Details

analyze43.0ms (4.5%)

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
25%	74.9%	0.1%	3
25%	62.4%	12.6%	4
37.5%	43.7%	18.8%	5
37.5%	34.3%	28.2%	6
43.7%	23.4%	32.9%	7
43.7%	18%	38.3%	8
46.8%	12.1%	41.1%	9
46.8%	9.2%	44%	10
48.4%	6.1%	45.5%	11
48.4%	4.6%	47%	12
49.2%	3.1%	47.7%	13
49.2%	2.3%	48.5%	14

Compiler

Compiled 5 to 5 computations (0% saved)

sample13.0ms (1.4%)

Algorithm

1×

intervals

Results

5.0ms	256×	body	128	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 9 to 11 computations (-22.2% saved)

simplify147.0ms (15.5%)

Algorithm

1×	egg-herbie

Rules

1× +-commutative_binary64_690

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_1023 erf-erfc_binary64_1022 erf-odd_binary64_1021 if-if-and-not_binary64_1020 if-if-and_binary64_1019 if-if-or-not_binary64_1018 if-if-or_binary64_1017 if-not_binary64_1016 if-same_binary64_1015 if-false_binary64_1014 if-true_binary64_1013 not-gte_binary64_1012 not-lte_binary64_1011 not-gt_binary64_1010 not-lt_binary64_1009 gte-same_binary64_1008 lte-same_binary64_1007 gt-same_binary64_1006 lt-same_binary64_1005 sinh---cosh_binary64_952 sinh-+-cosh_binary64_951 sinh-cosh_binary64_950 tanh-def-c_binary64_949 tanh-def-b_binary64_948 tanh-def-a_binary64_947 cosh-def_binary64_946 sinh-def_binary64_945 tan-neg_binary64_892 cos-neg_binary64_891 sin-neg_binary64_890 tan-0_binary64_889 cos-0_binary64_888 sin-0_binary64_887 hang-m-tan_binary64_886 hang-p-tan_binary64_885 hang-m0-tan_binary64_884 hang-p0-tan_binary64_883 hang-0m-tan_binary64_882 hang-0p-tan_binary64_881 tan-+PI/2_binary64_880 tan-+PI_binary64_879 tan-PI_binary64_878 tan-PI/3_binary64_877 tan-PI/4_binary64_876 tan-PI/6_binary64_875 cos-+PI/2_binary64_874 cos-+PI_binary64_873 cos-PI_binary64_872 cos-PI/2_binary64_871 cos-PI/3_binary64_870 cos-PI/4_binary64_869 cos-PI/6_binary64_868 sin-+PI/2_binary64_867 sin-+PI_binary64_866 sin-PI_binary64_865 sin-PI/2_binary64_864 sin-PI/3_binary64_863 sin-PI/4_binary64_862 sin-PI/6_binary64_861 sub-1-sin_binary64_860 sub-1-cos_binary64_859 -1-add-sin_binary64_858 -1-add-cos_binary64_857 1-sub-sin_binary64_856 1-sub-cos_binary64_855 cos-sin-sum_binary64_854 log-E_binary64_850 log-pow_binary64_849 log-rec_binary64_848 log-div_binary64_847 log-prod_binary64_846 pow-base-0_binary64_844 unpow1/3_binary64_827 unpow3_binary64_826 unpow2_binary64_825 unpow1/2_binary64_824 pow-plus_binary64_823 exp-to-pow_binary64_822 pow-base-1_binary64_820 unpow0_binary64_819 unpow1_binary64_818 unpow-1_binary64_817 exp-lft-cube_binary64_816 exp-lft-sqr_binary64_815 exp-cbrt_binary64_814 exp-sqrt_binary64_813 exp-prod_binary64_812 div-exp_binary64_811 rec-exp_binary64_810 prod-exp_binary64_809 exp-diff_binary64_808 exp-neg_binary64_807 exp-sum_binary64_806 e-exp-1_binary64_805 1-exp_binary64_804 exp-1-e_binary64_803 exp-0_binary64_802 rem-log-exp_binary64_801 rem-exp-log_binary64_800 cube-unmult_binary64_797 cube-mult_binary64_790 cube-div_binary64_789 cube-prod_binary64_788 cube-neg_binary64_787 rem-3cbrt-rft_binary64_786 rem-3cbrt-lft_binary64_785 rem-cbrt-cube_binary64_784 rem-cube-cbrt_binary64_783 sqr-abs_binary64_775 sqr-neg_binary64_774 rem-sqrt-square_binary64_773 rem-square-sqrt_binary64_772 times-frac_binary64_766 div-sub_binary64_765 neg-mul-1_binary64_756 neg-sub0_binary64_755 unsub-neg_binary64_754 sub-neg_binary64_753 mul-1-neg_binary64_752 /-rgt-identity_binary64_751 *-rgt-identity_binary64_750 *-lft-identity_binary64_749 remove-double-neg_binary64_748 sub0-neg_binary64_747 --rgt-identity_binary64_746 +-rgt-identity_binary64_745 +-lft-identity_binary64_744 mul0-rgt_binary64_743 mul0-lft_binary64_742 div0_binary64_741 *-inverses_binary64_740 +-inverses_binary64_739 lft-mult-inverse_binary64_738 rgt-mult-inverse_binary64_737 remove-double-div_binary64_736 pow-sqr_binary64_733 sqr-pow_binary64_732 difference-of-sqr--1_binary64_731 difference-of-sqr-1_binary64_730 difference-of-squares_binary64_729 unswap-sqr_binary64_728 swap-sqr_binary64_727 cancel-sign-sub-inv_binary64_726 cancel-sign-sub_binary64_725 distribute-neg-frac_binary64_724 distribute-frac-neg_binary64_723 distribute-neg-out_binary64_722 distribute-neg-in_binary64_721 distribute-rgt-neg-out_binary64_720 distribute-lft-neg-out_binary64_719 distribute-rgt-neg-in_binary64_718 distribute-lft-neg-in_binary64_717 distribute-rgt1-in_binary64_716 distribute-lft1-in_binary64_715 distribute-rgt-out--_binary64_714 distribute-rgt-out_binary64_713 distribute-lft-out--_binary64_712 distribute-lft-out_binary64_711 distribute-rgt-in_binary64_710 distribute-lft-in_binary64_709 count-2_binary64_708 associate-/l/_binary64_707 associate-/r/_binary64_706 associate-/l*_binary64_705 associate-/r*_binary64_704 associate-*l/_binary64_703 associate-*r/_binary64_702 associate-*l*_binary64_701 associate-*r*_binary64_700 associate--r-_binary64_699 associate--l-_binary64_698 associate--l+_binary64_697 associate--r+_binary64_696 associate-+l-_binary64_695 associate-+r-_binary64_694 associate-+l+_binary64_693 associate-+r+_binary64_692 *-commutative_binary64_691

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	6	6

prune2.0ms (0.2%)

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

0.0b

Counts

1 → 1

Compiler

Compiled 4 to 4 computations (0% saved)

localize7.0ms (0.7%)

Local error

Found 1 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x y))

rewrite14.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

4×	`sqrt-prod_binary64_776` `*-un-lft-identity_binary64_760`
3×	`add-sqr-sqrt_binary64_782`
2×	`pow1_binary64_821` `add-cube-cbrt_binary64_795` `sqrt-div_binary64_777`
1×	`pow1/2_binary64_840` `add-log-exp_binary64_799` `add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `sqrt-pow1_binary64_778` `flip3-+_binary64_763` `flip-+_binary64_734` `distribute-lft-out_binary64_711` `rem-sqrt-square_binary64_773`

Counts

1 → 16

Calls

1 calls:

3.0ms

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

Compiler

Compiled 159 to 56 computations (64.8% saved)

series63.0ms (6.7%)

Error

0.0b

Counts

1 → 10

Calls

1 calls:

55.0ms

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

Compiler

Compiled 258 to 218 computations (15.5% saved)

simplify154.0ms (16.2%)

Algorithm

1×	egg-herbie

Rules

727×	`times-frac_binary64_766`
506×	`cancel-sign-sub-inv_binary64_726`
286×	`associate-l_binary64_701`
261×	`distribute-rgt-in_binary64_710`
255×	`associate-/l*_binary64_705`
254×	`associate-/l/_binary64_707`
234×	`associate-r_binary64_700`
206×	`distribute-lft-in_binary64_709`
184×	`associate-/r*_binary64_704`
139×	`neg-mul-1_binary64_756`
121×	`associate-*r/_binary64_702`
109×	`distribute-rgt-out_binary64_713`
91×	`sub-neg_binary64_753`
90×	`distribute-rgt-neg-in_binary64_718`
89×	`distribute-lft-neg-in_binary64_717`
82×	`associate--r+_binary64_696` `associate-+r+_binary64_692`
80×	`distribute-rgt-out--_binary64_714` `associate-*l/_binary64_703`
78×	`unswap-sqr_binary64_728`
77×	`*-commutative_binary64_691`
76×	`distribute-lft-out_binary64_711` `associate-/r/_binary64_706`
67×	`associate-+l+_binary64_693`
62×	`associate-+l-_binary64_695`
59×	`+-commutative_binary64_690`
51×	`distribute-lft-out--_binary64_712`
47×	`unsub-neg_binary64_754`
42×	`sqr-pow_binary64_732`
39×	`associate-+r-_binary64_694`
32×	`distribute-lft-neg-out_binary64_719`
30×	`neg-sub0_binary64_755` `distribute-neg-in_binary64_721`
27×	`pow-sqr_binary64_733` `associate--l+_binary64_697`
26×	`cube-prod_binary64_788`
25×	`distribute-rgt-neg-out_binary64_720`
22×	`pow-plus_binary64_823`
19×	`exp-prod_binary64_812` `cube-unmult_binary64_797`
17×	`sub0-neg_binary64_747`
16×	`cube-div_binary64_789`
14×	`+-rgt-identity_binary64_745`
10×	`associate--r-_binary64_699`
9×	`div-exp_binary64_811` `prod-exp_binary64_809` `div-sub_binary64_765` `mul0-rgt_binary64_743` `mul0-lft_binary64_742`
8×	`rem-sqrt-square_binary64_773` `*-rgt-identity_binary64_750`
7×	`unpow3_binary64_826`
4×	`distribute-neg-out_binary64_722` `associate--l-_binary64_698`
3×	`rec-exp_binary64_810` `cube-mult_binary64_790` `/-rgt-identity_binary64_751` `difference-of-squares_binary64_729` `cancel-sign-sub_binary64_725` `distribute-rgt1-in_binary64_716`
2×	`exp-sum_binary64_806` `sqr-neg_binary64_774` `*-lft-identity_binary64_749` `swap-sqr_binary64_727` `count-2_binary64_708`
1×	`unpow2_binary64_825` `unpow1_binary64_818` `1-exp_binary64_804` `cube-neg_binary64_787` `rem-square-sqrt_binary64_772` `mul-1-neg_binary64_752` `remove-double-neg_binary64_748` `*-inverses_binary64_740` `rgt-mult-inverse_binary64_737`
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_1023` `erf-erfc_binary64_1022` `erf-odd_binary64_1021` `if-if-and-not_binary64_1020` `if-if-and_binary64_1019` `if-if-or-not_binary64_1018` `if-if-or_binary64_1017` `if-not_binary64_1016` `if-same_binary64_1015` `if-false_binary64_1014` `if-true_binary64_1013` `not-gte_binary64_1012` `not-lte_binary64_1011` `not-gt_binary64_1010` `not-lt_binary64_1009` `gte-same_binary64_1008` `lte-same_binary64_1007` `gt-same_binary64_1006` `lt-same_binary64_1005` `sinh---cosh_binary64_952` `sinh-+-cosh_binary64_951` `sinh-cosh_binary64_950` `tanh-def-c_binary64_949` `tanh-def-b_binary64_948` `tanh-def-a_binary64_947` `cosh-def_binary64_946` `sinh-def_binary64_945` `tan-neg_binary64_892` `cos-neg_binary64_891` `sin-neg_binary64_890` `tan-0_binary64_889` `cos-0_binary64_888` `sin-0_binary64_887` `hang-m-tan_binary64_886` `hang-p-tan_binary64_885` `hang-m0-tan_binary64_884` `hang-p0-tan_binary64_883` `hang-0m-tan_binary64_882` `hang-0p-tan_binary64_881` `tan-+PI/2_binary64_880` `tan-+PI_binary64_879` `tan-PI_binary64_878` `tan-PI/3_binary64_877` `tan-PI/4_binary64_876` `tan-PI/6_binary64_875` `cos-+PI/2_binary64_874` `cos-+PI_binary64_873` `cos-PI_binary64_872` `cos-PI/2_binary64_871` `cos-PI/3_binary64_870` `cos-PI/4_binary64_869` `cos-PI/6_binary64_868` `sin-+PI/2_binary64_867` `sin-+PI_binary64_866` `sin-PI_binary64_865` `sin-PI/2_binary64_864` `sin-PI/3_binary64_863` `sin-PI/4_binary64_862` `sin-PI/6_binary64_861` `sub-1-sin_binary64_860` `sub-1-cos_binary64_859` `-1-add-sin_binary64_858` `-1-add-cos_binary64_857` `1-sub-sin_binary64_856` `1-sub-cos_binary64_855` `cos-sin-sum_binary64_854` `log-E_binary64_850` `log-pow_binary64_849` `log-rec_binary64_848` `log-div_binary64_847` `log-prod_binary64_846` `pow-base-0_binary64_844` `unpow1/3_binary64_827` `unpow1/2_binary64_824` `exp-to-pow_binary64_822` `pow-base-1_binary64_820` `unpow0_binary64_819` `unpow-1_binary64_817` `exp-lft-cube_binary64_816` `exp-lft-sqr_binary64_815` `exp-cbrt_binary64_814` `exp-sqrt_binary64_813` `exp-diff_binary64_808` `exp-neg_binary64_807` `e-exp-1_binary64_805` `exp-1-e_binary64_803` `exp-0_binary64_802` `rem-log-exp_binary64_801` `rem-exp-log_binary64_800` `rem-3cbrt-rft_binary64_786` `rem-3cbrt-lft_binary64_785` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `--rgt-identity_binary64_746` `+-lft-identity_binary64_744` `div0_binary64_741` `+-inverses_binary64_739` `lft-mult-inverse_binary64_738` `remove-double-div_binary64_736` `difference-of-sqr--1_binary64_731` `difference-of-sqr-1_binary64_730` `distribute-neg-frac_binary64_724` `distribute-frac-neg_binary64_723` `distribute-lft1-in_binary64_715`

Counts

26 → 34

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	66	311
1	138	308
2	300	308
3	621	302
4	1642	299
5	4831	299

prune35.0ms (3.7%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	34	1	35

Error

0.0b

Counts

35 → 1

Compiler

Compiled 584 to 312 computations (46.6% saved)

regimes34.0ms (3.6%)

Accuracy

Total 0.0b remaining (5.6%)

Threshold costs 0.0b (5.6%)

Compiler

Compiled 50 to 62 computations (-24% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1× +-commutative_binary64_690

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	6	6

Proof

(sqrt f64 (+ f64 h0 h1))

end0.0ms (0%)

sample434.0ms (45.7%)

Algorithm

1×

intervals

Results

169.0ms	8000×	body	128	valid
4.0ms	265×	body	128	nan

Compiler

Compiled 17 to 21 computations (-23.5% saved)

Details

analyze43.0ms (4.5%)

sample13.0ms (1.4%)

simplify147.0ms (15.5%)

prune2.0ms (0.2%)

localize7.0ms (0.7%)

rewrite14.0ms (1.4%)

series63.0ms (6.7%)

simplify154.0ms (16.2%)

prune35.0ms (3.7%)

regimes34.0ms (3.6%)

bsearch0.0ms (0%)

simplify3.0ms (0.3%)

end0.0ms (0%)

sample434.0ms (45.7%)

Profiling