Details

analyze308.0ms (2.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample33.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	198×	body	128	valid
7.0ms	15×	body	4096	valid
3.0ms	16×	body	2048	valid
2.0ms	12×	body	1024	valid
1.0ms	11×	body	512	valid
0.0ms	4×	body	256	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify152.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64_3419`
2×	`distribute-rgt-in_binary64_3438` `distribute-lft-in_binary64_3437` `+-commutative_binary64_3418`
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_3751` `erf-erfc_binary64_3750` `erf-odd_binary64_3749` `if-if-and-not_binary64_3748` `if-if-and_binary64_3747` `if-if-or-not_binary64_3746` `if-if-or_binary64_3745` `if-not_binary64_3744` `if-same_binary64_3743` `if-false_binary64_3742` `if-true_binary64_3741` `not-gte_binary64_3740` `not-lte_binary64_3739` `not-gt_binary64_3738` `not-lt_binary64_3737` `gte-same_binary64_3736` `lte-same_binary64_3735` `gt-same_binary64_3734` `lt-same_binary64_3733` `sinh---cosh_binary64_3680` `sinh-+-cosh_binary64_3679` `sinh-cosh_binary64_3678` `tanh-def-c_binary64_3677` `tanh-def-b_binary64_3676` `tanh-def-a_binary64_3675` `cosh-def_binary64_3674` `sinh-def_binary64_3673` `tan-neg_binary64_3620` `cos-neg_binary64_3619` `sin-neg_binary64_3618` `tan-0_binary64_3617` `cos-0_binary64_3616` `sin-0_binary64_3615` `hang-m-tan_binary64_3614` `hang-p-tan_binary64_3613` `hang-m0-tan_binary64_3612` `hang-p0-tan_binary64_3611` `hang-0m-tan_binary64_3610` `hang-0p-tan_binary64_3609` `tan-+PI/2_binary64_3608` `tan-+PI_binary64_3607` `tan-PI_binary64_3606` `tan-PI/3_binary64_3605` `tan-PI/4_binary64_3604` `tan-PI/6_binary64_3603` `cos-+PI/2_binary64_3602` `cos-+PI_binary64_3601` `cos-PI_binary64_3600` `cos-PI/2_binary64_3599` `cos-PI/3_binary64_3598` `cos-PI/4_binary64_3597` `cos-PI/6_binary64_3596` `sin-+PI/2_binary64_3595` `sin-+PI_binary64_3594` `sin-PI_binary64_3593` `sin-PI/2_binary64_3592` `sin-PI/3_binary64_3591` `sin-PI/4_binary64_3590` `sin-PI/6_binary64_3589` `sub-1-sin_binary64_3588` `sub-1-cos_binary64_3587` `-1-add-sin_binary64_3586` `-1-add-cos_binary64_3585` `1-sub-sin_binary64_3584` `1-sub-cos_binary64_3583` `cos-sin-sum_binary64_3582` `log-E_binary64_3578` `log-pow_binary64_3577` `log-rec_binary64_3576` `log-div_binary64_3575` `log-prod_binary64_3574` `pow-base-0_binary64_3572` `unpow1/3_binary64_3555` `unpow3_binary64_3554` `unpow2_binary64_3553` `unpow1/2_binary64_3552` `pow-plus_binary64_3551` `exp-to-pow_binary64_3550` `pow-base-1_binary64_3548` `unpow0_binary64_3547` `unpow1_binary64_3546` `unpow-1_binary64_3545` `exp-lft-cube_binary64_3544` `exp-lft-sqr_binary64_3543` `exp-cbrt_binary64_3542` `exp-sqrt_binary64_3541` `exp-prod_binary64_3540` `div-exp_binary64_3539` `rec-exp_binary64_3538` `prod-exp_binary64_3537` `exp-diff_binary64_3536` `exp-neg_binary64_3535` `exp-sum_binary64_3534` `e-exp-1_binary64_3533` `1-exp_binary64_3532` `exp-1-e_binary64_3531` `exp-0_binary64_3530` `rem-log-exp_binary64_3529` `rem-exp-log_binary64_3528` `cube-unmult_binary64_3525` `cube-mult_binary64_3518` `cube-div_binary64_3517` `cube-prod_binary64_3516` `cube-neg_binary64_3515` `rem-3cbrt-rft_binary64_3514` `rem-3cbrt-lft_binary64_3513` `rem-cbrt-cube_binary64_3512` `rem-cube-cbrt_binary64_3511` `sqr-abs_binary64_3503` `sqr-neg_binary64_3502` `rem-sqrt-square_binary64_3501` `rem-square-sqrt_binary64_3500` `times-frac_binary64_3494` `div-sub_binary64_3493` `neg-mul-1_binary64_3484` `neg-sub0_binary64_3483` `unsub-neg_binary64_3482` `sub-neg_binary64_3481` `mul-1-neg_binary64_3480` `/-rgt-identity_binary64_3479` `-rgt-identity_binary64_3478` `-lft-identity_binary64_3477` `remove-double-neg_binary64_3476` `sub0-neg_binary64_3475` `--rgt-identity_binary64_3474` `+-rgt-identity_binary64_3473` `+-lft-identity_binary64_3472` `mul0-rgt_binary64_3471` `mul0-lft_binary64_3470` `div0_binary64_3469` `-inverses_binary64_3468` `+-inverses_binary64_3467` `lft-mult-inverse_binary64_3466` `rgt-mult-inverse_binary64_3465` `remove-double-div_binary64_3464` `pow-sqr_binary64_3461` `sqr-pow_binary64_3460` `difference-of-sqr--1_binary64_3459` `difference-of-sqr-1_binary64_3458` `difference-of-squares_binary64_3457` `unswap-sqr_binary64_3456` `swap-sqr_binary64_3455` `cancel-sign-sub-inv_binary64_3454` `cancel-sign-sub_binary64_3453` `distribute-neg-frac_binary64_3452` `distribute-frac-neg_binary64_3451` `distribute-neg-out_binary64_3450` `distribute-neg-in_binary64_3449` `distribute-rgt-neg-out_binary64_3448` `distribute-lft-neg-out_binary64_3447` `distribute-rgt-neg-in_binary64_3446` `distribute-lft-neg-in_binary64_3445` `distribute-rgt1-in_binary64_3444` `distribute-lft1-in_binary64_3443` `distribute-rgt-out--_binary64_3442` `distribute-rgt-out_binary64_3441` `distribute-lft-out--_binary64_3440` `distribute-lft-out_binary64_3439` `count-2_binary64_3436` `associate-/l/_binary64_3435` `associate-/r/_binary64_3434` `associate-/l_binary64_3433` `associate-/r_binary64_3432` `associate-l/_binary64_3431` `associate-r/_binary64_3430` `associate-l_binary64_3429` `associate-r*_binary64_3428` `associate--r-_binary64_3427` `associate--l-_binary64_3426` `associate--l+_binary64_3425` `associate--r+_binary64_3424` `associate-+l-_binary64_3423` `associate-+r-_binary64_3422` `associate-+l+_binary64_3421` `associate-+r+_binary64_3420`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	23	23
2	25	23

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

36.9b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.8b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
27.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite79.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

36.7b

Rules

7×	`pow1_binary64_3549`
6×	`*-un-lft-identity_binary64_3488`
5×	`add-log-exp_binary64_3527` `add-sqr-sqrt_binary64_3510`
4×	`add-cube-cbrt_binary64_3523` `sqrt-div_binary64_3505` `sqrt-prod_binary64_3504`
3×	`add-exp-log_binary64_3526` `add-cbrt-cube_binary64_3524` `sqrt-pow1_binary64_3506` `flip3-+_binary64_3491` `flip-+_binary64_3462`
2×	`pow1/2_binary64_3568` `associate-*r/_binary64_3430`
1×	`rem-sqrt-square_binary64_3501` `sum-log_binary64_3579` `distribute-lft-out_binary64_3439` `+-commutative_binary64_3418` `pow-prod-down_binary64_3559`

Counts

3 → 40

Calls

3 calls:

11.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
9.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 1030 to 354 computations (65.6% saved)

series537.0ms (4.8%)

Error

7.2b

Counts

3 → 49

Calls

3 calls:

171.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
163.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
144.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))

Compiler

Compiled 2092 to 1786 computations (14.6% saved)

simplify195.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

613×	`cancel-sign-sub-inv_binary64_3454`
363×	`unswap-sqr_binary64_3456`
306×	`associate-r_binary64_3428`
278×	`associate-l_binary64_3429`
213×	`sub-neg_binary64_3481`
136×	`*-commutative_binary64_3419`
111×	`sqr-pow_binary64_3460`
105×	`distribute-rgt-in_binary64_3438`
98×	`neg-sub0_binary64_3483`
96×	`associate-/l*_binary64_3433`
93×	`associate-/r*_binary64_3432`
88×	`neg-mul-1_binary64_3484`
80×	`distribute-lft-in_binary64_3437`
79×	`associate-+l+_binary64_3421` `+-commutative_binary64_3418`
76×	`distribute-rgt-neg-in_binary64_3446`
75×	`pow-sqr_binary64_3461`
74×	`times-frac_binary64_3494`
58×	`distribute-lft-neg-in_binary64_3445`
57×	`associate-+l-_binary64_3423` `associate-+r+_binary64_3420`
53×	`difference-of-squares_binary64_3457`
51×	`associate-*l/_binary64_3431`
49×	`associate-*r/_binary64_3430`
44×	`pow-plus_binary64_3551`
43×	`associate-+r-_binary64_3422`
37×	`unsub-neg_binary64_3482` `distribute-neg-frac_binary64_3452`
33×	`associate--l+_binary64_3425`
32×	`+-rgt-identity_binary64_3473`
30×	`div-sub_binary64_3493`
26×	`sub0-neg_binary64_3475`
23×	`associate-/r/_binary64_3434`
22×	`associate--r+_binary64_3424`
19×	`distribute-lft-neg-out_binary64_3447`
17×	`cube-unmult_binary64_3525`
13×	`distribute-neg-in_binary64_3449` `associate-/l/_binary64_3435`
12×	`cube-prod_binary64_3516`
10×	`mul-1-neg_binary64_3480` `distribute-rgt-out--_binary64_3442` `distribute-rgt-out_binary64_3441`
9×	`unpow3_binary64_3554`
7×	`rem-sqrt-square_binary64_3501`
5×	`exp-prod_binary64_3540` `cube-mult_binary64_3518`
4×	`exp-sum_binary64_3534` `distribute-rgt-neg-out_binary64_3448` `associate--l-_binary64_3426`
3×	`unpow2_binary64_3553` `unpow1_binary64_3546` `rem-square-sqrt_binary64_3500`
2×	`exp-diff_binary64_3536` `-rgt-identity_binary64_3478` `-inverses_binary64_3468` `+-inverses_binary64_3467` `swap-sqr_binary64_3455`
1×	`prod-exp_binary64_3537` `1-exp_binary64_3532` `mul0-rgt_binary64_3471` `mul0-lft_binary64_3470` `rgt-mult-inverse_binary64_3465` `distribute-rgt1-in_binary64_3444` `distribute-lft-out--_binary64_3440` `distribute-lft-out_binary64_3439` `count-2_binary64_3436`
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_3751` `erf-erfc_binary64_3750` `erf-odd_binary64_3749` `if-if-and-not_binary64_3748` `if-if-and_binary64_3747` `if-if-or-not_binary64_3746` `if-if-or_binary64_3745` `if-not_binary64_3744` `if-same_binary64_3743` `if-false_binary64_3742` `if-true_binary64_3741` `not-gte_binary64_3740` `not-lte_binary64_3739` `not-gt_binary64_3738` `not-lt_binary64_3737` `gte-same_binary64_3736` `lte-same_binary64_3735` `gt-same_binary64_3734` `lt-same_binary64_3733` `sinh---cosh_binary64_3680` `sinh-+-cosh_binary64_3679` `sinh-cosh_binary64_3678` `tanh-def-c_binary64_3677` `tanh-def-b_binary64_3676` `tanh-def-a_binary64_3675` `cosh-def_binary64_3674` `sinh-def_binary64_3673` `tan-neg_binary64_3620` `cos-neg_binary64_3619` `sin-neg_binary64_3618` `tan-0_binary64_3617` `cos-0_binary64_3616` `sin-0_binary64_3615` `hang-m-tan_binary64_3614` `hang-p-tan_binary64_3613` `hang-m0-tan_binary64_3612` `hang-p0-tan_binary64_3611` `hang-0m-tan_binary64_3610` `hang-0p-tan_binary64_3609` `tan-+PI/2_binary64_3608` `tan-+PI_binary64_3607` `tan-PI_binary64_3606` `tan-PI/3_binary64_3605` `tan-PI/4_binary64_3604` `tan-PI/6_binary64_3603` `cos-+PI/2_binary64_3602` `cos-+PI_binary64_3601` `cos-PI_binary64_3600` `cos-PI/2_binary64_3599` `cos-PI/3_binary64_3598` `cos-PI/4_binary64_3597` `cos-PI/6_binary64_3596` `sin-+PI/2_binary64_3595` `sin-+PI_binary64_3594` `sin-PI_binary64_3593` `sin-PI/2_binary64_3592` `sin-PI/3_binary64_3591` `sin-PI/4_binary64_3590` `sin-PI/6_binary64_3589` `sub-1-sin_binary64_3588` `sub-1-cos_binary64_3587` `-1-add-sin_binary64_3586` `-1-add-cos_binary64_3585` `1-sub-sin_binary64_3584` `1-sub-cos_binary64_3583` `cos-sin-sum_binary64_3582` `log-E_binary64_3578` `log-pow_binary64_3577` `log-rec_binary64_3576` `log-div_binary64_3575` `log-prod_binary64_3574` `pow-base-0_binary64_3572` `unpow1/3_binary64_3555` `unpow1/2_binary64_3552` `exp-to-pow_binary64_3550` `pow-base-1_binary64_3548` `unpow0_binary64_3547` `unpow-1_binary64_3545` `exp-lft-cube_binary64_3544` `exp-lft-sqr_binary64_3543` `exp-cbrt_binary64_3542` `exp-sqrt_binary64_3541` `div-exp_binary64_3539` `rec-exp_binary64_3538` `exp-neg_binary64_3535` `e-exp-1_binary64_3533` `exp-1-e_binary64_3531` `exp-0_binary64_3530` `rem-log-exp_binary64_3529` `rem-exp-log_binary64_3528` `cube-div_binary64_3517` `cube-neg_binary64_3515` `rem-3cbrt-rft_binary64_3514` `rem-3cbrt-lft_binary64_3513` `rem-cbrt-cube_binary64_3512` `rem-cube-cbrt_binary64_3511` `sqr-abs_binary64_3503` `sqr-neg_binary64_3502` `/-rgt-identity_binary64_3479` `*-lft-identity_binary64_3477` `remove-double-neg_binary64_3476` `--rgt-identity_binary64_3474` `+-lft-identity_binary64_3472` `div0_binary64_3469` `lft-mult-inverse_binary64_3466` `remove-double-div_binary64_3464` `difference-of-sqr--1_binary64_3459` `difference-of-sqr-1_binary64_3458` `cancel-sign-sub_binary64_3453` `distribute-frac-neg_binary64_3451` `distribute-neg-out_binary64_3450` `distribute-lft1-in_binary64_3443` `associate--r-_binary64_3427`

Counts

89 → 192

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	152	1675
1	397	1617
2	1168	1593
3	3124	1587

prune277.0ms (2.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	184	8	192
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	185	8	193

Error

4.5b

Counts

193 → 8

Compiler

Compiled 4852 to 2671 computations (45% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
0.7b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
27.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.6b	(sqrt.f64 (.f64 2 (.f64 im im)))

rewrite192.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

4.5b

Rules

51×	`add-sqr-sqrt_binary64_3510`
50×	`sqrt-prod_binary64_3504`
38×	`*-un-lft-identity_binary64_3488`
36×	`times-frac_binary64_3494`
26×	`add-cube-cbrt_binary64_3523`
12×	`difference-of-squares_binary64_3457`
11×	`pow1_binary64_3549`
9×	`associate-/r*_binary64_3432`
6×	`add-log-exp_binary64_3527` `add-exp-log_binary64_3526` `add-cbrt-cube_binary64_3524` `distribute-lft-out--_binary64_3440`
4×	`sqrt-pow1_binary64_3506` `sqrt-div_binary64_3505` `associate-/l*_binary64_3433`
3×	`pow-prod-down_binary64_3559` `cancel-sign-sub-inv_binary64_3454`
2×	`pow1/2_binary64_3568` `flip3--_binary64_3492` `flip--_binary64_3463` `associate-/r/_binary64_3434`
1×	`flip3-+_binary64_3491` `flip-+_binary64_3462` `rem-sqrt-square_binary64_3501` `diff-log_binary64_3580` `sub-neg_binary64_3481` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `sqrt-undiv_binary64_3509` `frac-2neg_binary64_3499` `clear-num_binary64_3487` `div-inv_binary64_3485`

Counts

4 → 108

Calls

4 calls:

15.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (.f64 2 (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 3656 to 1176 computations (67.8% saved)

series666.0ms (5.9%)

Error

1.1b

Counts

4 → 51

Calls

4 calls:

191.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
188.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
175.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
47.0ms	(sqrt.f64 (.f64 2 (.f64 im im)))

Compiler

Compiled 2619 to 2052 computations (21.6% saved)

simplify325.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

551×	`associate-l_binary64_3429`
486×	`associate-r_binary64_3428`
430×	`times-frac_binary64_3494`
322×	`associate-/l*_binary64_3433`
257×	`associate-/r*_binary64_3432`
156×	`associate-*l/_binary64_3431`
133×	`associate-/l/_binary64_3435`
124×	`cancel-sign-sub-inv_binary64_3454`
123×	`associate-*r/_binary64_3430`
117×	`associate-/r/_binary64_3434`
109×	`sub-neg_binary64_3481` `distribute-rgt-in_binary64_3438`
85×	`distribute-rgt-neg-in_binary64_3446`
83×	`distribute-lft-in_binary64_3437`
71×	`distribute-lft-neg-in_binary64_3445`
68×	`*-commutative_binary64_3419`
64×	`unswap-sqr_binary64_3456`
58×	`sqr-pow_binary64_3460`
52×	`neg-sub0_binary64_3483`
49×	`neg-mul-1_binary64_3484` `distribute-lft-neg-out_binary64_3447`
47×	`+-commutative_binary64_3418`
41×	`distribute-neg-frac_binary64_3452`
34×	`pow-sqr_binary64_3461`
33×	`distribute-neg-in_binary64_3449`
30×	`associate--r+_binary64_3424`
24×	`unsub-neg_binary64_3482` `distribute-rgt-neg-out_binary64_3448` `associate-+l+_binary64_3421`
20×	`difference-of-squares_binary64_3457`
19×	`pow-plus_binary64_3551`
18×	`exp-prod_binary64_3540`
16×	`div-sub_binary64_3493` `*-rgt-identity_binary64_3478`
13×	`associate-+r+_binary64_3420`
12×	`cube-prod_binary64_3516` `associate--l+_binary64_3425`
11×	`distribute-rgt-out_binary64_3441`
10×	`div-exp_binary64_3539` `rem-sqrt-square_binary64_3501` `associate-+r-_binary64_3422`
9×	`prod-exp_binary64_3537`
8×	`cube-unmult_binary64_3525` `distribute-rgt-out--_binary64_3442`
7×	`unpow3_binary64_3554` `+-rgt-identity_binary64_3473`
6×	`/-rgt-identity_binary64_3479`
5×	`log-div_binary64_3575` `cube-mult_binary64_3518` `rem-square-sqrt_binary64_3500` `mul-1-neg_binary64_3480` `swap-sqr_binary64_3455`
3×	`log-prod_binary64_3574` `unpow2_binary64_3553` `unpow1_binary64_3546` `rec-exp_binary64_3538` `exp-sum_binary64_3534` `cancel-sign-sub_binary64_3453` `associate-+l-_binary64_3423`
2×	`exp-diff_binary64_3536` `cube-div_binary64_3517` `*-lft-identity_binary64_3477` `sub0-neg_binary64_3475` `count-2_binary64_3436`
1×	`log-rec_binary64_3576` `1-exp_binary64_3532` `rem-log-exp_binary64_3529` `rem-3cbrt-lft_binary64_3513` `*-inverses_binary64_3468` `+-inverses_binary64_3467` `distribute-frac-neg_binary64_3451` `distribute-neg-out_binary64_3450` `distribute-rgt1-in_binary64_3444` `distribute-lft-out--_binary64_3440` `distribute-lft-out_binary64_3439`
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_3751` `erf-erfc_binary64_3750` `erf-odd_binary64_3749` `if-if-and-not_binary64_3748` `if-if-and_binary64_3747` `if-if-or-not_binary64_3746` `if-if-or_binary64_3745` `if-not_binary64_3744` `if-same_binary64_3743` `if-false_binary64_3742` `if-true_binary64_3741` `not-gte_binary64_3740` `not-lte_binary64_3739` `not-gt_binary64_3738` `not-lt_binary64_3737` `gte-same_binary64_3736` `lte-same_binary64_3735` `gt-same_binary64_3734` `lt-same_binary64_3733` `sinh---cosh_binary64_3680` `sinh-+-cosh_binary64_3679` `sinh-cosh_binary64_3678` `tanh-def-c_binary64_3677` `tanh-def-b_binary64_3676` `tanh-def-a_binary64_3675` `cosh-def_binary64_3674` `sinh-def_binary64_3673` `tan-neg_binary64_3620` `cos-neg_binary64_3619` `sin-neg_binary64_3618` `tan-0_binary64_3617` `cos-0_binary64_3616` `sin-0_binary64_3615` `hang-m-tan_binary64_3614` `hang-p-tan_binary64_3613` `hang-m0-tan_binary64_3612` `hang-p0-tan_binary64_3611` `hang-0m-tan_binary64_3610` `hang-0p-tan_binary64_3609` `tan-+PI/2_binary64_3608` `tan-+PI_binary64_3607` `tan-PI_binary64_3606` `tan-PI/3_binary64_3605` `tan-PI/4_binary64_3604` `tan-PI/6_binary64_3603` `cos-+PI/2_binary64_3602` `cos-+PI_binary64_3601` `cos-PI_binary64_3600` `cos-PI/2_binary64_3599` `cos-PI/3_binary64_3598` `cos-PI/4_binary64_3597` `cos-PI/6_binary64_3596` `sin-+PI/2_binary64_3595` `sin-+PI_binary64_3594` `sin-PI_binary64_3593` `sin-PI/2_binary64_3592` `sin-PI/3_binary64_3591` `sin-PI/4_binary64_3590` `sin-PI/6_binary64_3589` `sub-1-sin_binary64_3588` `sub-1-cos_binary64_3587` `-1-add-sin_binary64_3586` `-1-add-cos_binary64_3585` `1-sub-sin_binary64_3584` `1-sub-cos_binary64_3583` `cos-sin-sum_binary64_3582` `log-E_binary64_3578` `log-pow_binary64_3577` `pow-base-0_binary64_3572` `unpow1/3_binary64_3555` `unpow1/2_binary64_3552` `exp-to-pow_binary64_3550` `pow-base-1_binary64_3548` `unpow0_binary64_3547` `unpow-1_binary64_3545` `exp-lft-cube_binary64_3544` `exp-lft-sqr_binary64_3543` `exp-cbrt_binary64_3542` `exp-sqrt_binary64_3541` `exp-neg_binary64_3535` `e-exp-1_binary64_3533` `exp-1-e_binary64_3531` `exp-0_binary64_3530` `rem-exp-log_binary64_3528` `cube-neg_binary64_3515` `rem-3cbrt-rft_binary64_3514` `rem-cbrt-cube_binary64_3512` `rem-cube-cbrt_binary64_3511` `sqr-abs_binary64_3503` `sqr-neg_binary64_3502` `remove-double-neg_binary64_3476` `--rgt-identity_binary64_3474` `+-lft-identity_binary64_3472` `mul0-rgt_binary64_3471` `mul0-lft_binary64_3470` `div0_binary64_3469` `lft-mult-inverse_binary64_3466` `rgt-mult-inverse_binary64_3465` `remove-double-div_binary64_3464` `difference-of-sqr--1_binary64_3459` `difference-of-sqr-1_binary64_3458` `distribute-lft1-in_binary64_3443` `associate--r-_binary64_3427` `associate--l-_binary64_3426`

Counts

159 → 297

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	245	4558
1	537	4397
2	1549	4376

prune579.0ms (5.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	293	4	297
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	294	11	305

Error

1.1b

Counts

305 → 11

Compiler

Compiled 10113 to 4313 computations (57.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (.f64 (sqrt.f64 2) (fabs.f64 im)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.5b	(*.f64 (sqrt.f64 2) (fabs.f64 im))
0.7b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
27.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite157.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

Rules

30×	`add-sqr-sqrt_binary64_3510`
22×	`sqrt-prod_binary64_3504`
19×	`*-un-lft-identity_binary64_3488`
13×	`add-cube-cbrt_binary64_3523`
11×	`add-exp-log_binary64_3526` `add-cbrt-cube_binary64_3524`
9×	`times-frac_binary64_3494` `associate-/r*_binary64_3432`
7×	`pow1_binary64_3549`
6×	`add-log-exp_binary64_3527` `difference-of-squares_binary64_3457` `associate-l_binary64_3429`
4×	`sqrt-div_binary64_3505`
3×	`cancel-sign-sub-inv_binary64_3454` `distribute-lft-out--_binary64_3440` `associate-r_binary64_3428`
2×	`flip3--_binary64_3492` `flip--_binary64_3463` `prod-exp_binary64_3537` `cbrt-unprod_binary64_3521` `unswap-sqr_binary64_3456` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `associate-/r/_binary64_3434`
1×	`pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `flip3-+_binary64_3491` `flip-+_binary64_3462` `rem-sqrt-square_binary64_3501` `diff-log_binary64_3580` `sub-neg_binary64_3481` `pow-prod-down_binary64_3559` `-commutative_binary64_3419` `frac-2neg_binary64_3499` `clear-num_binary64_3487` `div-inv_binary64_3485` `associate-/l_binary64_3433`

Counts

4 → 89

Calls

4 calls:

14.0ms	(/.f64 (.f64 (sqrt.f64 2) (fabs.f64 im)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(*.f64 (sqrt.f64 2) (fabs.f64 im))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 2639 to 894 computations (66.1% saved)

series628.0ms (5.6%)

Error

0.5b

Counts

4 → 50

Calls

4 calls:

192.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
165.0ms	(/.f64 (.f64 (sqrt.f64 2) (fabs.f64 im)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
159.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
47.0ms	(*.f64 (sqrt.f64 2) (fabs.f64 im))

Compiler

Compiled 2626 to 2087 computations (20.5% saved)

simplify253.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

444×	`associate-/r*_binary64_3432`
430×	`associate-*l/_binary64_3431`
417×	`associate-/r/_binary64_3434`
373×	`associate-/l/_binary64_3435`
155×	`cancel-sign-sub-inv_binary64_3454`
132×	`associate-r_binary64_3428`
126×	`associate-l_binary64_3429`
120×	`associate-/l*_binary64_3433`
117×	`sub-neg_binary64_3481`
111×	`distribute-rgt-in_binary64_3438`
104×	`distribute-rgt-neg-in_binary64_3446`
98×	`unswap-sqr_binary64_3456`
87×	`distribute-lft-neg-in_binary64_3445`
85×	`distribute-lft-in_binary64_3437`
79×	`*-commutative_binary64_3419`
72×	`times-frac_binary64_3494`
70×	`sqr-pow_binary64_3460`
53×	`neg-sub0_binary64_3483`
51×	`distribute-neg-frac_binary64_3452`
50×	`distribute-lft-neg-out_binary64_3447`
49×	`neg-mul-1_binary64_3484`
48×	`+-commutative_binary64_3418`
38×	`pow-sqr_binary64_3461`
35×	`associate-*r/_binary64_3430`
33×	`distribute-neg-in_binary64_3449`
32×	`difference-of-squares_binary64_3457`
30×	`associate--r+_binary64_3424`
29×	`exp-prod_binary64_3540` `div-sub_binary64_3493`
28×	`*-rgt-identity_binary64_3478`
27×	`log-div_binary64_3575`
25×	`unsub-neg_binary64_3482`
24×	`associate-+l+_binary64_3421`
23×	`distribute-rgt-neg-out_binary64_3448`
21×	`cube-prod_binary64_3516`
20×	`pow-plus_binary64_3551`
19×	`cube-div_binary64_3517` `/-rgt-identity_binary64_3479`
15×	`log-prod_binary64_3574`
14×	`associate--l+_binary64_3425`
13×	`distribute-rgt-out_binary64_3441` `associate-+r+_binary64_3420`
11×	`swap-sqr_binary64_3455`
10×	`*-lft-identity_binary64_3477` `associate-+r-_binary64_3422`
9×	`cube-unmult_binary64_3525` `distribute-rgt-out--_binary64_3442`
8×	`rem-sqrt-square_binary64_3501`
7×	`unpow3_binary64_3554` `+-rgt-identity_binary64_3473`
5×	`cube-mult_binary64_3518` `mul-1-neg_binary64_3480`
4×	`log-rec_binary64_3576` `rem-square-sqrt_binary64_3500`
3×	`unpow2_binary64_3553` `unpow1_binary64_3546` `exp-sum_binary64_3534` `*-inverses_binary64_3468` `cancel-sign-sub_binary64_3453` `associate-+l-_binary64_3423`
2×	`div-exp_binary64_3539` `exp-diff_binary64_3536` `sub0-neg_binary64_3475` `distribute-frac-neg_binary64_3451` `count-2_binary64_3436`
1×	`exp-sqrt_binary64_3541` `rec-exp_binary64_3538` `prod-exp_binary64_3537` `1-exp_binary64_3532` `exp-1-e_binary64_3531` `rem-log-exp_binary64_3529` `rem-3cbrt-lft_binary64_3513` `sqr-abs_binary64_3503` `+-inverses_binary64_3467` `distribute-neg-out_binary64_3450` `distribute-rgt1-in_binary64_3444` `distribute-lft1-in_binary64_3443` `distribute-lft-out--_binary64_3440` `distribute-lft-out_binary64_3439`
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_3751` `erf-erfc_binary64_3750` `erf-odd_binary64_3749` `if-if-and-not_binary64_3748` `if-if-and_binary64_3747` `if-if-or-not_binary64_3746` `if-if-or_binary64_3745` `if-not_binary64_3744` `if-same_binary64_3743` `if-false_binary64_3742` `if-true_binary64_3741` `not-gte_binary64_3740` `not-lte_binary64_3739` `not-gt_binary64_3738` `not-lt_binary64_3737` `gte-same_binary64_3736` `lte-same_binary64_3735` `gt-same_binary64_3734` `lt-same_binary64_3733` `sinh---cosh_binary64_3680` `sinh-+-cosh_binary64_3679` `sinh-cosh_binary64_3678` `tanh-def-c_binary64_3677` `tanh-def-b_binary64_3676` `tanh-def-a_binary64_3675` `cosh-def_binary64_3674` `sinh-def_binary64_3673` `tan-neg_binary64_3620` `cos-neg_binary64_3619` `sin-neg_binary64_3618` `tan-0_binary64_3617` `cos-0_binary64_3616` `sin-0_binary64_3615` `hang-m-tan_binary64_3614` `hang-p-tan_binary64_3613` `hang-m0-tan_binary64_3612` `hang-p0-tan_binary64_3611` `hang-0m-tan_binary64_3610` `hang-0p-tan_binary64_3609` `tan-+PI/2_binary64_3608` `tan-+PI_binary64_3607` `tan-PI_binary64_3606` `tan-PI/3_binary64_3605` `tan-PI/4_binary64_3604` `tan-PI/6_binary64_3603` `cos-+PI/2_binary64_3602` `cos-+PI_binary64_3601` `cos-PI_binary64_3600` `cos-PI/2_binary64_3599` `cos-PI/3_binary64_3598` `cos-PI/4_binary64_3597` `cos-PI/6_binary64_3596` `sin-+PI/2_binary64_3595` `sin-+PI_binary64_3594` `sin-PI_binary64_3593` `sin-PI/2_binary64_3592` `sin-PI/3_binary64_3591` `sin-PI/4_binary64_3590` `sin-PI/6_binary64_3589` `sub-1-sin_binary64_3588` `sub-1-cos_binary64_3587` `-1-add-sin_binary64_3586` `-1-add-cos_binary64_3585` `1-sub-sin_binary64_3584` `1-sub-cos_binary64_3583` `cos-sin-sum_binary64_3582` `log-E_binary64_3578` `log-pow_binary64_3577` `pow-base-0_binary64_3572` `unpow1/3_binary64_3555` `unpow1/2_binary64_3552` `exp-to-pow_binary64_3550` `pow-base-1_binary64_3548` `unpow0_binary64_3547` `unpow-1_binary64_3545` `exp-lft-cube_binary64_3544` `exp-lft-sqr_binary64_3543` `exp-cbrt_binary64_3542` `exp-neg_binary64_3535` `e-exp-1_binary64_3533` `exp-0_binary64_3530` `rem-exp-log_binary64_3528` `cube-neg_binary64_3515` `rem-3cbrt-rft_binary64_3514` `rem-cbrt-cube_binary64_3512` `rem-cube-cbrt_binary64_3511` `sqr-neg_binary64_3502` `remove-double-neg_binary64_3476` `--rgt-identity_binary64_3474` `+-lft-identity_binary64_3472` `mul0-rgt_binary64_3471` `mul0-lft_binary64_3470` `div0_binary64_3469` `lft-mult-inverse_binary64_3466` `rgt-mult-inverse_binary64_3465` `remove-double-div_binary64_3464` `difference-of-sqr--1_binary64_3459` `difference-of-sqr-1_binary64_3458` `associate--r-_binary64_3427` `associate--l-_binary64_3426`

Counts

139 → 213

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	232	3078
1	567	2870
2	2050	2843

prune337.0ms (3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	210	3	213
Fresh	2	7	9
Picked	1	0	1
Done	1	0	1
Total	214	10	224

Error

0.4b

Counts

224 → 10

Compiler

Compiled 6264 to 2928 computations (53.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (fabs.f64 im) (sqrt.f64 (sqrt.f64 2)))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
0.3b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (fabs.f64 im) (sqrt.f64 (sqrt.f64 2))))
0.7b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
27.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite212.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

27×	`sqrt-prod_binary64_3504`
26×	`add-sqr-sqrt_binary64_3510`
19×	`*-un-lft-identity_binary64_3488`
18×	`add-exp-log_binary64_3526` `add-cbrt-cube_binary64_3524`
13×	`add-cube-cbrt_binary64_3523`
10×	`pow1_binary64_3549`
9×	`associate-l_binary64_3429` `times-frac_binary64_3494` `associate-/r*_binary64_3432`
6×	`add-log-exp_binary64_3527` `difference-of-squares_binary64_3457` `prod-exp_binary64_3537` `cbrt-unprod_binary64_3521`
4×	`sqrt-div_binary64_3505`
3×	`cancel-sign-sub-inv_binary64_3454` `distribute-lft-out--_binary64_3440` `pow-prod-down_binary64_3559` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522`
2×	`flip3--_binary64_3492` `flip--_binary64_3463` `associate-/r/_binary64_3434`
1×	`pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `flip3-+_binary64_3491` `flip-+_binary64_3462` `rem-sqrt-square_binary64_3501` `diff-log_binary64_3580` `sub-neg_binary64_3481` `associate-r_binary64_3428` `-commutative_binary64_3419` `frac-2neg_binary64_3499` `clear-num_binary64_3487` `div-inv_binary64_3485` `associate-/l_binary64_3433`

Counts

4 → 93

Calls

4 calls:

18.0ms	(/.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (fabs.f64 im) (sqrt.f64 (sqrt.f64 2)))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
11.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (fabs.f64 im) (sqrt.f64 (sqrt.f64 2))))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 3330 to 1521 computations (54.3% saved)

series635.0ms (5.6%)

Error

0.4b

Counts

4 → 50

Calls

4 calls:

181.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
169.0ms	(/.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (fabs.f64 im) (sqrt.f64 (sqrt.f64 2)))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
158.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
49.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (fabs.f64 im) (sqrt.f64 (sqrt.f64 2))))

Compiler

Compiled 3051 to 2512 computations (17.7% saved)

simplify332.0ms (3%)

Algorithm

1×	egg-herbie

Rules

550×	`associate-/r*_binary64_3432`
324×	`associate-*l/_binary64_3431`
301×	`associate-*r/_binary64_3430`
284×	`associate-/r/_binary64_3434`
247×	`associate-/l/_binary64_3435`
151×	`associate-r_binary64_3428`
146×	`cancel-sign-sub-inv_binary64_3454`
144×	`associate-l_binary64_3429`
118×	`sub-neg_binary64_3481`
111×	`associate-/l*_binary64_3433`
109×	`distribute-rgt-in_binary64_3438`
105×	`distribute-rgt-neg-in_binary64_3446`
91×	`unswap-sqr_binary64_3456`
87×	`times-frac_binary64_3494` `distribute-lft-neg-in_binary64_3445`
83×	`distribute-lft-in_binary64_3437` `*-commutative_binary64_3419`
68×	`sqr-pow_binary64_3460`
54×	`neg-sub0_binary64_3483` `distribute-lft-neg-out_binary64_3447`
50×	`neg-mul-1_binary64_3484`
49×	`+-commutative_binary64_3418`
44×	`distribute-neg-frac_binary64_3452`
39×	`pow-sqr_binary64_3461`
37×	`div-sub_binary64_3493`
33×	`distribute-neg-in_binary64_3449`
32×	`difference-of-squares_binary64_3457`
30×	`associate--r+_binary64_3424`
25×	`exp-prod_binary64_3540` `unsub-neg_binary64_3482` `distribute-rgt-neg-out_binary64_3448` `associate-+l+_binary64_3421`
21×	`log-div_binary64_3575` `pow-plus_binary64_3551`
20×	`*-rgt-identity_binary64_3478`
16×	`cube-prod_binary64_3516` `swap-sqr_binary64_3455` `associate--l+_binary64_3425`
15×	`associate-+r+_binary64_3420`
13×	`cube-div_binary64_3517` `distribute-rgt-out_binary64_3441`
10×	`cube-unmult_binary64_3525` `associate-+r-_binary64_3422`
9×	`distribute-rgt-out--_binary64_3442`
8×	`log-prod_binary64_3574`
7×	`unpow3_binary64_3554` `rem-sqrt-square_binary64_3501` `+-rgt-identity_binary64_3473`
5×	`cube-mult_binary64_3518` `rem-square-sqrt_binary64_3500` `mul-1-neg_binary64_3480`
3×	`unpow2_binary64_3553` `unpow1_binary64_3546` `exp-sum_binary64_3534` `cancel-sign-sub_binary64_3453` `count-2_binary64_3436` `associate-+l-_binary64_3423`
2×	`exp-diff_binary64_3536` `/-rgt-identity_binary64_3479` `-lft-identity_binary64_3477` `sub0-neg_binary64_3475` `-inverses_binary64_3468` `distribute-frac-neg_binary64_3451`
1×	`log-rec_binary64_3576` `div-exp_binary64_3539` `prod-exp_binary64_3537` `1-exp_binary64_3532` `rem-log-exp_binary64_3529` `rem-3cbrt-lft_binary64_3513` `sqr-abs_binary64_3503` `+-inverses_binary64_3467` `distribute-neg-out_binary64_3450` `distribute-rgt1-in_binary64_3444` `distribute-lft-out--_binary64_3440` `distribute-lft-out_binary64_3439`
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_3751` `erf-erfc_binary64_3750` `erf-odd_binary64_3749` `if-if-and-not_binary64_3748` `if-if-and_binary64_3747` `if-if-or-not_binary64_3746` `if-if-or_binary64_3745` `if-not_binary64_3744` `if-same_binary64_3743` `if-false_binary64_3742` `if-true_binary64_3741` `not-gte_binary64_3740` `not-lte_binary64_3739` `not-gt_binary64_3738` `not-lt_binary64_3737` `gte-same_binary64_3736` `lte-same_binary64_3735` `gt-same_binary64_3734` `lt-same_binary64_3733` `sinh---cosh_binary64_3680` `sinh-+-cosh_binary64_3679` `sinh-cosh_binary64_3678` `tanh-def-c_binary64_3677` `tanh-def-b_binary64_3676` `tanh-def-a_binary64_3675` `cosh-def_binary64_3674` `sinh-def_binary64_3673` `tan-neg_binary64_3620` `cos-neg_binary64_3619` `sin-neg_binary64_3618` `tan-0_binary64_3617` `cos-0_binary64_3616` `sin-0_binary64_3615` `hang-m-tan_binary64_3614` `hang-p-tan_binary64_3613` `hang-m0-tan_binary64_3612` `hang-p0-tan_binary64_3611` `hang-0m-tan_binary64_3610` `hang-0p-tan_binary64_3609` `tan-+PI/2_binary64_3608` `tan-+PI_binary64_3607` `tan-PI_binary64_3606` `tan-PI/3_binary64_3605` `tan-PI/4_binary64_3604` `tan-PI/6_binary64_3603` `cos-+PI/2_binary64_3602` `cos-+PI_binary64_3601` `cos-PI_binary64_3600` `cos-PI/2_binary64_3599` `cos-PI/3_binary64_3598` `cos-PI/4_binary64_3597` `cos-PI/6_binary64_3596` `sin-+PI/2_binary64_3595` `sin-+PI_binary64_3594` `sin-PI_binary64_3593` `sin-PI/2_binary64_3592` `sin-PI/3_binary64_3591` `sin-PI/4_binary64_3590` `sin-PI/6_binary64_3589` `sub-1-sin_binary64_3588` `sub-1-cos_binary64_3587` `-1-add-sin_binary64_3586` `-1-add-cos_binary64_3585` `1-sub-sin_binary64_3584` `1-sub-cos_binary64_3583` `cos-sin-sum_binary64_3582` `log-E_binary64_3578` `log-pow_binary64_3577` `pow-base-0_binary64_3572` `unpow1/3_binary64_3555` `unpow1/2_binary64_3552` `exp-to-pow_binary64_3550` `pow-base-1_binary64_3548` `unpow0_binary64_3547` `unpow-1_binary64_3545` `exp-lft-cube_binary64_3544` `exp-lft-sqr_binary64_3543` `exp-cbrt_binary64_3542` `exp-sqrt_binary64_3541` `rec-exp_binary64_3538` `exp-neg_binary64_3535` `e-exp-1_binary64_3533` `exp-1-e_binary64_3531` `exp-0_binary64_3530` `rem-exp-log_binary64_3528` `cube-neg_binary64_3515` `rem-3cbrt-rft_binary64_3514` `rem-cbrt-cube_binary64_3512` `rem-cube-cbrt_binary64_3511` `sqr-neg_binary64_3502` `remove-double-neg_binary64_3476` `--rgt-identity_binary64_3474` `+-lft-identity_binary64_3472` `mul0-rgt_binary64_3471` `mul0-lft_binary64_3470` `div0_binary64_3469` `lft-mult-inverse_binary64_3466` `rgt-mult-inverse_binary64_3465` `remove-double-div_binary64_3464` `difference-of-sqr--1_binary64_3459` `difference-of-sqr-1_binary64_3458` `distribute-lft1-in_binary64_3443` `associate--r-_binary64_3427` `associate--l-_binary64_3426`

Counts

143 → 250

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	241	3769
1	613	3060
2	2078	3033

prune464.0ms (4.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	249	1	250
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	249	11	260

Error

0.4b

Counts

260 → 11

Compiler

Compiled 8008 to 4115 computations (48.6% saved)

regimes2.1s (18.6%)

Accuracy

Total 17.3b remaining (99.2%)

Threshold costs 0b (0%)

Compiler

Compiled 14790 to 10729 computations (27.5% saved)

bsearch94.0ms (0.8%)

Steps

Iters	Range	Point
7	5.89673183955801e+101	1.5855399042473302e+103	3.1200050919961303e+102
6	1.211407107765241e-306	8.573342148616013e-306	1.2893888095222202e-306
9	-8.381900621877904e+156	-3.291518980484572e+148	-2.45305725845355e+153

Iters

Range

Point

5.89673183955801e+101

1.5855399042473302e+103

3.1200050919961303e+102

1.211407107765241e-306

8.573342148616013e-306

1.2893888095222202e-306

-8.381900621877904e+156

-3.291518980484572e+148

-2.45305725845355e+153

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary64_3419`
14×	`+-commutative_binary64_3418`
10×	`sub-neg_binary64_3481`
8×	`neg-mul-1_binary64_3484` `neg-sub0_binary64_3483`
4×	`distribute-neg-out_binary64_3450`
2×	`unsub-neg_binary64_3482` `distribute-rgt-neg-in_binary64_3446` `distribute-lft-neg-in_binary64_3445`
1×	`distribute-neg-frac_binary64_3452`
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_3748` `if-if-and_binary64_3747` `if-if-or-not_binary64_3746` `if-if-or_binary64_3745` `if-not_binary64_3744` `if-same_binary64_3743` `if-false_binary64_3742` `if-true_binary64_3741` `tan-0_binary64_3617` `cos-0_binary64_3616` `sin-0_binary64_3615` `unpow1_binary64_3546` `e-exp-1_binary64_3533` `1-exp_binary64_3532` `exp-1-e_binary64_3531` `exp-0_binary64_3530` `sqr-abs_binary64_3503` `sqr-neg_binary64_3502` `mul-1-neg_binary64_3480` `/-rgt-identity_binary64_3479` `-rgt-identity_binary64_3478` `-lft-identity_binary64_3477` `remove-double-neg_binary64_3476` `sub0-neg_binary64_3475` `--rgt-identity_binary64_3474` `+-rgt-identity_binary64_3473` `+-lft-identity_binary64_3472` `cancel-sign-sub-inv_binary64_3454` `cancel-sign-sub_binary64_3453` `distribute-frac-neg_binary64_3451` `distribute-neg-in_binary64_3449` `distribute-rgt-neg-out_binary64_3448` `distribute-lft-neg-out_binary64_3447`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	116
1	61	116
2	72	116
3	92	116
4	102	116
5	110	116
6	113	116

Proof

(if real (<= f64 h0 -2453057258453549852170831102178119874748091443047603249682727206688103170464259220196324747857762803392340872672086930421198012534988258765219419150876672) (* f64 1/2 (/ f64 (* f64 (sqrt f64 2) (fabs f64 h1)) (sqrt f64 (- f64 (- f64 (neg f64 h0) (/ f64 (=> (* f64 h1 1/2)) (/ f64 h0 h1))) h0)))) (if real (<= f64 h0 8155475013641503/6325070415853456823515479584966165845298645305129441198653167438357198111499854590373761990669910140474596183259900372230931523043306046152094168748148078435047419508642698792639590866940413010663742739952273283392562733857021646831815729864036236135650314266011211548510419206725953204130822734645187695728365866909171712) (* f64 1/2 (/ f64 (* f64 (sqrt f64 2) (fabs f64 h1)) (sqrt f64 (- f64 (sqrt f64 (+ f64 (* f64 h0 h0) (* f64 h1 h1))) h0)))) (if real (<= f64 h0 3120005091996130305402014839741132664404797108401382223938605411635930498268784191785564982702067679232) (* f64 1/2 (sqrt f64 (* f64 2 (+ f64 (sqrt f64 (+ f64 (* f64 h0 h0) (* f64 h1 h1))) h0)))) (* f64 1/2 (sqrt f64 (* f64 2 (+ f64 h0 h0)))))))
*-commutative_binary64_3419 =>
(if real (<= f64 h0 -2453057258453549852170831102178119874748091443047603249682727206688103170464259220196324747857762803392340872672086930421198012534988258765219419150876672) (* f64 1/2 (/ f64 (* f64 (sqrt f64 2) (fabs f64 h1)) (sqrt f64 (- f64 (- f64 (neg f64 h0) (/ f64 (* f64 1/2 h1) (/ f64 h0 h1))) h0)))) (if real (<= f64 h0 8155475013641503/6325070415853456823515479584966165845298645305129441198653167438357198111499854590373761990669910140474596183259900372230931523043306046152094168748148078435047419508642698792639590866940413010663742739952273283392562733857021646831815729864036236135650314266011211548510419206725953204130822734645187695728365866909171712) (* f64 1/2 (/ f64 (* f64 (sqrt f64 2) (fabs f64 h1)) (sqrt f64 (- f64 (sqrt f64 (+ f64 (* f64 h0 h0) (* f64 h1 h1))) h0)))) (if real (<= f64 h0 3120005091996130305402014839741132664404797108401382223938605411635930498268784191785564982702067679232) (* f64 1/2 (sqrt f64 (* f64 2 (=> (+ f64 (sqrt f64 (+ f64 (* f64 h0 h0) (* f64 h1 h1))) h0))))) (* f64 1/2 (sqrt f64 (* f64 2 (+ f64 h0 h0)))))))
+-commutative_binary64_3418 =>
(if real (<= f64 h0 -2453057258453549852170831102178119874748091443047603249682727206688103170464259220196324747857762803392340872672086930421198012534988258765219419150876672) (* f64 1/2 (/ f64 (* f64 (sqrt f64 2) (fabs f64 h1)) (sqrt f64 (- f64 (- f64 (neg f64 h0) (/ f64 (* f64 1/2 h1) (/ f64 h0 h1))) h0)))) (if real (<= f64 h0 8155475013641503/6325070415853456823515479584966165845298645305129441198653167438357198111499854590373761990669910140474596183259900372230931523043306046152094168748148078435047419508642698792639590866940413010663742739952273283392562733857021646831815729864036236135650314266011211548510419206725953204130822734645187695728365866909171712) (* f64 1/2 (/ f64 (* f64 (sqrt f64 2) (fabs f64 h1)) (sqrt f64 (- f64 (sqrt f64 (+ f64 (* f64 h0 h0) (* f64 h1 h1))) h0)))) (if real (<= f64 h0 3120005091996130305402014839741132664404797108401382223938605411635930498268784191785564982702067679232) (* f64 1/2 (sqrt f64 (* f64 2 (+ f64 h0 (sqrt f64 (+ f64 (* f64 h0 h0) (* f64 h1 h1))))))) (* f64 1/2 (sqrt f64 (* f64 2 (+ f64 h0 h0)))))))

end0.0ms (0%)

sample2.6s (23.4%)

Algorithm

1×

intervals

Results

281.0ms	6030×	body	128	valid
159.0ms	679×	body	2048	valid
141.0ms	518×	body	4096	valid
77.0ms	411×	body	1024	valid
31.0ms	242×	body	512	valid
13.0ms	120×	body	256	valid

Compiler

Compiled 2069 to 1505 computations (27.3% saved)

Details

analyze308.0ms (2.7%)

sample33.0ms (0.3%)

simplify152.0ms (1.4%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite79.0ms (0.7%)

series537.0ms (4.8%)

simplify195.0ms (1.7%)

prune277.0ms (2.5%)

localize15.0ms (0.1%)

rewrite192.0ms (1.7%)

series666.0ms (5.9%)

simplify325.0ms (2.9%)

prune579.0ms (5.1%)

localize13.0ms (0.1%)

rewrite157.0ms (1.4%)

series628.0ms (5.6%)

simplify253.0ms (2.2%)

prune337.0ms (3%)

localize14.0ms (0.1%)

rewrite212.0ms (1.9%)

series635.0ms (5.6%)

simplify332.0ms (3%)

prune464.0ms (4.1%)

regimes2.1s (18.6%)

bsearch94.0ms (0.8%)

simplify11.0ms (0.1%)

end0.0ms (0%)

sample2.6s (23.4%)

Profiling