Details

analyze1.1s (6.3%)

Algorithm

1×	search
2×	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`
9×	`+-commutative_binary64_349`
6×	`distribute-rgt-in_binary64_369`
4×	`distribute-lft-out_binary64_370`
3×	`associate-/r*_binary64_363`
1×	`swap-a1-a2`
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` `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)

Iter	Nodes	Cost
0	25	80
1	65	80
2	120	80
3	174	80
4	228	80
5	258	80
6	285	80
7	279	80
8	279	80
0	3	3
1	3	3

Search

True	Other	False	Iter
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)

sample94.0ms (0.5%)

Algorithm

1×

intervals

Results

18.0ms	53×	body	1024	invalid
14.0ms	44×	body	1024	valid
14.0ms	173×	body	128	valid
6.0ms	24×	body	512	valid
5.0ms	21×	body	512	invalid
3.0ms	18×	body	256	invalid
2.0ms	15×	body	256	valid
1.0ms	16×	body	128	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

23×	`*-commutative_binary64_350`
20×	`associate-/l*_binary64_364`
11×	`associate-/r/_binary64_365`
9×	`distribute-rgt-out_binary64_372` `associate-*r/_binary64_361`
6×	`associate-r_binary64_359`
5×	`associate-*l/_binary64_362`
4×	`associate-/l/_binary64_366` `associate-l_binary64_360`
3×	`+-commutative_binary64_349`
2×	`distribute-rgt-in_binary64_369` `associate-/r*_binary64_363`
1×	`distribute-lft-out_binary64_370`
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` `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)

Iter	Nodes	Cost
0	13	20
1	26	20
2	46	20
3	66	20
4	85	20
5	97	20
6	108	20
7	106	20
8	106	20

prune5.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.4b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.1b	(.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))

rewrite174.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

40×	`add-sqr-sqrt_binary64_441`
38×	`times-frac_binary64_425`
32×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
22×	`sqrt-prod_binary64_435` `associate-r_binary64_359`
10×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
6×	`associate-/r*_binary64_363`
5×	`pow1_binary64_480` `add-log-exp_binary64_458`
3×	`associate-/l_binary64_364` `unswap-sqr_binary64_387` `associate-l*_binary64_360`
2×	`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`
1×	`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

3 → 94

Calls

3 calls:

13.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
8.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
5.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 2362 to 862 computations (63.5% saved)

series1.1s (6%)

Error

0.4b

Counts

3 → 41

Calls

3 calls:

619.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
288.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
138.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 1585 to 1399 computations (11.7% saved)

simplify118.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

867×	`distribute-rgt-in_binary64_369`
302×	`cancel-sign-sub-inv_binary64_385`
301×	`associate-/l*_binary64_364`
273×	`unswap-sqr_binary64_387` `*-commutative_binary64_350`
266×	`associate-*r/_binary64_361`
261×	`associate-*l/_binary64_362`
137×	`sub-neg_binary64_412`
127×	`distribute-lft-in_binary64_368`
114×	`associate-l_binary64_360`
112×	`distribute-rgt-neg-in_binary64_377`
111×	`associate-/r/_binary64_365`
108×	`associate-/r*_binary64_363`
107×	`associate-r_binary64_359`
105×	`associate-/l/_binary64_366`
103×	`distribute-lft-neg-in_binary64_376`
98×	`times-frac_binary64_425`
80×	`associate-+l+_binary64_352`
65×	`sqr-pow_binary64_391`
63×	`+-commutative_binary64_349`
58×	`associate--l+_binary64_356`
52×	`associate-+r+_binary64_351`
46×	`*-rgt-identity_binary64_409` `distribute-neg-frac_binary64_383`
44×	`*-lft-identity_binary64_408` `difference-of-squares_binary64_388`
42×	`distribute-rgt-out_binary64_372`
40×	`neg-mul-1_binary64_415` `neg-sub0_binary64_414`
35×	`unsub-neg_binary64_413`
30×	`/-rgt-identity_binary64_410`
26×	`cube-prod_binary64_447`
24×	`log-prod_binary64_505` `exp-prod_binary64_471` `distribute-rgt-out--_binary64_373`
23×	`associate-+l-_binary64_354`
20×	`log-div_binary64_506` `associate-+r-_binary64_353`
19×	`div-sub_binary64_424`
18×	`cube-div_binary64_448`
17×	`swap-sqr_binary64_386` `distribute-lft-neg-out_binary64_378`
16×	`+-rgt-identity_binary64_404` `associate--r+_binary64_355`
15×	`distribute-neg-in_binary64_380`
14×	`pow-sqr_binary64_392`
13×	`distribute-lft-out_binary64_370`
10×	`unpow3_binary64_485` `cube-unmult_binary64_456`
8×	`pow-plus_binary64_482` `sub0-neg_binary64_406`
7×	`distribute-rgt-neg-out_binary64_379`
5×	`cube-mult_binary64_449`
4×	`unpow1/2_binary64_483` `rem-sqrt-square_binary64_432`
3×	`log-rec_binary64_507` `unpow2_binary64_484` `unpow1_binary64_477` `associate--l-_binary64_357`
2×	`remove-double-div_binary64_395`
1×	`prod-exp_binary64_468` `exp-sum_binary64_465` `1-exp_binary64_463` `exp-1-e_binary64_462` `rem-square-sqrt_binary64_431` `distribute-lft-out--_binary64_371`
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` `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` `--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` `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

135 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	158	3137
1	401	2898
2	1319	2865
3	3340	2865
4	5689	2865

prune166.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	117	8	125
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	119	8	127

Error

0.0b

Counts

127 → 8

Compiler

Compiled 2695 to 1077 computations (60% saved)

localize20.0ms (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))))
7.4b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
7.4b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite536.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

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`
9×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/r*_binary64_363`
6×	`sqrt-div_binary64_436` `associate-/l*_binary64_364`
4×	`add-log-exp_binary64_458`
3×	`flip3-+_binary64_422` `flip-+_binary64_393` `pow-prod-down_binary64_490` `associate-*r/_binary64_361`
2×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `div-inv_binary64_416` `associate-/l/_binary64_366`
1×	`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:

36.0ms	(.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))))
9.0ms	(/.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)

series1.4s (7.7%)

Error

0.0b

Counts

4 → 53

Calls

4 calls:

620.0ms	(.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))))
426.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
130.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
126.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 4222 to 3376 computations (20% saved)

simplify262.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

384×	`associate-/r/_binary64_365`
342×	`associate-l_binary64_360`
293×	`associate-r_binary64_359`
241×	`cancel-sign-sub-inv_binary64_385`
210×	`associate-*r/_binary64_361`
200×	`*-commutative_binary64_350`
196×	`associate-*l/_binary64_362`
181×	`associate-/l*_binary64_364`
121×	`distribute-rgt-neg-in_binary64_377`
119×	`times-frac_binary64_425`
109×	`unswap-sqr_binary64_387`
105×	`distribute-lft-neg-in_binary64_376`
102×	`log-prod_binary64_505`
101×	`sub-neg_binary64_412` `distribute-rgt-in_binary64_369`
91×	`cube-prod_binary64_447`
85×	`associate-/r*_binary64_363`
78×	`distribute-lft-in_binary64_368`
67×	`associate-/l/_binary64_366`
65×	`log-div_binary64_506` `cube-div_binary64_448`
54×	`distribute-neg-frac_binary64_383`
50×	`exp-prod_binary64_471`
48×	`+-commutative_binary64_349`
47×	`*-rgt-identity_binary64_409`
42×	`sqr-pow_binary64_391`
37×	`neg-sub0_binary64_414` `*-lft-identity_binary64_408`
33×	`unpow3_binary64_485` `neg-mul-1_binary64_415`
27×	`cube-mult_binary64_449` `swap-sqr_binary64_386`
25×	`distribute-rgt-out_binary64_372`
22×	`associate-+l+_binary64_352`
21×	`distribute-rgt-out--_binary64_373`
18×	`associate--l+_binary64_356`
16×	`distribute-lft-neg-out_binary64_378` `associate--r+_binary64_355`
15×	`cube-unmult_binary64_456`
13×	`associate-+r-_binary64_353`
12×	`difference-of-squares_binary64_388`
11×	`unsub-neg_binary64_413` `/-rgt-identity_binary64_410` `distribute-lft-out_binary64_370`
10×	`pow-plus_binary64_482` `associate-+r+_binary64_351`
9×	`distribute-neg-in_binary64_380` `associate-+l-_binary64_354`
4×	`unpow1/2_binary64_483` `rem-sqrt-square_binary64_432` `mul-1-neg_binary64_411` `pow-sqr_binary64_392` `distribute-lft-out--_binary64_371`
3×	`unpow2_binary64_484` `unpow1_binary64_477` `rem-square-sqrt_binary64_431`
2×	`+-rgt-identity_binary64_404` `distribute-rgt-neg-out_binary64_379`
1×	`log-pow_binary64_508` `unpow1/3_binary64_486` `1-exp_binary64_463` `exp-1-e_binary64_462` `rem-3cbrt-lft_binary64_444` `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-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

254 → 185

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	311	10097
1	774	8173
2	3120	8078
3	4759	8078
4	4985	8078

prune364.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	183	2	185
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	184	9	193

Error

Counts

193 → 9

Compiler

Compiled 6918 to 3258 computations (52.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
0.3b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
7.4b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
7.4b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite289.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

84×	`sqrt-prod_binary64_435`
72×	`times-frac_binary64_425`
61×	`add-sqr-sqrt_binary64_441`
59×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
40×	`associate-r_binary64_359`
18×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
11×	`pow1_binary64_480`
10×	`sqrt-div_binary64_436`
6×	`associate-/l_binary64_364` `associate-/r_binary64_363` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
5×	`flip3-+_binary64_422` `flip-+_binary64_393` `associate-*r/_binary64_361`
4×	`add-log-exp_binary64_458`
3×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `pow-prod-down_binary64_490`
2×	`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`
1×	`sqrt-undiv_binary64_440` `frac-2neg_binary64_430` `clear-num_binary64_418` `associate-l_binary64_360` `*-commutative_binary64_350`

Counts

4 → 157

Calls

4 calls:

25.0ms	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
8.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (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 5839 to 1470 computations (74.8% saved)

series1.1s (6.3%)

Error

Counts

4 → 53

Calls

4 calls:

619.0ms	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
213.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
126.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
121.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 3202 to 2331 computations (27.2% saved)

simplify187.0ms (1%)

Algorithm

1×	egg-herbie

Rules

794×	`times-frac_binary64_425`
238×	`associate-l_binary64_360`
210×	`associate-/l/_binary64_366`
199×	`associate-r_binary64_359`
180×	`associate-/r/_binary64_365`
172×	`distribute-rgt-in_binary64_369`
160×	`cancel-sign-sub-inv_binary64_385`
154×	`*-commutative_binary64_350`
150×	`distribute-lft-in_binary64_368`
131×	`associate-/l*_binary64_364`
110×	`associate-*r/_binary64_361`
98×	`neg-sub0_binary64_414`
94×	`neg-mul-1_binary64_415`
87×	`distribute-rgt-neg-in_binary64_377`
83×	`sub-neg_binary64_412`
79×	`unswap-sqr_binary64_387`
75×	`distribute-lft-neg-in_binary64_376`
69×	`associate-*l/_binary64_362`
50×	`distribute-neg-frac_binary64_383`
46×	`log-prod_binary64_505`
45×	`associate-/r*_binary64_363`
44×	`+-commutative_binary64_349`
42×	`cube-prod_binary64_447`
37×	`exp-prod_binary64_471` `sqr-pow_binary64_391`
27×	`*-rgt-identity_binary64_409`
24×	`div-sub_binary64_424`
23×	`log-div_binary64_506` `cube-div_binary64_448` `*-lft-identity_binary64_408`
18×	`unpow3_binary64_485`
17×	`associate--l+_binary64_356` `associate-+l+_binary64_352`
16×	`swap-sqr_binary64_386`
15×	`cube-unmult_binary64_456`
14×	`distribute-lft-neg-out_binary64_378` `associate--r+_binary64_355`
12×	`cube-mult_binary64_449` `difference-of-squares_binary64_388` `distribute-rgt-out--_binary64_373`
10×	`unsub-neg_binary64_413` `associate-+r+_binary64_351`
8×	`pow-plus_binary64_482` `/-rgt-identity_binary64_410` `distribute-neg-in_binary64_380` `distribute-rgt-out_binary64_372`
7×	`rem-sqrt-square_binary64_432` `associate-+r-_binary64_353`
4×	`unpow1/2_binary64_483` `mul-1-neg_binary64_411` `pow-sqr_binary64_392`
3×	`unpow2_binary64_484` `unpow1_binary64_477` `rem-square-sqrt_binary64_431` `distribute-lft-out_binary64_370` `associate-+l-_binary64_354`
2×	`+-rgt-identity_binary64_404` `distribute-rgt-neg-out_binary64_379` `distribute-lft-out--_binary64_371`
1×	`1-exp_binary64_463` `exp-1-e_binary64_462` `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` `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` `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-3cbrt-lft_binary64_444` `rem-cbrt-cube_binary64_443` `rem-cube-cbrt_binary64_442` `sqr-abs_binary64_434` `sqr-neg_binary64_433` `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

210 → 150

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	5672
1	630	5378
2	2153	5315
3	4737	5315
4	4977	5315

prune214.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	152	7	159

Error

Counts

159 → 7

Compiler

Compiled 4490 to 1468 computations (67.3% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a2 a2) (.f64 a1 a1))
0.1b	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
0.3b	(/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))
0.3b	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

rewrite629.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

195×	`times-frac_binary64_425`
111×	`add-sqr-sqrt_binary64_441`
94×	`cbrt-prod_binary64_450`
91×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
67×	`associate-r_binary64_359`
47×	`sqrt-prod_binary64_435`
32×	`add-exp-log_binary64_457`
22×	`div-inv_binary64_416`
20×	`add-cbrt-cube_binary64_455`
12×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
10×	`associate-/l_binary64_364` `associate-/r_binary64_363`
7×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `unswap-sqr_binary64_387`
6×	`pow1_binary64_480` `add-log-exp_binary64_458`
3×	`associate-/l/_binary64_366` `associate-l_binary64_360`
2×	`frac-2neg_binary64_430` `clear-num_binary64_418` `flip3-+_binary64_422` `flip-+_binary64_393`
1×	`pow-prod-down_binary64_490` `associate-r/_binary64_361` `-commutative_binary64_350` `sum-log_binary64_510` `+-commutative_binary64_349`

Counts

4 → 225

Calls

4 calls:

36.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
15.0ms	(/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))
11.0ms	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
4.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 8603 to 5119 computations (40.5% saved)

series2.0s (11.2%)

Error

Counts

4 → 53

Calls

4 calls:

944.0ms	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
615.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
268.0ms	(/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))
144.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 2659 to 2437 computations (8.3% saved)

simplify388.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

446×	`associate-/r/_binary64_365`
213×	`associate-l_binary64_360`
211×	`sub-neg_binary64_412`
205×	`associate-r_binary64_359`
202×	`associate-/l/_binary64_366`
185×	`associate-/l*_binary64_364`
160×	`associate-*r/_binary64_361`
153×	`*-commutative_binary64_350`
133×	`cancel-sign-sub-inv_binary64_385`
131×	`distribute-rgt-in_binary64_369`
115×	`div-sub_binary64_424` `associate-/r*_binary64_363`
113×	`distribute-lft-in_binary64_368`
107×	`unswap-sqr_binary64_387`
105×	`times-frac_binary64_425`
101×	`associate-*l/_binary64_362`
95×	`associate-+l+_binary64_352`
77×	`*-rgt-identity_binary64_409`
74×	`cube-prod_binary64_447`
73×	`log-prod_binary64_505`
72×	`+-commutative_binary64_349`
71×	`neg-mul-1_binary64_415` `neg-sub0_binary64_414`
70×	`associate--l+_binary64_356`
65×	`log-div_binary64_506`
62×	`*-lft-identity_binary64_408`
59×	`associate-+r+_binary64_351`
58×	`cube-div_binary64_448`
53×	`distribute-rgt-neg-in_binary64_377`
46×	`distribute-lft-neg-in_binary64_376`
44×	`sqr-pow_binary64_391`
43×	`unsub-neg_binary64_413`
42×	`associate-+l-_binary64_354`
40×	`exp-prod_binary64_471`
35×	`associate-+r-_binary64_353`
34×	`unpow3_binary64_485`
30×	`distribute-neg-frac_binary64_383`
28×	`distribute-rgt-out_binary64_372`
27×	`cube-mult_binary64_449`
20×	`associate--r+_binary64_355`
19×	`/-rgt-identity_binary64_410`
16×	`distribute-lft-out_binary64_370`
14×	`pow-plus_binary64_482`
12×	`cube-unmult_binary64_456` `associate--l-_binary64_357`
11×	`distribute-lft-neg-out_binary64_378`
10×	`swap-sqr_binary64_386`
8×	`rem-sqrt-square_binary64_432` `distribute-neg-in_binary64_380` `distribute-rgt-out--_binary64_373`
7×	`log-pow_binary64_508` `log-rec_binary64_507` `pow-sqr_binary64_392` `difference-of-squares_binary64_388`
5×	`unpow2_binary64_484` `unpow1/2_binary64_483`
4×	`unpow1_binary64_477` `distribute-rgt-neg-out_binary64_379`
2×	`associate--r-_binary64_358`
1×	`unpow1/3_binary64_486` `prod-exp_binary64_468` `exp-sum_binary64_465` `1-exp_binary64_463` `exp-1-e_binary64_462` `rem-3cbrt-rft_binary64_445` `rem-square-sqrt_binary64_431` `div0_binary64_400` `remove-double-div_binary64_395` `distribute-neg-out_binary64_381` `distribute-lft1-in_binary64_374` `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` `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` `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-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` `*-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`

Counts

278 → 267

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	310	9946
1	770	9324
2	2729	9261
3	4441	8675
4	4940	8675
5	4957	8675
6	5050	8675

prune470.0ms (2.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	267	0	267
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	267	7	274

Error

Counts

274 → 7

Compiler

Compiled 7875 to 4373 computations (44.5% saved)

regimes2.1s (11.7%)

Accuracy

Total 0.3b remaining (99.9%)

Threshold costs 0.3b (99.9%)

Compiler

Compiled 23847 to 17551 computations (26.4% saved)

bsearch0.0ms (0%)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64_350`
1×	`+-commutative_binary64_349`
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` `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)

Iter	Nodes	Cost
0	15	34
1	17	34
2	17	34

Remove

(sort a1 a2)

Compiler

Compiled 44 to 26 computations (40.9% saved)

end0.0ms (0%)

sample5.3s (29%)

Algorithm

1×

intervals

Results

590.0ms	1772×	body	1024	valid
514.0ms	1521×	body	1024	invalid
398.0ms	4908×	body	128	valid
232.0ms	890×	body	512	valid
182.0ms	767×	body	512	invalid
72.0ms	423×	body	256	valid
71.0ms	395×	body	256	invalid
63.0ms	658×	body	128	invalid
3.0ms	7×	body	2048	valid

Compiler

Compiled 3008 to 2209 computations (26.6% saved)

Details

analyze1.1s (6.3%)

sample94.0ms (0.5%)

simplify11.0ms (0.1%)

prune5.0ms (0%)

localize11.0ms (0.1%)

rewrite174.0ms (1%)

series1.1s (6%)

simplify118.0ms (0.6%)

prune166.0ms (0.9%)

localize20.0ms (0.1%)

rewrite536.0ms (3%)

series1.4s (7.7%)

simplify262.0ms (1.4%)

prune364.0ms (2%)

localize16.0ms (0.1%)

rewrite289.0ms (1.6%)

series1.1s (6.3%)

simplify187.0ms (1%)

prune214.0ms (1.2%)

localize15.0ms (0.1%)

rewrite629.0ms (3.5%)

series2.0s (11.2%)

simplify388.0ms (2.1%)

prune470.0ms (2.6%)

regimes2.1s (11.7%)

bsearch0.0ms (0%)

simplify11.0ms (0.1%)

end0.0ms (0%)

sample5.3s (29%)

Profiling