Details

analyze870.0ms (5.9%)

Algorithm

1×	search
2×	egg-herbie

Rules

655×	`div-sub_binary64_765` `sub-neg_binary64_753`
605×	`distribute-rgt-in_binary64_710`
539×	`associate-/l*_binary64_705`
495×	`neg-mul-1_binary64_756`
466×	`distribute-rgt-neg-in_binary64_718`
456×	`neg-sub0_binary64_755`
426×	`associate-/r*_binary64_704`
388×	`distribute-neg-frac_binary64_724`
289×	`distribute-rgt-neg-out_binary64_720` `distribute-lft-neg-out_binary64_719`
277×	`remove-double-neg_binary64_748`
251×	`cancel-sign-sub-inv_binary64_726`
242×	`distribute-frac-neg_binary64_723` `associate-l_binary64_701`
237×	`associate-r_binary64_700`
227×	`distribute-lft-neg-in_binary64_717`
208×	`*-commutative_binary64_691`
151×	`unsub-neg_binary64_754`
146×	`cancel-sign-sub_binary64_725`
128×	`associate-*l/_binary64_703`
119×	`distribute-neg-in_binary64_721` `associate--r+_binary64_696`
115×	`+-commutative_binary64_690`
112×	`times-frac_binary64_766`
107×	`associate-*r/_binary64_702`
94×	`associate-/r/_binary64_706`
79×	`distribute-lft-in_binary64_709`
77×	`associate--l-_binary64_698`
72×	`associate-/l/_binary64_707`
70×	`sub0-neg_binary64_747`
65×	`associate-+l-_binary64_695`
60×	`div0_binary64_741`
58×	`distribute-rgt-out--_binary64_714`
51×	`*-lft-identity_binary64_749`
50×	`associate--r-_binary64_699`
45×	`/-rgt-identity_binary64_751`
37×	`distribute-lft-out_binary64_711`
29×	`*-rgt-identity_binary64_750`
28×	`associate-+r-_binary64_694`
27×	`+-rgt-identity_binary64_745` `associate-+r+_binary64_692`
23×	`distribute-neg-out_binary64_722`
21×	`mul0-rgt_binary64_743` `mul0-lft_binary64_742`
20×	`distribute-rgt-out_binary64_713`
15×	`--rgt-identity_binary64_746`
13×	`associate--l+_binary64_697`
10×	`associate-+l+_binary64_693`
7×	`distribute-lft-out--_binary64_712`
6×	`mul-1-neg_binary64_752` `swap-sqr_binary64_727`
3×	`sqr-neg_binary64_774` `remove-double-div_binary64_736`
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` `+-lft-identity_binary64_744` `*-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` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `count-2_binary64_708`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	104
1	97	104
2	268	104
3	634	96
4	998	96
5	1695	96
6	3585	96
7	4103	96
8	3917	96
9	3960	96
10	4011	96
11	4065	96
12	4496	96
13	4413	96
14	4472	96
15	4499	96
16	4514	96
17	4517	96
18	4517	96
19	4810	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	168×	body	128	valid
8.0ms	28×	body	2048	valid
6.0ms	30×	body	1024	valid
4.0ms	12×	body	4096	valid
2.0ms	13×	body	512	valid
1.0ms	14×	body	128	nan
1.0ms	13×	body	128	invalid
1.0ms	5×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify325.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1319×	`div-sub_binary64_765`
932×	`unsub-neg_binary64_754`
843×	`associate-/l*_binary64_705`
678×	`distribute-rgt-in_binary64_710`
643×	`distribute-lft-in_binary64_709`
485×	`associate-/l/_binary64_707`
481×	`associate-/r/_binary64_706`
474×	`sub-neg_binary64_753`
459×	`cancel-sign-sub-inv_binary64_726`
405×	`times-frac_binary64_766`
321×	`distribute-rgt-neg-in_binary64_718`
316×	`neg-mul-1_binary64_756`
286×	`neg-sub0_binary64_755`
273×	`distribute-lft-neg-in_binary64_717`
261×	`*-commutative_binary64_691`
254×	`distribute-neg-frac_binary64_724`
228×	`associate-/r*_binary64_704`
200×	`distribute-neg-in_binary64_721`
198×	`associate-*l/_binary64_703`
136×	`mul0-rgt_binary64_743`
134×	`mul0-lft_binary64_742`
122×	`+-lft-identity_binary64_744` `associate--r+_binary64_696`
115×	`distribute-rgt-neg-out_binary64_720`
102×	`+-commutative_binary64_690`
96×	`distribute-rgt-out_binary64_713`
88×	`+-rgt-identity_binary64_745`
80×	`remove-double-neg_binary64_748`
77×	`distribute-frac-neg_binary64_723`
75×	`distribute-lft-neg-out_binary64_719`
74×	`div0_binary64_741`
72×	`distribute-rgt-out--_binary64_714` `associate--r-_binary64_699`
58×	`associate-*r/_binary64_702`
54×	`cancel-sign-sub_binary64_725`
48×	`associate-l_binary64_701` `associate-r_binary64_700`
39×	`distribute-neg-out_binary64_722`
38×	`associate--l-_binary64_698`
36×	`/-rgt-identity_binary64_751`
23×	`*-lft-identity_binary64_749`
22×	`remove-double-div_binary64_736`
20×	`associate--l+_binary64_697`
19×	`sub0-neg_binary64_747`
18×	`mul-1-neg_binary64_752`
16×	`associate-+l-_binary64_695`
9×	`*-rgt-identity_binary64_750`
8×	`--rgt-identity_binary64_746` `associate-+r-_binary64_694` `associate-+r+_binary64_692`
6×	`distribute-lft-out_binary64_711`
4×	`associate-+l+_binary64_693`
2×	`swap-sqr_binary64_727`
1×	`1-exp_binary64_804` `sqr-neg_binary64_774`
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` `*-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` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `distribute-lft-out--_binary64_712` `count-2_binary64_708`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	37	26
2	93	26
3	213	24
4	320	24
5	522	24
6	913	24
7	995	24
8	1154	24
9	1806	24
10	2663	24
11	2356	24
12	2303	24
13	2372	24
14	2398	24
15	2585	24
16	3881	24
17	3563	24
18	3397	24
19	3505	24
20	3509	24
21	3623	24
22	3691	24
23	3691	24
24	2163	24
25	2363	24
26	2081	24
27	2083	24
28	2083	24
29	2083	24
30	1834	24

prune5.0ms (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

35.2b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
24.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite164.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

35.0b

Rules

24×	`*-un-lft-identity_binary64_760`
15×	`add-sqr-sqrt_binary64_782`
14×	`add-cube-cbrt_binary64_795`
12×	`times-frac_binary64_766`
8×	`add-log-exp_binary64_799`
6×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
5×	`pow1_binary64_821` `distribute-lft-out_binary64_711`
4×	`associate-/l*_binary64_705`
3×	`sqrt-prod_binary64_776` `associate-/r*_binary64_704`
2×	`flip3--_binary64_764` `sqrt-div_binary64_777` `flip--_binary64_735` `flip3-+_binary64_763` `flip-+_binary64_734` `associate-/l/_binary64_707`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `sum-log_binary64_851` `+-commutative_binary64_690` `diff-log_binary64_852` `sub-neg_binary64_753` `cancel-sign-sub-inv_binary64_726` `div-exp_binary64_811` `cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757`

Counts

4 → 72

Calls

4 calls:

9.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
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 2053 to 1050 computations (48.9% saved)

series1.1s (7.4%)

Error

6.6b

Counts

4 → 77

Calls

4 calls:

325.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
242.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
229.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
204.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3528 to 2676 computations (24.1% saved)

simplify91.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

737×	`associate-l_binary64_701`
569×	`times-frac_binary64_766`
447×	`associate-/l*_binary64_705`
306×	`associate-/r*_binary64_704`
171×	`cancel-sign-sub-inv_binary64_726`
133×	`distribute-rgt-neg-in_binary64_718`
132×	`associate-*l/_binary64_703`
121×	`distribute-lft-neg-in_binary64_717`
117×	`associate-/r/_binary64_706`
114×	`associate-*r/_binary64_702`
113×	`distribute-rgt-in_binary64_710`
100×	`distribute-lft-in_binary64_709`
84×	`unswap-sqr_binary64_728`
81×	`associate-/l/_binary64_707` `associate-r_binary64_700`
70×	`*-commutative_binary64_691`
63×	`sub-neg_binary64_753`
55×	`+-commutative_binary64_690`
49×	`sqr-pow_binary64_732`
38×	`distribute-neg-frac_binary64_724`
34×	`neg-sub0_binary64_755`
33×	`neg-mul-1_binary64_756`
30×	`distribute-rgt-out_binary64_713`
26×	`exp-prod_binary64_812`
23×	`associate-+r+_binary64_692`
22×	`associate-+l+_binary64_693`
16×	`distribute-lft-neg-out_binary64_719`
14×	`distribute-neg-in_binary64_721`
13×	`cube-prod_binary64_788`
12×	`swap-sqr_binary64_727`
11×	`associate--l+_binary64_697`
9×	`distribute-lft-out_binary64_711`
8×	`unpow3_binary64_826` `cube-mult_binary64_790` `unsub-neg_binary64_754` `associate--r+_binary64_696`
7×	`difference-of-squares_binary64_729` `distribute-rgt-neg-out_binary64_720` `distribute-rgt-out--_binary64_714`
6×	`distribute-lft-out--_binary64_712`
4×	`pow-plus_binary64_823` `cube-unmult_binary64_797` `div-sub_binary64_765` `/-rgt-identity_binary64_751` `*-rgt-identity_binary64_750` `pow-sqr_binary64_733`
3×	`log-div_binary64_847` `unpow2_binary64_825` `unpow1/2_binary64_824` `unpow1_binary64_818` `exp-diff_binary64_808` `exp-sum_binary64_806` `rem-sqrt-square_binary64_773` `associate-+r-_binary64_694`
2×	`log-prod_binary64_846` `count-2_binary64_708` `associate-+l-_binary64_695`
1×	`log-pow_binary64_849` `div-exp_binary64_811` `prod-exp_binary64_809` `1-exp_binary64_804` `cube-div_binary64_789` `rem-square-sqrt_binary64_772` `mul-1-neg_binary64_752` `*-lft-identity_binary64_749` `remove-double-neg_binary64_748` `+-rgt-identity_binary64_745` `+-inverses_binary64_739` `cancel-sign-sub_binary64_725` `distribute-neg-out_binary64_722` `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-lft-sqr_binary64_815` `exp-cbrt_binary64_814` `exp-sqrt_binary64_813` `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` `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` `sub0-neg_binary64_747` `--rgt-identity_binary64_746` `+-lft-identity_binary64_744` `mul0-rgt_binary64_743` `mul0-lft_binary64_742` `div0_binary64_741` `*-inverses_binary64_740` `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

149 → 85

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	191	3307
1	478	3103
2	1426	3085
3	5314	3085

prune117.0ms (0.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	73	12	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	12	86

Error

10.1b

Counts

86 → 12

Compiler

Compiled 1929 to 1054 computations (45.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
3.5b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
9.8b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
24.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite327.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

10.1b

Rules

66×	`times-frac_binary64_766`
59×	`add-sqr-sqrt_binary64_782`
44×	`*-un-lft-identity_binary64_760`
30×	`add-cube-cbrt_binary64_795`
27×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
14×	`difference-of-squares_binary64_729`
13×	`sqrt-prod_binary64_776` `associate-/l*_binary64_705`
10×	`div-exp_binary64_811` `cbrt-undiv_binary64_794` `associate-/r/_binary64_706`
9×	`associate-/r*_binary64_704`
7×	`flip3--_binary64_764` `flip--_binary64_735` `distribute-lft-out--_binary64_712`
6×	`add-log-exp_binary64_799` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `div-inv_binary64_757` `cancel-sign-sub-inv_binary64_726`
5×	`pow1_binary64_821`
2×	`sqrt-div_binary64_777` `frac-2neg_binary64_771` `clear-num_binary64_759`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `associate-/l/_binary64_707` `diff-log_binary64_852` `sub-neg_binary64_753`

Counts

4 → 136

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
15.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
8.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 5265 to 2649 computations (49.7% saved)

series1.6s (11%)

Error

6.4b

Counts

4 → 76

Calls

4 calls:

579.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
535.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
218.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
202.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 4742 to 3406 computations (28.2% saved)

simplify250.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

277×	`cancel-sign-sub-inv_binary64_726`
258×	`associate-/l*_binary64_705`
246×	`times-frac_binary64_766` `distribute-rgt-neg-in_binary64_718`
164×	`associate-/l/_binary64_707`
158×	`associate-/r*_binary64_704`
146×	`associate-r_binary64_700`
144×	`*-commutative_binary64_691`
130×	`sub-neg_binary64_753`
113×	`distribute-neg-frac_binary64_724`
109×	`associate-l_binary64_701`
104×	`unswap-sqr_binary64_728`
82×	`associate-*l/_binary64_703`
80×	`neg-mul-1_binary64_756` `neg-sub0_binary64_755`
78×	`associate-*r/_binary64_702`
77×	`log-prod_binary64_846`
73×	`+-commutative_binary64_690`
71×	`div-sub_binary64_765`
67×	`log-div_binary64_847`
62×	`exp-prod_binary64_812`
59×	`associate-/r/_binary64_706`
58×	`distribute-neg-in_binary64_721`
50×	`sqr-pow_binary64_732`
40×	`unpow3_binary64_826` `distribute-rgt-in_binary64_710`
38×	`distribute-lft-neg-out_binary64_719`
33×	`distribute-lft-neg-in_binary64_717` `distribute-lft-in_binary64_709`
29×	`cube-prod_binary64_788` `associate-+l+_binary64_693`
28×	`associate-+r+_binary64_692`
26×	`swap-sqr_binary64_727`
25×	`distribute-rgt-neg-out_binary64_720`
24×	`*-rgt-identity_binary64_750`
23×	`cube-div_binary64_789` `unsub-neg_binary64_754` `associate--l+_binary64_697`
21×	`*-lft-identity_binary64_749` `associate--r+_binary64_696`
13×	`/-rgt-identity_binary64_751`
11×	`difference-of-squares_binary64_729`
9×	`log-pow_binary64_849` `cube-mult_binary64_790`
8×	`distribute-frac-neg_binary64_723` `distribute-rgt-out_binary64_713`
7×	`pow-plus_binary64_823`
6×	`rem-sqrt-square_binary64_773` `distribute-lft-out--_binary64_712`
5×	`exp-sum_binary64_806` `cube-unmult_binary64_797` `associate-+r-_binary64_694`
4×	`log-rec_binary64_848` `unpow2_binary64_825` `unpow1/2_binary64_824` `unpow1_binary64_818` `distribute-lft-out_binary64_711`
3×	`rem-square-sqrt_binary64_772` `+-rgt-identity_binary64_745`
2×	`exp-diff_binary64_808` `mul-1-neg_binary64_752` `remove-double-neg_binary64_748` `div0_binary64_741` `associate--r-_binary64_699` `associate--l-_binary64_698` `associate-+l-_binary64_695`
1×	`div-exp_binary64_811` `1-exp_binary64_804` `rem-3cbrt-lft_binary64_785` `*-inverses_binary64_740` `+-inverses_binary64_739` `pow-sqr_binary64_733` `distribute-neg-out_binary64_722`
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` `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-3cbrt-rft_binary64_786` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `sub0-neg_binary64_747` `--rgt-identity_binary64_746` `+-lft-identity_binary64_744` `mul0-rgt_binary64_743` `mul0-lft_binary64_742` `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` `cancel-sign-sub_binary64_725` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `distribute-rgt-out--_binary64_714` `count-2_binary64_708`

Counts

212 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	326	7161
1	881	6516
2	3275	6373
3	4829	6373
4	4994	6373
5	4943	6373

prune213.0ms (1.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	139	5	144
Fresh	6	5	11
Picked	0	1	1
Done	0	0	0
Total	145	11	156

Error

8.1b

Counts

156 → 11

Compiler

Compiled 4277 to 2287 computations (46.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.8b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
24.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite180.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

8.1b

Rules

39×	`add-sqr-sqrt_binary64_782`
28×	`*-un-lft-identity_binary64_760`
18×	`add-cube-cbrt_binary64_795` `times-frac_binary64_766`
11×	`sqrt-prod_binary64_776`
10×	`difference-of-squares_binary64_729`
8×	`add-log-exp_binary64_799`
7×	`cancel-sign-sub-inv_binary64_726`
6×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `associate-/r*_binary64_704`
5×	`pow1_binary64_821` `distribute-lft-out--_binary64_712`
4×	`flip3--_binary64_764` `flip--_binary64_735`
3×	`associate-/l*_binary64_705`
2×	`sqrt-div_binary64_777` `diff-log_binary64_852` `sub-neg_binary64_753` `associate-/r/_binary64_706`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `div-exp_binary64_811` `cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757`

Counts

4 → 88

Calls

4 calls:

12.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
9.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
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 2944 to 1670 computations (43.3% saved)

series1.2s (8.2%)

Error

6.4b

Counts

4 → 74

Calls

4 calls:

441.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
246.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
230.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
209.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 4188 to 3320 computations (20.7% saved)

simplify106.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

794×	`times-frac_binary64_766`
549×	`associate-/l*_binary64_705`
219×	`cancel-sign-sub-inv_binary64_726`
166×	`distribute-rgt-neg-in_binary64_718`
148×	`distribute-lft-neg-in_binary64_717`
142×	`associate-/r/_binary64_706`
112×	`associate-/l/_binary64_707`
104×	`distribute-rgt-in_binary64_710`
100×	`sub-neg_binary64_753`
96×	`unswap-sqr_binary64_728`
82×	`distribute-lft-in_binary64_709`
77×	`associate-r_binary64_700`
71×	`*-commutative_binary64_691`
65×	`associate-l_binary64_701`
63×	`neg-sub0_binary64_755`
62×	`neg-mul-1_binary64_756`
58×	`distribute-neg-frac_binary64_724`
55×	`sqr-pow_binary64_732`
54×	`+-commutative_binary64_690`
41×	`distribute-neg-in_binary64_721`
39×	`exp-prod_binary64_812`
38×	`associate-/r*_binary64_704`
31×	`distribute-rgt-out_binary64_713` `associate-l/_binary64_703` `associate-r/_binary64_702`
23×	`distribute-lft-neg-out_binary64_719`
18×	`associate--r+_binary64_696`
17×	`cube-prod_binary64_788` `associate-+r+_binary64_692`
16×	`unsub-neg_binary64_754`
15×	`div-sub_binary64_765` `associate-+l+_binary64_693`
12×	`*-rgt-identity_binary64_750` `associate--l+_binary64_697`
11×	`difference-of-squares_binary64_729` `swap-sqr_binary64_727`
10×	`distribute-rgt-neg-out_binary64_720`
9×	`unpow3_binary64_826` `cube-mult_binary64_790`
8×	`distribute-rgt-out--_binary64_714` `distribute-lft-out_binary64_711`
6×	`exp-sum_binary64_806` `rem-sqrt-square_binary64_773` `distribute-lft-out--_binary64_712`
5×	`log-prod_binary64_846` `exp-diff_binary64_808` `cube-unmult_binary64_797` `associate-+r-_binary64_694`
4×	`unpow2_binary64_825` `unpow1/2_binary64_824` `pow-plus_binary64_823` `unpow1_binary64_818` `cube-div_binary64_789` `/-rgt-identity_binary64_751` `pow-sqr_binary64_733`
3×	`log-div_binary64_847` `rem-square-sqrt_binary64_772` `mul-1-neg_binary64_752` `+-rgt-identity_binary64_745` `distribute-frac-neg_binary64_723`
2×	`div-exp_binary64_811` `remove-double-neg_binary64_748` `count-2_binary64_708` `associate--r-_binary64_699`
1×	`log-pow_binary64_849` `1-exp_binary64_804` `rem-3cbrt-lft_binary64_785` `*-lft-identity_binary64_749` `div0_binary64_741` `+-inverses_binary64_739` `distribute-rgt1-in_binary64_716` `associate-+l-_binary64_695`
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-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-3cbrt-rft_binary64_786` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `sub0-neg_binary64_747` `--rgt-identity_binary64_746` `+-lft-identity_binary64_744` `mul0-rgt_binary64_743` `mul0-lft_binary64_742` `*-inverses_binary64_740` `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` `cancel-sign-sub_binary64_725` `distribute-neg-out_binary64_722` `distribute-lft1-in_binary64_715` `associate--l-_binary64_698`

Counts

162 → 99

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	211	3825
1	528	3623
2	1581	3594
3	4945	3594

prune138.0ms (0.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	3	6	9
Picked	0	1	1
Done	0	1	1
Total	101	9	110

Error

6.4b

Counts

110 → 9

Compiler

Compiled 2551 to 1527 computations (40.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.8b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
17.8b	(/.f64 (.f64 4 (.f64 a c)) (.f64 a (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
24.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite159.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

6.4b

Rules

25×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
12×	`add-sqr-sqrt_binary64_782`
9×	`*-un-lft-identity_binary64_760` `prod-exp_binary64_809` `cbrt-unprod_binary64_793`
8×	`add-log-exp_binary64_799`
7×	`add-cube-cbrt_binary64_795` `sqrt-prod_binary64_776` `cancel-sign-sub-inv_binary64_726`
6×	`div-exp_binary64_811` `cbrt-undiv_binary64_794`
5×	`pow1_binary64_821`
4×	`flip3--_binary64_764` `flip--_binary64_735`
2×	`sqrt-div_binary64_777` `associate-*r/_binary64_702` `associate-/r/_binary64_706` `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` `frac-2neg_binary64_771` `times-frac_binary64_766` `clear-num_binary64_759` `div-inv_binary64_757` `associate-/l_binary64_705` `associate-/r_binary64_704` `distribute-lft-out--_binary64_712`

Counts

4 → 74

Calls

4 calls:

14.0ms	(/.f64 (.f64 4 (.f64 a c)) (.f64 a (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
8.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
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 2674 to 1363 computations (49% saved)

series1.2s (8.5%)

Error

6.4b

Counts

4 → 74

Calls

4 calls:

497.0ms	(/.f64 (.f64 4 (.f64 a c)) (.f64 a (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
249.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
217.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
202.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 4336 to 3096 computations (28.6% saved)

simplify157.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

355×	`times-frac_binary64_766`
253×	`cancel-sign-sub-inv_binary64_726`
215×	`distribute-rgt-neg-in_binary64_718`
196×	`distribute-rgt-in_binary64_710`
195×	`distribute-lft-neg-in_binary64_717`
176×	`distribute-lft-in_binary64_709` `associate-/l*_binary64_705`
145×	`log-prod_binary64_846`
144×	`associate-r_binary64_700`
139×	`associate-/r*_binary64_704`
126×	`associate-l_binary64_701`
123×	`exp-prod_binary64_812`
115×	`sub-neg_binary64_753` `unswap-sqr_binary64_728`
106×	`*-commutative_binary64_691`
68×	`neg-mul-1_binary64_756` `neg-sub0_binary64_755`
62×	`distribute-neg-frac_binary64_724` `+-commutative_binary64_690`
56×	`sqr-pow_binary64_732`
54×	`log-div_binary64_847`
48×	`distribute-neg-in_binary64_721`
45×	`associate-*r/_binary64_702`
44×	`associate-*l/_binary64_703`
42×	`div-sub_binary64_765`
37×	`distribute-rgt-out_binary64_713`
34×	`unpow3_binary64_826`
33×	`exp-sum_binary64_806`
30×	`distribute-lft-neg-out_binary64_719`
26×	`cube-mult_binary64_790`
24×	`cube-prod_binary64_788`
22×	`swap-sqr_binary64_727` `associate--r+_binary64_696`
21×	`associate-/r/_binary64_706` `associate--l+_binary64_697`
20×	`unsub-neg_binary64_754`
19×	`associate-+l+_binary64_693` `associate-+r+_binary64_692`
18×	`distribute-rgt-neg-out_binary64_720`
15×	`exp-diff_binary64_808`
12×	`cube-unmult_binary64_797`
11×	`difference-of-squares_binary64_729` `distribute-lft-out_binary64_711`
10×	`log-pow_binary64_849`
9×	`pow-plus_binary64_823` `cube-div_binary64_789`
7×	`distribute-rgt-out--_binary64_714`
6×	`distribute-lft-out--_binary64_712`
5×	`unpow2_binary64_825` `rem-sqrt-square_binary64_773` `associate-+r-_binary64_694`
4×	`unpow1/2_binary64_824` `unpow1_binary64_818` `pow-sqr_binary64_733` `distribute-frac-neg_binary64_723`
3×	`rem-square-sqrt_binary64_772` `-rgt-identity_binary64_750` `+-rgt-identity_binary64_745` `-inverses_binary64_740` `associate-/l/_binary64_707`
2×	`div-exp_binary64_811` `mul-1-neg_binary64_752` `remove-double-neg_binary64_748` `distribute-rgt1-in_binary64_716`
1×	`log-rec_binary64_848` `1-exp_binary64_804` `rem-3cbrt-lft_binary64_785` `/-rgt-identity_binary64_751` `*-lft-identity_binary64_749` `+-inverses_binary64_739` `associate--r-_binary64_699` `associate-+l-_binary64_695`
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` `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-3cbrt-rft_binary64_786` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `sub0-neg_binary64_747` `--rgt-identity_binary64_746` `+-lft-identity_binary64_744` `mul0-rgt_binary64_743` `mul0-lft_binary64_742` `div0_binary64_741` `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` `cancel-sign-sub_binary64_725` `distribute-neg-out_binary64_722` `distribute-lft1-in_binary64_715` `count-2_binary64_708` `associate--l-_binary64_698`

Counts

148 → 101

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	226	3672
1	629	2989
2	2603	2918
3	4697	2918
4	4986	2918
5	5005	2918

prune128.0ms (0.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	101	9	110

Error

6.4b

Counts

110 → 9

Compiler

Compiled 2459 to 1282 computations (47.9% saved)

regimes2.2s (14.9%)

Accuracy

Total 1.5b remaining (20.9%)

Threshold costs 0b (0%)

Compiler

Compiled 14104 to 10118 computations (28.3% saved)

bsearch107.0ms (0.7%)

Steps

Iters	Range	Point
2	2.4848932620839945e+72	2.718455955070719e+72	2.6892606184473783e+72
8	7.240030896940518e-119	2.7473432819822515e-114	7.387487850441641e-119
9	-3.6764914492777714e+155	-1.9435009923106308e+149	-1.2147252142309174e+151

Iters

Range

Point

2.4848932620839945e+72

2.718455955070719e+72

2.6892606184473783e+72

7.240030896940518e-119

2.7473432819822515e-114

7.387487850441641e-119

-3.6764914492777714e+155

-1.9435009923106308e+149

-1.2147252142309174e+151

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

19×	`*-commutative_binary64_691`
13×	`+-commutative_binary64_690`
12×	`sub-neg_binary64_753`
9×	`neg-mul-1_binary64_756` `neg-sub0_binary64_755`
6×	`distribute-rgt-neg-in_binary64_718`
4×	`cancel-sign-sub-inv_binary64_726` `distribute-lft-neg-in_binary64_717`
2×	`distribute-lft-neg-out_binary64_719`
1×	`1-exp_binary64_804` `*-lft-identity_binary64_749` `distribute-neg-frac_binary64_724`
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` `exp-1-e_binary64_803` `exp-0_binary64_802` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `unsub-neg_binary64_754` `mul-1-neg_binary64_752` `/-rgt-identity_binary64_751` `*-rgt-identity_binary64_750` `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	38	98
1	63	98
2	83	98
3	104	98
4	117	98
5	123	98
6	125	98
7	124	98

end0.0ms (0%)

sample3.9s (26.7%)

Algorithm

1×

intervals

Results

297.0ms	5241×	body	128	valid
286.0ms	1088×	body	2048	valid
153.0ms	724×	body	1024	valid
129.0ms	399×	body	4096	valid
56.0ms	371×	body	512	valid
36.0ms	658×	body	128	nan
23.0ms	390×	body	128	invalid
18.0ms	177×	body	256	valid

Compiler

Compiled 3642 to 2608 computations (28.4% saved)

Details

analyze870.0ms (5.9%)

sample43.0ms (0.3%)

simplify325.0ms (2.2%)

prune5.0ms (0%)

localize15.0ms (0.1%)

rewrite164.0ms (1.1%)

series1.1s (7.4%)

simplify91.0ms (0.6%)

prune117.0ms (0.8%)

localize13.0ms (0.1%)

rewrite327.0ms (2.2%)

series1.6s (11%)

simplify250.0ms (1.7%)

prune213.0ms (1.4%)

localize14.0ms (0.1%)

rewrite180.0ms (1.2%)

series1.2s (8.2%)

simplify106.0ms (0.7%)

prune138.0ms (0.9%)

localize13.0ms (0.1%)

rewrite159.0ms (1.1%)

series1.2s (8.5%)

simplify157.0ms (1.1%)

prune128.0ms (0.9%)

regimes2.2s (14.9%)

bsearch107.0ms (0.7%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample3.9s (26.7%)

Profiling