Details

analyze3.9s (11.2%)

Algorithm

1×

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)

sample456.0ms (1.3%)

Algorithm

1×

intervals

Results

289.0ms	425×	body	128	nan
61.0ms	256×	body	128	valid
5.0ms	44×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify467.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

450×	`associate-/l*_binary64_364`
385×	`distribute-rgt-neg-out_binary64_379`
361×	`unsub-neg_binary64_413`
360×	`cancel-sign-sub-inv_binary64_385`
356×	`distribute-lft-neg-out_binary64_378`
323×	`distribute-neg-frac_binary64_383`
282×	`distribute-rgt-in_binary64_369`
276×	`distribute-lft-in_binary64_368`
264×	`associate-*r/_binary64_361`
259×	`associate-*l/_binary64_362`
237×	`distribute-rgt-neg-in_binary64_377`
214×	`associate-/r/_binary64_365`
208×	`times-frac_binary64_425`
195×	`distribute-lft-neg-in_binary64_376`
185×	`*-commutative_binary64_350`
151×	`neg-sub0_binary64_414`
145×	`neg-mul-1_binary64_415`
117×	`distribute-neg-in_binary64_380`
94×	`associate-/l/_binary64_366` `associate-r_binary64_359`
90×	`associate-l_binary64_360`
89×	`sub-neg_binary64_412`
84×	`distribute-neg-out_binary64_381`
37×	`associate-+r+_binary64_351`
34×	`remove-double-neg_binary64_407`
30×	`distribute-rgt-out_binary64_372` `distribute-lft-out_binary64_370`
29×	`associate-+l+_binary64_352`
27×	`div-sub_binary64_424`
23×	`mul0-rgt_binary64_402` `mul0-lft_binary64_401`
20×	`associate--r+_binary64_355`
19×	`+-commutative_binary64_349`
16×	`associate-+l-_binary64_354` `associate-+r-_binary64_353`
13×	`distribute-rgt-out--_binary64_373`
11×	`unswap-sqr_binary64_387` `distribute-lft-out--_binary64_371`
10×	`associate-/r*_binary64_363`
9×	`sub0-neg_binary64_406`
8×	`sqr-pow_binary64_391`
7×	`associate--l+_binary64_356`
6×	`+-rgt-identity_binary64_404` `associate--r-_binary64_358`
5×	`pow-plus_binary64_482` `associate--l-_binary64_357`
4×	`cube-unmult_binary64_456` `--rgt-identity_binary64_405` `pow-sqr_binary64_392`
3×	`/-rgt-identity_binary64_410`
2×	`div0_binary64_400` `swap-sqr_binary64_386` `distribute-rgt1-in_binary64_375`
1×	`unpow2_binary64_484` `unpow1_binary64_477` `div-exp_binary64_470` `rec-exp_binary64_469` `prod-exp_binary64_468` `1-exp_binary64_463` `-rgt-identity_binary64_409` `-inverses_binary64_399` `rgt-mult-inverse_binary64_396` `cancel-sign-sub_binary64_384` `distribute-frac-neg_binary64_382` `distribute-lft1-in_binary64_374` `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` `log-div_binary64_506` `log-prod_binary64_505` `pow-base-0_binary64_503` `unpow1/3_binary64_486` `unpow3_binary64_485` `unpow1/2_binary64_483` `exp-to-pow_binary64_481` `pow-base-1_binary64_479` `unpow0_binary64_478` `unpow-1_binary64_476` `exp-lft-cube_binary64_475` `exp-lft-sqr_binary64_474` `exp-cbrt_binary64_473` `exp-sqrt_binary64_472` `exp-prod_binary64_471` `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` `sqr-neg_binary64_433` `rem-sqrt-square_binary64_432` `rem-square-sqrt_binary64_431` `mul-1-neg_binary64_411` `*-lft-identity_binary64_408` `+-lft-identity_binary64_403` `+-inverses_binary64_398` `lft-mult-inverse_binary64_397` `remove-double-div_binary64_395` `difference-of-sqr--1_binary64_390` `difference-of-sqr-1_binary64_389` `difference-of-squares_binary64_388`

Counts

1 → 5

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	42
1	56	42
2	187	42
3	740	39
4	2746	39

prune11.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	3	2	5
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	3	3	6

Error

28.2b

Counts

6 → 3

Compiler

Compiled 218 to 141 computations (35.3% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

5.0b	(*.f64 n (/.f64 l Om))
6.0b	(.f64 U (.f64 (.f64 2 n) (-.f64 t (.f64 (/.f64 l Om) (-.f64 (.f64 2 l) (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om))))))))
8.2b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
21.5b	(sqrt.f64 (.f64 U (.f64 (.f64 2 n) (-.f64 t (.f64 (/.f64 l Om) (-.f64 (.f64 2 l) (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))))))))

rewrite702.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

23.3b

Rules

30×	`pow1_binary64_480`
27×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
21×	`add-sqr-sqrt_binary64_441`
16×	`pow-prod-down_binary64_490` `*-un-lft-identity_binary64_419`
15×	`associate-r_binary64_359`
14×	`add-cube-cbrt_binary64_454`
13×	`associate-*r/_binary64_361` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
11×	`associate-l_binary64_360`
10×	`times-frac_binary64_425`
8×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
4×	`add-log-exp_binary64_458` `sqrt-pow1_binary64_437` `flip3--_binary64_423` `flip--_binary64_394` `sub-neg_binary64_412` `cancel-sign-sub-inv_binary64_385`
3×	`*-commutative_binary64_350`
2×	`sqrt-div_binary64_436` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `frac-times_binary64_429` `associate-*l/_binary64_362` `unswap-sqr_binary64_387`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371` `div-inv_binary64_416`

Counts

4 → 105

Calls

4 calls:

32.0ms	(sqrt.f64 (.f64 U (.f64 (.f64 2 n) (-.f64 t (.f64 (/.f64 l Om) (-.f64 (.f64 2 l) (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))))))))
9.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
8.0ms	(.f64 U (.f64 (.f64 2 n) (-.f64 t (.f64 (/.f64 l Om) (-.f64 (.f64 2 l) (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om))))))))
6.0ms	(*.f64 n (/.f64 l Om))

Compiler

Compiled 3926 to 1618 computations (58.8% saved)

series3.1s (8.9%)

Error

20.9b

Counts

4 → 94

Calls

4 calls:

1.8s	(sqrt.f64 (.f64 U (.f64 (.f64 2 n) (-.f64 t (.f64 (/.f64 l Om) (-.f64 (.f64 2 l) (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))))))))
1.0s	(.f64 U (.f64 (.f64 2 n) (-.f64 t (.f64 (/.f64 l Om) (-.f64 (.f64 2 l) (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om))))))))
126.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
50.0ms	(*.f64 n (/.f64 l Om))

Compiler

Compiled 11079 to 8316 computations (24.9% saved)

simplify806.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

687×	`associate-r_binary64_359`
664×	`associate-l_binary64_360`
296×	`associate-/l*_binary64_364`
239×	`times-frac_binary64_425`
196×	`associate-*r/_binary64_361`
192×	`*-commutative_binary64_350`
176×	`associate-*l/_binary64_362`
153×	`associate-/r*_binary64_363`
84×	`cancel-sign-sub-inv_binary64_385`
72×	`distribute-rgt-in_binary64_369`
67×	`distribute-lft-in_binary64_368`
61×	`sub-neg_binary64_412`
60×	`distribute-rgt-neg-in_binary64_377`
56×	`associate-/r/_binary64_365`
49×	`neg-sub0_binary64_414`
44×	`associate-/l/_binary64_366`
43×	`neg-mul-1_binary64_415`
41×	`distribute-lft-neg-in_binary64_376`
33×	`sqr-pow_binary64_391`
27×	`+-commutative_binary64_349`
24×	`distribute-lft-neg-out_binary64_378`
23×	`unswap-sqr_binary64_387`
18×	`distribute-neg-frac_binary64_383`
17×	`swap-sqr_binary64_386`
16×	`distribute-neg-in_binary64_380`
11×	`log-prod_binary64_505` `exp-prod_binary64_471`
10×	`unpow3_binary64_485` `cube-unmult_binary64_456` `mul-1-neg_binary64_411`
9×	`cube-mult_binary64_449` `div-sub_binary64_424` `pow-sqr_binary64_392`
8×	`distribute-rgt-out_binary64_372` `associate--l+_binary64_356` `associate--r+_binary64_355`
7×	`distribute-rgt-neg-out_binary64_379` `distribute-lft-out--_binary64_371` `associate-+r+_binary64_351`
6×	`difference-of-squares_binary64_388`
5×	`unpow2_binary64_484` `pow-plus_binary64_482`
4×	`log-div_binary64_506` `cube-prod_binary64_447`
3×	`cube-div_binary64_448` `/-rgt-identity_binary64_410` `distribute-rgt-out--_binary64_373` `distribute-lft-out_binary64_370`
2×	`*-rgt-identity_binary64_409`
1×	`div-exp_binary64_470` `rec-exp_binary64_469` `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` `*-inverses_binary64_399` `associate-+r-_binary64_353` `associate-+l+_binary64_352`
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` `unpow1/2_binary64_483` `exp-to-pow_binary64_481` `pow-base-1_binary64_479` `unpow0_binary64_478` `unpow1_binary64_477` `unpow-1_binary64_476` `exp-lft-cube_binary64_475` `exp-lft-sqr_binary64_474` `exp-cbrt_binary64_473` `exp-sqrt_binary64_472` `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` `*-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_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` `associate-+l-_binary64_354`

Counts

199 → 433

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	481	7371
1	1331	6761

prune425.0ms (1.2%)

Pruning

28 alts after pruning (27 fresh and 1 done)

	Pruned	Kept	Total
New	407	26	433
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	408	28	436

Error

13.0b

Counts

436 → 28

Compiler

Compiled 18346 to 7028 computations (61.7% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.1b	(/.f64 (*.f64 n l) Om)
6.9b	(.f64 U (.f64 (.f64 (.f64 n 2) (/.f64 (neg.f64 l) Om)) (-.f64 (.f64 2 l) (.f64 (-.f64 U* U) (/.f64 (*.f64 n l) Om)))))
8.2b	(.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om))
21.5b	(sqrt.f64 (+.f64 (.f64 (.f64 t (.f64 2 n)) U) (.f64 U (.f64 (.f64 (.f64 n 2) (/.f64 (neg.f64 l) Om)) (-.f64 (.f64 2 l) (.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om)))))))

rewrite159.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

12.3b

Rules

43×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
22×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
21×	`pow1_binary64_480`
16×	`add-sqr-sqrt_binary64_441`
13×	`*-un-lft-identity_binary64_419`
11×	`add-cube-cbrt_binary64_454` `pow-prod-down_binary64_490` `associate-*r/_binary64_361`
8×	`associate-l_binary64_360` `associate-r_binary64_359` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
6×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `times-frac_binary64_425`
4×	`add-log-exp_binary64_458` `flip3--_binary64_423` `frac-times_binary64_429` `flip--_binary64_394` `sub-neg_binary64_412` `cancel-sign-sub-inv_binary64_385`
3×	`sqrt-prod_binary64_435` `associate-l/_binary64_362` `associate-/r_binary64_363`
2×	`sqrt-div_binary64_436` `div-inv_binary64_416` `*-commutative_binary64_350` `distribute-rgt-neg-out_binary64_379`
1×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `flip3-+_binary64_422` `flip-+_binary64_393` `rem-sqrt-square_binary64_432` `unswap-sqr_binary64_387` `difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371` `distribute-frac-neg_binary64_382` `distribute-lft-neg-out_binary64_378` `frac-2neg_binary64_430` `clear-num_binary64_418` `associate-/l*_binary64_364`

Counts

4 → 111

Calls

4 calls:

16.0ms	(.f64 U (.f64 (.f64 (.f64 n 2) (/.f64 (neg.f64 l) Om)) (-.f64 (.f64 2 l) (.f64 (-.f64 U* U) (/.f64 (*.f64 n l) Om)))))
11.0ms	(.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om))
6.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 t (.f64 2 n)) U) (.f64 U (.f64 (.f64 (.f64 n 2) (/.f64 (neg.f64 l) Om)) (-.f64 (.f64 2 l) (.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om)))))))
5.0ms	(/.f64 (*.f64 n l) Om)

Compiler

Compiled 5254 to 2259 computations (57% saved)

series1.4s (4%)

Error

10.8b

Counts

4 → 80

Calls

4 calls:

616.0ms	(.f64 U (.f64 (.f64 (.f64 n 2) (/.f64 (neg.f64 l) Om)) (-.f64 (.f64 2 l) (.f64 (-.f64 U* U) (/.f64 (*.f64 n l) Om)))))
484.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 t (.f64 2 n)) U) (.f64 U (.f64 (.f64 (.f64 n 2) (/.f64 (neg.f64 l) Om)) (-.f64 (.f64 2 l) (.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om)))))))
163.0ms	(.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om))
50.0ms	(/.f64 (*.f64 n l) Om)

Compiler

Compiled 9492 to 7003 computations (26.2% saved)

simplify644.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

731×	`associate-l_binary64_360`
287×	`associate-/l*_binary64_364`
228×	`times-frac_binary64_425`
219×	`associate-*r/_binary64_361`
199×	`associate-*l/_binary64_362`
167×	`*-commutative_binary64_350`
142×	`associate-/r*_binary64_363`
95×	`associate-r_binary64_359`
88×	`cancel-sign-sub-inv_binary64_385`
86×	`distribute-rgt-in_binary64_369`
83×	`distribute-lft-in_binary64_368`
69×	`distribute-rgt-neg-in_binary64_377`
65×	`distribute-rgt-neg-out_binary64_379`
63×	`sub-neg_binary64_412`
61×	`distribute-lft-neg-out_binary64_378`
53×	`neg-sub0_binary64_414`
52×	`distribute-lft-neg-in_binary64_376`
48×	`neg-mul-1_binary64_415`
46×	`associate-/r/_binary64_365`
42×	`unswap-sqr_binary64_387`
33×	`associate-/l/_binary64_366`
30×	`sqr-pow_binary64_391`
27×	`swap-sqr_binary64_386`
25×	`distribute-neg-frac_binary64_383`
24×	`distribute-frac-neg_binary64_382`
21×	`+-commutative_binary64_349`
17×	`cube-prod_binary64_447`
13×	`unpow3_binary64_485`
12×	`log-prod_binary64_505`
11×	`pow-sqr_binary64_392`
10×	`log-div_binary64_506` `div-sub_binary64_424` `distribute-neg-in_binary64_380`
9×	`distribute-lft-out--_binary64_371`
8×	`cube-unmult_binary64_456` `cube-mult_binary64_449`
7×	`exp-prod_binary64_471` `mul-1-neg_binary64_411` `distribute-rgt-out--_binary64_373`
6×	`cube-div_binary64_448` `difference-of-squares_binary64_388` `associate--r+_binary64_355`
5×	`associate--l+_binary64_356`
4×	`unpow2_binary64_484` `pow-plus_binary64_482` `distribute-rgt-out_binary64_372`
3×	`associate-+r-_binary64_353`
2×	`exp-diff_binary64_467` `exp-sum_binary64_465` `sqr-neg_binary64_433` `rem-sqrt-square_binary64_432` `/-rgt-identity_binary64_410` `associate-+l+_binary64_352` `associate-+r+_binary64_351`
1×	`1-exp_binary64_463` `rem-square-sqrt_binary64_431` `-rgt-identity_binary64_409` `-lft-identity_binary64_408` `*-inverses_binary64_399` `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` `pow-base-0_binary64_503` `unpow1/3_binary64_486` `unpow1/2_binary64_483` `exp-to-pow_binary64_481` `pow-base-1_binary64_479` `unpow0_binary64_478` `unpow1_binary64_477` `unpow-1_binary64_476` `exp-lft-cube_binary64_475` `exp-lft-sqr_binary64_474` `exp-cbrt_binary64_473` `exp-sqrt_binary64_472` `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` `unsub-neg_binary64_413` `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_398` `lft-mult-inverse_binary64_397` `rgt-mult-inverse_binary64_396` `remove-double-div_binary64_395` `difference-of-sqr--1_binary64_390` `difference-of-sqr-1_binary64_389` `cancel-sign-sub_binary64_384` `distribute-neg-out_binary64_381` `distribute-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

191 → 467

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	456	6495
1	1292	6066

prune515.0ms (1.5%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	455	12	467
Fresh	10	16	26
Picked	1	0	1
Done	0	1	1
Total	466	29	495

Error

9.6b

Counts

495 → 29

Compiler

Compiled 22419 to 9504 computations (57.6% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.0b	(/.f64 Om (.f64 n (.f64 l U)))
5.1b	(/.f64 Om (*.f64 l U))
6.9b	(/.f64 n (/.f64 Om (*.f64 l U)))
16.4b	(sqrt.f64 (+.f64 (.f64 (.f64 t (.f64 2 n)) U) (.f64 -2 (/.f64 (+.f64 (/.f64 n (/.f64 Om (.f64 l U))) (.f64 2 l)) (/.f64 Om (.f64 n (.f64 l U)))))))

rewrite116.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

9.6b

Rules

39×	`times-frac_binary64_425`
27×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
26×	`add-sqr-sqrt_binary64_441`
25×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
10×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
9×	`associate-/l_binary64_364` `associate-/r_binary64_363`
7×	`div-inv_binary64_416`
5×	`pow1_binary64_480` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
4×	`add-log-exp_binary64_458`
3×	`sqrt-prod_binary64_435` `frac-2neg_binary64_430` `clear-num_binary64_418`
2×	`sqrt-div_binary64_436`
1×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `flip3-+_binary64_422` `flip-+_binary64_393` `rem-sqrt-square_binary64_432` `associate-/r/_binary64_365`

Counts

4 → 107

Calls

4 calls:

8.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 t (.f64 2 n)) U) (.f64 -2 (/.f64 (+.f64 (/.f64 n (/.f64 Om (.f64 l U))) (.f64 2 l)) (/.f64 Om (.f64 n (.f64 l U)))))))
7.0ms	(/.f64 Om (.f64 n (.f64 l U)))
6.0ms	(/.f64 n (/.f64 Om (*.f64 l U)))
4.0ms	(/.f64 Om (*.f64 l U))

Compiler

Compiled 4285 to 1791 computations (58.2% saved)

series559.0ms (1.6%)

Error

9.6b

Counts

4 → 53

Calls

4 calls:

283.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 t (.f64 2 n)) U) (.f64 -2 (/.f64 (+.f64 (/.f64 n (/.f64 Om (.f64 l U))) (.f64 2 l)) (/.f64 Om (.f64 n (.f64 l U)))))))
98.0ms	(/.f64 Om (.f64 n (.f64 l U)))
87.0ms	(/.f64 n (/.f64 Om (*.f64 l U)))
54.0ms	(/.f64 Om (*.f64 l U))

Compiler

Compiled 5260 to 3758 computations (28.6% saved)

simplify486.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

305×	`distribute-rgt-neg-in_binary64_377`
276×	`associate-r_binary64_359`
271×	`distribute-lft-neg-in_binary64_376`
231×	`cancel-sign-sub-inv_binary64_385`
223×	`associate-l_binary64_360`
222×	`times-frac_binary64_425`
194×	`associate-/l*_binary64_364`
177×	`associate-/r*_binary64_363`
160×	`distribute-neg-frac_binary64_383`
129×	`*-commutative_binary64_350`
127×	`associate-*l/_binary64_362`
121×	`associate-/r/_binary64_365`
101×	`associate-*r/_binary64_361`
99×	`associate-/l/_binary64_366`
98×	`distribute-rgt-in_binary64_369`
96×	`unswap-sqr_binary64_387`
89×	`neg-sub0_binary64_414`
88×	`neg-mul-1_binary64_415`
80×	`distribute-lft-in_binary64_368`
77×	`sub-neg_binary64_412`
64×	`sqr-pow_binary64_391`
59×	`cube-prod_binary64_447`
57×	`swap-sqr_binary64_386`
52×	`log-div_binary64_506`
49×	`unpow3_binary64_485` `+-commutative_binary64_349`
45×	`log-prod_binary64_505`
41×	`distribute-lft-neg-out_binary64_378`
37×	`*-rgt-identity_binary64_409`
30×	`cube-div_binary64_448`
28×	`associate-+r-_binary64_353`
27×	`associate-+l-_binary64_354`
25×	`distribute-neg-in_binary64_380`
23×	`pow-sqr_binary64_392` `associate--r+_binary64_355` `associate-+l+_binary64_352`
17×	`cube-mult_binary64_449` `associate-+r+_binary64_351`
16×	`div-sub_binary64_424`
14×	`unsub-neg_binary64_413`
13×	`distribute-rgt-out--_binary64_373` `associate--l+_binary64_356`
12×	`pow-plus_binary64_482` `distribute-lft-out--_binary64_371`
11×	`distribute-rgt-out_binary64_372` `associate--r-_binary64_358`
9×	`log-pow_binary64_508` `div-exp_binary64_470` `prod-exp_binary64_468` `cube-unmult_binary64_456` `/-rgt-identity_binary64_410`
7×	`log-rec_binary64_507` `exp-prod_binary64_471` `*-lft-identity_binary64_408` `distribute-rgt-neg-out_binary64_379` `associate--l-_binary64_357`
5×	`unpow2_binary64_484` `unpow1_binary64_477`
4×	`rem-sqrt-square_binary64_432` `mul-1-neg_binary64_411` `distribute-frac-neg_binary64_382`
3×	`rec-exp_binary64_469`
2×	`rem-square-sqrt_binary64_431` `distribute-lft-out_binary64_370`
1×	`1-exp_binary64_463` `rem-log-exp_binary64_460` `remove-double-neg_binary64_407` `div0_binary64_400` `*-inverses_binary64_399` `remove-double-div_binary64_395` `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` `unpow1/2_binary64_483` `exp-to-pow_binary64_481` `pow-base-1_binary64_479` `unpow0_binary64_478` `unpow-1_binary64_476` `exp-lft-cube_binary64_475` `exp-lft-sqr_binary64_474` `exp-cbrt_binary64_473` `exp-sqrt_binary64_472` `exp-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-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` `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_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-neg-out_binary64_381` `distribute-rgt1-in_binary64_375` `distribute-lft1-in_binary64_374` `count-2_binary64_367`

Counts

160 → 567

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	288	3582
1	755	3309
2	3276	3201
3	4957	3201

prune562.0ms (1.6%)

Pruning

30 alts after pruning (28 fresh and 2 done)

	Pruned	Kept	Total
New	565	2	567
Fresh	1	26	27
Picked	0	1	1
Done	0	1	1
Total	566	30	596

Error

9.3b

Counts

596 → 30

Compiler

Compiled 25279 to 10265 computations (59.4% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.2b	(.f64 (-.f64 U U) (*.f64 (/.f64 n Om) l))
8.2b	(.f64 (-.f64 U U) (*.f64 (/.f64 n Om) l))
22.7b	(cbrt.f64 (.f64 U (+.f64 (.f64 n (.f64 2 (.f64 (/.f64 (neg.f64 l) Om) (-.f64 (.f64 2 l) (.f64 (-.f64 U* U) (.f64 (/.f64 n Om) l)))))) (.f64 2 (*.f64 n t)))))
22.7b	(cbrt.f64 (.f64 U (+.f64 (.f64 n (.f64 2 (.f64 (/.f64 (neg.f64 l) Om) (-.f64 (.f64 2 l) (.f64 (-.f64 U* U) (.f64 (/.f64 n Om) l)))))) (.f64 2 (*.f64 n t)))))

rewrite170.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

9.3b

Rules

22×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
14×	`pow1_binary64_480`
10×	`add-sqr-sqrt_binary64_441` `-un-lft-identity_binary64_419` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-l/_binary64_362` `associate-l_binary64_360`
6×	`add-cube-cbrt_binary64_454` `associate-*r/_binary64_361` `pow-prod-down_binary64_490`
4×	`add-log-exp_binary64_458` `cbrt-div_binary64_451` `flip3--_binary64_423` `frac-times_binary64_429` `flip--_binary64_394`
2×	`pow1/3_binary64_501` `flip3-+_binary64_422` `flip-+_binary64_393` `cbrt-prod_binary64_450` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371` `associate-r_binary64_359` `*-commutative_binary64_350`

Counts

4 → 76

Calls

4 calls:

18.0ms	(cbrt.f64 (.f64 U (+.f64 (.f64 n (.f64 2 (.f64 (/.f64 (neg.f64 l) Om) (-.f64 (.f64 2 l) (.f64 (-.f64 U* U) (.f64 (/.f64 n Om) l)))))) (.f64 2 (*.f64 n t)))))
16.0ms	(cbrt.f64 (.f64 U (+.f64 (.f64 n (.f64 2 (.f64 (/.f64 (neg.f64 l) Om) (-.f64 (.f64 2 l) (.f64 (-.f64 U* U) (.f64 (/.f64 n Om) l)))))) (.f64 2 (*.f64 n t)))))
9.0ms	(.f64 (-.f64 U U) (*.f64 (/.f64 n Om) l))
9.0ms	(.f64 (-.f64 U U) (*.f64 (/.f64 n Om) l))

Compiler

Compiled 6034 to 2480 computations (58.9% saved)

series4.7s (13.5%)

Error

9.3b

Counts

4 → 79

Calls

4 calls:

3.2s	(cbrt.f64 (.f64 U (+.f64 (.f64 n (.f64 2 (.f64 (/.f64 (neg.f64 l) Om) (-.f64 (.f64 2 l) (.f64 (-.f64 U* U) (.f64 (/.f64 n Om) l)))))) (.f64 2 (*.f64 n t)))))
1.1s	(cbrt.f64 (.f64 U (+.f64 (.f64 n (.f64 2 (.f64 (/.f64 (neg.f64 l) Om) (-.f64 (.f64 2 l) (.f64 (-.f64 U* U) (.f64 (/.f64 n Om) l)))))) (.f64 2 (*.f64 n t)))))
169.0ms	(.f64 (-.f64 U U) (*.f64 (/.f64 n Om) l))
154.0ms	(.f64 (-.f64 U U) (*.f64 (/.f64 n Om) l))

Compiler

Compiled 18660 to 12628 computations (32.3% saved)

simplify656.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

347×	`cancel-sign-sub-inv_binary64_385`
300×	`associate-r_binary64_359`
248×	`associate-l_binary64_360`
192×	`*-commutative_binary64_350`
156×	`times-frac_binary64_425`
153×	`associate-/l*_binary64_364`
152×	`sub-neg_binary64_412`
146×	`log-prod_binary64_505`
126×	`sqr-pow_binary64_391`
114×	`distribute-neg-frac_binary64_383`
113×	`neg-mul-1_binary64_415`
112×	`neg-sub0_binary64_414`
91×	`exp-sum_binary64_465` `associate-/r*_binary64_363`
87×	`associate-*r/_binary64_361`
76×	`log-div_binary64_506` `distribute-rgt-neg-out_binary64_379` `associate-*l/_binary64_362`
61×	`+-commutative_binary64_349`
58×	`distribute-rgt-neg-in_binary64_377`
50×	`pow-sqr_binary64_392`
49×	`distribute-rgt-in_binary64_369`
48×	`distribute-lft-in_binary64_368`
45×	`exp-prod_binary64_471`
44×	`unswap-sqr_binary64_387`
40×	`swap-sqr_binary64_386`
37×	`distribute-lft-neg-in_binary64_376`
35×	`cube-prod_binary64_447` `distribute-neg-in_binary64_380`
32×	`unsub-neg_binary64_413`
26×	`distribute-lft-neg-out_binary64_378`
21×	`div-sub_binary64_424` `associate--l+_binary64_356`
20×	`associate-/r/_binary64_365`
19×	`unpow1/3_binary64_486` `associate-+l+_binary64_352`
16×	`cube-div_binary64_448`
15×	`exp-diff_binary64_467`
14×	`associate--r+_binary64_355`
13×	`unpow3_binary64_485`
12×	`cube-mult_binary64_449` `remove-double-neg_binary64_407`
9×	`pow-plus_binary64_482` `distribute-lft-out--_binary64_371`
7×	`cube-unmult_binary64_456`
6×	`distribute-rgt-out--_binary64_373` `associate-+r+_binary64_351`
5×	`log-rec_binary64_507` `cancel-sign-sub_binary64_384`
4×	`log-pow_binary64_508` `unpow2_binary64_484` `exp-to-pow_binary64_481` `unpow1_binary64_477` `mul-1-neg_binary64_411` `difference-of-squares_binary64_388` `associate--r-_binary64_358` `associate-+r-_binary64_353`
3×	`cube-neg_binary64_446` `sqr-neg_binary64_433` `distribute-frac-neg_binary64_382` `distribute-rgt-out_binary64_372` `associate-+l-_binary64_354`
2×	`--rgt-identity_binary64_405` `distribute-lft-out_binary64_370`
1×	`1-exp_binary64_463` `rem-log-exp_binary64_460` `rem-3cbrt-lft_binary64_444` `-rgt-identity_binary64_409` `div0_binary64_400` `-inverses_binary64_399`
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` `unpow1/2_binary64_483` `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-exp-log_binary64_459` `rem-3cbrt-rft_binary64_445` `rem-cbrt-cube_binary64_443` `rem-cube-cbrt_binary64_442` `sqr-abs_binary64_434` `rem-sqrt-square_binary64_432` `rem-square-sqrt_binary64_431` `/-rgt-identity_binary64_410` `*-lft-identity_binary64_408` `sub0-neg_binary64_406` `+-rgt-identity_binary64_404` `+-lft-identity_binary64_403` `mul0-rgt_binary64_402` `mul0-lft_binary64_401` `+-inverses_binary64_398` `lft-mult-inverse_binary64_397` `rgt-mult-inverse_binary64_396` `remove-double-div_binary64_395` `difference-of-sqr--1_binary64_390` `difference-of-sqr-1_binary64_389` `distribute-neg-out_binary64_381` `distribute-rgt1-in_binary64_375` `distribute-lft1-in_binary64_374` `count-2_binary64_367` `associate-/l/_binary64_366` `associate--l-_binary64_357`

Counts

155 → 551

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	328	5066
1	960	4692
2	3488	4634

prune1.2s (3.5%)

Pruning

30 alts after pruning (28 fresh and 2 done)

	Pruned	Kept	Total
New	550	1	551
Fresh	0	27	27
Picked	0	1	1
Done	1	1	2
Total	551	30	581

Error

9.3b

Counts

581 → 30

Compiler

Compiled 44615 to 18562 computations (58.4% saved)

regimes3.3s (9.4%)

Accuracy

Total 19.6b remaining (70.1%)

Threshold costs 0b (0%)

Compiler

Compiled 51194 to 36586 computations (28.5% saved)

bsearch172.0ms (0.5%)

Steps

Iters	Range		Point
6	4.793679950587205e+134	2.8026176026947286e+135	2.772988692385023e+135
6	-3.7926419831087285e+225	-7.369337618295341e+224	-1.8141662603144044e+225

Compiler

Compiled 1 to 6 computations (-500% saved)

simplify74.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

232×	`neg-mul-1_binary64_415` `neg-sub0_binary64_414`
194×	`unsub-neg_binary64_413`
191×	`distribute-rgt-neg-in_binary64_377`
179×	`distribute-rgt-neg-out_binary64_379`
152×	`distribute-neg-out_binary64_381`
131×	`distribute-lft-neg-out_binary64_378`
126×	`distribute-lft-neg-in_binary64_376`
99×	`cancel-sign-sub-inv_binary64_385`
75×	`remove-double-neg_binary64_407`
74×	`sub-neg_binary64_412`
70×	`*-commutative_binary64_350`
63×	`distribute-neg-in_binary64_380`
56×	`+-commutative_binary64_349`
14×	`distribute-frac-neg_binary64_382`
9×	`distribute-neg-frac_binary64_383`
2×	`sqr-neg_binary64_433`
1×	`--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` `+-rgt-identity_binary64_404` `+-lft-identity_binary64_403` `cancel-sign-sub_binary64_384`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	63	162
1	112	162
2	165	162
3	235	162
4	324	160
5	412	160
6	598	160
7	941	160
8	887	160
9	933	160
10	972	160
11	1018	160
12	1056	160
13	1086	160
14	1101	160
15	1105	160
16	1105	160

Proof

(if real (<= f64 h0 -1814166260314404422947506509472034874826589041472300679717874962722517490483781621807946692596512301534408456805020279248906501522976269774510795590322468755848152374207171914118282888081140328818338822119409949039069086351360) (* f64 (sqrt f64 (* f64 (* f64 h1 h2) (- f64 (* f64 (/ f64 h1 h3) (/ f64 h4 h3)) (+ f64 (/ f64 2 h3) (* f64 (/ f64 h1 (* f64 h3 h3)) h2))))) (neg f64 (* f64 (sqrt f64 2) h0))) (if real (<= f64 h0 2772988692385023087469996441391698009735755660052512759581547813830841443968204856060581660343635181422519447361689608799692542493851648) (sqrt f64 (+ f64 (* f64 (* f64 h5 (* f64 2 h1)) h2) (* f64 h2 (* f64 (* f64 (* f64 h1 2) (=> (/ f64 (neg f64 h0) h3))) (- f64 (* f64 2 h0) (* f64 (- f64 h4 h2) (/ f64 (* f64 h1 h0) h3))))))) (* f64 h0 (sqrt f64 (- f64 (* f64 2 (- f64 (/ f64 (/ f64 (* f64 h1 h1) (/ f64 (/ f64 h3 h2) h4)) h3) (/ f64 (* f64 h1 h1) (* f64 (/ f64 h3 h2) (/ f64 h3 h2))))) (* f64 4 (* f64 (/ f64 h1 h3) h2)))))))
distribute-frac-neg_binary64_382 =>
(if real (<= f64 h0 -1814166260314404422947506509472034874826589041472300679717874962722517490483781621807946692596512301534408456805020279248906501522976269774510795590322468755848152374207171914118282888081140328818338822119409949039069086351360) (* f64 (sqrt f64 (* f64 (* f64 h1 h2) (- f64 (* f64 (/ f64 h1 h3) (/ f64 h4 h3)) (+ f64 (/ f64 2 h3) (* f64 (/ f64 h1 (* f64 h3 h3)) h2))))) (=> (neg f64 (* f64 (sqrt f64 2) h0)))) (if real (<= f64 h0 2772988692385023087469996441391698009735755660052512759581547813830841443968204856060581660343635181422519447361689608799692542493851648) (sqrt f64 (+ f64 (* f64 (* f64 h5 (* f64 2 h1)) h2) (* f64 h2 (* f64 (* f64 (* f64 h1 2) (neg f64 (/ f64 h0 h3))) (- f64 (* f64 2 h0) (* f64 (- f64 h4 h2) (/ f64 (* f64 h1 h0) h3))))))) (* f64 h0 (sqrt f64 (- f64 (* f64 2 (- f64 (/ f64 (/ f64 (* f64 h1 h1) (/ f64 (/ f64 h3 h2) h4)) h3) (/ f64 (* f64 h1 h1) (* f64 (/ f64 h3 h2) (/ f64 h3 h2))))) (* f64 4 (* f64 (/ f64 h1 h3) h2)))))))
distribute-rgt-neg-in_binary64_377 =>
(if real (<= f64 h0 -1814166260314404422947506509472034874826589041472300679717874962722517490483781621807946692596512301534408456805020279248906501522976269774510795590322468755848152374207171914118282888081140328818338822119409949039069086351360) (* f64 (sqrt f64 (* f64 (* f64 h1 h2) (- f64 (* f64 (/ f64 h1 h3) (/ f64 h4 h3)) (+ f64 (/ f64 2 h3) (* f64 (/ f64 h1 (* f64 h3 h3)) h2))))) (* f64 (sqrt f64 2) (neg f64 h0))) (if real (<= f64 h0 2772988692385023087469996441391698009735755660052512759581547813830841443968204856060581660343635181422519447361689608799692542493851648) (sqrt f64 (+ f64 (* f64 (* f64 h5 (* f64 2 h1)) h2) (* f64 h2 (* f64 (* f64 (=> (* f64 h1 2)) (neg f64 (/ f64 h0 h3))) (- f64 (* f64 2 h0) (* f64 (- f64 h4 h2) (/ f64 (* f64 h1 h0) h3))))))) (* f64 h0 (sqrt f64 (- f64 (* f64 2 (- f64 (/ f64 (/ f64 (* f64 h1 h1) (/ f64 (/ f64 h3 h2) h4)) h3) (/ f64 (* f64 h1 h1) (* f64 (/ f64 h3 h2) (/ f64 h3 h2))))) (* f64 4 (* f64 (/ f64 h1 h3) h2)))))))
*-commutative_binary64_350 =>
(if real (<= f64 h0 -1814166260314404422947506509472034874826589041472300679717874962722517490483781621807946692596512301534408456805020279248906501522976269774510795590322468755848152374207171914118282888081140328818338822119409949039069086351360) (* f64 (sqrt f64 (* f64 (* f64 h1 h2) (- f64 (* f64 (/ f64 h1 h3) (/ f64 h4 h3)) (+ f64 (/ f64 2 h3) (=> (* f64 (/ f64 h1 (* f64 h3 h3)) h2)))))) (* f64 (sqrt f64 2) (neg f64 h0))) (if real (<= f64 h0 2772988692385023087469996441391698009735755660052512759581547813830841443968204856060581660343635181422519447361689608799692542493851648) (sqrt f64 (+ f64 (* f64 (* f64 h5 (* f64 2 h1)) h2) (* f64 h2 (* f64 (* f64 (* f64 2 h1) (neg f64 (/ f64 h0 h3))) (- f64 (* f64 2 h0) (* f64 (- f64 h4 h2) (/ f64 (* f64 h1 h0) h3))))))) (* f64 h0 (sqrt f64 (- f64 (* f64 2 (- f64 (/ f64 (/ f64 (* f64 h1 h1) (/ f64 (/ f64 h3 h2) h4)) h3) (/ f64 (* f64 h1 h1) (* f64 (/ f64 h3 h2) (/ f64 h3 h2))))) (* f64 4 (* f64 (/ f64 h1 h3) h2)))))))
*-commutative_binary64_350 =>
(if real (<= f64 h0 -1814166260314404422947506509472034874826589041472300679717874962722517490483781621807946692596512301534408456805020279248906501522976269774510795590322468755848152374207171914118282888081140328818338822119409949039069086351360) (* f64 (sqrt f64 (* f64 (* f64 h1 h2) (- f64 (* f64 (/ f64 h1 h3) (/ f64 h4 h3)) (+ f64 (/ f64 2 h3) (* f64 h2 (/ f64 h1 (* f64 h3 h3))))))) (* f64 (sqrt f64 2) (neg f64 h0))) (if real (<= f64 h0 2772988692385023087469996441391698009735755660052512759581547813830841443968204856060581660343635181422519447361689608799692542493851648) (sqrt f64 (+ f64 (=> (* f64 (* f64 h5 (* f64 2 h1)) h2)) (* f64 h2 (* f64 (* f64 (* f64 2 h1) (neg f64 (/ f64 h0 h3))) (- f64 (* f64 2 h0) (* f64 (- f64 h4 h2) (/ f64 (* f64 h1 h0) h3))))))) (* f64 h0 (sqrt f64 (- f64 (* f64 2 (- f64 (/ f64 (/ f64 (* f64 h1 h1) (/ f64 (/ f64 h3 h2) h4)) h3) (/ f64 (* f64 h1 h1) (* f64 (/ f64 h3 h2) (/ f64 h3 h2))))) (* f64 4 (* f64 (/ f64 h1 h3) h2)))))))
*-commutative_binary64_350 =>
(if real (<= f64 h0 -1814166260314404422947506509472034874826589041472300679717874962722517490483781621807946692596512301534408456805020279248906501522976269774510795590322468755848152374207171914118282888081140328818338822119409949039069086351360) (* f64 (sqrt f64 (* f64 (* f64 h1 h2) (- f64 (* f64 (/ f64 h1 h3) (/ f64 h4 h3)) (+ f64 (/ f64 2 h3) (* f64 h2 (/ f64 h1 (* f64 h3 h3))))))) (* f64 (sqrt f64 2) (neg f64 h0))) (if real (<= f64 h0 2772988692385023087469996441391698009735755660052512759581547813830841443968204856060581660343635181422519447361689608799692542493851648) (sqrt f64 (+ f64 (* f64 h2 (* f64 h5 (* f64 2 h1))) (* f64 h2 (* f64 (* f64 (* f64 2 h1) (neg f64 (/ f64 h0 h3))) (- f64 (* f64 2 h0) (* f64 (- f64 h4 h2) (/ f64 (* f64 h1 h0) h3))))))) (* f64 h0 (sqrt f64 (- f64 (* f64 2 (- f64 (/ f64 (/ f64 (* f64 h1 h1) (/ f64 (/ f64 h3 h2) h4)) h3) (/ f64 (* f64 h1 h1) (* f64 (/ f64 h3 h2) (/ f64 h3 h2))))) (* f64 4 (* f64 (/ f64 h1 h3) h2)))))))
<= *-commutative_binary64_350
(if real (<= f64 h0 -1814166260314404422947506509472034874826589041472300679717874962722517490483781621807946692596512301534408456805020279248906501522976269774510795590322468755848152374207171914118282888081140328818338822119409949039069086351360) (* f64 (sqrt f64 (* f64 (* f64 h1 h2) (- f64 (* f64 (/ f64 h1 h3) (/ f64 h4 h3)) (+ f64 (/ f64 2 h3) (* f64 h2 (/ f64 h1 (* f64 h3 h3))))))) (* f64 (sqrt f64 2) (neg f64 h0))) (if real (<= f64 h0 2772988692385023087469996441391698009735755660052512759581547813830841443968204856060581660343635181422519447361689608799692542493851648) (sqrt f64 (+ f64 (* f64 h2 (* f64 h5 (<= (* f64 h1 2)))) (* f64 h2 (* f64 (* f64 (* f64 2 h1) (neg f64 (/ f64 h0 h3))) (- f64 (* f64 2 h0) (* f64 (- f64 h4 h2) (/ f64 (* f64 h1 h0) h3))))))) (* f64 h0 (sqrt f64 (- f64 (* f64 2 (- f64 (/ f64 (/ f64 (* f64 h1 h1) (/ f64 (/ f64 h3 h2) h4)) h3) (/ f64 (* f64 h1 h1) (* f64 (/ f64 h3 h2) (/ f64 h3 h2))))) (* f64 4 (=> (* f64 (/ f64 h1 h3) h2))))))))
*-commutative_binary64_350 =>
(if real (<= f64 h0 -1814166260314404422947506509472034874826589041472300679717874962722517490483781621807946692596512301534408456805020279248906501522976269774510795590322468755848152374207171914118282888081140328818338822119409949039069086351360) (* f64 (sqrt f64 (* f64 (* f64 h1 h2) (- f64 (* f64 (/ f64 h1 h3) (/ f64 h4 h3)) (+ f64 (/ f64 2 h3) (* f64 h2 (/ f64 h1 (* f64 h3 h3))))))) (* f64 (sqrt f64 2) (neg f64 h0))) (if real (<= f64 h0 2772988692385023087469996441391698009735755660052512759581547813830841443968204856060581660343635181422519447361689608799692542493851648) (sqrt f64 (+ f64 (* f64 h2 (* f64 h5 (* f64 h1 2))) (* f64 h2 (* f64 (=> (* f64 (* f64 2 h1) (neg f64 (/ f64 h0 h3)))) (- f64 (* f64 2 h0) (* f64 (- f64 h4 h2) (/ f64 (* f64 h1 h0) h3))))))) (* f64 h0 (sqrt f64 (- f64 (* f64 2 (- f64 (/ f64 (/ f64 (* f64 h1 h1) (/ f64 (/ f64 h3 h2) h4)) h3) (/ f64 (* f64 h1 h1) (* f64 (/ f64 h3 h2) (/ f64 h3 h2))))) (* f64 4 (* f64 h2 (/ f64 h1 h3))))))))
distribute-rgt-neg-out_binary64_379 =>
(if real (<= f64 h0 -1814166260314404422947506509472034874826589041472300679717874962722517490483781621807946692596512301534408456805020279248906501522976269774510795590322468755848152374207171914118282888081140328818338822119409949039069086351360) (* f64 (sqrt f64 (* f64 (* f64 h1 h2) (- f64 (* f64 (/ f64 h1 h3) (/ f64 h4 h3)) (+ f64 (/ f64 2 h3) (* f64 h2 (/ f64 h1 (* f64 h3 h3))))))) (* f64 (sqrt f64 2) (neg f64 h0))) (if real (<= f64 h0 2772988692385023087469996441391698009735755660052512759581547813830841443968204856060581660343635181422519447361689608799692542493851648) (sqrt f64 (+ f64 (* f64 h2 (* f64 h5 (* f64 h1 2))) (* f64 h2 (=> (* f64 (neg f64 (* f64 (* f64 2 h1) (/ f64 h0 h3))) (- f64 (* f64 2 h0) (* f64 (- f64 h4 h2) (/ f64 (* f64 h1 h0) h3)))))))) (* f64 h0 (sqrt f64 (- f64 (* f64 2 (- f64 (/ f64 (/ f64 (* f64 h1 h1) (/ f64 (/ f64 h3 h2) h4)) h3) (/ f64 (* f64 h1 h1) (* f64 (/ f64 h3 h2) (/ f64 h3 h2))))) (* f64 4 (* f64 h2 (/ f64 h1 h3))))))))
distribute-lft-neg-out_binary64_378 =>
(if real (<= f64 h0 -1814166260314404422947506509472034874826589041472300679717874962722517490483781621807946692596512301534408456805020279248906501522976269774510795590322468755848152374207171914118282888081140328818338822119409949039069086351360) (* f64 (sqrt f64 (* f64 (* f64 h1 h2) (- f64 (* f64 (/ f64 h1 h3) (/ f64 h4 h3)) (+ f64 (/ f64 2 h3) (* f64 h2 (/ f64 h1 (* f64 h3 h3))))))) (* f64 (sqrt f64 2) (neg f64 h0))) (if real (<= f64 h0 2772988692385023087469996441391698009735755660052512759581547813830841443968204856060581660343635181422519447361689608799692542493851648) (sqrt f64 (+ f64 (* f64 h2 (* f64 h5 (* f64 h1 2))) (* f64 h2 (=> (neg f64 (* f64 (* f64 (* f64 2 h1) (/ f64 h0 h3)) (- f64 (* f64 2 h0) (* f64 (- f64 h4 h2) (/ f64 (* f64 h1 h0) h3))))))))) (* f64 h0 (sqrt f64 (- f64 (* f64 2 (- f64 (/ f64 (/ f64 (* f64 h1 h1) (/ f64 (/ f64 h3 h2) h4)) h3) (/ f64 (* f64 h1 h1) (* f64 (/ f64 h3 h2) (/ f64 h3 h2))))) (* f64 4 (* f64 h2 (/ f64 h1 h3))))))))
distribute-rgt-neg-in_binary64_377 =>
(if real (<= f64 h0 -1814166260314404422947506509472034874826589041472300679717874962722517490483781621807946692596512301534408456805020279248906501522976269774510795590322468755848152374207171914118282888081140328818338822119409949039069086351360) (* f64 (sqrt f64 (* f64 (* f64 h1 h2) (- f64 (* f64 (/ f64 h1 h3) (/ f64 h4 h3)) (+ f64 (/ f64 2 h3) (* f64 h2 (/ f64 h1 (* f64 h3 h3))))))) (* f64 (sqrt f64 2) (neg f64 h0))) (if real (<= f64 h0 2772988692385023087469996441391698009735755660052512759581547813830841443968204856060581660343635181422519447361689608799692542493851648) (sqrt f64 (+ f64 (* f64 h2 (* f64 h5 (* f64 h1 2))) (* f64 h2 (* f64 (* f64 (* f64 2 h1) (/ f64 h0 h3)) (neg f64 (=> (- f64 (* f64 2 h0) (* f64 (- f64 h4 h2) (/ f64 (* f64 h1 h0) h3))))))))) (* f64 h0 (sqrt f64 (- f64 (* f64 2 (- f64 (/ f64 (/ f64 (* f64 h1 h1) (/ f64 (/ f64 h3 h2) h4)) h3) (/ f64 (* f64 h1 h1) (* f64 (/ f64 h3 h2) (/ f64 h3 h2))))) (* f64 4 (* f64 h2 (/ f64 h1 h3))))))))
sub-neg_binary64_412 =>
(if real (<= f64 h0 -1814166260314404422947506509472034874826589041472300679717874962722517490483781621807946692596512301534408456805020279248906501522976269774510795590322468755848152374207171914118282888081140328818338822119409949039069086351360) (* f64 (sqrt f64 (* f64 (* f64 h1 h2) (- f64 (* f64 (/ f64 h1 h3) (/ f64 h4 h3)) (+ f64 (/ f64 2 h3) (* f64 h2 (/ f64 h1 (* f64 h3 h3))))))) (* f64 (sqrt f64 2) (neg f64 h0))) (if real (<= f64 h0 2772988692385023087469996441391698009735755660052512759581547813830841443968204856060581660343635181422519447361689608799692542493851648) (sqrt f64 (+ f64 (* f64 h2 (* f64 h5 (* f64 h1 2))) (* f64 h2 (* f64 (* f64 (* f64 2 h1) (/ f64 h0 h3)) (neg f64 (+ f64 (* f64 2 h0) (neg f64 (* f64 (- f64 h4 h2) (/ f64 (* f64 h1 h0) h3))))))))) (* f64 h0 (sqrt f64 (- f64 (* f64 2 (- f64 (/ f64 (/ f64 (* f64 h1 h1) (/ f64 (/ f64 h3 h2) h4)) h3) (/ f64 (* f64 h1 h1) (* f64 (/ f64 h3 h2) (/ f64 h3 h2))))) (* f64 4 (* f64 h2 (/ f64 h1 h3))))))))
<= *-commutative_binary64_350
(if real (<= f64 h0 -1814166260314404422947506509472034874826589041472300679717874962722517490483781621807946692596512301534408456805020279248906501522976269774510795590322468755848152374207171914118282888081140328818338822119409949039069086351360) (* f64 (sqrt f64 (* f64 (* f64 h1 h2) (- f64 (* f64 (/ f64 h1 h3) (/ f64 h4 h3)) (+ f64 (/ f64 2 h3) (* f64 h2 (/ f64 h1 (* f64 h3 h3))))))) (* f64 (sqrt f64 2) (neg f64 h0))) (if real (<= f64 h0 2772988692385023087469996441391698009735755660052512759581547813830841443968204856060581660343635181422519447361689608799692542493851648) (sqrt f64 (+ f64 (* f64 h2 (* f64 h5 (* f64 h1 2))) (* f64 h2 (* f64 (* f64 (<= (* f64 h1 2)) (/ f64 h0 h3)) (neg f64 (=> (+ f64 (* f64 2 h0) (neg f64 (* f64 (- f64 h4 h2) (/ f64 (* f64 h1 h0) h3)))))))))) (* f64 h0 (sqrt f64 (- f64 (* f64 2 (- f64 (/ f64 (/ f64 (* f64 h1 h1) (/ f64 (/ f64 h3 h2) h4)) h3) (/ f64 (* f64 h1 h1) (* f64 (/ f64 h3 h2) (/ f64 h3 h2))))) (* f64 4 (* f64 h2 (/ f64 h1 h3))))))))
+-commutative_binary64_349 =>
(if real (<= f64 h0 -1814166260314404422947506509472034874826589041472300679717874962722517490483781621807946692596512301534408456805020279248906501522976269774510795590322468755848152374207171914118282888081140328818338822119409949039069086351360) (* f64 (sqrt f64 (* f64 (* f64 h1 h2) (- f64 (* f64 (/ f64 h1 h3) (/ f64 h4 h3)) (+ f64 (/ f64 2 h3) (* f64 h2 (/ f64 h1 (* f64 h3 h3))))))) (* f64 (sqrt f64 2) (neg f64 h0))) (if real (<= f64 h0 2772988692385023087469996441391698009735755660052512759581547813830841443968204856060581660343635181422519447361689608799692542493851648) (sqrt f64 (+ f64 (* f64 h2 (* f64 h5 (* f64 h1 2))) (* f64 h2 (* f64 (* f64 (* f64 h1 2) (/ f64 h0 h3)) (=> (neg f64 (+ f64 (neg f64 (* f64 (- f64 h4 h2) (/ f64 (* f64 h1 h0) h3))) (* f64 2 h0)))))))) (* f64 h0 (sqrt f64 (- f64 (* f64 2 (- f64 (/ f64 (/ f64 (* f64 h1 h1) (/ f64 (/ f64 h3 h2) h4)) h3) (/ f64 (* f64 h1 h1) (* f64 (/ f64 h3 h2) (/ f64 h3 h2))))) (* f64 4 (* f64 h2 (/ f64 h1 h3))))))))
distribute-neg-in_binary64_380 =>
(if real (<= f64 h0 -1814166260314404422947506509472034874826589041472300679717874962722517490483781621807946692596512301534408456805020279248906501522976269774510795590322468755848152374207171914118282888081140328818338822119409949039069086351360) (* f64 (sqrt f64 (* f64 (* f64 h1 h2) (- f64 (* f64 (/ f64 h1 h3) (/ f64 h4 h3)) (+ f64 (/ f64 2 h3) (* f64 h2 (/ f64 h1 (* f64 h3 h3))))))) (* f64 (sqrt f64 2) (neg f64 h0))) (if real (<= f64 h0 2772988692385023087469996441391698009735755660052512759581547813830841443968204856060581660343635181422519447361689608799692542493851648) (sqrt f64 (+ f64 (* f64 h2 (* f64 h5 (* f64 h1 2))) (* f64 h2 (* f64 (* f64 (* f64 h1 2) (/ f64 h0 h3)) (=> (+ f64 (neg f64 (neg f64 (* f64 (- f64 h4 h2) (/ f64 (* f64 h1 h0) h3)))) (neg f64 (* f64 2 h0)))))))) (* f64 h0 (sqrt f64 (- f64 (* f64 2 (- f64 (/ f64 (/ f64 (* f64 h1 h1) (/ f64 (/ f64 h3 h2) h4)) h3) (/ f64 (* f64 h1 h1) (* f64 (/ f64 h3 h2) (/ f64 h3 h2))))) (* f64 4 (* f64 h2 (/ f64 h1 h3))))))))
unsub-neg_binary64_413 =>
(if real (<= f64 h0 -1814166260314404422947506509472034874826589041472300679717874962722517490483781621807946692596512301534408456805020279248906501522976269774510795590322468755848152374207171914118282888081140328818338822119409949039069086351360) (* f64 (sqrt f64 (* f64 (* f64 h1 h2) (- f64 (* f64 (/ f64 h1 h3) (/ f64 h4 h3)) (+ f64 (/ f64 2 h3) (* f64 h2 (/ f64 h1 (* f64 h3 h3))))))) (* f64 (sqrt f64 2) (neg f64 h0))) (if real (<= f64 h0 2772988692385023087469996441391698009735755660052512759581547813830841443968204856060581660343635181422519447361689608799692542493851648) (sqrt f64 (+ f64 (* f64 h2 (* f64 h5 (* f64 h1 2))) (* f64 h2 (* f64 (* f64 (* f64 h1 2) (/ f64 h0 h3)) (- f64 (neg f64 (neg f64 (* f64 (- f64 h4 h2) (/ f64 (* f64 h1 h0) h3)))) (=> (* f64 2 h0))))))) (* f64 h0 (sqrt f64 (- f64 (* f64 2 (- f64 (/ f64 (/ f64 (* f64 h1 h1) (/ f64 (/ f64 h3 h2) h4)) h3) (/ f64 (* f64 h1 h1) (* f64 (/ f64 h3 h2) (/ f64 h3 h2))))) (* f64 4 (* f64 h2 (/ f64 h1 h3))))))))
*-commutative_binary64_350 =>
(if real (<= f64 h0 -1814166260314404422947506509472034874826589041472300679717874962722517490483781621807946692596512301534408456805020279248906501522976269774510795590322468755848152374207171914118282888081140328818338822119409949039069086351360) (* f64 (sqrt f64 (* f64 (* f64 h1 h2) (- f64 (* f64 (/ f64 h1 h3) (/ f64 h4 h3)) (+ f64 (/ f64 2 h3) (* f64 h2 (/ f64 h1 (* f64 h3 h3))))))) (* f64 (sqrt f64 2) (neg f64 h0))) (if real (<= f64 h0 2772988692385023087469996441391698009735755660052512759581547813830841443968204856060581660343635181422519447361689608799692542493851648) (sqrt f64 (+ f64 (* f64 h2 (* f64 h5 (* f64 h1 2))) (* f64 h2 (* f64 (* f64 (* f64 h1 2) (/ f64 h0 h3)) (- f64 (=> (neg f64 (neg f64 (* f64 (- f64 h4 h2) (/ f64 (* f64 h1 h0) h3))))) (* f64 h0 2)))))) (* f64 h0 (sqrt f64 (- f64 (* f64 2 (- f64 (/ f64 (/ f64 (* f64 h1 h1) (/ f64 (/ f64 h3 h2) h4)) h3) (/ f64 (* f64 h1 h1) (* f64 (/ f64 h3 h2) (/ f64 h3 h2))))) (* f64 4 (* f64 h2 (/ f64 h1 h3))))))))
remove-double-neg_binary64_407 =>
(if real (<= f64 h0 -1814166260314404422947506509472034874826589041472300679717874962722517490483781621807946692596512301534408456805020279248906501522976269774510795590322468755848152374207171914118282888081140328818338822119409949039069086351360) (* f64 (sqrt f64 (* f64 (* f64 h1 h2) (- f64 (* f64 (/ f64 h1 h3) (/ f64 h4 h3)) (+ f64 (/ f64 2 h3) (* f64 h2 (/ f64 h1 (* f64 h3 h3))))))) (* f64 (sqrt f64 2) (neg f64 h0))) (if real (<= f64 h0 2772988692385023087469996441391698009735755660052512759581547813830841443968204856060581660343635181422519447361689608799692542493851648) (sqrt f64 (+ f64 (* f64 h2 (* f64 h5 (* f64 h1 2))) (* f64 h2 (* f64 (* f64 (* f64 h1 2) (/ f64 h0 h3)) (- f64 (* f64 (- f64 h4 h2) (/ f64 (=> (* f64 h1 h0)) h3)) (* f64 h0 2)))))) (* f64 h0 (sqrt f64 (- f64 (* f64 2 (- f64 (/ f64 (/ f64 (* f64 h1 h1) (/ f64 (/ f64 h3 h2) h4)) h3) (/ f64 (* f64 h1 h1) (* f64 (/ f64 h3 h2) (/ f64 h3 h2))))) (* f64 4 (* f64 h2 (/ f64 h1 h3))))))))
*-commutative_binary64_350 =>
(if real (<= f64 h0 -1814166260314404422947506509472034874826589041472300679717874962722517490483781621807946692596512301534408456805020279248906501522976269774510795590322468755848152374207171914118282888081140328818338822119409949039069086351360) (* f64 (sqrt f64 (* f64 (* f64 h1 h2) (- f64 (* f64 (/ f64 h1 h3) (/ f64 h4 h3)) (+ f64 (/ f64 2 h3) (* f64 h2 (/ f64 h1 (* f64 h3 h3))))))) (* f64 (sqrt f64 2) (neg f64 h0))) (if real (<= f64 h0 2772988692385023087469996441391698009735755660052512759581547813830841443968204856060581660343635181422519447361689608799692542493851648) (sqrt f64 (+ f64 (* f64 h2 (* f64 h5 (* f64 h1 2))) (* f64 h2 (* f64 (* f64 (* f64 h1 2) (/ f64 h0 h3)) (- f64 (* f64 (- f64 h4 h2) (/ f64 (* f64 h0 h1) h3)) (* f64 h0 2)))))) (* f64 h0 (sqrt f64 (- f64 (* f64 2 (- f64 (/ f64 (/ f64 (* f64 h1 h1) (/ f64 (/ f64 h3 h2) h4)) h3) (/ f64 (* f64 h1 h1) (* f64 (/ f64 h3 h2) (/ f64 h3 h2))))) (* f64 4 (* f64 h2 (/ f64 h1 h3))))))))

end0.0ms (0%)

sample10.1s (29.2%)

Algorithm

1×

intervals

Results

2.2s	12760×	body	128	nan
1.5s	8000×	body	128	valid
368.0ms	1197×	body	128	invalid

Compiler

Compiled 6519 to 4648 computations (28.7% saved)

Details

analyze3.9s (11.2%)

sample456.0ms (1.3%)

simplify467.0ms (1.3%)

prune11.0ms (0%)

localize17.0ms (0%)

rewrite702.0ms (2%)

series3.1s (8.9%)

simplify806.0ms (2.3%)

prune425.0ms (1.2%)

localize25.0ms (0.1%)

rewrite159.0ms (0.5%)

series1.4s (4%)

simplify644.0ms (1.9%)

prune515.0ms (1.5%)

localize20.0ms (0.1%)

rewrite116.0ms (0.3%)

series559.0ms (1.6%)

simplify486.0ms (1.4%)

prune562.0ms (1.6%)

localize28.0ms (0.1%)

rewrite170.0ms (0.5%)

series4.7s (13.5%)

simplify656.0ms (1.9%)

prune1.2s (3.5%)

regimes3.3s (9.4%)

bsearch172.0ms (0.5%)

simplify74.0ms (0.2%)

end0.0ms (0%)

sample10.1s (29.2%)

Profiling