Details

analyze736.0ms (5.1%)

Algorithm

1×	search
2×	egg-herbie

Rules

715×	`div-sub_binary64_765`
690×	`sub-neg_binary64_753`
580×	`neg-mul-1_binary64_756`
490×	`neg-sub0_binary64_755`
476×	`associate-/r*_binary64_704`
402×	`distribute-neg-frac_binary64_724`
320×	`distribute-rgt-neg-in_binary64_718`
280×	`distribute-rgt-neg-out_binary64_720`
254×	`distribute-lft-neg-in_binary64_717`
248×	`distribute-lft-neg-out_binary64_719`
231×	`+-commutative_binary64_690`
226×	`associate-/r/_binary64_706`
220×	`associate-/l*_binary64_705`
217×	`associate-*l/_binary64_703`
200×	`associate-+l-_binary64_695`
198×	`remove-double-neg_binary64_748`
189×	`distribute-rgt-in_binary64_710`
185×	`cancel-sign-sub-inv_binary64_726`
144×	`times-frac_binary64_766`
140×	`unsub-neg_binary64_754`
131×	`associate-/l/_binary64_707`
119×	`associate-*r/_binary64_702`
117×	`associate--r+_binary64_696`
100×	`distribute-lft-in_binary64_709`
93×	`distribute-frac-neg_binary64_723`
88×	`sub0-neg_binary64_747`
76×	`cancel-sign-sub_binary64_725`
72×	`*-lft-identity_binary64_749`
71×	`associate--l-_binary64_698`
68×	`distribute-neg-in_binary64_721`
65×	`*-commutative_binary64_691`
61×	`+-lft-identity_binary64_744`
57×	`associate--r-_binary64_699`
54×	`/-rgt-identity_binary64_751`
53×	`+-rgt-identity_binary64_745`
48×	`associate-r_binary64_700`
40×	`associate-+r-_binary64_694` `associate-+l+_binary64_693`
36×	`div0_binary64_741`
34×	`associate-l_binary64_701`
24×	`--rgt-identity_binary64_746`
18×	`mul0-rgt_binary64_743` `mul0-lft_binary64_742` `associate--l+_binary64_697`
17×	`associate-+r+_binary64_692`
6×	`*-rgt-identity_binary64_750`
3×	`sqr-neg_binary64_774` `swap-sqr_binary64_727`
1×	`1-exp_binary64_804`
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` `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` `rem-sqrt-square_binary64_773` `rem-square-sqrt_binary64_772` `mul-1-neg_binary64_752` `*-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` `distribute-neg-out_binary64_722` `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` `count-2_binary64_708`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	104
1	82	96
2	160	96
3	321	96
4	480	96
5	786	96
6	1384	96
7	2448	96
8	3546	96
9	4339	96
10	4614	96
11	4871	96
12	4961	96
13	5132	96
0	3	3
1	3	3

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample43.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	174×	body	128	valid
9.0ms	34×	body	2048	valid
5.0ms	17×	body	4096	valid
2.0ms	11×	body	1024	valid
2.0ms	14×	body	512	valid
1.0ms	28×	body	128	nan
1.0ms	6×	body	256	valid
0.0ms	8×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify339.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1228×	`associate-/l*_binary64_705`
1150×	`div-sub_binary64_765`
630×	`distribute-rgt-in_binary64_710`
619×	`times-frac_binary64_766`
588×	`associate-/r*_binary64_704`
554×	`distribute-lft-in_binary64_709`
519×	`unsub-neg_binary64_754`
479×	`associate-/r/_binary64_706`
457×	`cancel-sign-sub-inv_binary64_726`
434×	`sub-neg_binary64_753`
393×	`*-commutative_binary64_691`
381×	`associate-/l/_binary64_707`
225×	`distribute-rgt-neg-in_binary64_718`
224×	`associate-*l/_binary64_703`
212×	`distribute-rgt-out--_binary64_714`
198×	`distribute-lft-neg-in_binary64_717`
184×	`distribute-neg-frac_binary64_724`
179×	`neg-mul-1_binary64_756`
156×	`distribute-rgt-out_binary64_713`
141×	`neg-sub0_binary64_755`
121×	`associate--r+_binary64_696`
120×	`distribute-rgt-neg-out_binary64_720`
101×	`associate--r-_binary64_699` `+-commutative_binary64_690`
98×	`associate-*r/_binary64_702`
87×	`distribute-lft-neg-out_binary64_719`
86×	`mul0-rgt_binary64_743`
80×	`mul0-lft_binary64_742`
69×	`distribute-frac-neg_binary64_723`
68×	`distribute-neg-out_binary64_722`
64×	`distribute-lft-out_binary64_711`
62×	`div0_binary64_741`
61×	`associate--l-_binary64_698`
60×	`*-lft-identity_binary64_749`
57×	`associate-r_binary64_700`
51×	`associate-l_binary64_701`
48×	`distribute-lft-out--_binary64_712`
30×	`+-lft-identity_binary64_744` `distribute-neg-in_binary64_721`
28×	`associate--l+_binary64_697`
27×	`remove-double-neg_binary64_748`
26×	`/-rgt-identity_binary64_751`
24×	`associate-+r-_binary64_694`
19×	`sub0-neg_binary64_747` `--rgt-identity_binary64_746`
17×	`*-rgt-identity_binary64_750`
16×	`mul-1-neg_binary64_752`
14×	`remove-double-div_binary64_736` `associate-+l+_binary64_693`
13×	`associate-+l-_binary64_695`
7×	`associate-+r+_binary64_692`
5×	`+-rgt-identity_binary64_745`
1×	`1-exp_binary64_804` `swap-sqr_binary64_727`
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` `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` `*-inverses_binary64_740` `+-inverses_binary64_739` `lft-mult-inverse_binary64_738` `rgt-mult-inverse_binary64_737` `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` `cancel-sign-sub_binary64_725` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `count-2_binary64_708`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	33	24
2	62	24
3	121	24
4	172	24
5	282	24
6	460	24
7	748	24
8	1084	24
9	1128	24
10	1799	24
11	2594	24
12	2001	24
13	2089	24
14	2153	24
15	2179	24
16	2431	24
17	2909	24
18	2913	24
19	2991	24
20	3053	24
21	3065	24
22	3035	24
23	3211	24
24	3211	24
25	2043	24
26	2195	24
27	2097	24
28	2107	24
29	2107	24
30	2107	24
31	2107	24
32	1834	24

prune7.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

34.4b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
24.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite161.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

34.1b

Rules

21×	`add-sqr-sqrt_binary64_782`
14×	`*-un-lft-identity_binary64_760`
9×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
8×	`add-log-exp_binary64_799` `add-cube-cbrt_binary64_795`
6×	`sqrt-prod_binary64_776` `difference-of-squares_binary64_729` `times-frac_binary64_766` `associate-/l*_binary64_705`
5×	`pow1_binary64_821`
4×	`flip3--_binary64_764` `flip--_binary64_735` `cancel-sign-sub-inv_binary64_726`
3×	`distribute-lft-out--_binary64_712`
2×	`sqrt-div_binary64_777` `diff-log_binary64_852` `sub-neg_binary64_753` `div-exp_binary64_811` `cbrt-undiv_binary64_794` `associate-/l/_binary64_707`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `frac-2neg_binary64_771` `div-sub_binary64_765` `clear-num_binary64_759` `div-inv_binary64_757` `associate-/r*_binary64_704`

Counts

4 → 74

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 2100 to 1088 computations (48.2% saved)

series1.0s (7.2%)

Error

7.9b

Counts

4 → 68

Calls

4 calls:

330.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
222.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
219.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
198.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3015 to 2294 computations (23.9% saved)

simplify124.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

552×	`times-frac_binary64_766`
422×	`associate-/l*_binary64_705`
329×	`div-sub_binary64_765`
316×	`associate-/r*_binary64_704`
178×	`distribute-rgt-in_binary64_710`
174×	`distribute-lft-in_binary64_709`
156×	`associate-*l/_binary64_703`
150×	`cancel-sign-sub-inv_binary64_726`
138×	`distribute-rgt-neg-in_binary64_718`
121×	`distribute-lft-neg-in_binary64_717`
115×	`exp-prod_binary64_812`
99×	`sub-neg_binary64_753`
86×	`associate-/l/_binary64_707` `*-commutative_binary64_691`
83×	`associate-l_binary64_701`
82×	`associate-r_binary64_700`
78×	`associate-/r/_binary64_706`
52×	`neg-sub0_binary64_755`
49×	`neg-mul-1_binary64_756`
46×	`+-commutative_binary64_690`
43×	`cube-prod_binary64_788`
37×	`sqr-pow_binary64_732` `distribute-neg-frac_binary64_724` `distribute-rgt-out_binary64_713`
35×	`unswap-sqr_binary64_728`
23×	`distribute-lft-neg-out_binary64_719` `associate-*r/_binary64_702`
21×	`exp-sum_binary64_806`
16×	`unpow3_binary64_826`
15×	`exp-diff_binary64_808` `swap-sqr_binary64_727`
13×	`distribute-neg-in_binary64_721`
12×	`distribute-lft-out_binary64_711` `associate--l+_binary64_697`
11×	`cube-mult_binary64_790` `distribute-rgt-neg-out_binary64_720` `associate-+r-_binary64_694`
10×	`+-rgt-identity_binary64_745`
9×	`cube-unmult_binary64_797` `unsub-neg_binary64_754`
8×	`pow-plus_binary64_823` `difference-of-squares_binary64_729` `associate--r+_binary64_696`
7×	`log-div_binary64_847` `associate-+l+_binary64_693`
6×	`rem-sqrt-square_binary64_773` `mul-1-neg_binary64_752`
5×	`cube-div_binary64_789` `distribute-lft-out--_binary64_712` `associate-+r+_binary64_692`
4×	`log-prod_binary64_846` `unpow2_binary64_825` `exp-sqrt_binary64_813` `pow-sqr_binary64_733`
3×	`unpow1/2_binary64_824` `unpow1_binary64_818` `exp-lft-sqr_binary64_815` `distribute-rgt-out--_binary64_714` `associate-+l-_binary64_695`
2×	`log-pow_binary64_849` `div-exp_binary64_811` `sqr-neg_binary64_774` `rem-square-sqrt_binary64_772`
1×	`prod-exp_binary64_809` `1-exp_binary64_804` `cube-neg_binary64_787` `rem-3cbrt-lft_binary64_785` `remove-double-neg_binary64_748` `div0_binary64_741` `*-inverses_binary64_740` `cancel-sign-sub_binary64_725` `distribute-neg-out_binary64_722` `count-2_binary64_708` `associate--r-_binary64_699` `associate--l-_binary64_698`
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-rec_binary64_848` `pow-base-0_binary64_844` `unpow1/3_binary64_827` `exp-to-pow_binary64_822` `pow-base-1_binary64_820` `unpow0_binary64_819` `unpow-1_binary64_817` `exp-lft-cube_binary64_816` `exp-cbrt_binary64_814` `rec-exp_binary64_810` `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-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `/-rgt-identity_binary64_751` `-rgt-identity_binary64_750` `-lft-identity_binary64_749` `sub0-neg_binary64_747` `--rgt-identity_binary64_746` `+-lft-identity_binary64_744` `mul0-rgt_binary64_743` `mul0-lft_binary64_742` `+-inverses_binary64_739` `lft-mult-inverse_binary64_738` `rgt-mult-inverse_binary64_737` `remove-double-div_binary64_736` `difference-of-sqr--1_binary64_731` `difference-of-sqr-1_binary64_730` `distribute-frac-neg_binary64_723` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715`

Counts

142 → 90

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	2997
1	501	2750
2	1476	2744
3	4694	2744
4	5535	2744

prune112.0ms (0.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	81	9	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	9	91

Error

7.8b

Counts

91 → 9

Compiler

Compiled 1827 to 972 computations (46.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
24.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite156.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

7.8b

Rules

28×	`add-sqr-sqrt_binary64_782`
18×	`*-un-lft-identity_binary64_760`
14×	`add-cube-cbrt_binary64_795`
13×	`associate-r_binary64_700`
10×	`times-frac_binary64_766`
9×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
8×	`add-log-exp_binary64_799`
7×	`pow1_binary64_821`
6×	`associate-l_binary64_701`
5×	`flip3--_binary64_764` `flip--_binary64_735` `sqrt-prod_binary64_776`
4×	`difference-of-squares_binary64_729` `cancel-sign-sub-inv_binary64_726`
2×	`sqrt-div_binary64_777` `diff-log_binary64_852` `sub-neg_binary64_753` `distribute-lft-out--_binary64_712` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `frac-times_binary64_770` `unswap-sqr_binary64_728` `associate-*l/_binary64_703`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `pow-prod-down_binary64_831` `div-exp_binary64_811` `cbrt-undiv_binary64_794` `associate-r/_binary64_702` `div-inv_binary64_757` `-commutative_binary64_691`

Counts

4 → 83

Calls

4 calls:

16.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2366 to 1240 computations (47.6% saved)

series1.0s (7.3%)

Error

7.8b

Counts

4 → 68

Calls

4 calls:

326.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
242.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
228.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
188.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3015 to 2294 computations (23.9% saved)

simplify350.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

456×	`times-frac_binary64_766`
388×	`associate-/l*_binary64_705`
288×	`distribute-rgt-in_binary64_710`
282×	`distribute-lft-in_binary64_709`
139×	`cancel-sign-sub-inv_binary64_726`
127×	`distribute-rgt-neg-in_binary64_718`
115×	`associate-l_binary64_701`
113×	`distribute-lft-neg-in_binary64_717`
110×	`associate-r_binary64_700`
109×	`*-commutative_binary64_691`
103×	`exp-prod_binary64_812`
90×	`sub-neg_binary64_753`
82×	`associate-/r/_binary64_706`
60×	`associate-/l/_binary64_707`
58×	`associate-*r/_binary64_702`
48×	`+-commutative_binary64_690`
43×	`cube-prod_binary64_788` `neg-sub0_binary64_755` `sqr-pow_binary64_732`
40×	`neg-mul-1_binary64_756`
38×	`associate-*l/_binary64_703`
37×	`distribute-lft-neg-out_binary64_719`
36×	`div-sub_binary64_765`
34×	`distribute-neg-frac_binary64_724`
33×	`unswap-sqr_binary64_728` `distribute-rgt-out_binary64_713`
30×	`exp-sum_binary64_806`
27×	`distribute-rgt-neg-out_binary64_720`
25×	`log-prod_binary64_846` `associate-/r*_binary64_704`
24×	`log-div_binary64_847`
19×	`*-rgt-identity_binary64_750`
18×	`*-lft-identity_binary64_749`
17×	`unpow3_binary64_826`
15×	`swap-sqr_binary64_727`
13×	`cube-mult_binary64_790` `cube-div_binary64_789`
12×	`exp-diff_binary64_808` `associate--l+_binary64_697` `associate-+r-_binary64_694`
10×	`+-rgt-identity_binary64_745`
9×	`cube-unmult_binary64_797`
8×	`pow-plus_binary64_823` `unsub-neg_binary64_754` `difference-of-squares_binary64_729` `distribute-neg-in_binary64_721` `distribute-lft-out_binary64_711` `associate-+l+_binary64_693`
6×	`mul-1-neg_binary64_752`
5×	`/-rgt-identity_binary64_751` `pow-sqr_binary64_733` `distribute-lft-out--_binary64_712` `associate--r+_binary64_696` `associate-+r+_binary64_692`
4×	`log-rec_binary64_848` `unpow2_binary64_825` `unpow1/2_binary64_824` `sqr-neg_binary64_774` `rem-sqrt-square_binary64_773` `associate-+l-_binary64_695`
3×	`log-pow_binary64_849` `unpow1_binary64_818` `exp-neg_binary64_807` `distribute-rgt-out--_binary64_714`
2×	`div-exp_binary64_811` `rem-square-sqrt_binary64_772`
1×	`1-exp_binary64_804` `exp-1-e_binary64_803` `rem-3cbrt-lft_binary64_785` `div0_binary64_741` `*-inverses_binary64_740` `cancel-sign-sub_binary64_725` `distribute-neg-out_binary64_722` `count-2_binary64_708` `associate--l-_binary64_698`
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` `pow-base-0_binary64_844` `unpow1/3_binary64_827` `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` `rec-exp_binary64_810` `prod-exp_binary64_809` `e-exp-1_binary64_805` `exp-0_binary64_802` `rem-log-exp_binary64_801` `rem-exp-log_binary64_800` `cube-neg_binary64_787` `rem-3cbrt-rft_binary64_786` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `remove-double-neg_binary64_748` `sub0-neg_binary64_747` `--rgt-identity_binary64_746` `+-lft-identity_binary64_744` `mul0-rgt_binary64_743` `mul0-lft_binary64_742` `+-inverses_binary64_739` `lft-mult-inverse_binary64_738` `rgt-mult-inverse_binary64_737` `remove-double-div_binary64_736` `difference-of-sqr--1_binary64_731` `difference-of-sqr-1_binary64_730` `distribute-frac-neg_binary64_723` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `associate--r-_binary64_699`

Counts

151 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	210	3239
1	533	2996
2	1701	2990
3	4770	2990
4	4988	2990
5	4946	2990

prune99.0ms (0.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	87	11	98

Error

7.8b

Counts

98 → 11

Compiler

Compiled 1753 to 942 computations (46.3% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
24.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite993.0ms (6.9%)

Algorithm

1×	rewrite-expression-head

Error

7.8b

Rules

693×	`times-frac_binary64_766`
439×	`add-sqr-sqrt_binary64_782`
364×	`*-un-lft-identity_binary64_760`
290×	`add-cube-cbrt_binary64_795`
74×	`difference-of-squares_binary64_729`
71×	`associate-/r*_binary64_704`
40×	`sqrt-prod_binary64_776`
37×	`distribute-lft-out--_binary64_712`
25×	`add-exp-log_binary64_798`
17×	`div-inv_binary64_757`
15×	`div-exp_binary64_811`
13×	`add-cbrt-cube_binary64_796`
8×	`add-log-exp_binary64_799`
6×	`pow1_binary64_821` `cbrt-undiv_binary64_794`
5×	`associate-/r/_binary64_706`
4×	`cancel-sign-sub-inv_binary64_726`
3×	`flip3--_binary64_764` `flip--_binary64_735` `1-exp_binary64_804` `rec-exp_binary64_810` `associate-/l*_binary64_705`
2×	`sqrt-div_binary64_777` `diff-log_binary64_852` `sub-neg_binary64_753`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `inv-pow_binary64_845` `pow-flip_binary64_834` `frac-2neg_binary64_771` `clear-num_binary64_759`

Counts

4 → 356

Calls

4 calls:

25.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 14021 to 8305 computations (40.8% saved)

series1.0s (7.2%)

Error

7.8b

Counts

4 → 68

Calls

4 calls:

313.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
237.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
225.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
196.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3277 to 2556 computations (22% saved)

simplify505.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

476×	`associate-/r/_binary64_706`
323×	`associate-*l/_binary64_703`
319×	`*-commutative_binary64_691`
279×	`associate-/l/_binary64_707`
263×	`associate-*r/_binary64_702`
198×	`associate-/r*_binary64_704`
190×	`associate-/l*_binary64_705`
147×	`cancel-sign-sub-inv_binary64_726`
146×	`associate-r_binary64_700`
125×	`div-sub_binary64_765`
112×	`sub-neg_binary64_753`
110×	`neg-mul-1_binary64_756`
99×	`times-frac_binary64_766`
90×	`associate-l_binary64_701`
84×	`exp-prod_binary64_812`
76×	`*-rgt-identity_binary64_750`
59×	`neg-sub0_binary64_755`
53×	`cube-prod_binary64_788`
51×	`+-commutative_binary64_690`
49×	`unswap-sqr_binary64_728`
45×	`distribute-neg-frac_binary64_724`
41×	`sqr-pow_binary64_732`
37×	`distribute-rgt-in_binary64_710`
35×	`distribute-lft-in_binary64_709`
33×	`distribute-rgt-neg-in_binary64_718`
29×	`distribute-lft-neg-in_binary64_717`
26×	`log-prod_binary64_846`
25×	`log-div_binary64_847` `*-lft-identity_binary64_749` `remove-double-div_binary64_736`
24×	`exp-sum_binary64_806`
22×	`cube-div_binary64_789`
20×	`unpow3_binary64_826`
19×	`/-rgt-identity_binary64_751` `swap-sqr_binary64_727`
16×	`cube-mult_binary64_790` `associate-+r-_binary64_694`
14×	`distribute-neg-in_binary64_721` `associate-+r+_binary64_692`
13×	`exp-diff_binary64_808` `unsub-neg_binary64_754`
12×	`associate--l+_binary64_697`
11×	`+-rgt-identity_binary64_745`
10×	`cube-unmult_binary64_797` `associate--r+_binary64_696`
8×	`pow-plus_binary64_823` `difference-of-squares_binary64_729`
7×	`log-rec_binary64_848` `associate-+l+_binary64_693`
6×	`mul-1-neg_binary64_752`
5×	`rem-sqrt-square_binary64_773` `distribute-rgt-out_binary64_713` `distribute-lft-out--_binary64_712`
4×	`unpow2_binary64_825` `pow-sqr_binary64_733` `distribute-lft-neg-out_binary64_719`
3×	`unpow1/2_binary64_824` `unpow1_binary64_818` `associate--r-_binary64_699` `associate-+l-_binary64_695`
2×	`log-pow_binary64_849` `exp-sqrt_binary64_813` `div-exp_binary64_811` `rem-square-sqrt_binary64_772` `+-lft-identity_binary64_744` `distribute-neg-out_binary64_722`
1×	`1-exp_binary64_804` `exp-1-e_binary64_803` `rem-3cbrt-lft_binary64_785` `sqr-neg_binary64_774` `remove-double-neg_binary64_748` `sub0-neg_binary64_747` `div0_binary64_741` `*-inverses_binary64_740` `cancel-sign-sub_binary64_725` `distribute-rgt-neg-out_binary64_720` `distribute-rgt-out--_binary64_714` `distribute-lft-out_binary64_711` `associate--l-_binary64_698`
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` `pow-base-0_binary64_844` `unpow1/3_binary64_827` `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` `rec-exp_binary64_810` `prod-exp_binary64_809` `exp-neg_binary64_807` `e-exp-1_binary64_805` `exp-0_binary64_802` `rem-log-exp_binary64_801` `rem-exp-log_binary64_800` `cube-neg_binary64_787` `rem-3cbrt-rft_binary64_786` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `--rgt-identity_binary64_746` `mul0-rgt_binary64_743` `mul0-lft_binary64_742` `+-inverses_binary64_739` `lft-mult-inverse_binary64_738` `rgt-mult-inverse_binary64_737` `difference-of-sqr--1_binary64_731` `difference-of-sqr-1_binary64_730` `distribute-frac-neg_binary64_723` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `count-2_binary64_708`

Counts

424 → 362

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	505	18107
1	1216	17244
2	4201	17051
3	4648	17051
4	4975	17051

prune774.0ms (5.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	360	2	362
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	361	12	373

Error

7.8b

Counts

373 → 12

Compiler

Compiled 11740 to 6480 computations (44.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.0b	(/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (sqrt.f64 2))
24.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite176.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

7.8b

Rules

15×	`add-sqr-sqrt_binary64_782`
12×	`*-un-lft-identity_binary64_760`
10×	`add-cube-cbrt_binary64_795` `sqrt-prod_binary64_776`
9×	`add-exp-log_binary64_798`
8×	`add-log-exp_binary64_799`
7×	`add-cbrt-cube_binary64_796`
6×	`times-frac_binary64_766` `associate-/r*_binary64_704`
5×	`pow1_binary64_821`
4×	`cancel-sign-sub-inv_binary64_726`
3×	`flip3--_binary64_764` `flip--_binary64_735`
2×	`sqrt-div_binary64_777` `div-exp_binary64_811` `cbrt-undiv_binary64_794` `diff-log_binary64_852` `sub-neg_binary64_753` `difference-of-squares_binary64_729`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757` `associate-/l*_binary64_705` `distribute-lft-out--_binary64_712`

Counts

4 → 71

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
7.0ms	(/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (sqrt.f64 2))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 2716 to 1916 computations (29.5% saved)

series780.0ms (5.4%)

Error

7.8b

Counts

4 → 52

Calls

4 calls:

246.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
227.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
219.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
0.0ms	(/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (sqrt.f64 2))

Compiler

Compiled 4034 to 3478 computations (13.8% saved)

simplify107.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

629×	`associate-l_binary64_701`
531×	`associate-r_binary64_700`
318×	`unswap-sqr_binary64_728`
286×	`times-frac_binary64_766`
204×	`associate-/l*_binary64_705`
157×	`sub-neg_binary64_753`
155×	`*-commutative_binary64_691`
130×	`associate-/r*_binary64_704`
118×	`exp-prod_binary64_812`
113×	`associate-*l/_binary64_703`
104×	`cancel-sign-sub-inv_binary64_726`
103×	`distribute-rgt-neg-in_binary64_718`
99×	`sqr-pow_binary64_732`
98×	`neg-sub0_binary64_755`
92×	`neg-mul-1_binary64_756` `distribute-lft-neg-in_binary64_717`
88×	`associate-*r/_binary64_702`
83×	`associate-/l/_binary64_707`
75×	`associate-/r/_binary64_706`
70×	`distribute-lft-in_binary64_709`
67×	`distribute-rgt-in_binary64_710`
62×	`unsub-neg_binary64_754`
48×	`cube-prod_binary64_788`
36×	`+-commutative_binary64_690`
35×	`associate-+l-_binary64_695`
34×	`associate-+l+_binary64_693`
32×	`associate-+r-_binary64_694`
31×	`distribute-rgt-out_binary64_713`
27×	`log-div_binary64_847` `associate-+r+_binary64_692`
24×	`+-rgt-identity_binary64_745`
23×	`difference-of-squares_binary64_729` `distribute-neg-frac_binary64_724`
21×	`log-prod_binary64_846`
19×	`exp-sum_binary64_806` `sub0-neg_binary64_747`
16×	`unpow3_binary64_826` `associate--l+_binary64_697`
15×	`cube-unmult_binary64_797` `cube-div_binary64_789` `div-sub_binary64_765` `distribute-lft-neg-out_binary64_719`
13×	`pow-plus_binary64_823` `mul0-rgt_binary64_743` `mul0-lft_binary64_742`
12×	`exp-diff_binary64_808` `pow-sqr_binary64_733` `swap-sqr_binary64_727`
11×	`cube-mult_binary64_790` `*-rgt-identity_binary64_750`
9×	`associate--l-_binary64_698`
8×	`distribute-rgt-neg-out_binary64_720` `distribute-lft-out_binary64_711`
7×	`associate--r+_binary64_696`
6×	`rem-sqrt-square_binary64_773`
5×	`log-rec_binary64_848` `mul-1-neg_binary64_752` `/-rgt-identity_binary64_751` `*-lft-identity_binary64_749` `remove-double-div_binary64_736`
4×	`unpow2_binary64_825` `distribute-neg-in_binary64_721`
3×	`unpow1/2_binary64_824` `unpow1_binary64_818` `rem-square-sqrt_binary64_772` `distribute-rgt-out--_binary64_714`
2×	`div-exp_binary64_811` `rem-3cbrt-lft_binary64_785` `sqr-neg_binary64_774` `remove-double-neg_binary64_748` `distribute-lft-out--_binary64_712` `count-2_binary64_708`
1×	`1-exp_binary64_804` `rem-3cbrt-rft_binary64_786` `--rgt-identity_binary64_746` `div0_binary64_741` `+-inverses_binary64_739` `cancel-sign-sub_binary64_725` `distribute-neg-out_binary64_722` `associate--r-_binary64_699`
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` `pow-base-0_binary64_844` `unpow1/3_binary64_827` `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` `rec-exp_binary64_810` `prod-exp_binary64_809` `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` `cube-neg_binary64_787` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `+-lft-identity_binary64_744` `*-inverses_binary64_740` `lft-mult-inverse_binary64_738` `rgt-mult-inverse_binary64_737` `difference-of-sqr--1_binary64_731` `difference-of-sqr-1_binary64_730` `distribute-frac-neg_binary64_723` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715`

Counts

123 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	162	2168
1	375	1996
2	1047	1963
3	4144	1963
4	5072	1963

prune133.0ms (0.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	1	8	9
Picked	1	0	1
Done	0	2	2
Total	75	12	87

Error

7.8b

Counts

87 → 12

Compiler

Compiled 2311 to 1679 computations (27.3% saved)

regimes1.8s (12.6%)

Accuracy

Total 4.3b remaining (43.5%)

Threshold costs 0b (0%)

Compiler

Compiled 11844 to 9026 computations (23.8% saved)

bsearch70.0ms (0.5%)

Steps

Iters	Range		Point
6	1.9552026207765497e-92	2.1446087013644353e-91	1.778320156513799e-91
9	-3.6764914492777714e+155	-8.845415570980643e+145	-2.972045709025322e+148

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`sub-neg_binary64_753` `*-commutative_binary64_691` `+-commutative_binary64_690`
8×	`neg-sub0_binary64_755`
7×	`neg-mul-1_binary64_756`
4×	`distribute-rgt-neg-in_binary64_718`
3×	`distribute-lft-neg-in_binary64_717`
2×	`cancel-sign-sub-inv_binary64_726` `distribute-neg-frac_binary64_724`
1×	`mul-1-neg_binary64_752` `distribute-lft-neg-out_binary64_719`
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_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` `tan-0_binary64_889` `cos-0_binary64_888` `sin-0_binary64_887` `unpow1_binary64_818` `e-exp-1_binary64_805` `1-exp_binary64_804` `exp-1-e_binary64_803` `exp-0_binary64_802` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `unsub-neg_binary64_754` `/-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` `cancel-sign-sub_binary64_725` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722` `distribute-neg-in_binary64_721` `distribute-rgt-neg-out_binary64_720`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	52
1	40	52
2	59	52
3	77	52
4	88	52
5	92	52
6	93	52
7	93	52

end0.0ms (0%)

sample3.7s (26%)

Algorithm

1×

intervals

Results

292.0ms	5211×	body	128	valid
289.0ms	1122×	body	2048	valid
153.0ms	728×	body	1024	valid
130.0ms	386×	body	4096	valid
55.0ms	371×	body	512	valid
36.0ms	658×	body	128	nan
18.0ms	182×	body	256	valid
18.0ms	334×	body	128	invalid

Compiler

Compiled 3046 to 2313 computations (24.1% saved)

Details

analyze736.0ms (5.1%)

sample43.0ms (0.3%)

simplify339.0ms (2.4%)

prune7.0ms (0%)

localize11.0ms (0.1%)

rewrite161.0ms (1.1%)

series1.0s (7.2%)

simplify124.0ms (0.9%)

prune112.0ms (0.8%)

localize11.0ms (0.1%)

rewrite156.0ms (1.1%)

series1.0s (7.3%)

simplify350.0ms (2.4%)

prune99.0ms (0.7%)

localize15.0ms (0.1%)

rewrite993.0ms (6.9%)

series1.0s (7.2%)

simplify505.0ms (3.5%)

prune774.0ms (5.4%)

localize19.0ms (0.1%)

rewrite176.0ms (1.2%)

series780.0ms (5.4%)

simplify107.0ms (0.7%)

prune133.0ms (0.9%)

regimes1.8s (12.6%)

bsearch70.0ms (0.5%)

simplify6.0ms (0%)

end0.0ms (0%)

sample3.7s (26%)

Profiling