Details

analyze101.0ms (1.4%)

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
37.5%	62.4%	0.1%	6
56.2%	43.7%	0.1%	7
65.6%	34.3%	0.1%	8
76.5%	23.4%	0.1%	9
82%	18%	0.1%	10
87.8%	12.1%	0.1%	11
90.7%	9.2%	0.1%	12
93.8%	6.1%	0.1%	13
95.3%	4.6%	0.1%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample21.0ms (0.3%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

128

valid

Compiler

Compiled 17 to 15 computations (11.8% saved)

simplify159.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1× +-commutative_binary64_32744

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_33077 erf-erfc_binary64_33076 erf-odd_binary64_33075 if-if-and-not_binary64_33074 if-if-and_binary64_33073 if-if-or-not_binary64_33072 if-if-or_binary64_33071 if-not_binary64_33070 if-same_binary64_33069 if-false_binary64_33068 if-true_binary64_33067 not-gte_binary64_33066 not-lte_binary64_33065 not-gt_binary64_33064 not-lt_binary64_33063 gte-same_binary64_33062 lte-same_binary64_33061 gt-same_binary64_33060 lt-same_binary64_33059 sinh---cosh_binary64_33006 sinh-+-cosh_binary64_33005 sinh-cosh_binary64_33004 tanh-def-c_binary64_33003 tanh-def-b_binary64_33002 tanh-def-a_binary64_33001 cosh-def_binary64_33000 sinh-def_binary64_32999 tan-neg_binary64_32946 cos-neg_binary64_32945 sin-neg_binary64_32944 tan-0_binary64_32943 cos-0_binary64_32942 sin-0_binary64_32941 hang-m-tan_binary64_32940 hang-p-tan_binary64_32939 hang-m0-tan_binary64_32938 hang-p0-tan_binary64_32937 hang-0m-tan_binary64_32936 hang-0p-tan_binary64_32935 tan-+PI/2_binary64_32934 tan-+PI_binary64_32933 tan-PI_binary64_32932 tan-PI/3_binary64_32931 tan-PI/4_binary64_32930 tan-PI/6_binary64_32929 cos-+PI/2_binary64_32928 cos-+PI_binary64_32927 cos-PI_binary64_32926 cos-PI/2_binary64_32925 cos-PI/3_binary64_32924 cos-PI/4_binary64_32923 cos-PI/6_binary64_32922 sin-+PI/2_binary64_32921 sin-+PI_binary64_32920 sin-PI_binary64_32919 sin-PI/2_binary64_32918 sin-PI/3_binary64_32917 sin-PI/4_binary64_32916 sin-PI/6_binary64_32915 sub-1-sin_binary64_32914 sub-1-cos_binary64_32913 -1-add-sin_binary64_32912 -1-add-cos_binary64_32911 1-sub-sin_binary64_32910 1-sub-cos_binary64_32909 cos-sin-sum_binary64_32908 log-E_binary64_32904 log-pow_binary64_32903 log-rec_binary64_32902 log-div_binary64_32901 log-prod_binary64_32900 pow-base-0_binary64_32898 unpow1/3_binary64_32881 unpow3_binary64_32880 unpow2_binary64_32879 unpow1/2_binary64_32878 pow-plus_binary64_32877 exp-to-pow_binary64_32876 pow-base-1_binary64_32874 unpow0_binary64_32873 unpow1_binary64_32872 unpow-1_binary64_32871 exp-lft-cube_binary64_32870 exp-lft-sqr_binary64_32869 exp-cbrt_binary64_32868 exp-sqrt_binary64_32867 exp-prod_binary64_32866 div-exp_binary64_32865 rec-exp_binary64_32864 prod-exp_binary64_32863 exp-diff_binary64_32862 exp-neg_binary64_32861 exp-sum_binary64_32860 e-exp-1_binary64_32859 1-exp_binary64_32858 exp-1-e_binary64_32857 exp-0_binary64_32856 rem-log-exp_binary64_32855 rem-exp-log_binary64_32854 cube-unmult_binary64_32851 cube-mult_binary64_32844 cube-div_binary64_32843 cube-prod_binary64_32842 cube-neg_binary64_32841 rem-3cbrt-rft_binary64_32840 rem-3cbrt-lft_binary64_32839 rem-cbrt-cube_binary64_32838 rem-cube-cbrt_binary64_32837 sqr-abs_binary64_32829 sqr-neg_binary64_32828 rem-sqrt-square_binary64_32827 rem-square-sqrt_binary64_32826 times-frac_binary64_32820 div-sub_binary64_32819 neg-mul-1_binary64_32810 neg-sub0_binary64_32809 unsub-neg_binary64_32808 sub-neg_binary64_32807 mul-1-neg_binary64_32806 /-rgt-identity_binary64_32805 *-rgt-identity_binary64_32804 *-lft-identity_binary64_32803 remove-double-neg_binary64_32802 sub0-neg_binary64_32801 --rgt-identity_binary64_32800 +-rgt-identity_binary64_32799 +-lft-identity_binary64_32798 mul0-rgt_binary64_32797 mul0-lft_binary64_32796 div0_binary64_32795 *-inverses_binary64_32794 +-inverses_binary64_32793 lft-mult-inverse_binary64_32792 rgt-mult-inverse_binary64_32791 remove-double-div_binary64_32790 pow-sqr_binary64_32787 sqr-pow_binary64_32786 difference-of-sqr--1_binary64_32785 difference-of-sqr-1_binary64_32784 difference-of-squares_binary64_32783 unswap-sqr_binary64_32782 swap-sqr_binary64_32781 cancel-sign-sub-inv_binary64_32780 cancel-sign-sub_binary64_32779 distribute-neg-frac_binary64_32778 distribute-frac-neg_binary64_32777 distribute-neg-out_binary64_32776 distribute-neg-in_binary64_32775 distribute-rgt-neg-out_binary64_32774 distribute-lft-neg-out_binary64_32773 distribute-rgt-neg-in_binary64_32772 distribute-lft-neg-in_binary64_32771 distribute-rgt1-in_binary64_32770 distribute-lft1-in_binary64_32769 distribute-rgt-out--_binary64_32768 distribute-rgt-out_binary64_32767 distribute-lft-out--_binary64_32766 distribute-lft-out_binary64_32765 distribute-rgt-in_binary64_32764 distribute-lft-in_binary64_32763 count-2_binary64_32762 associate-/l/_binary64_32761 associate-/r/_binary64_32760 associate-/l*_binary64_32759 associate-/r*_binary64_32758 associate-*l/_binary64_32757 associate-*r/_binary64_32756 associate-*l*_binary64_32755 associate-*r*_binary64_32754 associate--r-_binary64_32753 associate--l-_binary64_32752 associate--l+_binary64_32751 associate--r+_binary64_32750 associate-+l-_binary64_32749 associate-+r-_binary64_32748 associate-+l+_binary64_32747 associate-+r+_binary64_32746 *-commutative_binary64_32745

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	8	12

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

28.7b

Counts

1 → 1

Compiler

Compiled 8 to 6 computations (25% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

26.9b

(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

28.7b

Rules

3×	`add-sqr-sqrt_binary64_32836` `sqrt-prod_binary64_32830`
2×	`pow1_binary64_32875` `add-cube-cbrt_binary64_32849` `sqrt-div_binary64_32831` `*-un-lft-identity_binary64_32814`
1×	`pow1/2_binary64_32894` `add-log-exp_binary64_32853` `add-exp-log_binary64_32852` `add-cbrt-cube_binary64_32850` `sqrt-pow1_binary64_32832` `flip3-+_binary64_32817` `flip-+_binary64_32788` `rem-sqrt-square_binary64_32827`

Counts

1 → 15

Calls

1 calls:

6.0ms

(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))

Compiler

Compiled 264 to 55 computations (79.2% saved)

series115.0ms (1.7%)

Error

0.3b

Counts

1 → 11

Calls

1 calls:

104.0ms

(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 y y)))

Compiler

Compiled 259 to 216 computations (16.6% saved)

simplify101.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

845×	`times-frac_binary64_32820`
394×	`cancel-sign-sub-inv_binary64_32780`
268×	`unswap-sqr_binary64_32782`
148×	`distribute-rgt-in_binary64_32764`
147×	`distribute-rgt-neg-in_binary64_32772`
130×	`distribute-lft-neg-in_binary64_32771` `associate-r_binary64_32754`
120×	`associate-l_binary64_32755`
118×	`associate-/l/_binary64_32761`
117×	`sub-neg_binary64_32807`
111×	`distribute-lft-in_binary64_32763`
98×	`sqr-pow_binary64_32786`
76×	`associate-/l*_binary64_32759`
65×	`pow-sqr_binary64_32787`
51×	`associate-/r*_binary64_32758`
49×	`*-commutative_binary64_32745`
48×	`difference-of-squares_binary64_32783`
45×	`neg-sub0_binary64_32809`
43×	`distribute-neg-frac_binary64_32778`
42×	`neg-mul-1_binary64_32810`
40×	`pow-plus_binary64_32877`
37×	`distribute-rgt-out_binary64_32767` `associate-*l/_binary64_32757`
32×	`distribute-lft-neg-out_binary64_32773`
29×	`associate-*r/_binary64_32756` `+-commutative_binary64_32744`
24×	`associate-+l-_binary64_32749`
23×	`associate-+r-_binary64_32748`
22×	`associate-+l+_binary64_32747`
20×	`distribute-rgt-out--_binary64_32768`
19×	`unsub-neg_binary64_32808` `associate-+r+_binary64_32746`
18×	`+-rgt-identity_binary64_32799` `distribute-neg-in_binary64_32775`
15×	`associate--r+_binary64_32750`
13×	`cube-unmult_binary64_32851`
12×	`cube-prod_binary64_32842` `distribute-rgt-neg-out_binary64_32774`
11×	`sub0-neg_binary64_32801`
10×	`associate-/r/_binary64_32760`
9×	`div-sub_binary64_32819` `distribute-lft-out--_binary64_32766`
8×	`unpow3_binary64_32880`
7×	`cancel-sign-sub_binary64_32779`
6×	`distribute-lft-out_binary64_32765`
5×	`associate--l+_binary64_32751`
4×	`cube-mult_binary64_32844` `distribute-neg-out_binary64_32776` `associate--l-_binary64_32752`
2×	`unpow2_binary64_32879` `unpow1_binary64_32872` `rem-sqrt-square_binary64_32827` `mul-1-neg_binary64_32806` `swap-sqr_binary64_32781` `count-2_binary64_32762`
1×	`1-exp_binary64_32858` `rem-square-sqrt_binary64_32826` `-rgt-identity_binary64_32804` `-inverses_binary64_32794` `rgt-mult-inverse_binary64_32791` `distribute-rgt1-in_binary64_32770`
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_33077` `erf-erfc_binary64_33076` `erf-odd_binary64_33075` `if-if-and-not_binary64_33074` `if-if-and_binary64_33073` `if-if-or-not_binary64_33072` `if-if-or_binary64_33071` `if-not_binary64_33070` `if-same_binary64_33069` `if-false_binary64_33068` `if-true_binary64_33067` `not-gte_binary64_33066` `not-lte_binary64_33065` `not-gt_binary64_33064` `not-lt_binary64_33063` `gte-same_binary64_33062` `lte-same_binary64_33061` `gt-same_binary64_33060` `lt-same_binary64_33059` `sinh---cosh_binary64_33006` `sinh-+-cosh_binary64_33005` `sinh-cosh_binary64_33004` `tanh-def-c_binary64_33003` `tanh-def-b_binary64_33002` `tanh-def-a_binary64_33001` `cosh-def_binary64_33000` `sinh-def_binary64_32999` `tan-neg_binary64_32946` `cos-neg_binary64_32945` `sin-neg_binary64_32944` `tan-0_binary64_32943` `cos-0_binary64_32942` `sin-0_binary64_32941` `hang-m-tan_binary64_32940` `hang-p-tan_binary64_32939` `hang-m0-tan_binary64_32938` `hang-p0-tan_binary64_32937` `hang-0m-tan_binary64_32936` `hang-0p-tan_binary64_32935` `tan-+PI/2_binary64_32934` `tan-+PI_binary64_32933` `tan-PI_binary64_32932` `tan-PI/3_binary64_32931` `tan-PI/4_binary64_32930` `tan-PI/6_binary64_32929` `cos-+PI/2_binary64_32928` `cos-+PI_binary64_32927` `cos-PI_binary64_32926` `cos-PI/2_binary64_32925` `cos-PI/3_binary64_32924` `cos-PI/4_binary64_32923` `cos-PI/6_binary64_32922` `sin-+PI/2_binary64_32921` `sin-+PI_binary64_32920` `sin-PI_binary64_32919` `sin-PI/2_binary64_32918` `sin-PI/3_binary64_32917` `sin-PI/4_binary64_32916` `sin-PI/6_binary64_32915` `sub-1-sin_binary64_32914` `sub-1-cos_binary64_32913` `-1-add-sin_binary64_32912` `-1-add-cos_binary64_32911` `1-sub-sin_binary64_32910` `1-sub-cos_binary64_32909` `cos-sin-sum_binary64_32908` `log-E_binary64_32904` `log-pow_binary64_32903` `log-rec_binary64_32902` `log-div_binary64_32901` `log-prod_binary64_32900` `pow-base-0_binary64_32898` `unpow1/3_binary64_32881` `unpow1/2_binary64_32878` `exp-to-pow_binary64_32876` `pow-base-1_binary64_32874` `unpow0_binary64_32873` `unpow-1_binary64_32871` `exp-lft-cube_binary64_32870` `exp-lft-sqr_binary64_32869` `exp-cbrt_binary64_32868` `exp-sqrt_binary64_32867` `exp-prod_binary64_32866` `div-exp_binary64_32865` `rec-exp_binary64_32864` `prod-exp_binary64_32863` `exp-diff_binary64_32862` `exp-neg_binary64_32861` `exp-sum_binary64_32860` `e-exp-1_binary64_32859` `exp-1-e_binary64_32857` `exp-0_binary64_32856` `rem-log-exp_binary64_32855` `rem-exp-log_binary64_32854` `cube-div_binary64_32843` `cube-neg_binary64_32841` `rem-3cbrt-rft_binary64_32840` `rem-3cbrt-lft_binary64_32839` `rem-cbrt-cube_binary64_32838` `rem-cube-cbrt_binary64_32837` `sqr-abs_binary64_32829` `sqr-neg_binary64_32828` `/-rgt-identity_binary64_32805` `*-lft-identity_binary64_32803` `remove-double-neg_binary64_32802` `--rgt-identity_binary64_32800` `+-lft-identity_binary64_32798` `mul0-rgt_binary64_32797` `mul0-lft_binary64_32796` `div0_binary64_32795` `+-inverses_binary64_32793` `lft-mult-inverse_binary64_32792` `remove-double-div_binary64_32790` `difference-of-sqr--1_binary64_32785` `difference-of-sqr-1_binary64_32784` `distribute-frac-neg_binary64_32777` `distribute-lft1-in_binary64_32769` `associate--r-_binary64_32753`

Counts

26 → 56

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	72	413
1	188	404
2	627	404
3	1654	404

prune72.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	51	5	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	51	6	57

Error

16.2b

Counts

57 → 6

Compiler

Compiled 1246 to 530 computations (57.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
0.3b	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 y y) (.f64 x x)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
27.9b	(cbrt.f64 (+.f64 (.f64 y y) (.f64 x x)))
27.9b	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite125.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

16.2b

Rules

20×	`add-sqr-sqrt_binary64_32836`
14×	`cbrt-prod_binary64_32845` `sqrt-prod_binary64_32830`
12×	`add-cube-cbrt_binary64_32849` `*-un-lft-identity_binary64_32814`
9×	`associate-r_binary64_32754`
8×	`cbrt-div_binary64_32846`
7×	`pow1_binary64_32875`
6×	`add-exp-log_binary64_32852` `add-cbrt-cube_binary64_32850`
4×	`add-log-exp_binary64_32853` `flip3-+_binary64_32817` `flip-+_binary64_32788` `sqrt-div_binary64_32831`
3×	`pow1/3_binary64_32896` `unswap-sqr_binary64_32782` `associate-l_binary64_32755`
2×	`associate-*r/_binary64_32756` `sqrt-pow1_binary64_32832` `rem-sqrt-square_binary64_32827`
1×	`pow-prod-down_binary64_32885` `prod-exp_binary64_32863` `cbrt-unprod_binary64_32847` `*-commutative_binary64_32745` `pow1/2_binary64_32894`

Counts

4 → 74

Calls

4 calls:

10.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 y y) (.f64 x x)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
8.0ms	(cbrt.f64 (+.f64 (.f64 y y) (.f64 x x)))
5.0ms	(sqrt.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
4.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 2308 to 292 computations (87.3% saved)

series1.2s (17.9%)

Error

16.2b

Counts

4 → 54

Calls

4 calls:

357.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
348.0ms	(cbrt.f64 (+.f64 (.f64 y y) (.f64 x x)))
288.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 y y) (.f64 x x)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
163.0ms	(sqrt.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))))

Compiler

Compiled 3920 to 2977 computations (24.1% saved)

simplify662.0ms (9.5%)

Algorithm

1×	egg-herbie

Rules

603×	`unswap-sqr_binary64_32782`
318×	`cancel-sign-sub-inv_binary64_32780`
290×	`times-frac_binary64_32820`
289×	`*-commutative_binary64_32745`
234×	`sqr-pow_binary64_32786`
190×	`associate-r_binary64_32754`
176×	`associate-l_binary64_32755`
158×	`pow-sqr_binary64_32787`
115×	`sub-neg_binary64_32807`
99×	`distribute-rgt-neg-in_binary64_32772`
89×	`log-prod_binary64_32900`
80×	`distribute-lft-neg-in_binary64_32771`
62×	`distribute-rgt-in_binary64_32764`
60×	`+-commutative_binary64_32744`
57×	`neg-sub0_binary64_32809` `associate-*r/_binary64_32756`
55×	`neg-mul-1_binary64_32810`
52×	`difference-of-squares_binary64_32783`
48×	`distribute-lft-in_binary64_32763`
43×	`associate-*l/_binary64_32757`
41×	`associate-+l+_binary64_32747`
34×	`associate-+r+_binary64_32746`
32×	`pow-plus_binary64_32877`
28×	`associate--l+_binary64_32751`
27×	`*-rgt-identity_binary64_32804` `associate-+r-_binary64_32748`
23×	`*-lft-identity_binary64_32803` `+-rgt-identity_binary64_32799`
21×	`associate-/r*_binary64_32758`
20×	`exp-prod_binary64_32866` `distribute-lft-neg-out_binary64_32773` `associate-+l-_binary64_32749`
19×	`cube-prod_binary64_32842`
18×	`associate-/l/_binary64_32761`
15×	`log-div_binary64_32901` `unsub-neg_binary64_32808` `distribute-rgt-out--_binary64_32768`
14×	`unpow1/3_binary64_32881` `rem-sqrt-square_binary64_32827`
12×	`log-pow_binary64_32903`
11×	`distribute-neg-frac_binary64_32778`
10×	`cube-unmult_binary64_32851` `sub0-neg_binary64_32801`
9×	`unpow3_binary64_32880` `cube-div_binary64_32843`
8×	`exp-sqrt_binary64_32867` `distribute-rgt-out_binary64_32767`
7×	`swap-sqr_binary64_32781`
2×	`unpow2_binary64_32879` `unpow1_binary64_32872` `cube-mult_binary64_32844` `rem-3cbrt-lft_binary64_32839` `mul-1-neg_binary64_32806` `distribute-rgt-neg-out_binary64_32774` `distribute-lft-out--_binary64_32766` `count-2_binary64_32762`
1×	`exp-lft-sqr_binary64_32869` `prod-exp_binary64_32863` `exp-diff_binary64_32862` `1-exp_binary64_32858` `exp-1-e_binary64_32857` `rem-log-exp_binary64_32855` `sqr-abs_binary64_32829` `rem-square-sqrt_binary64_32826` `*-inverses_binary64_32794` `rgt-mult-inverse_binary64_32791`
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_33077` `erf-erfc_binary64_33076` `erf-odd_binary64_33075` `if-if-and-not_binary64_33074` `if-if-and_binary64_33073` `if-if-or-not_binary64_33072` `if-if-or_binary64_33071` `if-not_binary64_33070` `if-same_binary64_33069` `if-false_binary64_33068` `if-true_binary64_33067` `not-gte_binary64_33066` `not-lte_binary64_33065` `not-gt_binary64_33064` `not-lt_binary64_33063` `gte-same_binary64_33062` `lte-same_binary64_33061` `gt-same_binary64_33060` `lt-same_binary64_33059` `sinh---cosh_binary64_33006` `sinh-+-cosh_binary64_33005` `sinh-cosh_binary64_33004` `tanh-def-c_binary64_33003` `tanh-def-b_binary64_33002` `tanh-def-a_binary64_33001` `cosh-def_binary64_33000` `sinh-def_binary64_32999` `tan-neg_binary64_32946` `cos-neg_binary64_32945` `sin-neg_binary64_32944` `tan-0_binary64_32943` `cos-0_binary64_32942` `sin-0_binary64_32941` `hang-m-tan_binary64_32940` `hang-p-tan_binary64_32939` `hang-m0-tan_binary64_32938` `hang-p0-tan_binary64_32937` `hang-0m-tan_binary64_32936` `hang-0p-tan_binary64_32935` `tan-+PI/2_binary64_32934` `tan-+PI_binary64_32933` `tan-PI_binary64_32932` `tan-PI/3_binary64_32931` `tan-PI/4_binary64_32930` `tan-PI/6_binary64_32929` `cos-+PI/2_binary64_32928` `cos-+PI_binary64_32927` `cos-PI_binary64_32926` `cos-PI/2_binary64_32925` `cos-PI/3_binary64_32924` `cos-PI/4_binary64_32923` `cos-PI/6_binary64_32922` `sin-+PI/2_binary64_32921` `sin-+PI_binary64_32920` `sin-PI_binary64_32919` `sin-PI/2_binary64_32918` `sin-PI/3_binary64_32917` `sin-PI/4_binary64_32916` `sin-PI/6_binary64_32915` `sub-1-sin_binary64_32914` `sub-1-cos_binary64_32913` `-1-add-sin_binary64_32912` `-1-add-cos_binary64_32911` `1-sub-sin_binary64_32910` `1-sub-cos_binary64_32909` `cos-sin-sum_binary64_32908` `log-E_binary64_32904` `log-rec_binary64_32902` `pow-base-0_binary64_32898` `unpow1/2_binary64_32878` `exp-to-pow_binary64_32876` `pow-base-1_binary64_32874` `unpow0_binary64_32873` `unpow-1_binary64_32871` `exp-lft-cube_binary64_32870` `exp-cbrt_binary64_32868` `div-exp_binary64_32865` `rec-exp_binary64_32864` `exp-neg_binary64_32861` `exp-sum_binary64_32860` `e-exp-1_binary64_32859` `exp-0_binary64_32856` `rem-exp-log_binary64_32854` `cube-neg_binary64_32841` `rem-3cbrt-rft_binary64_32840` `rem-cbrt-cube_binary64_32838` `rem-cube-cbrt_binary64_32837` `sqr-neg_binary64_32828` `div-sub_binary64_32819` `/-rgt-identity_binary64_32805` `remove-double-neg_binary64_32802` `--rgt-identity_binary64_32800` `+-lft-identity_binary64_32798` `mul0-rgt_binary64_32797` `mul0-lft_binary64_32796` `div0_binary64_32795` `+-inverses_binary64_32793` `lft-mult-inverse_binary64_32792` `remove-double-div_binary64_32790` `difference-of-sqr--1_binary64_32785` `difference-of-sqr-1_binary64_32784` `cancel-sign-sub_binary64_32779` `distribute-frac-neg_binary64_32777` `distribute-neg-out_binary64_32776` `distribute-neg-in_binary64_32775` `distribute-rgt1-in_binary64_32770` `distribute-lft1-in_binary64_32769` `distribute-lft-out_binary64_32765` `associate-/r/_binary64_32760` `associate-/l*_binary64_32759` `associate--r-_binary64_32753` `associate--l-_binary64_32752` `associate--r+_binary64_32750`

Counts

128 → 255

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	197	3614
1	459	3512
2	1435	3448
3	2623	3448

prune437.0ms (6.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	254	1	255
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	254	7	261

Error

16.2b

Counts

261 → 7

Compiler

Compiled 9131 to 3090 computations (66.2% saved)

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

16.2b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 16.2b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

prune4.0ms (0.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	2	2
Total	7	7

Error

16.2b

Counts

7 → 7

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (neg.f64 y) (*.f64 1/2 (/.f64 x (/.f64 y x))))
0.2b	(/.f64 x (/.f64 y x))

rewrite109.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

16.2b

Rules

75×	`times-frac_binary64_32820`
44×	`add-cube-cbrt_binary64_32849` `add-sqr-sqrt_binary64_32836` `*-un-lft-identity_binary64_32814`
13×	`associate-/r*_binary64_32758`
7×	`add-exp-log_binary64_32852` `add-cbrt-cube_binary64_32850`
6×	`add-log-exp_binary64_32853`
5×	`div-inv_binary64_32811`
3×	`div-exp_binary64_32865` `cbrt-undiv_binary64_32848` `associate-/l*_binary64_32759`
2×	`pow1_binary64_32875` `diff-log_binary64_32906`
1×	`frac-2neg_binary64_32825` `clear-num_binary64_32813` `associate-/r/_binary64_32760` `neg-log_binary64_32907` `flip3--_binary64_32818` `sub-neg_binary64_32807` `flip--_binary64_32789` `cancel-sign-sub-inv_binary64_32780` `neg-sub0_binary64_32809` `associate--l-_binary64_32752`

Counts

2 → 84

Calls

2 calls:

6.0ms	(/.f64 x (/.f64 y x))
5.0ms	(-.f64 (neg.f64 y) (*.f64 1/2 (/.f64 x (/.f64 y x))))

Compiler

Compiled 1639 to 601 computations (63.3% saved)

series320.0ms (4.6%)

Error

16.2b

Counts

2 → 18

Calls

2 calls:

194.0ms	(-.f64 (neg.f64 y) (*.f64 1/2 (/.f64 x (/.f64 y x))))
114.0ms	(/.f64 x (/.f64 y x))

Compiler

Compiled 420 to 351 computations (16.4% saved)

simplify962.0ms (13.8%)

Algorithm

1×	egg-herbie

Rules

392×	`associate-/r*_binary64_32758`
321×	`*-commutative_binary64_32745`
298×	`distribute-rgt-neg-in_binary64_32772`
270×	`cancel-sign-sub-inv_binary64_32780`
260×	`distribute-lft-neg-in_binary64_32771`
196×	`distribute-neg-frac_binary64_32778`
175×	`unsub-neg_binary64_32808`
162×	`div-sub_binary64_32819`
160×	`unswap-sqr_binary64_32782`
152×	`associate-/l*_binary64_32759`
145×	`associate-/r/_binary64_32760`
144×	`distribute-rgt-neg-out_binary64_32774`
141×	`associate-/l/_binary64_32761`
138×	`neg-mul-1_binary64_32810`
137×	`neg-sub0_binary64_32809`
126×	`distribute-lft-neg-out_binary64_32773`
117×	`distribute-frac-neg_binary64_32777`
100×	`sqr-pow_binary64_32786`
94×	`associate-*r/_binary64_32756`
92×	`sub-neg_binary64_32807`
84×	`associate-r_binary64_32754`
82×	`associate-*l/_binary64_32757`
81×	`distribute-neg-out_binary64_32776`
72×	`exp-prod_binary64_32866`
69×	`swap-sqr_binary64_32781`
68×	`times-frac_binary64_32820`
65×	`cube-prod_binary64_32842`
57×	`distribute-rgt-in_binary64_32764`
54×	`cube-div_binary64_32843`
51×	`distribute-lft-in_binary64_32763`
48×	`log-prod_binary64_32900`
47×	`associate-l_binary64_32755`
46×	`div-exp_binary64_32865`
43×	`log-div_binary64_32901`
42×	`pow-sqr_binary64_32787`
37×	`prod-exp_binary64_32863`
34×	`distribute-rgt-out_binary64_32767`
27×	`exp-sum_binary64_32860`
23×	`distribute-lft-out_binary64_32765`
22×	`unpow3_binary64_32880` `/-rgt-identity_binary64_32805` `difference-of-squares_binary64_32783` `distribute-rgt-out--_binary64_32768`
21×	`+-commutative_binary64_32744`
20×	`*-rgt-identity_binary64_32804`
19×	`associate-+l-_binary64_32749`
17×	`cube-mult_binary64_32844` `mul0-lft_binary64_32796`
16×	`remove-double-neg_binary64_32802` `mul0-rgt_binary64_32797` `distribute-neg-in_binary64_32775`
15×	`associate-+r-_binary64_32748`
13×	`sub0-neg_binary64_32801`
12×	`exp-diff_binary64_32862`
11×	`log-rec_binary64_32902` `pow-plus_binary64_32877` `+-rgt-identity_binary64_32799` `div0_binary64_32795`
9×	`rec-exp_binary64_32864`
8×	`log-pow_binary64_32903` `cube-unmult_binary64_32851`
6×	`*-lft-identity_binary64_32803`
5×	`remove-double-div_binary64_32790` `distribute-rgt1-in_binary64_32770`
4×	`associate--r+_binary64_32750` `associate-+l+_binary64_32747`
3×	`sqr-neg_binary64_32828` `rem-sqrt-square_binary64_32827` `cancel-sign-sub_binary64_32779` `distribute-lft-out--_binary64_32766` `associate--l-_binary64_32752` `associate-+r+_binary64_32746`
2×	`unpow1/2_binary64_32878` `exp-neg_binary64_32861` `cube-neg_binary64_32841` `--rgt-identity_binary64_32800` `associate--r-_binary64_32753`
1×	`unpow2_binary64_32879` `pow-base-1_binary64_32874` `unpow1_binary64_32872` `1-exp_binary64_32858` `rem-log-exp_binary64_32855` `rem-3cbrt-rft_binary64_32840` `rem-3cbrt-lft_binary64_32839` `rem-square-sqrt_binary64_32826` `mul-1-neg_binary64_32806` `*-inverses_binary64_32794` `rgt-mult-inverse_binary64_32791` `count-2_binary64_32762`
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_33077` `erf-erfc_binary64_33076` `erf-odd_binary64_33075` `if-if-and-not_binary64_33074` `if-if-and_binary64_33073` `if-if-or-not_binary64_33072` `if-if-or_binary64_33071` `if-not_binary64_33070` `if-same_binary64_33069` `if-false_binary64_33068` `if-true_binary64_33067` `not-gte_binary64_33066` `not-lte_binary64_33065` `not-gt_binary64_33064` `not-lt_binary64_33063` `gte-same_binary64_33062` `lte-same_binary64_33061` `gt-same_binary64_33060` `lt-same_binary64_33059` `sinh---cosh_binary64_33006` `sinh-+-cosh_binary64_33005` `sinh-cosh_binary64_33004` `tanh-def-c_binary64_33003` `tanh-def-b_binary64_33002` `tanh-def-a_binary64_33001` `cosh-def_binary64_33000` `sinh-def_binary64_32999` `tan-neg_binary64_32946` `cos-neg_binary64_32945` `sin-neg_binary64_32944` `tan-0_binary64_32943` `cos-0_binary64_32942` `sin-0_binary64_32941` `hang-m-tan_binary64_32940` `hang-p-tan_binary64_32939` `hang-m0-tan_binary64_32938` `hang-p0-tan_binary64_32937` `hang-0m-tan_binary64_32936` `hang-0p-tan_binary64_32935` `tan-+PI/2_binary64_32934` `tan-+PI_binary64_32933` `tan-PI_binary64_32932` `tan-PI/3_binary64_32931` `tan-PI/4_binary64_32930` `tan-PI/6_binary64_32929` `cos-+PI/2_binary64_32928` `cos-+PI_binary64_32927` `cos-PI_binary64_32926` `cos-PI/2_binary64_32925` `cos-PI/3_binary64_32924` `cos-PI/4_binary64_32923` `cos-PI/6_binary64_32922` `sin-+PI/2_binary64_32921` `sin-+PI_binary64_32920` `sin-PI_binary64_32919` `sin-PI/2_binary64_32918` `sin-PI/3_binary64_32917` `sin-PI/4_binary64_32916` `sin-PI/6_binary64_32915` `sub-1-sin_binary64_32914` `sub-1-cos_binary64_32913` `-1-add-sin_binary64_32912` `-1-add-cos_binary64_32911` `1-sub-sin_binary64_32910` `1-sub-cos_binary64_32909` `cos-sin-sum_binary64_32908` `log-E_binary64_32904` `pow-base-0_binary64_32898` `unpow1/3_binary64_32881` `exp-to-pow_binary64_32876` `unpow0_binary64_32873` `unpow-1_binary64_32871` `exp-lft-cube_binary64_32870` `exp-lft-sqr_binary64_32869` `exp-cbrt_binary64_32868` `exp-sqrt_binary64_32867` `e-exp-1_binary64_32859` `exp-1-e_binary64_32857` `exp-0_binary64_32856` `rem-exp-log_binary64_32854` `rem-cbrt-cube_binary64_32838` `rem-cube-cbrt_binary64_32837` `sqr-abs_binary64_32829` `+-lft-identity_binary64_32798` `+-inverses_binary64_32793` `lft-mult-inverse_binary64_32792` `difference-of-sqr--1_binary64_32785` `difference-of-sqr-1_binary64_32784` `distribute-lft1-in_binary64_32769` `associate--l+_binary64_32751`

Counts

102 → 534

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	1820
1	410	1646
2	1497	1574
3	2875	1574

prune602.0ms (8.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	530	4	534
Fresh	0	3	3
Picked	1	0	1
Done	0	3	3
Total	531	10	541

Error

16.1b

Counts

541 → 10

Compiler

Compiled 11402 to 3301 computations (71% saved)

regimes713.0ms (10.2%)

Accuracy

Total 17.7b remaining (99.1%)

Threshold costs 0b (0%)

Compiler

Compiled 5728 to 3063 computations (46.5% saved)

bsearch31.0ms (0.4%)

Steps

Iters	Range		Point
7	3.6345089841164763e+95	1.521738340503539e+97	1.2142329415337049e+97
8	-1.3608891685309633e+94	-1.7447627592974023e+90	-1.3398376281346736e+94

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64_32744`
1×	`neg-mul-1_binary64_32810` `neg-sub0_binary64_32809` `sub-neg_binary64_32807` `*-commutative_binary64_32745`
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_33074` `if-if-and_binary64_33073` `if-if-or-not_binary64_33072` `if-if-or_binary64_33071` `if-not_binary64_33070` `if-same_binary64_33069` `if-false_binary64_33068` `if-true_binary64_33067` `tan-0_binary64_32943` `cos-0_binary64_32942` `sin-0_binary64_32941` `unpow1_binary64_32872` `e-exp-1_binary64_32859` `1-exp_binary64_32858` `exp-1-e_binary64_32857` `exp-0_binary64_32856` `sqr-abs_binary64_32829` `sqr-neg_binary64_32828` `unsub-neg_binary64_32808` `mul-1-neg_binary64_32806` `/-rgt-identity_binary64_32805` `-rgt-identity_binary64_32804` `-lft-identity_binary64_32803` `remove-double-neg_binary64_32802` `sub0-neg_binary64_32801` `--rgt-identity_binary64_32800` `+-rgt-identity_binary64_32799` `+-lft-identity_binary64_32798` `cancel-sign-sub-inv_binary64_32780` `cancel-sign-sub_binary64_32779` `distribute-neg-frac_binary64_32778` `distribute-frac-neg_binary64_32777` `distribute-neg-out_binary64_32776` `distribute-neg-in_binary64_32775` `distribute-rgt-neg-out_binary64_32774` `distribute-lft-neg-out_binary64_32773` `distribute-rgt-neg-in_binary64_32772` `distribute-lft-neg-in_binary64_32771`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	28
1	20	28
2	22	28
3	23	28

Proof

(if real (<= f64 h0 -13398376281346736101461237098228976092576829853887438119763789170143345925589100659045690245120) (neg f64 h0) (if real (<= f64 h0 12142329415337049042930683231226286227750274403034604956886288535698748009006538008125279110692864) (sqrt f64 (+ f64 (* f64 h0 h0) (* f64 h1 h1))) h0))

end0.0ms (0%)

sample1.1s (16.1%)

Algorithm

1×

intervals

Results

251.0ms

8000×

body

128

valid

Compiler

Compiled 864 to 481 computations (44.3% saved)

Details

analyze101.0ms (1.4%)

sample21.0ms (0.3%)

simplify159.0ms (2.3%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite22.0ms (0.3%)

series115.0ms (1.7%)

simplify101.0ms (1.5%)

prune72.0ms (1%)

localize12.0ms (0.2%)

rewrite125.0ms (1.8%)

series1.2s (17.9%)

simplify662.0ms (9.5%)

prune437.0ms (6.3%)

localize2.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify10.0ms (0.1%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

rewrite109.0ms (1.6%)

series320.0ms (4.6%)

simplify962.0ms (13.8%)

prune602.0ms (8.6%)

regimes713.0ms (10.2%)

bsearch31.0ms (0.4%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.1s (16.1%)

Profiling