Details

analyze1.1s (7.8%)

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)

sample86.0ms (0.6%)

Algorithm

1×

intervals

Results

19.0ms	48×	body	1024	invalid
14.0ms	49×	body	1024	valid
12.0ms	163×	body	128	valid
5.0ms	25×	body	512	valid
4.0ms	17×	body	512	invalid
3.0ms	19×	body	256	valid
2.0ms	14×	body	256	invalid
1.0ms	16×	body	128	invalid
0.0ms	1×	body	2048	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

0.6b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.3b	(.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))

rewrite160.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

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:

11.0ms	(.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))

Compiler

Compiled 2362 to 862 computations (63.5% saved)

series1.1s (7.8%)

Error

0.5b

Counts

3 → 42

Calls

3 calls:

587.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
282.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
139.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 1676 to 1476 computations (11.9% saved)

simplify119.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

367×	`sub-neg_binary64_412`
341×	`unswap-sqr_binary64_387`
336×	`associate-/l*_binary64_364`
303×	`*-commutative_binary64_350`
272×	`associate-*r/_binary64_361`
269×	`associate-*l/_binary64_362`
169×	`associate--l+_binary64_356`
153×	`distribute-rgt-in_binary64_369`
148×	`associate-+l+_binary64_352`
138×	`associate--r+_binary64_355`
133×	`distribute-lft-in_binary64_368`
131×	`associate-/r*_binary64_363`
129×	`associate-/r/_binary64_365`
118×	`associate-l_binary64_360`
115×	`associate-r_binary64_359`
109×	`associate-/l/_binary64_366`
100×	`cancel-sign-sub-inv_binary64_385`
98×	`times-frac_binary64_425`
96×	`associate-+r+_binary64_351`
81×	`unsub-neg_binary64_413`
70×	`sqr-pow_binary64_391`
54×	`neg-mul-1_binary64_415` `neg-sub0_binary64_414`
46×	`*-rgt-identity_binary64_409`
44×	`*-lft-identity_binary64_408` `difference-of-squares_binary64_388`
40×	`+-commutative_binary64_349`
35×	`distribute-rgt-neg-in_binary64_377`
30×	`/-rgt-identity_binary64_410`
29×	`associate-+l-_binary64_354`
28×	`cube-prod_binary64_447` `distribute-lft-neg-in_binary64_376`
26×	`distribute-neg-in_binary64_380` `associate-+r-_binary64_353`
24×	`log-prod_binary64_505` `exp-prod_binary64_471`
20×	`log-div_binary64_506`
19×	`div-sub_binary64_424`
18×	`cube-div_binary64_448`
17×	`+-rgt-identity_binary64_404` `distribute-neg-frac_binary64_383`
16×	`distribute-rgt-out_binary64_372`
15×	`pow-sqr_binary64_392`
12×	`unpow3_binary64_485`
10×	`cube-unmult_binary64_456` `distribute-lft-neg-out_binary64_378`
9×	`sub0-neg_binary64_406`
7×	`pow-plus_binary64_482` `distribute-rgt-out--_binary64_373` `distribute-lft-out_binary64_370`
6×	`cube-mult_binary64_449` `swap-sqr_binary64_386` `associate--l-_binary64_357`
4×	`unpow1/2_binary64_483` `rem-sqrt-square_binary64_432`
3×	`log-rec_binary64_507` `unpow2_binary64_484` `unpow1_binary64_477` `distribute-rgt-neg-out_binary64_379`
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

136 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	3337
1	445	3089
2	1498	2993
3	4168	2993
4	5044	2993

prune170.0ms (1.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	116	10	126
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	118	10	128

Error

0.2b

Counts

128 → 10

Compiler

Compiled 2805 to 1151 computations (59% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 2))))
0.4b	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 2))
6.9b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
6.9b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite213.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

48×	`sqrt-prod_binary64_435`
37×	`add-sqr-sqrt_binary64_441`
36×	`times-frac_binary64_425`
35×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
15×	`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` `associate-*r/_binary64_361`
5×	`flip3-+_binary64_422` `flip-+_binary64_393` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
4×	`add-log-exp_binary64_458`
3×	`pow-prod-down_binary64_490` `associate-l_binary64_360`
2×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `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` `div-inv_binary64_416` `associate-r_binary64_359` `*-commutative_binary64_350`

Counts

4 → 118

Calls

4 calls:

19.0ms	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 2))))
8.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (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 4260 to 1117 computations (73.8% saved)

series1.1s (8.2%)

Error

0.2b

Counts

4 → 54

Calls

4 calls:

588.0ms	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 2))))
220.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 2))
116.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
106.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 3293 to 2431 computations (26.2% saved)

simplify176.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

627×	`associate-/l*_binary64_364`
623×	`times-frac_binary64_425`
310×	`associate-/r*_binary64_363`
150×	`cancel-sign-sub-inv_binary64_385`
145×	`associate-r_binary64_359`
132×	`associate-l_binary64_360`
130×	`associate-/r/_binary64_365`
128×	`distribute-rgt-in_binary64_369`
112×	`distribute-lft-in_binary64_368`
111×	`associate-/l/_binary64_366`
107×	`*-commutative_binary64_350`
99×	`sub-neg_binary64_412`
91×	`unswap-sqr_binary64_387`
77×	`distribute-rgt-neg-in_binary64_377`
70×	`distribute-lft-neg-in_binary64_376`
69×	`associate-*r/_binary64_361`
53×	`+-commutative_binary64_349`
52×	`log-div_binary64_506`
50×	`distribute-neg-frac_binary64_383`
48×	`associate-*l/_binary64_362`
37×	`neg-sub0_binary64_414`
36×	`sqr-pow_binary64_391`
33×	`neg-mul-1_binary64_415`
30×	`associate--l+_binary64_356`
28×	`distribute-neg-in_binary64_380`
24×	`log-prod_binary64_505` `associate-+l+_binary64_352`
23×	`associate--r+_binary64_355` `associate-+r+_binary64_351`
19×	`unpow3_binary64_485`
17×	`unsub-neg_binary64_413`
14×	`swap-sqr_binary64_386`
11×	`exp-prod_binary64_471`
10×	`cube-div_binary64_448` `cube-prod_binary64_447` `distribute-rgt-out_binary64_372`
8×	`cube-unmult_binary64_456` `distribute-lft-neg-out_binary64_378`
7×	`difference-of-squares_binary64_388` `distribute-rgt-out--_binary64_373`
6×	`*-rgt-identity_binary64_409` `associate-+r-_binary64_353`
5×	`log-rec_binary64_507` `pow-plus_binary64_482` `cube-mult_binary64_449` `/-rgt-identity_binary64_410` `distribute-lft-out_binary64_370`
4×	`mul-1-neg_binary64_411` `pow-sqr_binary64_392`
3×	`unpow2_binary64_484` `unpow1/2_binary64_483` `unpow1_binary64_477` `rem-sqrt-square_binary64_432` `div-sub_binary64_424` `associate-+l-_binary64_354`
2×	`rem-square-sqrt_binary64_431` `+-rgt-identity_binary64_404`
1×	`1-exp_binary64_463` `*-lft-identity_binary64_408` `distribute-rgt-neg-out_binary64_379` `distribute-lft-out--_binary64_371` `count-2_binary64_367`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_682` `erf-erfc_binary64_681` `erf-odd_binary64_680` `if-if-and-not_binary64_679` `if-if-and_binary64_678` `if-if-or-not_binary64_677` `if-if-or_binary64_676` `if-not_binary64_675` `if-same_binary64_674` `if-false_binary64_673` `if-true_binary64_672` `not-gte_binary64_671` `not-lte_binary64_670` `not-gt_binary64_669` `not-lt_binary64_668` `gte-same_binary64_667` `lte-same_binary64_666` `gt-same_binary64_665` `lt-same_binary64_664` `sinh---cosh_binary64_611` `sinh-+-cosh_binary64_610` `sinh-cosh_binary64_609` `tanh-def-c_binary64_608` `tanh-def-b_binary64_607` `tanh-def-a_binary64_606` `cosh-def_binary64_605` `sinh-def_binary64_604` `tan-neg_binary64_551` `cos-neg_binary64_550` `sin-neg_binary64_549` `tan-0_binary64_548` `cos-0_binary64_547` `sin-0_binary64_546` `hang-m-tan_binary64_545` `hang-p-tan_binary64_544` `hang-m0-tan_binary64_543` `hang-p0-tan_binary64_542` `hang-0m-tan_binary64_541` `hang-0p-tan_binary64_540` `tan-+PI/2_binary64_539` `tan-+PI_binary64_538` `tan-PI_binary64_537` `tan-PI/3_binary64_536` `tan-PI/4_binary64_535` `tan-PI/6_binary64_534` `cos-+PI/2_binary64_533` `cos-+PI_binary64_532` `cos-PI_binary64_531` `cos-PI/2_binary64_530` `cos-PI/3_binary64_529` `cos-PI/4_binary64_528` `cos-PI/6_binary64_527` `sin-+PI/2_binary64_526` `sin-+PI_binary64_525` `sin-PI_binary64_524` `sin-PI/2_binary64_523` `sin-PI/3_binary64_522` `sin-PI/4_binary64_521` `sin-PI/6_binary64_520` `sub-1-sin_binary64_519` `sub-1-cos_binary64_518` `-1-add-sin_binary64_517` `-1-add-cos_binary64_516` `1-sub-sin_binary64_515` `1-sub-cos_binary64_514` `cos-sin-sum_binary64_513` `log-E_binary64_509` `log-pow_binary64_508` `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-1-e_binary64_462` `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

172 → 145

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	236	4315
1	562	4053
2	1739	3957
3	4944	3957
4	4989	3957
5	4969	3957

prune194.0ms (1.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	146	9	155

Error

0.2b

Counts

155 → 9

Compiler

Compiled 4380 to 1554 computations (64.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) 2)))
0.3b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))))
6.9b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
7.0b	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))

rewrite203.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

41×	`add-sqr-sqrt_binary64_441`
39×	`sqrt-prod_binary64_435`
23×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
21×	`times-frac_binary64_425`
17×	`sqrt-div_binary64_436` `associate-r_binary64_359`
15×	`pow1_binary64_480`
11×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
9×	`associate-l_binary64_360`
7×	`associate-*r/_binary64_361`
6×	`pow-prod-down_binary64_490` `unswap-sqr_binary64_387`
5×	`flip3-+_binary64_422` `flip-+_binary64_393`
4×	`pow1/2_binary64_499` `add-log-exp_binary64_458` `sqrt-pow1_binary64_437` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `frac-times_binary64_429` `associate-*l/_binary64_362`
3×	`rem-sqrt-square_binary64_432`
2×	`div-inv_binary64_416` `*-commutative_binary64_350`
1×	`sqrt-unprod_binary64_439`

Counts

4 → 110

Calls

4 calls:

19.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) 2)))
14.0ms	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))))
5.0ms	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 3866 to 1050 computations (72.8% saved)

series1.2s (8.6%)

Error

0.2b

Counts

4 → 54

Calls

4 calls:

544.0ms	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))))
234.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) 2)))
181.0ms	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))
124.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 2904 to 2265 computations (22% saved)

simplify179.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

511×	`times-frac_binary64_425`
450×	`associate-/l*_binary64_364`
360×	`cancel-sign-sub-inv_binary64_385`
241×	`associate-r_binary64_359`
202×	`associate-l_binary64_360`
156×	`distribute-rgt-in_binary64_369`
147×	`*-commutative_binary64_350`
139×	`distribute-lft-in_binary64_368`
134×	`neg-sub0_binary64_414`
129×	`neg-mul-1_binary64_415`
127×	`sub-neg_binary64_412`
126×	`distribute-rgt-neg-in_binary64_377`
115×	`distribute-lft-neg-in_binary64_376`
103×	`associate-/r/_binary64_365`
76×	`distribute-rgt-out_binary64_372`
69×	`unswap-sqr_binary64_387`
52×	`+-commutative_binary64_349`
42×	`distribute-lft-out_binary64_370`
41×	`sqr-pow_binary64_391`
39×	`unsub-neg_binary64_413`
36×	`distribute-neg-frac_binary64_383` `associate-*l/_binary64_362`
35×	`associate-/r*_binary64_363`
29×	`associate-*r/_binary64_361`
28×	`distribute-neg-in_binary64_380`
27×	`cube-prod_binary64_447`
26×	`log-prod_binary64_505` `exp-prod_binary64_471` `associate-/l/_binary64_366` `associate--l+_binary64_356`
25×	`associate-+l+_binary64_352`
24×	`*-rgt-identity_binary64_409`
23×	`associate--r+_binary64_355`
20×	`associate-+r+_binary64_351`
19×	`*-lft-identity_binary64_408`
16×	`swap-sqr_binary64_386`
15×	`log-div_binary64_506` `cube-unmult_binary64_456`
14×	`unpow3_binary64_485` `div-sub_binary64_424` `distribute-rgt-out--_binary64_373`
10×	`cube-div_binary64_448` `distribute-lft-neg-out_binary64_378`
9×	`pow-plus_binary64_482` `cube-mult_binary64_449`
8×	`log-rec_binary64_507` `rem-sqrt-square_binary64_432`
7×	`difference-of-squares_binary64_388`
6×	`/-rgt-identity_binary64_410`
5×	`mul-1-neg_binary64_411`
4×	`unpow1/2_binary64_483` `pow-sqr_binary64_392`
3×	`unpow2_binary64_484` `unpow1_binary64_477` `associate-+r-_binary64_353`
2×	`rem-square-sqrt_binary64_431` `+-rgt-identity_binary64_404`
1×	`1-exp_binary64_463` `exp-1-e_binary64_462` `distribute-rgt-neg-out_binary64_379` `distribute-lft-out--_binary64_371` `associate-+l-_binary64_354`
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` `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` `count-2_binary64_367` `associate--r-_binary64_358` `associate--l-_binary64_357`

Counts

164 → 130

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	4486
1	570	4178
2	1882	4128
3	4678	4128
4	4995	4128
5	4969	4128

prune176.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	127	3	130
Fresh	6	2	8
Picked	0	1	1
Done	0	0	0
Total	133	6	139

Error

0.2b

Counts

139 → 6

Compiler

Compiled 3617 to 1209 computations (66.6% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a2 a2) (.f64 a1 a1))
0.1b	(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))
0.5b	(/.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))

rewrite89.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

11×	`add-sqr-sqrt_binary64_441`
10×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
9×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
6×	`times-frac_binary64_425` `sqrt-prod_binary64_435` `associate-/r*_binary64_363`
5×	`pow1_binary64_480` `add-log-exp_binary64_458`
4×	`associate-*l/_binary64_362`
3×	`flip3-+_binary64_422` `flip-+_binary64_393` `associate-l_binary64_360` `associate-r_binary64_359`
2×	`prod-exp_binary64_468` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `cbrt-unprod_binary64_452` `associate-/l/_binary64_366`
1×	`frac-2neg_binary64_430` `clear-num_binary64_418` `div-inv_binary64_416` `associate-/l_binary64_364` `pow-prod-down_binary64_490` `unswap-sqr_binary64_387` `-commutative_binary64_350` `sum-log_binary64_510` `+-commutative_binary64_349`

Counts

3 → 60

Calls

3 calls:

8.0ms	(/.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
7.0ms	(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))
4.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 1347 to 424 computations (68.5% saved)

series1.2s (8.5%)

Error

0.2b

Counts

3 → 48

Calls

3 calls:

590.0ms	(/.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
373.0ms	(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))
131.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 2074 to 1778 computations (14.3% saved)

simplify129.0ms (1%)

Algorithm

1×	egg-herbie

Rules

634×	`associate-/l*_binary64_364`
361×	`cancel-sign-sub-inv_binary64_385`
355×	`times-frac_binary64_425`
279×	`distribute-rgt-in_binary64_369`
254×	`distribute-lft-in_binary64_368`
194×	`associate-/l/_binary64_366`
163×	`associate-/r/_binary64_365`
130×	`sub-neg_binary64_412`
105×	`distribute-rgt-neg-in_binary64_377`
103×	`associate-l_binary64_360`
97×	`associate-r_binary64_359`
96×	`unswap-sqr_binary64_387`
92×	`distribute-lft-neg-in_binary64_376`
74×	`*-commutative_binary64_350`
63×	`+-commutative_binary64_349`
58×	`associate--l+_binary64_356`
50×	`distribute-neg-in_binary64_380`
47×	`distribute-rgt-out_binary64_372`
45×	`log-div_binary64_506`
40×	`neg-mul-1_binary64_415` `neg-sub0_binary64_414` `associate-+l+_binary64_352`
38×	`associate-+r+_binary64_351`
37×	`log-prod_binary64_505`
36×	`sqr-pow_binary64_391` `associate-*l/_binary64_362` `associate--r+_binary64_355`
28×	`associate-*r/_binary64_361`
27×	`unsub-neg_binary64_413`
22×	`distribute-neg-frac_binary64_383` `distribute-lft-out_binary64_370`
21×	`exp-prod_binary64_471`
17×	`*-rgt-identity_binary64_409` `distribute-lft-neg-out_binary64_378`
16×	`associate-/r*_binary64_363`
15×	`cube-div_binary64_448`
13×	`log-rec_binary64_507`
12×	`/-rgt-identity_binary64_410` `distribute-rgt-out--_binary64_373`
11×	`*-lft-identity_binary64_408`
10×	`cube-prod_binary64_447`
7×	`exp-sum_binary64_465` `pow-sqr_binary64_392` `difference-of-squares_binary64_388` `swap-sqr_binary64_386`
6×	`cube-unmult_binary64_456`
5×	`unpow3_binary64_485`
4×	`div-sub_binary64_424` `distribute-rgt-neg-out_binary64_379`
3×	`unpow2_binary64_484` `unpow1/2_binary64_483` `unpow1_binary64_477` `cube-mult_binary64_449` `distribute-rgt1-in_binary64_375`
2×	`pow-plus_binary64_482`
1×	`prod-exp_binary64_468` `1-exp_binary64_463` `exp-1-e_binary64_462` `rem-sqrt-square_binary64_432` `rem-square-sqrt_binary64_431` `distribute-lft-out--_binary64_371` `associate-+l-_binary64_354` `associate-+r-_binary64_353`
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` `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-lft1-in_binary64_374` `count-2_binary64_367` `associate--r-_binary64_358` `associate--l-_binary64_357`

Counts

108 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	2493
1	461	2188
2	1748	2050
3	4938	2050
4	5000	2050
5	4967	2050

prune93.0ms (0.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	97	6	103

Error

0.2b

Counts

103 → 6

Compiler

Compiled 1692 to 641 computations (62.1% saved)

regimes1.6s (11.5%)

Accuracy

Total 0.3b remaining (95.2%)

Threshold costs 0.3b (95.2%)

Compiler

Compiled 17147 to 12555 computations (26.8% 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	14	34
1	17	34
2	17	34

Remove

(sort a1 a2)

Compiler

Compiled 44 to 26 computations (40.9% saved)

end0.0ms (0%)

sample4.3s (32.3%)

Algorithm

1×

intervals

Results

696.0ms	1792×	body	1024	valid
469.0ms	1543×	body	1024	invalid
351.0ms	4866×	body	128	valid
203.0ms	903×	body	512	valid
165.0ms	727×	body	512	invalid
74.0ms	431×	body	256	valid
57.0ms	388×	body	256	invalid
46.0ms	599×	body	128	invalid
4.0ms	8×	body	2048	valid
0.0ms	1×	body	2048	invalid

Compiler

Compiled 2168 to 1582 computations (27% saved)

Details

analyze1.1s (7.8%)

sample86.0ms (0.6%)

simplify11.0ms (0.1%)

prune5.0ms (0%)

localize10.0ms (0.1%)

rewrite160.0ms (1.2%)

series1.1s (7.8%)

simplify119.0ms (0.9%)

prune170.0ms (1.3%)

localize12.0ms (0.1%)

rewrite213.0ms (1.6%)

series1.1s (8.2%)

simplify176.0ms (1.3%)

prune194.0ms (1.4%)

localize13.0ms (0.1%)

rewrite203.0ms (1.5%)

series1.2s (8.6%)

simplify179.0ms (1.3%)

prune176.0ms (1.3%)

localize10.0ms (0.1%)

rewrite89.0ms (0.7%)

series1.2s (8.5%)

simplify129.0ms (1%)

prune93.0ms (0.7%)

regimes1.6s (11.5%)

bsearch0.0ms (0%)

simplify11.0ms (0.1%)

end0.0ms (0%)

sample4.3s (32.3%)

Profiling