Details

analyze2.3s (14.2%)

Algorithm

1×	search
2×	egg-herbie

Rules

584×	`exp-prod_binary64_812`
582×	`exp-sum_binary64_806`
397×	`sub-neg_binary64_753`
308×	`exp-diff_binary64_808`
164×	`distribute-rgt-in_binary64_710`
152×	`times-frac_binary64_766`
144×	`distribute-lft-in_binary64_709`
130×	`neg-mul-1_binary64_756`
128×	`unsub-neg_binary64_754`
117×	`neg-sub0_binary64_755`
108×	`*-commutative_binary64_691`
107×	`+-commutative_binary64_690`
102×	`associate-+r-_binary64_694`
85×	`associate-r_binary64_700`
80×	`associate-+l-_binary64_695`
76×	`associate-l_binary64_701`
66×	`distribute-neg-in_binary64_721`
61×	`associate--r+_binary64_696`
53×	`associate-+l+_binary64_693`
44×	`associate-+r+_binary64_692`
41×	`associate-/l_binary64_705` `associate-l/_binary64_703`
40×	`associate-/r/_binary64_706`
37×	`sqr-pow_binary64_732`
33×	`associate--r-_binary64_699`
32×	`associate--l-_binary64_698` `associate--l+_binary64_697`
31×	`cancel-sign-sub-inv_binary64_726`
30×	`associate-*r/_binary64_702`
27×	`exp-neg_binary64_807`
26×	`distribute-lft-neg-in_binary64_717`
25×	`exp-sqrt_binary64_813`
22×	`distribute-neg-out_binary64_722` `associate-/r*_binary64_704`
21×	`div-exp_binary64_811` `sub0-neg_binary64_747` `distribute-lft-out_binary64_711`
18×	`distribute-rgt-neg-in_binary64_718`
11×	`prod-exp_binary64_809` `associate-/l/_binary64_707`
10×	`unpow2_binary64_825`
9×	`unpow3_binary64_826` `unpow1/2_binary64_824` `pow-plus_binary64_823` `unpow1_binary64_818` `cube-unmult_binary64_797` `rem-sqrt-square_binary64_773` `distribute-rgt-neg-out_binary64_720` `distribute-lft-neg-out_binary64_719`
8×	`remove-double-neg_binary64_748`
5×	`sqr-neg_binary64_774`
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` `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` `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-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-square-sqrt_binary64_772` `div-sub_binary64_765` `mul-1-neg_binary64_752` `/-rgt-identity_binary64_751` `-rgt-identity_binary64_750` `-lft-identity_binary64_749` `--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` `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_binary64_725` `distribute-neg-frac_binary64_724` `distribute-frac-neg_binary64_723` `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` `count-2_binary64_708`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	154	495
1	397	495
2	925	473
3	3020	473
4	4898	473
5	5136	473
0	5	5
1	5	5

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
12.5%	87.3%	0.2%	9
12.5%	87.3%	0.2%	10
18.7%	81.1%	0.2%	11
18.7%	81.1%	0.2%	12
18.7%	81.1%	0.2%	13
20.5%	79.3%	0.2%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample45.0ms (0.3%)

Algorithm

1×

intervals

Results

24.0ms	252×	body	128	valid
1.0ms	3×	body	512	invalid
1.0ms	9×	body	128	invalid
1.0ms	2×	body	1024	valid
1.0ms	2×	body	1024	invalid
1.0ms	2×	body	512	valid
0.0ms	1×	body	256	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify50.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

604×	`exp-prod_binary64_812`
534×	`exp-sum_binary64_806`
375×	`associate-l_binary64_701`
303×	`associate-r_binary64_700`
251×	`times-frac_binary64_766`
229×	`cancel-sign-sub-inv_binary64_726`
204×	`distribute-rgt-in_binary64_710`
182×	`associate-/l*_binary64_705`
169×	`exp-diff_binary64_808`
164×	`distribute-lft-in_binary64_709`
112×	`associate-/r_binary64_704` `associate-l/_binary64_703`
99×	`sub-neg_binary64_753`
92×	`distribute-neg-in_binary64_721`
87×	`unsub-neg_binary64_754`
86×	`associate-*r/_binary64_702`
74×	`associate--r-_binary64_699`
70×	`associate--l-_binary64_698`
68×	`distribute-rgt-neg-in_binary64_718`
60×	`exp-sqrt_binary64_813`
54×	`distribute-lft-neg-in_binary64_717` `associate-/l/_binary64_707`
52×	`associate-+l+_binary64_693`
48×	`sqr-pow_binary64_732`
47×	`distribute-rgt-neg-out_binary64_720`
44×	`associate-/r/_binary64_706`
43×	`div-exp_binary64_811`
42×	`distribute-lft-neg-out_binary64_719`
41×	`prod-exp_binary64_809`
40×	`neg-mul-1_binary64_756`
39×	`neg-sub0_binary64_755`
38×	`associate--r+_binary64_696`
35×	`associate-+r+_binary64_692`
34×	`*-commutative_binary64_691`
31×	`exp-neg_binary64_807`
30×	`associate--l+_binary64_697`
24×	`+-commutative_binary64_690`
23×	`unswap-sqr_binary64_728`
22×	`distribute-rgt-out_binary64_713`
21×	`distribute-neg-out_binary64_722`
20×	`associate-+l-_binary64_695`
19×	`distribute-rgt-out--_binary64_714` `associate-+r-_binary64_694`
17×	`div-sub_binary64_765`
15×	`distribute-neg-frac_binary64_724`
13×	`rec-exp_binary64_810` `remove-double-neg_binary64_748` `sub0-neg_binary64_747` `distribute-lft-out_binary64_711`
10×	`+-rgt-identity_binary64_745`
7×	`*-lft-identity_binary64_749` `--rgt-identity_binary64_746` `pow-sqr_binary64_733` `swap-sqr_binary64_727` `distribute-lft-out--_binary64_712`
6×	`/-rgt-identity_binary64_751` `distribute-frac-neg_binary64_723`
5×	`pow-plus_binary64_823` `mul0-rgt_binary64_743` `mul0-lft_binary64_742`
4×	`*-rgt-identity_binary64_750`
2×	`cube-unmult_binary64_797` `sqr-neg_binary64_774`
1×	`cos-neg_binary64_891` `unpow2_binary64_825` `unpow1/2_binary64_824` `unpow1_binary64_818` `1-exp_binary64_804` `exp-1-e_binary64_803` `rem-sqrt-square_binary64_773` `mul-1-neg_binary64_752` `cancel-sign-sub_binary64_725`
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` `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` `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` `e-exp-1_binary64_805` `exp-0_binary64_802` `rem-log-exp_binary64_801` `rem-exp-log_binary64_800` `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-square-sqrt_binary64_772` `+-lft-identity_binary64_744` `div0_binary64_741` `*-inverses_binary64_740` `+-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` `difference-of-squares_binary64_729` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `count-2_binary64_708`

Counts

1 → 1

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	45
1	56	45
2	121	43
3	355	43
4	1127	43
5	4019	43
6	5097	43

prune6.0ms (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

14.1b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 K (+.f64 m n))
0.0b	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
32.7b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite205.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

14.0b

Rules

22×	`*-un-lft-identity_binary64_760`
20×	`add-sqr-sqrt_binary64_782`
11×	`add-cube-cbrt_binary64_795`
10×	`add-log-exp_binary64_799`
7×	`cancel-sign-sub-inv_binary64_726` `pow1_binary64_821` `add-exp-log_binary64_798`
6×	`add-cbrt-cube_binary64_796` `unpow-prod-down_binary64_839` `exp-prod_binary64_812`
5×	`exp-sum_binary64_806`
4×	`cos-sum_binary64_894` `associate-r_binary64_700`
3×	`difference-of-squares_binary64_729` `distribute-lft-out--_binary64_712` `pow-unpow_binary64_837` `distribute-lft-out_binary64_711` `rem-exp-log_binary64_800` `associate-l_binary64_701`
2×	`sub-neg_binary64_753` `diff-log_binary64_852` `associate-*r/_binary64_702`
1×	`cos-diff_binary64_897` `times-frac_binary64_766` `pow-pow_binary64_832` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `unpow2_binary64_825` `sqr-pow_binary64_732` `exp-diff_binary64_808` `sum-log_binary64_851` `pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `unswap-sqr_binary64_728` `distribute-rgt-in_binary64_710` `distribute-lft-in_binary64_709` `flip3-+_binary64_763` `flip-+_binary64_734` `*-commutative_binary64_691`

Counts

4 → 78

Calls

4 calls:

18.0ms	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
14.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
10.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
6.0ms	(*.f64 K (+.f64 m n))

Compiler

Compiled 2906 to 1447 computations (50.2% saved)

series1.3s (7.9%)

Error

1.0b

Counts

4 → 68

Calls

4 calls:

431.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
341.0ms	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
280.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
106.0ms	(*.f64 K (+.f64 m n))

Compiler

Compiled 6937 to 4672 computations (32.7% saved)

simplify101.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

393×	`distribute-rgt-in_binary64_710`
347×	`distribute-lft-in_binary64_709`
318×	`cancel-sign-sub-inv_binary64_726`
232×	`sub-neg_binary64_753`
218×	`exp-sum_binary64_806`
157×	`associate-r_binary64_700`
155×	`distribute-rgt-neg-in_binary64_718`
144×	`distribute-neg-in_binary64_721` `associate-l_binary64_701`
138×	`distribute-lft-neg-in_binary64_717`
123×	`*-commutative_binary64_691`
105×	`+-commutative_binary64_690`
88×	`associate--l+_binary64_697`
87×	`sqr-pow_binary64_732`
85×	`associate--r+_binary64_696`
84×	`exp-diff_binary64_808`
75×	`exp-prod_binary64_812`
74×	`neg-mul-1_binary64_756`
72×	`associate-+l+_binary64_693`
70×	`neg-sub0_binary64_755`
69×	`associate-+r+_binary64_692`
64×	`unswap-sqr_binary64_728`
51×	`distribute-lft-neg-out_binary64_719`
47×	`distribute-rgt-neg-out_binary64_720`
44×	`times-frac_binary64_766` `unsub-neg_binary64_754`
29×	`distribute-rgt-out_binary64_713`
18×	`distribute-lft-out_binary64_711`
17×	`log-prod_binary64_846` `*-lft-identity_binary64_749`
16×	`*-rgt-identity_binary64_750` `cancel-sign-sub_binary64_725`
15×	`unpow2_binary64_825` `unpow1/2_binary64_824` `unpow1_binary64_818`
12×	`pow-sqr_binary64_733` `swap-sqr_binary64_727` `associate-+r-_binary64_694`
10×	`cube-unmult_binary64_797` `cube-prod_binary64_788` `+-rgt-identity_binary64_745`
8×	`distribute-neg-out_binary64_722` `distribute-rgt-out--_binary64_714`
7×	`prod-exp_binary64_809`
6×	`log-pow_binary64_849` `pow-plus_binary64_823`
5×	`rem-sqrt-square_binary64_773` `associate-/l*_binary64_705`
4×	`distribute-lft-out--_binary64_712`
3×	`cos-neg_binary64_891` `sin-neg_binary64_890` `log-div_binary64_847` `exp-neg_binary64_807` `rem-log-exp_binary64_801` `rem-square-sqrt_binary64_772` `difference-of-squares_binary64_729`
2×	`unpow3_binary64_826` `cube-mult_binary64_790` `cube-div_binary64_789` `rem-3cbrt-lft_binary64_785` `associate-/r_binary64_704` `associate-l/_binary64_703` `associate-*r/_binary64_702` `associate-+l-_binary64_695`
1×	`div-exp_binary64_811` `rec-exp_binary64_810` `1-exp_binary64_804` `exp-1-e_binary64_803` `rem-3cbrt-rft_binary64_786` `/-rgt-identity_binary64_751` `remove-double-neg_binary64_748` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `count-2_binary64_708` `associate-/r/_binary64_706`
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` `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` `e-exp-1_binary64_805` `exp-0_binary64_802` `rem-exp-log_binary64_800` `cube-neg_binary64_787` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `div-sub_binary64_765` `mul-1-neg_binary64_752` `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` `+-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-neg-frac_binary64_724` `distribute-frac-neg_binary64_723` `associate-/l/_binary64_707` `associate--r-_binary64_699` `associate--l-_binary64_698`

Counts

146 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	294	3329
1	742	3030
2	2100	2947
3	4980	2947

prune216.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	6	123

Error

1.0b

Counts

123 → 6

Compiler

Compiled 4430 to 2109 computations (52.4% saved)

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b

(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))

0.0b

(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))

0.0b

(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite150.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

1.0b

Rules

24×	`*-un-lft-identity_binary64_760`
17×	`add-sqr-sqrt_binary64_782`
14×	`add-log-exp_binary64_799`
8×	`add-cube-cbrt_binary64_795` `cancel-sign-sub-inv_binary64_726`
6×	`unpow-prod-down_binary64_839` `exp-prod_binary64_812`
5×	`distribute-lft-out--_binary64_712` `exp-sum_binary64_806`
4×	`difference-of-squares_binary64_729` `pow1_binary64_821` `add-exp-log_binary64_798` `distribute-lft-out_binary64_711` `diff-log_binary64_852`
3×	`pow-unpow_binary64_837` `add-cbrt-cube_binary64_796` `rem-exp-log_binary64_800`
2×	`sub-neg_binary64_753` `sum-log_binary64_851`
1×	`times-frac_binary64_766` `pow-pow_binary64_832` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `unpow2_binary64_825` `sqr-pow_binary64_732` `exp-diff_binary64_808` `flip3--_binary64_764` `flip--_binary64_735` `associate--r+_binary64_696`

Counts

3 → 63

Calls

3 calls:

18.0ms

(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))

17.0ms

(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))

11.0ms

(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

Compiler

Compiled 1950 to 990 computations (49.2% saved)

series1.8s (11.2%)

Error

1.0b

Counts

3 → 72

Calls

3 calls:

974.0ms

(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))

424.0ms

(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

324.0ms

(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))

Compiler

Compiled 5612 to 3895 computations (30.6% saved)

simplify136.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

380×	`associate--l+_binary64_697`
307×	`distribute-rgt-in_binary64_710`
266×	`associate-l_binary64_701`
265×	`distribute-lft-in_binary64_709`
259×	`associate-r_binary64_700`
254×	`sub-neg_binary64_753`
237×	`cancel-sign-sub-inv_binary64_726`
212×	`exp-sum_binary64_806`
135×	`distribute-neg-in_binary64_721`
108×	`associate--r+_binary64_696`
100×	`+-commutative_binary64_690`
80×	`associate-+l+_binary64_693`
79×	`exp-diff_binary64_808`
76×	`sqr-pow_binary64_732`
72×	`associate-+r+_binary64_692`
59×	`log-prod_binary64_846`
54×	`exp-prod_binary64_812`
50×	`unsub-neg_binary64_754`
46×	`neg-mul-1_binary64_756` `neg-sub0_binary64_755`
45×	`distribute-rgt-neg-in_binary64_718`
44×	`times-frac_binary64_766`
35×	`distribute-lft-neg-in_binary64_717`
32×	`unswap-sqr_binary64_728`
31×	`associate--l-_binary64_698`
29×	`log-pow_binary64_849` `associate-l/_binary64_703` `associate-r/_binary64_702`
28×	`*-commutative_binary64_691`
24×	`associate-/r*_binary64_704`
22×	`associate-/l*_binary64_705`
21×	`distribute-lft-out_binary64_711`
20×	`distribute-lft-neg-out_binary64_719`
19×	`distribute-rgt-out_binary64_713`
14×	`unpow2_binary64_825` `unpow1/2_binary64_824` `unpow1_binary64_818`
12×	`prod-exp_binary64_809` `distribute-rgt-neg-out_binary64_720` `distribute-rgt-out--_binary64_714`
11×	`pow-sqr_binary64_733`
10×	`log-div_binary64_847`
7×	`cube-unmult_binary64_797` `difference-of-squares_binary64_729` `distribute-lft-out--_binary64_712`
6×	`cube-prod_binary64_788` `swap-sqr_binary64_727` `associate--r-_binary64_699`
5×	`pow-plus_binary64_823` `rem-log-exp_binary64_801`
4×	`rem-sqrt-square_binary64_773` `associate-+r-_binary64_694`
3×	`div-exp_binary64_811` `exp-neg_binary64_807` `cube-div_binary64_789` `associate-/l/_binary64_707`
2×	`unpow3_binary64_826` `rec-exp_binary64_810` `cube-mult_binary64_790` `rem-square-sqrt_binary64_772` `mul-1-neg_binary64_752` `+-rgt-identity_binary64_745` `associate-+l-_binary64_695`
1×	`1-exp_binary64_804` `exp-1-e_binary64_803` `rem-3cbrt-rft_binary64_786` `rem-3cbrt-lft_binary64_785` `sqr-abs_binary64_775` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `count-2_binary64_708` `associate-/r/_binary64_706`
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` `e-exp-1_binary64_805` `exp-0_binary64_802` `rem-exp-log_binary64_800` `cube-neg_binary64_787` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-neg_binary64_774` `div-sub_binary64_765` `/-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` `+-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` `difference-of-sqr--1_binary64_731` `difference-of-sqr-1_binary64_730` `cancel-sign-sub_binary64_725` `distribute-neg-frac_binary64_724` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722`

Counts

135 → 123

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	4030
1	519	3650
2	1493	3488
3	4888	3488
4	4994	3488

prune167.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	123	6	129

Error

1.0b

Counts

129 → 6

Compiler

Compiled 3420 to 1575 computations (53.9% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 K)
0.6b	(cbrt.f64 K)
0.6b	(cbrt.f64 K)
32.8b	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (*.f64 (+.f64 n m) (cbrt.f64 K))) 2) M))

rewrite118.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.9b

Rules

9×	`cbrt-prod_binary64_791`
8×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
4×	`cos-sum_binary64_894` `pow1_binary64_821` `add-log-exp_binary64_799` `add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
3×	`cancel-sign-sub-inv_binary64_726` `pow1/3_binary64_842`
1×	`cos-diff_binary64_897` `sub-neg_binary64_753`

Counts

4 → 45

Calls

4 calls:

16.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (*.f64 (+.f64 n m) (cbrt.f64 K))) 2) M))
1.0ms	(cbrt.f64 K)
1.0ms	(cbrt.f64 K)
1.0ms	(cbrt.f64 K)

Compiler

Compiled 1951 to 795 computations (59.3% saved)

series696.0ms (4.3%)

Error

0.9b

Counts

4 → 26

Calls

4 calls:

307.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (*.f64 (+.f64 n m) (cbrt.f64 K))) 2) M))
119.0ms	(cbrt.f64 K)
119.0ms	(cbrt.f64 K)
108.0ms	(cbrt.f64 K)

Compiler

Compiled 2883 to 1993 computations (30.9% saved)

simplify98.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

546×	`distribute-rgt-neg-in_binary64_718`
482×	`distribute-lft-neg-in_binary64_717`
394×	`neg-mul-1_binary64_756`
393×	`neg-sub0_binary64_755`
344×	`*-commutative_binary64_691`
299×	`unswap-sqr_binary64_728`
230×	`distribute-rgt-in_binary64_710`
191×	`unsub-neg_binary64_754`
181×	`sub-neg_binary64_753`
172×	`cancel-sign-sub-inv_binary64_726`
148×	`distribute-rgt-neg-out_binary64_720`
136×	`distribute-neg-in_binary64_721`
134×	`associate-r_binary64_700`
130×	`distribute-lft-neg-out_binary64_719`
129×	`cancel-sign-sub_binary64_725`
115×	`log-prod_binary64_846`
101×	`associate-l_binary64_701`
77×	`distribute-rgt-out_binary64_713`
71×	`associate--r+_binary64_696`
68×	`associate-+l+_binary64_693`
62×	`+-commutative_binary64_690`
53×	`remove-double-neg_binary64_748`
50×	`associate-+r+_binary64_692`
39×	`distribute-lft-in_binary64_709`
37×	`sqr-pow_binary64_732`
30×	`swap-sqr_binary64_727`
29×	`distribute-neg-out_binary64_722`
27×	`distribute-lft-out_binary64_711`
22×	`associate-/l*_binary64_705`
19×	`rem-sqrt-square_binary64_773`
18×	`cube-prod_binary64_788`
17×	`distribute-rgt-out--_binary64_714`
15×	`associate-+r-_binary64_694`
14×	`log-pow_binary64_849` `associate-+l-_binary64_695`
12×	`sqr-neg_binary64_774` `div-sub_binary64_765` `associate-/r*_binary64_704`
11×	`cos-neg_binary64_891` `exp-prod_binary64_812`
10×	`+-rgt-identity_binary64_745`
9×	`pow-plus_binary64_823` `cube-unmult_binary64_797` `sub0-neg_binary64_747` `associate--l+_binary64_697`
7×	`associate-/r/_binary64_706`
6×	`sin-neg_binary64_890`
5×	`pow-sqr_binary64_733`
4×	`unpow2_binary64_825` `mul-1-neg_binary64_752`
3×	`unpow3_binary64_826` `unpow1/2_binary64_824` `unpow1_binary64_818` `associate-/l/_binary64_707` `associate--l-_binary64_698`
2×	`unpow1/3_binary64_827` `cube-mult_binary64_790` `rem-3cbrt-lft_binary64_785` `mul0-rgt_binary64_743` `mul0-lft_binary64_742` `distribute-rgt1-in_binary64_716`
1×	`exp-diff_binary64_808` `1-exp_binary64_804` `cube-neg_binary64_787` `rem-cube-cbrt_binary64_783` `rem-square-sqrt_binary64_772` `distribute-frac-neg_binary64_723` `distribute-lft-out--_binary64_712` `count-2_binary64_708`
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` `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` `log-div_binary64_847` `pow-base-0_binary64_844` `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` `div-exp_binary64_811` `rec-exp_binary64_810` `prod-exp_binary64_809` `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-div_binary64_789` `rem-3cbrt-rft_binary64_786` `rem-cbrt-cube_binary64_784` `sqr-abs_binary64_775` `times-frac_binary64_766` `/-rgt-identity_binary64_751` `-rgt-identity_binary64_750` `-lft-identity_binary64_749` `--rgt-identity_binary64_746` `+-lft-identity_binary64_744` `div0_binary64_741` `-inverses_binary64_740` `+-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` `difference-of-squares_binary64_729` `distribute-neg-frac_binary64_724` `distribute-lft1-in_binary64_715` `associate-l/_binary64_703` `associate-*r/_binary64_702` `associate--r-_binary64_699`

Counts

71 → 42

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	143	1287
1	319	971
2	944	951
3	2247	930
4	4519	930
5	5046	930

prune80.0ms (0.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	42	6	48

Error

1.0b

Counts

48 → 6

Compiler

Compiled 1627 to 801 computations (50.8% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.1b	(.f64 (.f64 K -1/2) (sin.f64 M))
4.4b	(.f64 (.f64 (*.f64 K -1/2) (sin.f64 M)) (+.f64 n m))
7.9b	(.f64 (-.f64 (cos.f64 M) (.f64 (.f64 (.f64 K -1/2) (sin.f64 M)) (+.f64 n m))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

rewrite248.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

1.0b

Rules

21×	`pow1_binary64_821`
20×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
18×	`add-sqr-sqrt_binary64_782`
17×	`*-un-lft-identity_binary64_760`
15×	`associate-r_binary64_700`
11×	`add-cube-cbrt_binary64_795`
10×	`pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793`
6×	`unpow-prod-down_binary64_839`
5×	`associate-l_binary64_701` `exp-sum_binary64_806`
4×	`add-log-exp_binary64_799` `cancel-sign-sub-inv_binary64_726`
3×	`exp-diff_binary64_808` `associate-r/_binary64_702` `-commutative_binary64_691` `pow-unpow_binary64_837`
2×	`flip3--_binary64_764` `frac-times_binary64_770` `flip--_binary64_735` `associate-*l/_binary64_703` `distribute-lft-out_binary64_711` `difference-of-squares_binary64_729`
1×	`unswap-sqr_binary64_728` `sub-neg_binary64_753` `distribute-rgt-in_binary64_710` `distribute-lft-in_binary64_709` `flip3-+_binary64_763` `flip-+_binary64_734` `times-frac_binary64_766` `distribute-lft-out--_binary64_712` `pow-pow_binary64_832` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `unpow2_binary64_825` `sqr-pow_binary64_732`

Counts

4 → 93

Calls

4 calls:

29.0ms	(.f64 (-.f64 (cos.f64 M) (.f64 (.f64 (.f64 K -1/2) (sin.f64 M)) (+.f64 n m))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
11.0ms	(.f64 (.f64 (*.f64 K -1/2) (sin.f64 M)) (+.f64 n m))
6.0ms	(.f64 (.f64 K -1/2) (sin.f64 M))

Compiler

Compiled 3972 to 1912 computations (51.9% saved)

series3.9s (23.9%)

Error

1.0b

Counts

4 → 76

Calls

4 calls:

2.8s	(.f64 (-.f64 (cos.f64 M) (.f64 (.f64 (.f64 K -1/2) (sin.f64 M)) (+.f64 n m))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
420.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
381.0ms	(.f64 (.f64 (*.f64 K -1/2) (sin.f64 M)) (+.f64 n m))
115.0ms	(.f64 (.f64 K -1/2) (sin.f64 M))

Compiler

Compiled 14106 to 8640 computations (38.7% saved)

simplify185.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

790×	`associate-r_binary64_700`
735×	`associate-l_binary64_701`
211×	`*-commutative_binary64_691`
166×	`exp-prod_binary64_812`
131×	`distribute-rgt-in_binary64_710`
121×	`associate--l+_binary64_697`
117×	`distribute-lft-in_binary64_709`
88×	`cancel-sign-sub-inv_binary64_726` `+-commutative_binary64_690`
83×	`sub-neg_binary64_753`
78×	`log-prod_binary64_846`
69×	`associate-*r/_binary64_702`
65×	`associate-*l/_binary64_703`
48×	`associate-+r+_binary64_692`
47×	`sqr-pow_binary64_732`
43×	`exp-sum_binary64_806`
40×	`distribute-rgt-neg-in_binary64_718`
39×	`distribute-neg-in_binary64_721`
36×	`distribute-rgt-out_binary64_713`
31×	`distribute-lft-neg-in_binary64_717`
29×	`neg-sub0_binary64_755`
27×	`neg-mul-1_binary64_756`
25×	`distribute-lft-out_binary64_711`
19×	`swap-sqr_binary64_727` `associate--r+_binary64_696`
15×	`exp-diff_binary64_808`
14×	`unpow2_binary64_825` `unpow1/2_binary64_824` `unpow1_binary64_818`
10×	`unpow3_binary64_826` `cube-prod_binary64_788`
7×	`cube-unmult_binary64_797`
5×	`log-pow_binary64_849` `pow-plus_binary64_823` `cube-mult_binary64_790` `distribute-lft-neg-out_binary64_719`
4×	`log-div_binary64_847` `*-rgt-identity_binary64_750` `pow-sqr_binary64_733` `unswap-sqr_binary64_728`
3×	`prod-exp_binary64_809` `mul-1-neg_binary64_752` `difference-of-squares_binary64_729` `associate-+l+_binary64_693`
2×	`rem-sqrt-square_binary64_773` `distribute-rgt-out--_binary64_714`
1×	`1-exp_binary64_804` `rem-log-exp_binary64_801` `rem-square-sqrt_binary64_772` `unsub-neg_binary64_754` `distribute-rgt1-in_binary64_716` `count-2_binary64_708` `associate-/l_binary64_705` `associate-/r_binary64_704` `associate-+r-_binary64_694`
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` `div-exp_binary64_811` `rec-exp_binary64_810` `exp-neg_binary64_807` `e-exp-1_binary64_805` `exp-1-e_binary64_803` `exp-0_binary64_802` `rem-exp-log_binary64_800` `cube-div_binary64_789` `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` `times-frac_binary64_766` `div-sub_binary64_765` `/-rgt-identity_binary64_751` `-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` `difference-of-sqr--1_binary64_731` `difference-of-sqr-1_binary64_730` `cancel-sign-sub_binary64_725` `distribute-neg-frac_binary64_724` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722` `distribute-rgt-neg-out_binary64_720` `distribute-lft1-in_binary64_715` `distribute-lft-out--_binary64_712` `associate-/l/_binary64_707` `associate-/r/_binary64_706` `associate--r-_binary64_699` `associate--l-_binary64_698` `associate-+l-_binary64_695`

Counts

169 → 150

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	473	8166
1	1387	6911
2	4847	6911
3	5152	6911

prune309.0ms (1.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	150	6	156

Error

1.0b

Counts

156 → 6

Compiler

Compiled 6984 to 2802 computations (59.9% saved)

regimes1.0s (6.3%)

Accuracy

Total 0.2b remaining (15.8%)

Threshold costs 0.2b (15.8%)

Compiler

Compiled 12608 to 9948 computations (21.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64_690`
8×	`sub-neg_binary64_753`
6×	`*-commutative_binary64_691`
5×	`neg-mul-1_binary64_756` `neg-sub0_binary64_755`
2×	`unsub-neg_binary64_754` `distribute-neg-in_binary64_721`
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` `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` `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-rgt-neg-out_binary64_720` `distribute-lft-neg-out_binary64_719` `distribute-rgt-neg-in_binary64_718` `distribute-lft-neg-in_binary64_717`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	31
1	26	31
2	41	31
3	53	31
4	60	31
5	62	31
6	62	31

end0.0ms (0%)

sample3.1s (18.8%)

Algorithm

1×

intervals

Results

777.0ms	7817×	body	128	valid
41.0ms	92×	body	1024	invalid
37.0ms	327×	body	128	invalid
31.0ms	71×	body	1024	valid
30.0ms	84×	body	512	invalid
24.0ms	76×	body	512	valid
11.0ms	21×	body	2048	invalid
9.0ms	45×	body	256	invalid
8.0ms	35×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 2140 to 1689 computations (21.1% saved)

Details

analyze2.3s (14.2%)

sample45.0ms (0.3%)

simplify50.0ms (0.3%)

prune6.0ms (0%)

localize24.0ms (0.1%)

rewrite205.0ms (1.3%)

series1.3s (7.9%)

simplify101.0ms (0.6%)

prune216.0ms (1.3%)

localize16.0ms (0.1%)

rewrite150.0ms (0.9%)

series1.8s (11.2%)

simplify136.0ms (0.8%)

prune167.0ms (1%)

localize24.0ms (0.1%)

rewrite118.0ms (0.7%)

series696.0ms (4.3%)

simplify98.0ms (0.6%)

prune80.0ms (0.5%)

localize23.0ms (0.1%)

rewrite248.0ms (1.5%)

series3.9s (23.9%)

simplify185.0ms (1.1%)

prune309.0ms (1.9%)

regimes1.0s (6.3%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.1s (18.8%)

Profiling