Details

analyze2.6s (5.8%)

Algorithm

1×	search
2×	egg-herbie

Rules

648×	`distribute-rgt-in_binary64_369`
636×	`distribute-lft-in_binary64_368`
356×	`cancel-sign-sub-inv_binary64_385`
251×	`distribute-rgt-neg-in_binary64_377`
235×	`distribute-lft-neg-in_binary64_376`
159×	`associate-l_binary64_360`
158×	`*-commutative_binary64_350`
132×	`sub-neg_binary64_412`
118×	`associate-r_binary64_359`
114×	`distribute-lft-neg-out_binary64_378`
112×	`neg-mul-1_binary64_415` `neg-sub0_binary64_414`
101×	`distribute-rgt-neg-out_binary64_379`
92×	`distribute-neg-in_binary64_380`
70×	`distribute-neg-frac_binary64_383`
55×	`+-commutative_binary64_349`
40×	`associate-*r/_binary64_361`
30×	`sqr-pow_binary64_391` `associate-*l/_binary64_362`
22×	`unsub-neg_binary64_413`
20×	`associate-/l*_binary64_364`
16×	`cancel-sign-sub_binary64_384` `distribute-neg-out_binary64_381` `associate--l-_binary64_357` `associate--l+_binary64_356` `associate-+l-_binary64_354` `associate-+l+_binary64_352`
10×	`unpow2_binary64_484` `unpow1/2_binary64_483` `unpow1_binary64_477` `associate-/r/_binary64_365`
6×	`times-frac_binary64_425`
1×	`1-exp_binary64_463`
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` `pow-plus_binary64_482` `exp-to-pow_binary64_481` `pow-base-1_binary64_479` `unpow0_binary64_478` `unpow-1_binary64_476` `exp-lft-cube_binary64_475` `exp-lft-sqr_binary64_474` `exp-cbrt_binary64_473` `exp-sqrt_binary64_472` `exp-prod_binary64_471` `div-exp_binary64_470` `rec-exp_binary64_469` `prod-exp_binary64_468` `exp-diff_binary64_467` `exp-neg_binary64_466` `exp-sum_binary64_465` `e-exp-1_binary64_464` `exp-1-e_binary64_462` `exp-0_binary64_461` `rem-log-exp_binary64_460` `rem-exp-log_binary64_459` `cube-unmult_binary64_456` `cube-mult_binary64_449` `cube-div_binary64_448` `cube-prod_binary64_447` `cube-neg_binary64_446` `rem-3cbrt-rft_binary64_445` `rem-3cbrt-lft_binary64_444` `rem-cbrt-cube_binary64_443` `rem-cube-cbrt_binary64_442` `sqr-abs_binary64_434` `sqr-neg_binary64_433` `rem-sqrt-square_binary64_432` `rem-square-sqrt_binary64_431` `div-sub_binary64_424` `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` `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` `distribute-frac-neg_binary64_382` `distribute-rgt1-in_binary64_375` `distribute-lft1-in_binary64_374` `distribute-rgt-out--_binary64_373` `distribute-rgt-out_binary64_372` `distribute-lft-out--_binary64_371` `distribute-lft-out_binary64_370` `count-2_binary64_367` `associate-/l/_binary64_366` `associate-/r_binary64_363` `associate--r-_binary64_358` `associate--r+_binary64_355` `associate-+r-_binary64_353` `associate-+r+_binary64_351`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	170	672
1	563	672
2	2019	672
3	5820	672
0	6	6
1	6	6

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	98.1%	1.9%	7
0%	98.1%	1.9%	8
0%	97.8%	2.2%	9
0%	96.8%	3.2%	10
0%	96.3%	3.7%	11
0%	94.3%	5.7%	12
0.4%	92.1%	7.5%	13
0.6%	90.8%	8.6%	14

Compiler

Compiled 29 to 24 computations (17.2% saved)

sample106.0ms (0.2%)

Algorithm

1×

intervals

Results

39.0ms	408×	body	128	nan
25.0ms	256×	body	128	valid
4.0ms	37×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify58.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

716×	`neg-mul-1_binary64_415` `neg-sub0_binary64_414`
377×	`distribute-rgt-neg-out_binary64_379`
358×	`cancel-sign-sub-inv_binary64_385`
354×	`distribute-lft-neg-out_binary64_378`
351×	`unsub-neg_binary64_413`
309×	`distribute-neg-frac_binary64_383`
281×	`distribute-rgt-in_binary64_369`
275×	`distribute-lft-in_binary64_368`
248×	`associate-*r/_binary64_361`
236×	`distribute-rgt-neg-in_binary64_377` `associate-*l/_binary64_362`
228×	`*-commutative_binary64_350`
125×	`distribute-neg-in_binary64_380`
106×	`div-sub_binary64_424`
95×	`associate-r_binary64_359`
88×	`associate-l_binary64_360`
87×	`sub-neg_binary64_412`
86×	`distribute-lft-neg-in_binary64_376`
85×	`distribute-neg-out_binary64_381`
61×	`times-frac_binary64_425`
43×	`associate-/l*_binary64_364`
35×	`remove-double-neg_binary64_407`
32×	`associate-+l+_binary64_352` `associate-+r+_binary64_351`
23×	`distribute-lft-out_binary64_370`
20×	`mul0-rgt_binary64_402` `mul0-lft_binary64_401` `associate--r+_binary64_355` `+-commutative_binary64_349`
16×	`associate-+l-_binary64_354`
12×	`distribute-rgt-out_binary64_372`
11×	`sub0-neg_binary64_406` `associate-+r-_binary64_353`
10×	`associate-/r/_binary64_365`
8×	`unswap-sqr_binary64_387`
7×	`sqr-pow_binary64_391` `associate--l+_binary64_356`
6×	`+-rgt-identity_binary64_404`
5×	`distribute-lft-out--_binary64_371` `associate--r-_binary64_358` `associate--l-_binary64_357`
4×	`*-lft-identity_binary64_408` `associate-/l/_binary64_366`
3×	`pow-plus_binary64_482` `cube-unmult_binary64_456` `--rgt-identity_binary64_405`
2×	`rem-sqrt-square_binary64_432` `-rgt-identity_binary64_409` `associate-/r_binary64_363`
1×	`unpow3_binary64_485` `unpow2_binary64_484` `unpow1/2_binary64_483` `unpow1_binary64_477` `1-exp_binary64_463` `sqr-neg_binary64_433` `div0_binary64_400` `cancel-sign-sub_binary64_384`
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` `exp-to-pow_binary64_481` `pow-base-1_binary64_479` `unpow0_binary64_478` `unpow-1_binary64_476` `exp-lft-cube_binary64_475` `exp-lft-sqr_binary64_474` `exp-cbrt_binary64_473` `exp-sqrt_binary64_472` `exp-prod_binary64_471` `div-exp_binary64_470` `rec-exp_binary64_469` `prod-exp_binary64_468` `exp-diff_binary64_467` `exp-neg_binary64_466` `exp-sum_binary64_465` `e-exp-1_binary64_464` `exp-1-e_binary64_462` `exp-0_binary64_461` `rem-log-exp_binary64_460` `rem-exp-log_binary64_459` `cube-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` `rem-square-sqrt_binary64_431` `mul-1-neg_binary64_411` `/-rgt-identity_binary64_410` `+-lft-identity_binary64_403` `*-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` `difference-of-sqr--1_binary64_390` `difference-of-sqr-1_binary64_389` `difference-of-squares_binary64_388` `swap-sqr_binary64_386` `distribute-frac-neg_binary64_382` `distribute-rgt1-in_binary64_375` `distribute-lft1-in_binary64_374` `distribute-rgt-out--_binary64_373` `count-2_binary64_367`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	42
1	58	42
2	180	42
3	719	39
4	2459	39
5	3993	39
6	5178	39

prune7.0ms (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

30.8b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

1.1b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
10.0b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
12.0b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))
18.0b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))

rewrite303.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

23.7b

Rules

30×	`pow1_binary64_480` `add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
29×	`add-sqr-sqrt_binary64_441`
27×	`associate-l_binary64_360`
24×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
19×	`times-frac_binary64_425`
18×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
16×	`pow-prod-down_binary64_490`
14×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
12×	`associate-*r/_binary64_361` `cancel-sign-sub-inv_binary64_385`
7×	`associate-r_binary64_359`
4×	`add-log-exp_binary64_458` `sqrt-pow1_binary64_437` `flip3-+_binary64_422` `flip-+_binary64_393` `frac-times_binary64_429` `sub-neg_binary64_412`
3×	`*-commutative_binary64_350` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
2×	`sqrt-div_binary64_436` `flip3--_binary64_423` `flip--_binary64_394` `associate-*l/_binary64_362` `div-inv_binary64_416` `unswap-sqr_binary64_387`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435`

Counts

4 → 131

Calls

4 calls:

14.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
11.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
10.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))
7.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))

Compiler

Compiled 5195 to 2032 computations (60.9% saved)

series6.3s (14%)

Error

19.2b

Counts

4 → 110

Calls

4 calls:

2.8s	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))
1.6s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))
1.2s	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
510.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 11462 to 8623 computations (24.8% saved)

simplify246.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

625×	`*-commutative_binary64_350`
235×	`associate-*l/_binary64_362`
227×	`associate-/l*_binary64_364`
222×	`distribute-rgt-in_binary64_369`
205×	`distribute-lft-in_binary64_368`
195×	`associate-*r/_binary64_361`
174×	`sub-neg_binary64_412`
159×	`exp-prod_binary64_471`
135×	`neg-sub0_binary64_414`
123×	`associate-r_binary64_359`
119×	`neg-mul-1_binary64_415`
108×	`+-commutative_binary64_349`
107×	`times-frac_binary64_425`
104×	`cancel-sign-sub-inv_binary64_385`
85×	`associate-/r*_binary64_363`
78×	`sqr-pow_binary64_391`
72×	`distribute-rgt-neg-in_binary64_377`
71×	`div-sub_binary64_424`
61×	`log-prod_binary64_505`
56×	`associate-l_binary64_360`
53×	`distribute-lft-neg-in_binary64_376`
48×	`cube-prod_binary64_447`
44×	`associate-/r/_binary64_365`
35×	`unpow3_binary64_485`
31×	`log-div_binary64_506`
29×	`unsub-neg_binary64_413`
28×	`distribute-neg-frac_binary64_383`
25×	`associate-+l+_binary64_352`
24×	`exp-sum_binary64_465`
23×	`distribute-lft-neg-out_binary64_378` `associate--r+_binary64_355`
21×	`swap-sqr_binary64_386`
20×	`associate--l+_binary64_356`
18×	`mul-1-neg_binary64_411`
17×	`cube-div_binary64_448`
14×	`distribute-rgt-neg-out_binary64_379`
13×	`distribute-neg-in_binary64_380` `associate-+r+_binary64_351`
12×	`cube-mult_binary64_449`
11×	`distribute-rgt-out--_binary64_373`
9×	`log-pow_binary64_508`
7×	`unpow1/2_binary64_483` `cube-unmult_binary64_456`
6×	`*-rgt-identity_binary64_409` `associate-+l-_binary64_354` `associate-+r-_binary64_353`
5×	`unpow2_binary64_484` `unpow1_binary64_477` `*-lft-identity_binary64_408` `unswap-sqr_binary64_387` `distribute-rgt-out_binary64_372`
4×	`exp-diff_binary64_467` `rem-sqrt-square_binary64_432` `pow-sqr_binary64_392` `difference-of-squares_binary64_388`
3×	`exp-lft-sqr_binary64_474` `distribute-lft-out_binary64_370`
2×	`pow-plus_binary64_482` `rem-square-sqrt_binary64_431` `+-rgt-identity_binary64_404` `distribute-lft-out--_binary64_371`
1×	`log-rec_binary64_507` `1-exp_binary64_463` `exp-1-e_binary64_462` `cube-neg_binary64_446` `rem-3cbrt-lft_binary64_444` `sqr-neg_binary64_433` `/-rgt-identity_binary64_410`
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` `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-cbrt_binary64_473` `exp-sqrt_binary64_472` `div-exp_binary64_470` `rec-exp_binary64_469` `prod-exp_binary64_468` `exp-neg_binary64_466` `e-exp-1_binary64_464` `exp-0_binary64_461` `rem-log-exp_binary64_460` `rem-exp-log_binary64_459` `rem-3cbrt-rft_binary64_445` `rem-cbrt-cube_binary64_443` `rem-cube-cbrt_binary64_442` `sqr-abs_binary64_434` `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-/l/_binary64_366` `associate--r-_binary64_358` `associate--l-_binary64_357`

Counts

241 → 222

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	521	8630
1	1607	8142
2	4256	7905
3	4923	7905
4	5053	7905

prune377.0ms (0.8%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	201	21	222
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	201	23	224

Error

14.2b

Counts

224 → 23

Compiler

Compiled 8312 to 3124 computations (62.4% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.2b	(/.f64 (.f64 l (-.f64 U U)) Om)
6.3b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
6.4b	(.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om))
18.0b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))

rewrite202.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

11.5b

Rules

31×	`pow1_binary64_480`
30×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
17×	`pow-prod-down_binary64_490`
13×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
11×	`add-sqr-sqrt_binary64_441` `associate-*r/_binary64_361`
9×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
8×	`associate-r_binary64_359`
6×	`times-frac_binary64_425`
5×	`sqrt-pow1_binary64_437`
4×	`add-log-exp_binary64_458` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-l_binary64_360` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
3×	`associate-/r*_binary64_363`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `flip-+_binary64_393` `div-inv_binary64_416` `*-commutative_binary64_350` `associate-/l/_binary64_366`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `unswap-sqr_binary64_387` `frac-2neg_binary64_430` `clear-num_binary64_418` `flip3--_binary64_423` `flip--_binary64_394` `associate-/l*_binary64_364`

Counts

4 → 94

Calls

4 calls:

10.0ms	(.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om))
10.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
8.0ms	(/.f64 (.f64 l (-.f64 U U)) Om)
7.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))

Compiler

Compiled 3589 to 1455 computations (59.5% saved)

series5.5s (12.2%)

Error

13.9b

Counts

4 → 102

Calls

4 calls:

2.9s	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
1.6s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))
503.0ms	(.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om))
317.0ms	(/.f64 (.f64 l (-.f64 U U)) Om)

Compiler

Compiled 10646 to 7866 computations (26.1% saved)

simplify165.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

582×	`associate-r_binary64_359`
500×	`associate-l_binary64_360`
207×	`associate-/l*_binary64_364`
167×	`*-commutative_binary64_350`
161×	`associate-*r/_binary64_361`
154×	`distribute-rgt-in_binary64_369`
145×	`distribute-lft-in_binary64_368`
141×	`times-frac_binary64_425`
127×	`associate-*l/_binary64_362`
102×	`associate-/r*_binary64_363`
78×	`cancel-sign-sub-inv_binary64_385`
69×	`div-sub_binary64_424`
64×	`log-prod_binary64_505`
63×	`sub-neg_binary64_412`
56×	`distribute-rgt-neg-in_binary64_377`
47×	`associate-/r/_binary64_365`
44×	`exp-prod_binary64_471`
43×	`neg-sub0_binary64_414` `distribute-lft-neg-in_binary64_376`
35×	`neg-mul-1_binary64_415`
34×	`log-div_binary64_506`
27×	`cube-div_binary64_448` `cube-prod_binary64_447`
26×	`+-commutative_binary64_349`
22×	`sqr-pow_binary64_391` `associate-/l/_binary64_366`
20×	`distribute-neg-frac_binary64_383`
16×	`swap-sqr_binary64_386`
15×	`distribute-neg-in_binary64_380`
13×	`mul-1-neg_binary64_411`
10×	`distribute-lft-neg-out_binary64_378` `distribute-rgt-out--_binary64_373`
9×	`cube-unmult_binary64_456`
8×	`exp-sum_binary64_465` `associate--l+_binary64_356` `associate--r+_binary64_355`
7×	`unpow3_binary64_485` `cube-mult_binary64_449`
6×	`unswap-sqr_binary64_387`
5×	`unpow2_binary64_484` `unpow1/2_binary64_483` `unpow1_binary64_477` `exp-diff_binary64_467`
4×	`log-pow_binary64_508` `pow-plus_binary64_482` `distribute-rgt-out_binary64_372`
3×	`exp-lft-sqr_binary64_474` `rem-sqrt-square_binary64_432` `distribute-lft-out_binary64_370` `associate-+r-_binary64_353` `associate-+r+_binary64_351`
2×	`/-rgt-identity_binary64_410` `distribute-lft-out--_binary64_371` `associate-+l+_binary64_352`
1×	`log-rec_binary64_507` `prod-exp_binary64_468` `1-exp_binary64_463` `exp-1-e_binary64_462` `rem-square-sqrt_binary64_431` `unsub-neg_binary64_413` `*-rgt-identity_binary64_409` `difference-of-squares_binary64_388`
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` `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-cbrt_binary64_473` `exp-sqrt_binary64_472` `div-exp_binary64_470` `rec-exp_binary64_469` `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` `-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` `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-rgt-neg-out_binary64_379` `distribute-rgt1-in_binary64_375` `distribute-lft1-in_binary64_374` `count-2_binary64_367` `associate--r-_binary64_358` `associate--l-_binary64_357` `associate-+l-_binary64_354`

Counts

196 → 173

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	409	6814
1	1176	6169
2	4681	6109
3	5011	6109

prune275.0ms (0.6%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	168	5	173
Fresh	5	16	21
Picked	1	0	1
Done	0	1	1
Total	174	22	196

Error

11.7b

Counts

196 → 22

Compiler

Compiled 6516 to 2530 computations (61.2% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.9b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2)))))
6.3b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2))))))
12.0b	(.f64 (/.f64 (-.f64 U U) Om) (*.f64 l n))
18.0b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2)))))))

rewrite209.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

11.7b

Rules

36×	`pow1_binary64_480`
30×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
23×	`add-sqr-sqrt_binary64_441` `associate-l_binary64_360`
21×	`*-un-lft-identity_binary64_419`
20×	`pow-prod-down_binary64_490`
15×	`add-cube-cbrt_binary64_454` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `times-frac_binary64_425`
10×	`associate-*r/_binary64_361`
5×	`sqrt-pow1_binary64_437` `associate-r_binary64_359` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
4×	`add-log-exp_binary64_458`
3×	`flip3-+_binary64_422` `flip-+_binary64_393` `difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371` `*-commutative_binary64_350`
2×	`sqrt-div_binary64_436` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `associate-*l/_binary64_362` `div-inv_binary64_416` `unswap-sqr_binary64_387`

Counts

4 → 105

Calls

4 calls:

11.0ms	(.f64 (/.f64 (-.f64 U U) Om) (*.f64 l n))
10.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2))))))
7.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2)))))))
6.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2)))))

Compiler

Compiled 4245 to 1677 computations (60.5% saved)

series7.4s (16.3%)

Error

11.5b

Counts

4 → 123

Calls

4 calls:

2.9s	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2))))))
2.2s	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2)))))
1.6s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2)))))))
453.0ms	(.f64 (/.f64 (-.f64 U U) Om) (*.f64 l n))

Compiler

Compiled 12708 to 9603 computations (24.4% saved)

simplify203.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

697×	`associate-r_binary64_359`
602×	`associate-l_binary64_360`
212×	`associate-/l*_binary64_364`
190×	`*-commutative_binary64_350`
145×	`distribute-rgt-in_binary64_369`
137×	`distribute-lft-in_binary64_368`
131×	`associate-*l/_binary64_362`
123×	`associate-*r/_binary64_361`
120×	`times-frac_binary64_425`
91×	`associate-/r*_binary64_363`
90×	`cancel-sign-sub-inv_binary64_385`
73×	`sub-neg_binary64_412`
64×	`log-prod_binary64_505`
59×	`distribute-rgt-neg-in_binary64_377`
47×	`distribute-lft-neg-in_binary64_376`
41×	`neg-sub0_binary64_414`
35×	`associate-/r/_binary64_365`
33×	`neg-mul-1_binary64_415`
26×	`+-commutative_binary64_349`
23×	`sqr-pow_binary64_391`
18×	`distribute-neg-frac_binary64_383`
17×	`log-div_binary64_506` `div-sub_binary64_424`
16×	`swap-sqr_binary64_386`
14×	`exp-prod_binary64_471` `distribute-neg-in_binary64_380`
13×	`mul-1-neg_binary64_411`
11×	`associate--r+_binary64_355`
10×	`associate--l+_binary64_356`
9×	`cube-unmult_binary64_456` `distribute-lft-neg-out_binary64_378` `distribute-rgt-out--_binary64_373`
6×	`unpow3_binary64_485` `cube-mult_binary64_449` `unswap-sqr_binary64_387`
5×	`unpow2_binary64_484` `unpow1_binary64_477`
4×	`log-pow_binary64_508` `associate-+r+_binary64_351`
3×	`pow-plus_binary64_482` `distribute-rgt-out_binary64_372` `distribute-lft-out_binary64_370`
2×	`cube-div_binary64_448` `cube-prod_binary64_447` `distribute-lft-out--_binary64_371` `associate-+l-_binary64_354` `associate-+l+_binary64_352`
1×	`exp-lft-sqr_binary64_474` `exp-diff_binary64_467` `exp-sum_binary64_465` `1-exp_binary64_463` `rem-sqrt-square_binary64_432` `rem-square-sqrt_binary64_431` `unsub-neg_binary64_413` `-rgt-identity_binary64_409` `-lft-identity_binary64_408` `difference-of-squares_binary64_388` `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-rec_binary64_507` `pow-base-0_binary64_503` `unpow1/3_binary64_486` `unpow1/2_binary64_483` `exp-to-pow_binary64_481` `pow-base-1_binary64_479` `unpow0_binary64_478` `unpow-1_binary64_476` `exp-lft-cube_binary64_475` `exp-cbrt_binary64_473` `exp-sqrt_binary64_472` `div-exp_binary64_470` `rec-exp_binary64_469` `prod-exp_binary64_468` `exp-neg_binary64_466` `e-exp-1_binary64_464` `exp-1-e_binary64_462` `exp-0_binary64_461` `rem-log-exp_binary64_460` `rem-exp-log_binary64_459` `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` `/-rgt-identity_binary64_410` `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` `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-rgt-neg-out_binary64_379` `distribute-rgt1-in_binary64_375` `distribute-lft1-in_binary64_374` `count-2_binary64_367` `associate-/l/_binary64_366` `associate--r-_binary64_358` `associate--l-_binary64_357`

Counts

228 → 206

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	438	9137
1	1279	8288
2	4919	8288
3	4987	8288

prune337.0ms (0.7%)

Pruning

26 alts after pruning (24 fresh and 2 done)

	Pruned	Kept	Total
New	200	6	206
Fresh	2	18	20
Picked	0	1	1
Done	0	1	1
Total	202	26	228

Error

11.0b

Counts

228 → 26

Compiler

Compiled 8180 to 2951 computations (63.9% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

18.0b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (.f64 l -2)))))) (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (.f64 l -2))))))) (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (*.f64 l -2))))))))
18.9b	(cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
18.9b	(cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
18.9b	(cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))

rewrite447.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

11.0b

Rules

68×	`associate-*r/_binary64_361`
60×	`cbrt-div_binary64_451`
30×	`flip3-+_binary64_422` `flip-+_binary64_393`
28×	`frac-times_binary64_429`
26×	`sqrt-div_binary64_436`
24×	`pow1_binary64_480`
15×	`sqrt-pow1_binary64_437`
14×	`associate-*l/_binary64_362`
12×	`pow1/3_binary64_501`
9×	`pow-prod-up_binary64_489`
6×	`pow-plus_binary64_482`
5×	`pow-prod-down_binary64_490`
4×	`add-log-exp_binary64_458` `add-exp-log_binary64_457` `add-cbrt-cube_binary64_455` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `*-un-lft-identity_binary64_419`
3×	`cbrt-prod_binary64_450` `pow-sqr_binary64_392`
2×	`pow2_binary64_500`
1×	`pow1/2_binary64_499` `pow3_binary64_502` `sqrt-prod_binary64_435`

Counts

4 → 83

Calls

4 calls:

14.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (.f64 l -2)))))) (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (.f64 l -2))))))) (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (*.f64 l -2))))))))
7.0ms	(cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
7.0ms	(cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
7.0ms	(cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))

Compiler

Compiled 10290 to 4030 computations (60.8% saved)

series8.2s (18.3%)

Error

11.0b

Counts

4 → 87

Calls

4 calls:

2.1s	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (.f64 l -2)))))) (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (.f64 l -2))))))) (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (*.f64 l -2))))))))
2.0s	(cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
1.9s	(cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
1.9s	(cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))

Compiler

Compiled 26674 to 18090 computations (32.2% saved)

simplify280.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

275×	`cancel-sign-sub-inv_binary64_385`
269×	`associate-r_binary64_359`
261×	`*-commutative_binary64_350`
260×	`associate-l_binary64_360`
162×	`times-frac_binary64_425`
158×	`associate-/l*_binary64_364`
145×	`sub-neg_binary64_412`
144×	`distribute-neg-frac_binary64_383`
112×	`neg-sub0_binary64_414`
99×	`neg-mul-1_binary64_415`
97×	`associate-/r*_binary64_363`
90×	`sqr-pow_binary64_391`
84×	`log-prod_binary64_505` `distribute-rgt-in_binary64_369`
82×	`distribute-lft-in_binary64_368`
79×	`exp-sum_binary64_465` `div-sub_binary64_424`
74×	`associate-*r/_binary64_361`
56×	`associate-*l/_binary64_362`
55×	`+-commutative_binary64_349`
53×	`distribute-rgt-neg-in_binary64_377`
45×	`distribute-lft-neg-in_binary64_376`
39×	`log-div_binary64_506`
35×	`unsub-neg_binary64_413`
34×	`exp-prod_binary64_471`
33×	`unswap-sqr_binary64_387`
28×	`associate-/r/_binary64_365`
25×	`associate--l+_binary64_356`
18×	`associate-+l+_binary64_352`
16×	`unpow1/3_binary64_486` `mul-1-neg_binary64_411`
15×	`exp-diff_binary64_467` `associate--r+_binary64_355`
13×	`pow-sqr_binary64_392`
11×	`remove-double-neg_binary64_407`
10×	`unpow3_binary64_485` `cube-mult_binary64_449` `distribute-neg-in_binary64_380`
8×	`distribute-lft-neg-out_binary64_378`
7×	`log-pow_binary64_508` `cube-prod_binary64_447`
6×	`cube-unmult_binary64_456` `distribute-rgt-neg-out_binary64_379`
5×	`log-rec_binary64_507` `rem-3cbrt-lft_binary64_444`
4×	`unpow2_binary64_484` `unpow1/2_binary64_483` `exp-to-pow_binary64_481` `unpow1_binary64_477` `rem-sqrt-square_binary64_432` `distribute-rgt-out--_binary64_373` `associate--r-_binary64_358` `associate-+r-_binary64_353` `associate-+r+_binary64_351`
3×	`cube-div_binary64_448` `cancel-sign-sub_binary64_384` `associate-+l-_binary64_354`
2×	`rem-cube-cbrt_binary64_442` `swap-sqr_binary64_386` `associate--l-_binary64_357`
1×	`1-exp_binary64_463` `rem-square-sqrt_binary64_431` `/-rgt-identity_binary64_410` `*-rgt-identity_binary64_409` `+-rgt-identity_binary64_404` `difference-of-squares_binary64_388` `distribute-rgt-out_binary64_372` `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` `pow-base-0_binary64_503` `pow-plus_binary64_482` `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-neg_binary64_466` `e-exp-1_binary64_464` `exp-1-e_binary64_462` `exp-0_binary64_461` `rem-log-exp_binary64_460` `rem-exp-log_binary64_459` `cube-neg_binary64_446` `rem-3cbrt-rft_binary64_445` `rem-cbrt-cube_binary64_443` `sqr-abs_binary64_434` `sqr-neg_binary64_433` `-lft-identity_binary64_408` `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` `distribute-frac-neg_binary64_382` `distribute-neg-out_binary64_381` `distribute-rgt1-in_binary64_375` `distribute-lft1-in_binary64_374` `distribute-lft-out--_binary64_371` `count-2_binary64_367` `associate-/l/_binary64_366`

Counts

170 → 158

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	451	13494
1	1081	13379
2	3599	13301
3	5017	13301

prune564.0ms (1.2%)

Pruning

26 alts after pruning (23 fresh and 3 done)

	Pruned	Kept	Total
New	154	4	158
Fresh	4	19	23
Picked	0	1	1
Done	0	2	2
Total	158	26	184

Error

10.7b

Counts

184 → 26

Compiler

Compiled 14181 to 5581 computations (60.6% saved)

regimes4.1s (9.1%)

Accuracy

Total 17.4b remaining (62.6%)

Threshold costs 0b (0%)

Compiler

Compiled 41482 to 30226 computations (27.1% saved)

bsearch14.0ms (0%)

Compiler: Compiled 27 to 22 computations (18.5% saved)

simplify69.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

320×	`neg-mul-1_binary64_415` `neg-sub0_binary64_414`
276×	`unsub-neg_binary64_413`
266×	`distribute-rgt-neg-out_binary64_379`
221×	`distribute-lft-neg-out_binary64_378`
207×	`distribute-neg-out_binary64_381`
196×	`distribute-rgt-neg-in_binary64_377`
128×	`distribute-lft-neg-in_binary64_376`
109×	`remove-double-neg_binary64_407`
98×	`*-commutative_binary64_350`
91×	`cancel-sign-sub-inv_binary64_385`
86×	`sub-neg_binary64_412`
69×	`+-commutative_binary64_349`
62×	`distribute-neg-in_binary64_380`
17×	`+-lft-identity_binary64_403`
16×	`+-rgt-identity_binary64_404`
13×	`distribute-frac-neg_binary64_382`
4×	`distribute-neg-frac_binary64_383`
1×	`sqr-neg_binary64_433` `--rgt-identity_binary64_405`
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` `mul-1-neg_binary64_411` `/-rgt-identity_binary64_410` `-rgt-identity_binary64_409` `-lft-identity_binary64_408` `sub0-neg_binary64_406` `cancel-sign-sub_binary64_384`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	298
1	131	298
2	174	298
3	215	298
4	253	298
5	291	298
6	319	298
7	525	298
8	791	298
9	719	298
10	812	298
11	904	298
12	1023	298
13	1131	298
14	1224	298
15	1283	298
16	1310	298
17	1315	298
18	1316	298
19	1316	298
20	1299	298

end0.0ms (0%)

sample7.0s (15.4%)

Algorithm

1×

intervals

Results

1.3s	13127×	body	128	nan
812.0ms	8000×	body	128	valid
126.0ms	1237×	body	128	invalid

Compiler

Compiled 5397 to 3898 computations (27.8% saved)

Details

analyze2.6s (5.8%)

sample106.0ms (0.2%)

simplify58.0ms (0.1%)

prune7.0ms (0%)

localize20.0ms (0%)

rewrite303.0ms (0.7%)

series6.3s (14%)

simplify246.0ms (0.5%)

prune377.0ms (0.8%)

localize24.0ms (0.1%)

rewrite202.0ms (0.4%)

series5.5s (12.2%)

simplify165.0ms (0.4%)

prune275.0ms (0.6%)

localize25.0ms (0.1%)

rewrite209.0ms (0.5%)

series7.4s (16.3%)

simplify203.0ms (0.5%)

prune337.0ms (0.7%)

localize28.0ms (0.1%)

rewrite447.0ms (1%)

series8.2s (18.3%)

simplify280.0ms (0.6%)

prune564.0ms (1.2%)

regimes4.1s (9.1%)

bsearch14.0ms (0%)

simplify69.0ms (0.2%)

end0.0ms (0%)

sample7.0s (15.4%)

Profiling