Details

analyze2.0s (52.7%)

Algorithm

1×

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)

sample52.0ms (1.4%)

Algorithm

1×

intervals

Results

28.0ms	245×	body	128	valid
2.0ms	5×	body	1024	valid
1.0ms	4×	body	512	valid
1.0ms	2×	body	2048	invalid
1.0ms	8×	body	128	invalid
1.0ms	2×	body	1024	invalid
1.0ms	2×	body	512	invalid
0.0ms	2×	body	256	valid
0.0ms	1×	body	256	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify133.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

333×	`associate-l_binary64_701`
286×	`associate-r_binary64_700`
262×	`times-frac_binary64_766`
236×	`exp-sum_binary64_806`
231×	`distribute-rgt-in_binary64_710`
230×	`cancel-sign-sub-inv_binary64_726`
196×	`distribute-lft-in_binary64_709`
184×	`associate-/l*_binary64_705`
139×	`exp-prod_binary64_812`
113×	`associate-/r*_binary64_704`
105×	`associate-*l/_binary64_703`
104×	`distribute-neg-in_binary64_721`
103×	`sub-neg_binary64_753`
92×	`exp-diff_binary64_808`
89×	`unsub-neg_binary64_754`
84×	`associate--r-_binary64_699`
82×	`associate-*r/_binary64_702`
70×	`associate--l-_binary64_698`
57×	`associate-/l/_binary64_707`
54×	`distribute-rgt-neg-in_binary64_718`
52×	`associate-+l+_binary64_693`
50×	`associate-/r/_binary64_706`
47×	`distribute-rgt-neg-out_binary64_720`
46×	`sqr-pow_binary64_732`
43×	`distribute-lft-neg-out_binary64_719`
41×	`neg-mul-1_binary64_756` `distribute-lft-neg-in_binary64_717`
40×	`associate--r+_binary64_696`
38×	`neg-sub0_binary64_755` `associate-+r+_binary64_692`
30×	`associate--l+_binary64_697` `*-commutative_binary64_691`
27×	`unswap-sqr_binary64_728`
24×	`+-commutative_binary64_690`
23×	`associate-+r-_binary64_694`
21×	`distribute-neg-out_binary64_722`
20×	`associate-+l-_binary64_695`
19×	`div-sub_binary64_765` `distribute-rgt-out--_binary64_714`
16×	`distribute-rgt-out_binary64_713`
15×	`exp-sqrt_binary64_813` `+-rgt-identity_binary64_745`
14×	`sub0-neg_binary64_747`
13×	`pow-sqr_binary64_733` `distribute-neg-frac_binary64_724`
12×	`remove-double-neg_binary64_748`
11×	`exp-neg_binary64_807` `--rgt-identity_binary64_746`
9×	`distribute-lft-out--_binary64_712`
8×	`div-exp_binary64_811`
7×	`swap-sqr_binary64_727`
6×	`pow-plus_binary64_823` `/-rgt-identity_binary64_751` `distribute-frac-neg_binary64_723`
5×	`prod-exp_binary64_809` `*-lft-identity_binary64_749` `mul0-lft_binary64_742` `distribute-lft-out_binary64_711`
4×	`*-rgt-identity_binary64_750` `mul0-rgt_binary64_743`
3×	`cube-unmult_binary64_797` `sqr-neg_binary64_774`
2×	`rec-exp_binary64_810` `mul-1-neg_binary64_752` `count-2_binary64_708`
1×	`cos-neg_binary64_891` `unpow2_binary64_825` `unpow1_binary64_818` `1-exp_binary64_804` `*-inverses_binary64_740` `rgt-mult-inverse_binary64_737` `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` `unpow1/2_binary64_824` `exp-to-pow_binary64_822` `pow-base-1_binary64_820` `unpow0_binary64_819` `unpow-1_binary64_817` `exp-lft-cube_binary64_816` `exp-lft-sqr_binary64_815` `exp-cbrt_binary64_814` `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-sqrt-square_binary64_773` `rem-square-sqrt_binary64_772` `+-lft-identity_binary64_744` `div0_binary64_741` `+-inverses_binary64_739` `lft-mult-inverse_binary64_738` `remove-double-div_binary64_736` `difference-of-sqr--1_binary64_731` `difference-of-sqr-1_binary64_730` `difference-of-squares_binary64_729` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715`

Counts

1 → 3

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	45
1	55	45
2	128	43
3	347	43
4	1108	43

prune8.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	2	1	3
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	3	1	4

Error

17.6b

Counts

4 → 1

Compiler

Compiled 113 to 73 computations (35.4% saved)

localize23.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (*.f64 (+.f64 m n) (/.f64 K 2)) M)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0b	(exp.f64 (-.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)))
36.3b	(cos.f64 (-.f64 (*.f64 (+.f64 m n) (/.f64 K 2)) M))

rewrite191.0ms (4.9%)

Algorithm

1×	rewrite-expression-head

Error

17.5b

Rules

28×	`add-sqr-sqrt_binary64_782`
21×	`*-un-lft-identity_binary64_760`
20×	`cancel-sign-sub-inv_binary64_726`
16×	`exp-sum_binary64_806`
13×	`unpow-prod-down_binary64_839`
12×	`add-cube-cbrt_binary64_795` `add-log-exp_binary64_799`
9×	`exp-prod_binary64_812`
8×	`difference-of-squares_binary64_729`
5×	`pow1_binary64_821` `add-exp-log_binary64_798` `distribute-lft-out--_binary64_712`
4×	`sub-neg_binary64_753` `cos-sum_binary64_894` `add-cbrt-cube_binary64_796` `associate--l+_binary64_697` `diff-log_binary64_852`
3×	`unpow2_binary64_825` `sqr-pow_binary64_732` `rem-exp-log_binary64_800` `pow-unpow_binary64_837`
2×	`times-frac_binary64_766`
1×	`cos-diff_binary64_897` `exp-diff_binary64_808` `pow-pow_binary64_832` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `flip3--_binary64_764` `flip--_binary64_735`

Counts

4 → 83

Calls

4 calls:

21.0ms	(exp.f64 (-.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)))
10.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
9.0ms	(cos.f64 (-.f64 (*.f64 (+.f64 m n) (/.f64 K 2)) M))
8.0ms	(-.f64 (*.f64 (+.f64 m n) (/.f64 K 2)) M)

Compiler

Compiled 3227 to 1612 computations (50% saved)

series1.0s (27.1%)

Error

2.5b

Counts

4 → 78

Calls

4 calls:

299.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
231.0ms	(exp.f64 (-.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)))
214.0ms	(-.f64 (*.f64 (+.f64 m n) (/.f64 K 2)) M)
197.0ms	(cos.f64 (-.f64 (*.f64 (+.f64 m n) (/.f64 K 2)) M))

Compiler

Compiled 7783 to 5236 computations (32.7% saved)

simplify377.0ms (9.7%)

Algorithm

1×	egg-herbie

Rules

408×	`distribute-rgt-in_binary64_710`
380×	`cancel-sign-sub-inv_binary64_726`
260×	`sub-neg_binary64_753`
256×	`exp-sum_binary64_806`
194×	`distribute-rgt-neg-in_binary64_718`
180×	`exp-prod_binary64_812`
158×	`distribute-neg-in_binary64_721` `distribute-lft-neg-in_binary64_717`
134×	`associate-r_binary64_700`
128×	`sqr-pow_binary64_732`
122×	`*-commutative_binary64_691`
118×	`+-commutative_binary64_690`
109×	`neg-mul-1_binary64_756`
104×	`associate-l_binary64_701`
102×	`exp-diff_binary64_808`
101×	`neg-sub0_binary64_755`
93×	`unswap-sqr_binary64_728`
90×	`associate--l+_binary64_697`
84×	`distribute-lft-neg-out_binary64_719`
82×	`associate--r+_binary64_696`
75×	`associate-+l+_binary64_693`
71×	`associate-+r+_binary64_692`
57×	`distribute-rgt-neg-out_binary64_720`
46×	`unsub-neg_binary64_754`
39×	`times-frac_binary64_766`
38×	`distribute-rgt-out_binary64_713`
27×	`pow-sqr_binary64_733`
25×	`pow-plus_binary64_823`
24×	`distribute-lft-in_binary64_709`
23×	`distribute-lft-out_binary64_711`
22×	`cube-prod_binary64_788`
17×	`cancel-sign-sub_binary64_725`
16×	`log-prod_binary64_846` `unpow2_binary64_825`
15×	`unpow1_binary64_818` `associate-+r-_binary64_694`
13×	`swap-sqr_binary64_727`
12×	`cube-unmult_binary64_797` `+-rgt-identity_binary64_745`
11×	`exp-neg_binary64_807` `associate-*l/_binary64_703`
10×	`distribute-neg-out_binary64_722` `distribute-rgt-out--_binary64_714` `associate-*r/_binary64_702`
8×	`log-pow_binary64_849` `prod-exp_binary64_809`
7×	`unpow3_binary64_826` `cube-mult_binary64_790` `rem-sqrt-square_binary64_773`
6×	`difference-of-squares_binary64_729`
5×	`cube-div_binary64_789` `*-lft-identity_binary64_749` `distribute-neg-frac_binary64_724` `associate-+l-_binary64_695`
4×	`cos-neg_binary64_891` `sin-neg_binary64_890` `log-div_binary64_847` `rem-3cbrt-lft_binary64_785` `rem-square-sqrt_binary64_772` `distribute-lft-out--_binary64_712`
3×	`pow-base-1_binary64_820` `exp-sqrt_binary64_813` `rem-log-exp_binary64_801`
2×	`div-sub_binary64_765` `remove-double-neg_binary64_748` `distribute-rgt1-in_binary64_716` `associate-/l*_binary64_705` `associate--l-_binary64_698`
1×	`div-exp_binary64_811` `1-exp_binary64_804` `exp-1-e_binary64_803` `rem-3cbrt-rft_binary64_786` `-rgt-identity_binary64_750` `sub0-neg_binary64_747` `-inverses_binary64_740` `rgt-mult-inverse_binary64_737` `distribute-lft1-in_binary64_715` `count-2_binary64_708` `associate-/l/_binary64_707` `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` `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` `unpow1/2_binary64_824` `exp-to-pow_binary64_822` `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-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` `mul-1-neg_binary64_752` `/-rgt-identity_binary64_751` `--rgt-identity_binary64_746` `+-lft-identity_binary64_744` `mul0-rgt_binary64_743` `mul0-lft_binary64_742` `div0_binary64_741` `+-inverses_binary64_739` `lft-mult-inverse_binary64_738` `remove-double-div_binary64_736` `difference-of-sqr--1_binary64_731` `difference-of-sqr-1_binary64_730` `distribute-frac-neg_binary64_723` `associate-/r/_binary64_706` `associate-/r*_binary64_704`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	328	4112
1	825	3732
2	2204	3596

Details

analyze2.0s (52.7%)

sample52.0ms (1.4%)

simplify133.0ms (3.4%)

prune8.0ms (0.2%)

localize23.0ms (0.6%)

rewrite191.0ms (4.9%)

series1.0s (27.1%)

simplify377.0ms (9.7%)

end0.0ms (0%)

Profiling