Details

analyze72.0ms (0.7%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	62.4%	12.6%	6
25%	40.6%	34.4%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample15.0ms (0.1%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 23 to 19 computations (17.4% saved)

simplify162.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64_7510`
3×	`associate-+l+_binary64_7513` `associate-+r+_binary64_7512`
2×	`*-commutative_binary64_7511`
1×	`distribute-rgt-out_binary64_7533` `distribute-lft-out_binary64_7531`
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_7843` `erf-erfc_binary64_7842` `erf-odd_binary64_7841` `if-if-and-not_binary64_7840` `if-if-and_binary64_7839` `if-if-or-not_binary64_7838` `if-if-or_binary64_7837` `if-not_binary64_7836` `if-same_binary64_7835` `if-false_binary64_7834` `if-true_binary64_7833` `not-gte_binary64_7832` `not-lte_binary64_7831` `not-gt_binary64_7830` `not-lt_binary64_7829` `gte-same_binary64_7828` `lte-same_binary64_7827` `gt-same_binary64_7826` `lt-same_binary64_7825` `sinh---cosh_binary64_7772` `sinh-+-cosh_binary64_7771` `sinh-cosh_binary64_7770` `tanh-def-c_binary64_7769` `tanh-def-b_binary64_7768` `tanh-def-a_binary64_7767` `cosh-def_binary64_7766` `sinh-def_binary64_7765` `tan-neg_binary64_7712` `cos-neg_binary64_7711` `sin-neg_binary64_7710` `tan-0_binary64_7709` `cos-0_binary64_7708` `sin-0_binary64_7707` `hang-m-tan_binary64_7706` `hang-p-tan_binary64_7705` `hang-m0-tan_binary64_7704` `hang-p0-tan_binary64_7703` `hang-0m-tan_binary64_7702` `hang-0p-tan_binary64_7701` `tan-+PI/2_binary64_7700` `tan-+PI_binary64_7699` `tan-PI_binary64_7698` `tan-PI/3_binary64_7697` `tan-PI/4_binary64_7696` `tan-PI/6_binary64_7695` `cos-+PI/2_binary64_7694` `cos-+PI_binary64_7693` `cos-PI_binary64_7692` `cos-PI/2_binary64_7691` `cos-PI/3_binary64_7690` `cos-PI/4_binary64_7689` `cos-PI/6_binary64_7688` `sin-+PI/2_binary64_7687` `sin-+PI_binary64_7686` `sin-PI_binary64_7685` `sin-PI/2_binary64_7684` `sin-PI/3_binary64_7683` `sin-PI/4_binary64_7682` `sin-PI/6_binary64_7681` `sub-1-sin_binary64_7680` `sub-1-cos_binary64_7679` `-1-add-sin_binary64_7678` `-1-add-cos_binary64_7677` `1-sub-sin_binary64_7676` `1-sub-cos_binary64_7675` `cos-sin-sum_binary64_7674` `log-E_binary64_7670` `log-pow_binary64_7669` `log-rec_binary64_7668` `log-div_binary64_7667` `log-prod_binary64_7666` `pow-base-0_binary64_7664` `unpow1/3_binary64_7647` `unpow3_binary64_7646` `unpow2_binary64_7645` `unpow1/2_binary64_7644` `pow-plus_binary64_7643` `exp-to-pow_binary64_7642` `pow-base-1_binary64_7640` `unpow0_binary64_7639` `unpow1_binary64_7638` `unpow-1_binary64_7637` `exp-lft-cube_binary64_7636` `exp-lft-sqr_binary64_7635` `exp-cbrt_binary64_7634` `exp-sqrt_binary64_7633` `exp-prod_binary64_7632` `div-exp_binary64_7631` `rec-exp_binary64_7630` `prod-exp_binary64_7629` `exp-diff_binary64_7628` `exp-neg_binary64_7627` `exp-sum_binary64_7626` `e-exp-1_binary64_7625` `1-exp_binary64_7624` `exp-1-e_binary64_7623` `exp-0_binary64_7622` `rem-log-exp_binary64_7621` `rem-exp-log_binary64_7620` `cube-unmult_binary64_7617` `cube-mult_binary64_7610` `cube-div_binary64_7609` `cube-prod_binary64_7608` `cube-neg_binary64_7607` `rem-3cbrt-rft_binary64_7606` `rem-3cbrt-lft_binary64_7605` `rem-cbrt-cube_binary64_7604` `rem-cube-cbrt_binary64_7603` `sqr-abs_binary64_7595` `sqr-neg_binary64_7594` `rem-sqrt-square_binary64_7593` `rem-square-sqrt_binary64_7592` `times-frac_binary64_7586` `div-sub_binary64_7585` `neg-mul-1_binary64_7576` `neg-sub0_binary64_7575` `unsub-neg_binary64_7574` `sub-neg_binary64_7573` `mul-1-neg_binary64_7572` `/-rgt-identity_binary64_7571` `-rgt-identity_binary64_7570` `-lft-identity_binary64_7569` `remove-double-neg_binary64_7568` `sub0-neg_binary64_7567` `--rgt-identity_binary64_7566` `+-rgt-identity_binary64_7565` `+-lft-identity_binary64_7564` `mul0-rgt_binary64_7563` `mul0-lft_binary64_7562` `div0_binary64_7561` `-inverses_binary64_7560` `+-inverses_binary64_7559` `lft-mult-inverse_binary64_7558` `rgt-mult-inverse_binary64_7557` `remove-double-div_binary64_7556` `pow-sqr_binary64_7553` `sqr-pow_binary64_7552` `difference-of-sqr--1_binary64_7551` `difference-of-sqr-1_binary64_7550` `difference-of-squares_binary64_7549` `unswap-sqr_binary64_7548` `swap-sqr_binary64_7547` `cancel-sign-sub-inv_binary64_7546` `cancel-sign-sub_binary64_7545` `distribute-neg-frac_binary64_7544` `distribute-frac-neg_binary64_7543` `distribute-neg-out_binary64_7542` `distribute-neg-in_binary64_7541` `distribute-rgt-neg-out_binary64_7540` `distribute-lft-neg-out_binary64_7539` `distribute-rgt-neg-in_binary64_7538` `distribute-lft-neg-in_binary64_7537` `distribute-rgt1-in_binary64_7536` `distribute-lft1-in_binary64_7535` `distribute-rgt-out--_binary64_7534` `distribute-lft-out--_binary64_7532` `distribute-rgt-in_binary64_7530` `distribute-lft-in_binary64_7529` `count-2_binary64_7528` `associate-/l/_binary64_7527` `associate-/r/_binary64_7526` `associate-/l_binary64_7525` `associate-/r_binary64_7524` `associate-l/_binary64_7523` `associate-r/_binary64_7522` `associate-l_binary64_7521` `associate-r*_binary64_7520` `associate--r-_binary64_7519` `associate--l-_binary64_7518` `associate--l+_binary64_7517` `associate--r+_binary64_7516` `associate-+l-_binary64_7515` `associate-+r-_binary64_7514`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	16	13
2	24	13
3	24	13

prune5.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Compiler

Compiled 38 to 26 computations (31.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
0.0b	(*.f64 x (+.f64 2 x))

rewrite47.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

6×	`add-sqr-sqrt_binary64_7602` `*-un-lft-identity_binary64_7580`
4×	`pow1_binary64_7641` `add-exp-log_binary64_7618` `add-log-exp_binary64_7619` `add-cbrt-cube_binary64_7616` `add-cube-cbrt_binary64_7615` `associate-r_binary64_7520`
3×	`associate-l_binary64_7521`
2×	`distribute-rgt-in_binary64_7530` `distribute-lft-in_binary64_7529` `flip3-+_binary64_7583` `associate-*r/_binary64_7522` `flip-+_binary64_7554` `associate-+l+_binary64_7513`
1×	`pow-prod-down_binary64_7651` `prod-exp_binary64_7629` `cbrt-unprod_binary64_7613` `unswap-sqr_binary64_7548` `distribute-lft-out_binary64_7531` `*-commutative_binary64_7511` `sum-log_binary64_7671` `+-commutative_binary64_7510`

Counts

2 → 36

Calls

2 calls:

7.0ms	(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
6.0ms	(*.f64 x (+.f64 2 x))

Compiler

Compiled 583 to 312 computations (46.5% saved)

series275.0ms (2.7%)

Error

0.0b

Counts

2 → 21

Calls

2 calls:

195.0ms	(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
64.0ms	(*.f64 x (+.f64 2 x))

Compiler

Compiled 425 to 348 computations (18.1% saved)

simplify146.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

641×	`associate-*l/_binary64_7523`
591×	`associate-*r/_binary64_7522`
483×	`distribute-rgt-in_binary64_7530`
467×	`distribute-lft-in_binary64_7529`
208×	`times-frac_binary64_7586`
195×	`unswap-sqr_binary64_7548`
176×	`cancel-sign-sub-inv_binary64_7546`
130×	`*-commutative_binary64_7511`
129×	`associate-+r+_binary64_7512`
112×	`associate-+l+_binary64_7513`
97×	`distribute-rgt-neg-in_binary64_7538`
95×	`associate-l_binary64_7521`
88×	`sqr-pow_binary64_7552`
86×	`associate-/l*_binary64_7525`
81×	`associate-/r*_binary64_7524`
80×	`associate-r_binary64_7520`
79×	`distribute-neg-in_binary64_7541`
75×	`distribute-lft-neg-in_binary64_7537`
74×	`sub-neg_binary64_7573`
70×	`distribute-rgt-out_binary64_7533`
66×	`associate-/r/_binary64_7526`
50×	`pow-sqr_binary64_7553`
31×	`exp-prod_binary64_7632` `*-rgt-identity_binary64_7570`
30×	`*-lft-identity_binary64_7569`
29×	`neg-mul-1_binary64_7576` `neg-sub0_binary64_7575`
28×	`pow-plus_binary64_7643`
25×	`unsub-neg_binary64_7574`
24×	`associate--r+_binary64_7516` `+-commutative_binary64_7510`
23×	`distribute-lft-neg-out_binary64_7539`
22×	`distribute-rgt-out--_binary64_7534`
19×	`distribute-neg-frac_binary64_7544`
17×	`associate-/l/_binary64_7527` `associate--l+_binary64_7517`
16×	`log-prod_binary64_7666`
14×	`cube-prod_binary64_7608`
12×	`exp-sum_binary64_7626`
11×	`difference-of-squares_binary64_7549` `associate-+r-_binary64_7514`
10×	`+-rgt-identity_binary64_7565` `swap-sqr_binary64_7547`
9×	`unpow3_binary64_7646` `exp-sqrt_binary64_7633` `distribute-rgt-neg-out_binary64_7540`
7×	`associate-+l-_binary64_7515`
6×	`log-div_binary64_7667` `cube-div_binary64_7609` `distribute-lft-out_binary64_7531`
5×	`cube-mult_binary64_7610` `sub0-neg_binary64_7567`
3×	`log-pow_binary64_7669` `prod-exp_binary64_7629` `cube-unmult_binary64_7617` `distribute-rgt1-in_binary64_7536` `count-2_binary64_7528`
2×	`unpow2_binary64_7645` `pow-base-1_binary64_7640` `unpow1_binary64_7638` `exp-lft-sqr_binary64_7635` `distribute-lft-out--_binary64_7532`
1×	`exp-diff_binary64_7628` `1-exp_binary64_7624` `exp-1-e_binary64_7623` `rem-log-exp_binary64_7621` `rem-sqrt-square_binary64_7593` `div-sub_binary64_7585` `*-inverses_binary64_7560` `cancel-sign-sub_binary64_7545`
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_7843` `erf-erfc_binary64_7842` `erf-odd_binary64_7841` `if-if-and-not_binary64_7840` `if-if-and_binary64_7839` `if-if-or-not_binary64_7838` `if-if-or_binary64_7837` `if-not_binary64_7836` `if-same_binary64_7835` `if-false_binary64_7834` `if-true_binary64_7833` `not-gte_binary64_7832` `not-lte_binary64_7831` `not-gt_binary64_7830` `not-lt_binary64_7829` `gte-same_binary64_7828` `lte-same_binary64_7827` `gt-same_binary64_7826` `lt-same_binary64_7825` `sinh---cosh_binary64_7772` `sinh-+-cosh_binary64_7771` `sinh-cosh_binary64_7770` `tanh-def-c_binary64_7769` `tanh-def-b_binary64_7768` `tanh-def-a_binary64_7767` `cosh-def_binary64_7766` `sinh-def_binary64_7765` `tan-neg_binary64_7712` `cos-neg_binary64_7711` `sin-neg_binary64_7710` `tan-0_binary64_7709` `cos-0_binary64_7708` `sin-0_binary64_7707` `hang-m-tan_binary64_7706` `hang-p-tan_binary64_7705` `hang-m0-tan_binary64_7704` `hang-p0-tan_binary64_7703` `hang-0m-tan_binary64_7702` `hang-0p-tan_binary64_7701` `tan-+PI/2_binary64_7700` `tan-+PI_binary64_7699` `tan-PI_binary64_7698` `tan-PI/3_binary64_7697` `tan-PI/4_binary64_7696` `tan-PI/6_binary64_7695` `cos-+PI/2_binary64_7694` `cos-+PI_binary64_7693` `cos-PI_binary64_7692` `cos-PI/2_binary64_7691` `cos-PI/3_binary64_7690` `cos-PI/4_binary64_7689` `cos-PI/6_binary64_7688` `sin-+PI/2_binary64_7687` `sin-+PI_binary64_7686` `sin-PI_binary64_7685` `sin-PI/2_binary64_7684` `sin-PI/3_binary64_7683` `sin-PI/4_binary64_7682` `sin-PI/6_binary64_7681` `sub-1-sin_binary64_7680` `sub-1-cos_binary64_7679` `-1-add-sin_binary64_7678` `-1-add-cos_binary64_7677` `1-sub-sin_binary64_7676` `1-sub-cos_binary64_7675` `cos-sin-sum_binary64_7674` `log-E_binary64_7670` `log-rec_binary64_7668` `pow-base-0_binary64_7664` `unpow1/3_binary64_7647` `unpow1/2_binary64_7644` `exp-to-pow_binary64_7642` `unpow0_binary64_7639` `unpow-1_binary64_7637` `exp-lft-cube_binary64_7636` `exp-cbrt_binary64_7634` `div-exp_binary64_7631` `rec-exp_binary64_7630` `exp-neg_binary64_7627` `e-exp-1_binary64_7625` `exp-0_binary64_7622` `rem-exp-log_binary64_7620` `cube-neg_binary64_7607` `rem-3cbrt-rft_binary64_7606` `rem-3cbrt-lft_binary64_7605` `rem-cbrt-cube_binary64_7604` `rem-cube-cbrt_binary64_7603` `sqr-abs_binary64_7595` `sqr-neg_binary64_7594` `rem-square-sqrt_binary64_7592` `mul-1-neg_binary64_7572` `/-rgt-identity_binary64_7571` `remove-double-neg_binary64_7568` `--rgt-identity_binary64_7566` `+-lft-identity_binary64_7564` `mul0-rgt_binary64_7563` `mul0-lft_binary64_7562` `div0_binary64_7561` `+-inverses_binary64_7559` `lft-mult-inverse_binary64_7558` `rgt-mult-inverse_binary64_7557` `remove-double-div_binary64_7556` `difference-of-sqr--1_binary64_7551` `difference-of-sqr-1_binary64_7550` `distribute-frac-neg_binary64_7543` `distribute-neg-out_binary64_7542` `distribute-lft1-in_binary64_7535` `associate--r-_binary64_7519` `associate--l-_binary64_7518`

Counts

57 → 47

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	70	662
1	213	632
2	781	626
3	2617	626

prune51.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	46	1	47
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	46	3	49

Error

Counts

49 → 3

Compiler

Compiled 820 to 454 computations (44.6% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
0.0b	(+.f64 (.f64 x 2) (.f64 x x))

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

9×	`add-log-exp_binary64_7619`
4×	`sum-log_binary64_7671`
2×	`pow1_binary64_7641` `add-exp-log_binary64_7618` `add-cbrt-cube_binary64_7616` `add-cube-cbrt_binary64_7615` `add-sqr-sqrt_binary64_7602` `flip3-+_binary64_7583` `*-un-lft-identity_binary64_7580` `flip-+_binary64_7554` `+-commutative_binary64_7510`
1×	`distribute-lft-out_binary64_7531` `associate-+l+_binary64_7513`

Counts

2 → 25

Calls

2 calls:

7.0ms	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
4.0ms	(+.f64 (.f64 x 2) (.f64 x x))

Compiler

Compiled 519 to 236 computations (54.5% saved)

series288.0ms (2.8%)

Error

Counts

2 → 21

Calls

2 calls:

197.0ms	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
78.0ms	(+.f64 (.f64 x 2) (.f64 x x))

Compiler

Compiled 425 to 348 computations (18.1% saved)

simplify124.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

427×	`cancel-sign-sub-inv_binary64_7546`
378×	`distribute-rgt-out_binary64_7533`
310×	`associate-l_binary64_7521`
286×	`unswap-sqr_binary64_7548`
285×	`distribute-rgt-in_binary64_7530`
265×	`associate-r_binary64_7520`
257×	`distribute-lft-in_binary64_7529`
234×	`distribute-lft-out_binary64_7531`
137×	`distribute-rgt-neg-in_binary64_7538`
109×	`distribute-lft-neg-in_binary64_7537`
101×	`associate--r+_binary64_7516`
99×	`sub-neg_binary64_7573`
91×	`sqr-pow_binary64_7552`
89×	`associate-+l+_binary64_7513`
82×	`associate-+l-_binary64_7515`
80×	`associate-+r-_binary64_7514`
79×	`*-commutative_binary64_7511`
70×	`associate--l+_binary64_7517`
65×	`associate-+r+_binary64_7512`
64×	`distribute-rgt-out--_binary64_7534`
55×	`pow-sqr_binary64_7553`
48×	`distribute-neg-in_binary64_7541` `distribute-lft-neg-out_binary64_7539`
43×	`+-commutative_binary64_7510`
42×	`associate-*l/_binary64_7523`
34×	`neg-sub0_binary64_7575`
33×	`pow-plus_binary64_7643`
32×	`neg-mul-1_binary64_7576` `distribute-lft-out--_binary64_7532` `associate-*r/_binary64_7522`
28×	`prod-exp_binary64_7629`
27×	`unsub-neg_binary64_7574`
21×	`difference-of-squares_binary64_7549` `associate-/r*_binary64_7524`
20×	`exp-prod_binary64_7632` `cube-prod_binary64_7608` `times-frac_binary64_7586`
19×	`distribute-rgt-neg-out_binary64_7540`
14×	`+-rgt-identity_binary64_7565` `associate-/r/_binary64_7526`
12×	`unpow3_binary64_7646`
11×	`cube-unmult_binary64_7617` `associate-/l/_binary64_7527`
9×	`associate-/l*_binary64_7525`
8×	`sub0-neg_binary64_7567`
7×	`swap-sqr_binary64_7547` `associate--r-_binary64_7519`
6×	`cube-mult_binary64_7610`
3×	`log-prod_binary64_7666` `unpow1_binary64_7638` `exp-sum_binary64_7626`
2×	`log-pow_binary64_7669` `unpow2_binary64_7645` `exp-lft-sqr_binary64_7635` `cancel-sign-sub_binary64_7545` `distribute-rgt1-in_binary64_7536` `count-2_binary64_7528`
1×	`exp-sqrt_binary64_7633` `1-exp_binary64_7624` `cube-div_binary64_7609` `-rgt-identity_binary64_7570` `-inverses_binary64_7560` `rgt-mult-inverse_binary64_7557` `distribute-neg-frac_binary64_7544` `distribute-lft1-in_binary64_7535`
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_7843` `erf-erfc_binary64_7842` `erf-odd_binary64_7841` `if-if-and-not_binary64_7840` `if-if-and_binary64_7839` `if-if-or-not_binary64_7838` `if-if-or_binary64_7837` `if-not_binary64_7836` `if-same_binary64_7835` `if-false_binary64_7834` `if-true_binary64_7833` `not-gte_binary64_7832` `not-lte_binary64_7831` `not-gt_binary64_7830` `not-lt_binary64_7829` `gte-same_binary64_7828` `lte-same_binary64_7827` `gt-same_binary64_7826` `lt-same_binary64_7825` `sinh---cosh_binary64_7772` `sinh-+-cosh_binary64_7771` `sinh-cosh_binary64_7770` `tanh-def-c_binary64_7769` `tanh-def-b_binary64_7768` `tanh-def-a_binary64_7767` `cosh-def_binary64_7766` `sinh-def_binary64_7765` `tan-neg_binary64_7712` `cos-neg_binary64_7711` `sin-neg_binary64_7710` `tan-0_binary64_7709` `cos-0_binary64_7708` `sin-0_binary64_7707` `hang-m-tan_binary64_7706` `hang-p-tan_binary64_7705` `hang-m0-tan_binary64_7704` `hang-p0-tan_binary64_7703` `hang-0m-tan_binary64_7702` `hang-0p-tan_binary64_7701` `tan-+PI/2_binary64_7700` `tan-+PI_binary64_7699` `tan-PI_binary64_7698` `tan-PI/3_binary64_7697` `tan-PI/4_binary64_7696` `tan-PI/6_binary64_7695` `cos-+PI/2_binary64_7694` `cos-+PI_binary64_7693` `cos-PI_binary64_7692` `cos-PI/2_binary64_7691` `cos-PI/3_binary64_7690` `cos-PI/4_binary64_7689` `cos-PI/6_binary64_7688` `sin-+PI/2_binary64_7687` `sin-+PI_binary64_7686` `sin-PI_binary64_7685` `sin-PI/2_binary64_7684` `sin-PI/3_binary64_7683` `sin-PI/4_binary64_7682` `sin-PI/6_binary64_7681` `sub-1-sin_binary64_7680` `sub-1-cos_binary64_7679` `-1-add-sin_binary64_7678` `-1-add-cos_binary64_7677` `1-sub-sin_binary64_7676` `1-sub-cos_binary64_7675` `cos-sin-sum_binary64_7674` `log-E_binary64_7670` `log-rec_binary64_7668` `log-div_binary64_7667` `pow-base-0_binary64_7664` `unpow1/3_binary64_7647` `unpow1/2_binary64_7644` `exp-to-pow_binary64_7642` `pow-base-1_binary64_7640` `unpow0_binary64_7639` `unpow-1_binary64_7637` `exp-lft-cube_binary64_7636` `exp-cbrt_binary64_7634` `div-exp_binary64_7631` `rec-exp_binary64_7630` `exp-diff_binary64_7628` `exp-neg_binary64_7627` `e-exp-1_binary64_7625` `exp-1-e_binary64_7623` `exp-0_binary64_7622` `rem-log-exp_binary64_7621` `rem-exp-log_binary64_7620` `cube-neg_binary64_7607` `rem-3cbrt-rft_binary64_7606` `rem-3cbrt-lft_binary64_7605` `rem-cbrt-cube_binary64_7604` `rem-cube-cbrt_binary64_7603` `sqr-abs_binary64_7595` `sqr-neg_binary64_7594` `rem-sqrt-square_binary64_7593` `rem-square-sqrt_binary64_7592` `div-sub_binary64_7585` `mul-1-neg_binary64_7572` `/-rgt-identity_binary64_7571` `*-lft-identity_binary64_7569` `remove-double-neg_binary64_7568` `--rgt-identity_binary64_7566` `+-lft-identity_binary64_7564` `mul0-rgt_binary64_7563` `mul0-lft_binary64_7562` `div0_binary64_7561` `+-inverses_binary64_7559` `lft-mult-inverse_binary64_7558` `remove-double-div_binary64_7556` `difference-of-sqr--1_binary64_7551` `difference-of-sqr-1_binary64_7550` `distribute-frac-neg_binary64_7543` `distribute-neg-out_binary64_7542` `associate--l-_binary64_7518`

Counts

46 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	58	604
1	196	565
2	743	559
3	2335	559

prune114.0ms (1.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	97	3	100

Error

Counts

100 → 3

Compiler

Compiled 2273 to 1223 computations (46.2% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (*.f64 y y) 3)
1.6b	(+.f64 (.f64 (.f64 x x) (.f64 (+.f64 2 x) (+.f64 2 x))) (.f64 (.f64 y y) (-.f64 (.f64 y y) (*.f64 x (+.f64 2 x)))))
3.9b	(.f64 (.f64 y y) (-.f64 (.f64 y y) (.f64 x (+.f64 2 x))))
35.8b	(/.f64 (+.f64 (pow.f64 (.f64 x (+.f64 2 x)) 3) (pow.f64 (.f64 y y) 3)) (+.f64 (.f64 (.f64 x x) (.f64 (+.f64 2 x) (+.f64 2 x))) (.f64 (.f64 y y) (-.f64 (.f64 y y) (*.f64 x (+.f64 2 x))))))

rewrite620.0ms (6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

74×	`associate-*r/_binary64_7522`
32×	`frac-add_binary64_7588`
27×	`flip3-+_binary64_7583` `flip-+_binary64_7554`
24×	`*-un-lft-identity_binary64_7580`
18×	`associate-/r/_binary64_7526`
17×	`pow1_binary64_7641` `add-sqr-sqrt_binary64_7602` `flip3--_binary64_7584` `flip--_binary64_7555`
16×	`add-cube-cbrt_binary64_7615` `frac-times_binary64_7590`
15×	`times-frac_binary64_7586`
14×	`add-exp-log_binary64_7618` `add-cbrt-cube_binary64_7616`
8×	`associate-*l/_binary64_7523` `distribute-rgt-in_binary64_7530` `distribute-lft-in_binary64_7529`
6×	`add-log-exp_binary64_7619` `pow-pow_binary64_7652`
5×	`associate-/l*_binary64_7525`
4×	`sum-cubes_binary64_7581` `distribute-lft-out_binary64_7531` `pow-prod-down_binary64_7651` `prod-exp_binary64_7629` `cbrt-unprod_binary64_7613` `sub-neg_binary64_7573` `cancel-sign-sub-inv_binary64_7546` `associate-+l+_binary64_7513` `associate-+r+_binary64_7512`
3×	`associate-/r_binary64_7524` `associate-r*_binary64_7520` `pow-unpow_binary64_7657`
2×	`associate-/l/_binary64_7527` `pow-exp_binary64_7648` `rem-cube-cbrt_binary64_7603`
1×	`div-exp_binary64_7631` `cbrt-undiv_binary64_7614` `frac-2neg_binary64_7591` `clear-num_binary64_7579` `div-inv_binary64_7577` `unswap-sqr_binary64_7548` `associate-l_binary64_7521` `*-commutative_binary64_7511` `sum-log_binary64_7671` `+-commutative_binary64_7510` `unpow-prod-down_binary64_7659` `pow2_binary64_7661` `pow-prod-up_binary64_7650` `pow-plus_binary64_7643` `pow-sqr_binary64_7553` `pow-to-exp_binary64_7649` `unpow3_binary64_7646` `cube-mult_binary64_7610` `cube-prod_binary64_7608` `sqr-pow_binary64_7552`

Counts

4 → 141

Calls

4 calls:

35.0ms	(/.f64 (+.f64 (pow.f64 (.f64 x (+.f64 2 x)) 3) (pow.f64 (.f64 y y) 3)) (+.f64 (.f64 (.f64 x x) (.f64 (+.f64 2 x) (+.f64 2 x))) (.f64 (.f64 y y) (-.f64 (.f64 y y) (*.f64 x (+.f64 2 x))))))
18.0ms	(+.f64 (.f64 (.f64 x x) (.f64 (+.f64 2 x) (+.f64 2 x))) (.f64 (.f64 y y) (-.f64 (.f64 y y) (*.f64 x (+.f64 2 x)))))
10.0ms	(.f64 (.f64 y y) (-.f64 (.f64 y y) (.f64 x (+.f64 2 x))))
4.0ms	(pow.f64 (*.f64 y y) 3)

Compiler

Compiled 10014 to 5509 computations (45% saved)

series2.5s (23.8%)

Error

Counts

4 → 54

Calls

4 calls:

1.4s	(/.f64 (+.f64 (pow.f64 (.f64 x (+.f64 2 x)) 3) (pow.f64 (.f64 y y) 3)) (+.f64 (.f64 (.f64 x x) (.f64 (+.f64 2 x) (+.f64 2 x))) (.f64 (.f64 y y) (-.f64 (.f64 y y) (*.f64 x (+.f64 2 x))))))
528.0ms	(+.f64 (.f64 (.f64 x x) (.f64 (+.f64 2 x) (+.f64 2 x))) (.f64 (.f64 y y) (-.f64 (.f64 y y) (*.f64 x (+.f64 2 x)))))
354.0ms	(.f64 (.f64 y y) (-.f64 (.f64 y y) (.f64 x (+.f64 2 x))))
65.0ms	(pow.f64 (*.f64 y y) 3)

Compiler

Compiled 4562 to 3463 computations (24.1% saved)

simplify1.7s (16.1%)

Algorithm

1×	egg-herbie

Rules

793×	`associate-l_binary64_7521`
744×	`associate-r_binary64_7520`
446×	`distribute-rgt-in_binary64_7530`
429×	`distribute-lft-in_binary64_7529`
135×	`unswap-sqr_binary64_7548`
111×	`cancel-sign-sub-inv_binary64_7546`
88×	`*-commutative_binary64_7511`
58×	`times-frac_binary64_7586`
53×	`associate-/l*_binary64_7525`
52×	`associate-/r*_binary64_7524`
49×	`sqr-pow_binary64_7552` `distribute-rgt-neg-in_binary64_7538`
46×	`+-commutative_binary64_7510`
44×	`sub-neg_binary64_7573`
40×	`associate-/l/_binary64_7527`
38×	`distribute-lft-neg-in_binary64_7537`
34×	`associate-*l/_binary64_7523`
24×	`exp-prod_binary64_7632`
23×	`pow-sqr_binary64_7553` `associate-/r/_binary64_7526` `associate-*r/_binary64_7522`
22×	`cube-prod_binary64_7608`
20×	`neg-sub0_binary64_7575`
19×	`neg-mul-1_binary64_7576`
16×	`swap-sqr_binary64_7547`
14×	`log-prod_binary64_7666` `associate-+r+_binary64_7512`
13×	`distribute-neg-in_binary64_7541`
12×	`distribute-lft-neg-out_binary64_7539`
11×	`unpow3_binary64_7646`
10×	`cube-mult_binary64_7610`
8×	`div-sub_binary64_7585` `difference-of-squares_binary64_7549` `distribute-rgt-out_binary64_7533`
6×	`distribute-rgt-out--_binary64_7534` `distribute-lft-out_binary64_7531`
5×	`/-rgt-identity_binary64_7571` `distribute-rgt-neg-out_binary64_7540` `associate--l+_binary64_7517` `associate--r+_binary64_7516`
4×	`pow-plus_binary64_7643` `cube-unmult_binary64_7617` `associate-+r-_binary64_7514`
3×	`log-div_binary64_7667` `unpow2_binary64_7645` `unsub-neg_binary64_7574` `*-rgt-identity_binary64_7570`
2×	`log-pow_binary64_7669` `exp-diff_binary64_7628` `rem-sqrt-square_binary64_7593` `mul-1-neg_binary64_7572` `distribute-neg-frac_binary64_7544` `count-2_binary64_7528`
1×	`unpow1_binary64_7638` `div-exp_binary64_7631` `rec-exp_binary64_7630` `prod-exp_binary64_7629` `exp-sum_binary64_7626` `1-exp_binary64_7624` `rem-cbrt-cube_binary64_7604` `-lft-identity_binary64_7569` `-inverses_binary64_7560` `distribute-rgt1-in_binary64_7536` `distribute-lft-out--_binary64_7532` `associate-+l+_binary64_7513`
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_7843` `erf-erfc_binary64_7842` `erf-odd_binary64_7841` `if-if-and-not_binary64_7840` `if-if-and_binary64_7839` `if-if-or-not_binary64_7838` `if-if-or_binary64_7837` `if-not_binary64_7836` `if-same_binary64_7835` `if-false_binary64_7834` `if-true_binary64_7833` `not-gte_binary64_7832` `not-lte_binary64_7831` `not-gt_binary64_7830` `not-lt_binary64_7829` `gte-same_binary64_7828` `lte-same_binary64_7827` `gt-same_binary64_7826` `lt-same_binary64_7825` `sinh---cosh_binary64_7772` `sinh-+-cosh_binary64_7771` `sinh-cosh_binary64_7770` `tanh-def-c_binary64_7769` `tanh-def-b_binary64_7768` `tanh-def-a_binary64_7767` `cosh-def_binary64_7766` `sinh-def_binary64_7765` `tan-neg_binary64_7712` `cos-neg_binary64_7711` `sin-neg_binary64_7710` `tan-0_binary64_7709` `cos-0_binary64_7708` `sin-0_binary64_7707` `hang-m-tan_binary64_7706` `hang-p-tan_binary64_7705` `hang-m0-tan_binary64_7704` `hang-p0-tan_binary64_7703` `hang-0m-tan_binary64_7702` `hang-0p-tan_binary64_7701` `tan-+PI/2_binary64_7700` `tan-+PI_binary64_7699` `tan-PI_binary64_7698` `tan-PI/3_binary64_7697` `tan-PI/4_binary64_7696` `tan-PI/6_binary64_7695` `cos-+PI/2_binary64_7694` `cos-+PI_binary64_7693` `cos-PI_binary64_7692` `cos-PI/2_binary64_7691` `cos-PI/3_binary64_7690` `cos-PI/4_binary64_7689` `cos-PI/6_binary64_7688` `sin-+PI/2_binary64_7687` `sin-+PI_binary64_7686` `sin-PI_binary64_7685` `sin-PI/2_binary64_7684` `sin-PI/3_binary64_7683` `sin-PI/4_binary64_7682` `sin-PI/6_binary64_7681` `sub-1-sin_binary64_7680` `sub-1-cos_binary64_7679` `-1-add-sin_binary64_7678` `-1-add-cos_binary64_7677` `1-sub-sin_binary64_7676` `1-sub-cos_binary64_7675` `cos-sin-sum_binary64_7674` `log-E_binary64_7670` `log-rec_binary64_7668` `pow-base-0_binary64_7664` `unpow1/3_binary64_7647` `unpow1/2_binary64_7644` `exp-to-pow_binary64_7642` `pow-base-1_binary64_7640` `unpow0_binary64_7639` `unpow-1_binary64_7637` `exp-lft-cube_binary64_7636` `exp-lft-sqr_binary64_7635` `exp-cbrt_binary64_7634` `exp-sqrt_binary64_7633` `exp-neg_binary64_7627` `e-exp-1_binary64_7625` `exp-1-e_binary64_7623` `exp-0_binary64_7622` `rem-log-exp_binary64_7621` `rem-exp-log_binary64_7620` `cube-div_binary64_7609` `cube-neg_binary64_7607` `rem-3cbrt-rft_binary64_7606` `rem-3cbrt-lft_binary64_7605` `rem-cube-cbrt_binary64_7603` `sqr-abs_binary64_7595` `sqr-neg_binary64_7594` `rem-square-sqrt_binary64_7592` `remove-double-neg_binary64_7568` `sub0-neg_binary64_7567` `--rgt-identity_binary64_7566` `+-rgt-identity_binary64_7565` `+-lft-identity_binary64_7564` `mul0-rgt_binary64_7563` `mul0-lft_binary64_7562` `div0_binary64_7561` `+-inverses_binary64_7559` `lft-mult-inverse_binary64_7558` `rgt-mult-inverse_binary64_7557` `remove-double-div_binary64_7556` `difference-of-sqr--1_binary64_7551` `difference-of-sqr-1_binary64_7550` `cancel-sign-sub_binary64_7545` `distribute-frac-neg_binary64_7543` `distribute-neg-out_binary64_7542` `distribute-lft1-in_binary64_7535` `associate--r-_binary64_7519` `associate--l-_binary64_7518` `associate-+l-_binary64_7515`

Counts

195 → 429

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	359	10343
1	1051	9962

prune3.3s (32.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	429	0	429
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	429	3	432

Error

Counts

432 → 3

Compiler

Compiled 32447 to 19778 computations (39% saved)

regimes164.0ms (1.6%)

Accuracy

Total 0.0b remaining (62.3%)

Threshold costs 0.0b (62.3%)

Compiler

Compiled 1206 to 942 computations (21.9% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64_7510`
1×	`*-commutative_binary64_7511`
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_7840` `if-if-and_binary64_7839` `if-if-or-not_binary64_7838` `if-if-or_binary64_7837` `if-not_binary64_7836` `if-same_binary64_7835` `if-false_binary64_7834` `if-true_binary64_7833` `tan-0_binary64_7709` `cos-0_binary64_7708` `sin-0_binary64_7707` `unpow1_binary64_7638` `e-exp-1_binary64_7625` `1-exp_binary64_7624` `exp-1-e_binary64_7623` `exp-0_binary64_7622` `sqr-abs_binary64_7595` `sqr-neg_binary64_7594` `neg-mul-1_binary64_7576` `neg-sub0_binary64_7575` `unsub-neg_binary64_7574` `sub-neg_binary64_7573` `mul-1-neg_binary64_7572` `/-rgt-identity_binary64_7571` `-rgt-identity_binary64_7570` `-lft-identity_binary64_7569` `remove-double-neg_binary64_7568` `sub0-neg_binary64_7567` `--rgt-identity_binary64_7566` `+-rgt-identity_binary64_7565` `+-lft-identity_binary64_7564` `cancel-sign-sub-inv_binary64_7546` `cancel-sign-sub_binary64_7545` `distribute-neg-frac_binary64_7544` `distribute-frac-neg_binary64_7543` `distribute-neg-out_binary64_7542` `distribute-neg-in_binary64_7541` `distribute-rgt-neg-out_binary64_7540` `distribute-lft-neg-out_binary64_7539` `distribute-rgt-neg-in_binary64_7538` `distribute-lft-neg-in_binary64_7537`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	12	16

Proof

(+ f64 (+ f64 (* f64 h0 2) (* f64 h0 h0)) (* f64 h1 h1))

end0.0ms (0%)

sample737.0ms (7.1%)

Algorithm

1×

intervals

Results

232.0ms	8000×	body	128	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 266 to 207 computations (22.2% saved)

Details

analyze72.0ms (0.7%)

sample15.0ms (0.1%)

simplify162.0ms (1.6%)

prune5.0ms (0%)

localize6.0ms (0.1%)

rewrite47.0ms (0.5%)

series275.0ms (2.7%)

simplify146.0ms (1.4%)

prune51.0ms (0.5%)

localize7.0ms (0.1%)

rewrite38.0ms (0.4%)

series288.0ms (2.8%)

simplify124.0ms (1.2%)

prune114.0ms (1.1%)

localize17.0ms (0.2%)

rewrite620.0ms (6%)

series2.5s (23.8%)

simplify1.7s (16.1%)

prune3.3s (32.1%)

regimes164.0ms (1.6%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample737.0ms (7.1%)

Profiling