_binary64_359
34×associate-/l*_binary64_364
22×div-inv_binary64_416
20×add-exp-log_binary64_457 add-cbrt-cube_binary64_455
18×associate-/r*_binary64_363
13×unswap-sqr_binary64_387
div-exp_binary64_470 cbrt-undiv_binary64_453
pow1_binary64_480 add-log-exp_binary64_458
associate-/l/_binary64_366 prod-exp_binary64_468 cbrt-unprod_binary64_452 associate-*l*_binary64_360
frac-2neg_binary64_430 clear-num_binary64_418 flip3-+_binary64_422 flip-+_binary64_393
pow-prod-down_binary64_490 associate-*r/_binary64_361 *-commutative_binary64_350 sum-log_binary64_510 +-commutative_binary64_349
Counts
4 → 713
Calls

4 calls:

88.0ms
(*.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
21.0ms
(/.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
9.0ms
(/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2)))
9.0ms
(+.f64 (*.f64 a2 a2) (*.f64 a1 a1))
Compiler

Compiled 27448 to 15232 computations (44.5% saved)

series1.4s (6.8%)

Error
0b
Counts
4 → 54
Calls

4 calls:

588.0ms
(*.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
362.0ms
(/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2)))
278.0ms
(/.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
144.0ms
(+.f64 (*.f64 a2 a2) (*.f64 a1 a1))
Compiler

Compiled 2486 to 2250 computations (9.5% saved)

simplify879.0ms (4.2%)

Algorithm
egg-herbie
Rules
669×associate-/r/_binary64_365
428×associate-/l/_binary64_366
287×associate-/l*_binary64_364
250×associate-*l*_binary64_360
222×associate-*r*_binary64_359
200×*-commutative_binary64_350
197×associate-*r/_binary64_361
140×associate-/r*_binary64_363
129×cancel-sign-sub-inv_binary64_385
118×distribute-rgt-in_binary64_369
115×times-frac_binary64_425
108×associate-*l/_binary64_362
104×unswap-sqr_binary64_387
100×*-rgt-identity_binary64_409
97×distribute-lft-in_binary64_368
82×sub-neg_binary64_412
80×*-lft-identity_binary64_408
75×neg-mul-1_binary64_415
74×neg-sub0_binary64_414
66×log-div_binary64_506
57×log-prod_binary64_505
56×cube-prod_binary64_447
44×distribute-rgt-neg-in_binary64_377
42×+-commutative_binary64_349
38×sqr-pow_binary64_391
37×distribute-lft-neg-in_binary64_376
34×exp-prod_binary64_471
32×cube-div_binary64_448
27×/-rgt-identity_binary64_410 associate--l+_binary64_356
26×distribute-neg-in_binary64_380
25×distribute-neg-frac_binary64_383 distribute-rgt-out_binary64_372
21×associate-+l+_binary64_352
20×div-sub_binary64_424 associate-+r+_binary64_351
18×associate--r+_binary64_355
16×swap-sqr_binary64_386
15×unpow3_binary64_485 cube-unmult_binary64_456
13×unsub-neg_binary64_413 distribute-lft-out_binary64_370
12×rem-sqrt-square_binary64_432
10×cube-mult_binary64_449 distribute-lft-neg-out_binary64_378
log-rec_binary64_507 pow-plus_binary64_482
pow-sqr_binary64_392
difference-of-squares_binary64_388 distribute-rgt-out--_binary64_373
rem-square-sqrt_binary64_431
associate-+r-_binary64_353
unpow1/2_binary64_483 remove-double-div_binary64_395 associate-+l-_binary64_354
unpow2_binary64_484 unpow1_binary64_477 distribute-rgt-neg-out_binary64_379
log-pow_binary64_508 prod-exp_binary64_468 exp-sum_binary64_465 1-exp_binary64_463 exp-1-e_binary64_462 rem-3cbrt-rft_binary64_445 rem-3cbrt-lft_binary64_444 sqr-abs_binary64_434 div0_binary64_400 distribute-neg-out_binary64_381 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 pow-base-0_binary64_503 unpow1/3_binary64_486 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 div-exp_binary64_470 rec-exp_binary64_469 exp-diff_binary64_467 exp-neg_binary64_466 e-exp-1_binary64_464 exp-0_binary64_461 rem-log-exp_binary64_460 rem-exp-log_binary64_459 cube-neg_binary64_446 rem-cbrt-cube_binary64_443 rem-cube-cbrt_binary64_442 sqr-neg_binary64_433 mul-1-neg_binary64_411 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 *-inverses_binary64_399 +-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-frac-neg_binary64_382 distribute-rgt1-in_binary64_375 distribute-lft1-in_binary64_374 associate--r-_binary64_358
Counts
767 → 756
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
047729575
1115627687
2327427043
3468726923
4497826923
5497026923

prune1.6s (7.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New7551756
Fresh145
Picked011
Done022
Total7568764
Error
0b
Counts
764 → 8
Compiler

Compiled 24311 to 11982 computations (50.7% saved)

regimes2.2s (10.6%)

Accuracy

Total 0.4b remaining (96.4%)

Threshold costs 0.4b (96.4%)

Compiler

Compiled 24927 to 18647 computations (25.2% saved)

bsearch0.0ms (0%)

simplify15.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64_350
+-commutative_binary64_349
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 1-exp_binary64_463 exp-1-e_binary64_462 exp-0_binary64_461 sqr-abs_binary64_434 sqr-neg_binary64_433 neg-mul-1_binary64_415 neg-sub0_binary64_414 unsub-neg_binary64_413 sub-neg_binary64_412 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-neg-frac_binary64_383 distribute-frac-neg_binary64_382 distribute-neg-out_binary64_381 distribute-neg-in_binary64_380 distribute-rgt-neg-out_binary64_379 distribute-lft-neg-out_binary64_378 distribute-rgt-neg-in_binary64_377 distribute-lft-neg-in_binary64_376
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01952
12052
22052
Remove

(sort a1 a2)

Compiler

Compiled 64 to 44 computations (31.3% saved)

end0.0ms (0%)

sample5.2s (24.5%)

Algorithm
intervals
Results
556.0ms1775×body1024valid
480.0ms1562×body1024invalid
379.0ms4857×body128valid
208.0ms913×body512valid
161.0ms724×body512invalid
71.0ms448×body256valid
59.0ms398×body256invalid
59.0ms693×body128invalid
3.0msbody2048valid
1.0msbody2048invalid
Compiler

Compiled 3153 to 2355 computations (25.3% saved)

Profiling

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