Details

analyze2.0s (5.5%)

Algorithm

1×	search
2×	egg-herbie

Rules

1154×	`associate-*r/_binary64_702`
696×	`associate-/r/_binary64_706`
564×	`associate-/l/_binary64_707`
492×	`unswap-sqr_binary64_728`
376×	`times-frac_binary64_766`
307×	`associate-*l/_binary64_703`
300×	`associate-/r*_binary64_704`
296×	`associate-/l*_binary64_705`
280×	`sqr-pow_binary64_732`
164×	`associate-l_binary64_701`
156×	`associate-r_binary64_700`
104×	`*-commutative_binary64_691`
72×	`pow-sqr_binary64_733`
60×	`pow-plus_binary64_823`
44×	`swap-sqr_binary64_727`
40×	`rem-sqrt-square_binary64_773`
28×	`cube-prod_binary64_788`
24×	`unpow3_binary64_826`
20×	`unpow2_binary64_825` `cube-unmult_binary64_797`
16×	`unpow1_binary64_818`
12×	`unpow1/2_binary64_824`
8×	`cube-mult_binary64_790`
4×	`+-commutative_binary64_690`
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` `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-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` `rem-square-sqrt_binary64_772` `div-sub_binary64_765` `neg-mul-1_binary64_756` `neg-sub0_binary64_755` `unsub-neg_binary64_754` `sub-neg_binary64_753` `mul-1-neg_binary64_752` `/-rgt-identity_binary64_751` `-rgt-identity_binary64_750` `-lft-identity_binary64_749` `remove-double-neg_binary64_748` `sub0-neg_binary64_747` `--rgt-identity_binary64_746` `+-rgt-identity_binary64_745` `+-lft-identity_binary64_744` `mul0-rgt_binary64_743` `mul0-lft_binary64_742` `div0_binary64_741` `*-inverses_binary64_740` `+-inverses_binary64_739` `lft-mult-inverse_binary64_738` `rgt-mult-inverse_binary64_737` `remove-double-div_binary64_736` `difference-of-sqr--1_binary64_731` `difference-of-sqr-1_binary64_730` `difference-of-squares_binary64_729` `cancel-sign-sub-inv_binary64_726` `cancel-sign-sub_binary64_725` `distribute-neg-frac_binary64_724` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722` `distribute-neg-in_binary64_721` `distribute-rgt-neg-out_binary64_720` `distribute-lft-neg-out_binary64_719` `distribute-rgt-neg-in_binary64_718` `distribute-lft-neg-in_binary64_717` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `distribute-rgt-out--_binary64_714` `distribute-rgt-out_binary64_713` `distribute-lft-out--_binary64_712` `distribute-lft-out_binary64_711` `distribute-rgt-in_binary64_710` `distribute-lft-in_binary64_709` `count-2_binary64_708` `associate--r-_binary64_699` `associate--l-_binary64_698` `associate--l+_binary64_697` `associate--r+_binary64_696` `associate-+l-_binary64_695` `associate-+r-_binary64_694` `associate-+l+_binary64_693` `associate-+r+_binary64_692`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	148
1	112	148
2	271	148
3	756	148
4	2792	148
5	3544	148
6	3772	148
7	4300	148
8	4407	148
9	4516	148
10	5366	148
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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
15.6%	84.3%	0.1%	8
15.6%	84.3%	0.1%	9
15.6%	84.3%	0.1%	10
30.4%	69.4%	0.1%	11
30.4%	69.4%	0.1%	12
30.4%	69.4%	0.1%	13
39.6%	60.3%	0.1%	14

Compiler

Compiled 25 to 23 computations (8% saved)

sample83.0ms (0.2%)

Algorithm

1×

intervals

Results

39.0ms	70×	body	1024	valid
15.0ms	140×	body	128	valid
11.0ms	28×	body	512	valid
4.0ms	18×	body	256	valid

Compiler

Compiled 49 to 48 computations (2% saved)

simplify92.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1043×	`associate-*l/_binary64_703`
692×	`associate-/l/_binary64_707`
651×	`associate-/r/_binary64_706`
525×	`associate-*r/_binary64_702`
474×	`associate-/l*_binary64_705`
398×	`times-frac_binary64_766`
330×	`unswap-sqr_binary64_728`
263×	`sqr-pow_binary64_732`
246×	`associate-/r*_binary64_704`
210×	`associate-l_binary64_701`
155×	`associate-r_binary64_700`
98×	`pow-sqr_binary64_733`
72×	`cube-prod_binary64_788`
66×	`*-commutative_binary64_691`
48×	`unpow3_binary64_826`
42×	`cube-mult_binary64_790`
36×	`pow-plus_binary64_823`
20×	`rem-sqrt-square_binary64_773`
12×	`swap-sqr_binary64_727`
7×	`unpow2_binary64_825` `unpow1_binary64_818`
6×	`unpow1/2_binary64_824`
5×	`cube-unmult_binary64_797`
1×	`1-exp_binary64_804` `+-commutative_binary64_690`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_1023` `erf-erfc_binary64_1022` `erf-odd_binary64_1021` `if-if-and-not_binary64_1020` `if-if-and_binary64_1019` `if-if-or-not_binary64_1018` `if-if-or_binary64_1017` `if-not_binary64_1016` `if-same_binary64_1015` `if-false_binary64_1014` `if-true_binary64_1013` `not-gte_binary64_1012` `not-lte_binary64_1011` `not-gt_binary64_1010` `not-lt_binary64_1009` `gte-same_binary64_1008` `lte-same_binary64_1007` `gt-same_binary64_1006` `lt-same_binary64_1005` `sinh---cosh_binary64_952` `sinh-+-cosh_binary64_951` `sinh-cosh_binary64_950` `tanh-def-c_binary64_949` `tanh-def-b_binary64_948` `tanh-def-a_binary64_947` `cosh-def_binary64_946` `sinh-def_binary64_945` `tan-neg_binary64_892` `cos-neg_binary64_891` `sin-neg_binary64_890` `tan-0_binary64_889` `cos-0_binary64_888` `sin-0_binary64_887` `hang-m-tan_binary64_886` `hang-p-tan_binary64_885` `hang-m0-tan_binary64_884` `hang-p0-tan_binary64_883` `hang-0m-tan_binary64_882` `hang-0p-tan_binary64_881` `tan-+PI/2_binary64_880` `tan-+PI_binary64_879` `tan-PI_binary64_878` `tan-PI/3_binary64_877` `tan-PI/4_binary64_876` `tan-PI/6_binary64_875` `cos-+PI/2_binary64_874` `cos-+PI_binary64_873` `cos-PI_binary64_872` `cos-PI/2_binary64_871` `cos-PI/3_binary64_870` `cos-PI/4_binary64_869` `cos-PI/6_binary64_868` `sin-+PI/2_binary64_867` `sin-+PI_binary64_866` `sin-PI_binary64_865` `sin-PI/2_binary64_864` `sin-PI/3_binary64_863` `sin-PI/4_binary64_862` `sin-PI/6_binary64_861` `sub-1-sin_binary64_860` `sub-1-cos_binary64_859` `-1-add-sin_binary64_858` `-1-add-cos_binary64_857` `1-sub-sin_binary64_856` `1-sub-cos_binary64_855` `cos-sin-sum_binary64_854` `log-E_binary64_850` `log-pow_binary64_849` `log-rec_binary64_848` `log-div_binary64_847` `log-prod_binary64_846` `pow-base-0_binary64_844` `unpow1/3_binary64_827` `exp-to-pow_binary64_822` `pow-base-1_binary64_820` `unpow0_binary64_819` `unpow-1_binary64_817` `exp-lft-cube_binary64_816` `exp-lft-sqr_binary64_815` `exp-cbrt_binary64_814` `exp-sqrt_binary64_813` `exp-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-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` `rem-square-sqrt_binary64_772` `div-sub_binary64_765` `neg-mul-1_binary64_756` `neg-sub0_binary64_755` `unsub-neg_binary64_754` `sub-neg_binary64_753` `mul-1-neg_binary64_752` `/-rgt-identity_binary64_751` `-rgt-identity_binary64_750` `-lft-identity_binary64_749` `remove-double-neg_binary64_748` `sub0-neg_binary64_747` `--rgt-identity_binary64_746` `+-rgt-identity_binary64_745` `+-lft-identity_binary64_744` `mul0-rgt_binary64_743` `mul0-lft_binary64_742` `div0_binary64_741` `*-inverses_binary64_740` `+-inverses_binary64_739` `lft-mult-inverse_binary64_738` `rgt-mult-inverse_binary64_737` `remove-double-div_binary64_736` `difference-of-sqr--1_binary64_731` `difference-of-sqr-1_binary64_730` `difference-of-squares_binary64_729` `cancel-sign-sub-inv_binary64_726` `cancel-sign-sub_binary64_725` `distribute-neg-frac_binary64_724` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722` `distribute-neg-in_binary64_721` `distribute-rgt-neg-out_binary64_720` `distribute-lft-neg-out_binary64_719` `distribute-rgt-neg-in_binary64_718` `distribute-lft-neg-in_binary64_717` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `distribute-rgt-out--_binary64_714` `distribute-rgt-out_binary64_713` `distribute-lft-out--_binary64_712` `distribute-lft-out_binary64_711` `distribute-rgt-in_binary64_710` `distribute-lft-in_binary64_709` `count-2_binary64_708` `associate--r-_binary64_699` `associate--l-_binary64_698` `associate--l+_binary64_697` `associate--r+_binary64_696` `associate-+l-_binary64_695` `associate-+r-_binary64_694` `associate-+l+_binary64_693` `associate-+r+_binary64_692`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	37
1	37	37
2	81	37
3	206	37
4	726	37
5	2240	37
6	2389	37
7	2768	37
8	2812	37
9	2915	37
10	3034	37
11	4545	37
12	4766	37
13	4871	37

prune8.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

15.4b

Counts

2 → 1

Compiler

Compiled 48 to 44 computations (8.3% saved)

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
0.3b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
6.4b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.1b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))

rewrite250.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

15.3b

Rules

28×	`add-exp-log_binary64_798`
20×	`pow1_binary64_821`
18×	`add-cbrt-cube_binary64_796`
15×	`*-un-lft-identity_binary64_760`
12×	`prod-exp_binary64_809` `add-sqr-sqrt_binary64_782`
11×	`add-cube-cbrt_binary64_795`
10×	`associate-r_binary64_700`
9×	`pow-prod-down_binary64_831` `cbrt-unprod_binary64_793`
8×	`sqrt-prod_binary64_776`
7×	`unpow-prod-down_binary64_839`
4×	`add-log-exp_binary64_799` `sqrt-div_binary64_777` `pow-exp_binary64_828`
3×	`times-frac_binary64_766` `pow-unpow_binary64_837` `div-exp_binary64_811`
2×	`flip3-+_binary64_763` `associate-r/_binary64_702` `flip-+_binary64_734` `associate-l_binary64_701` `distribute-lft-out_binary64_711` `-commutative_binary64_691`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `div-inv_binary64_757` `pow-pow_binary64_832` `pow-to-exp_binary64_829` `unpow2_binary64_825` `sqr-pow_binary64_732`

Counts

4 → 86

Calls

4 calls:

15.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
7.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
5.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 3141 to 2524 computations (19.6% saved)

series2.5s (6.8%)

Error

0.1b

Counts

4 → 56

Calls

4 calls:

924.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
866.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
468.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
175.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 4317 to 3703 computations (14.2% saved)

simplify170.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

951×	`times-frac_binary64_766`
277×	`associate-l_binary64_701`
207×	`associate-r_binary64_700`
148×	`distribute-rgt-in_binary64_710`
146×	`*-commutative_binary64_691`
144×	`cancel-sign-sub-inv_binary64_726`
138×	`log-prod_binary64_846`
115×	`exp-prod_binary64_812`
111×	`distribute-rgt-neg-in_binary64_718`
93×	`distribute-lft-neg-in_binary64_717`
92×	`sqr-pow_binary64_732`
91×	`unswap-sqr_binary64_728`
62×	`sub-neg_binary64_753`
60×	`associate-/r*_binary64_704`
57×	`distribute-neg-frac_binary64_724`
56×	`distribute-lft-neg-out_binary64_719`
44×	`associate-*r/_binary64_702`
42×	`associate-/l*_binary64_705`
41×	`neg-sub0_binary64_755`
40×	`neg-mul-1_binary64_756`
39×	`log-div_binary64_847` `cube-prod_binary64_788` `swap-sqr_binary64_727` `distribute-rgt-neg-out_binary64_720` `+-commutative_binary64_690`
38×	`associate-*l/_binary64_703`
29×	`unpow3_binary64_826`
28×	`log-pow_binary64_849`
25×	`*-lft-identity_binary64_749`
18×	`unpow1/2_binary64_824` `*-rgt-identity_binary64_750` `distribute-neg-in_binary64_721`
16×	`associate--r+_binary64_696`
15×	`unpow2_binary64_825` `unpow1_binary64_818` `distribute-lft-in_binary64_709`
14×	`pow-plus_binary64_823`
13×	`associate-+l+_binary64_693`
11×	`unsub-neg_binary64_754`
10×	`cube-unmult_binary64_797` `pow-sqr_binary64_733`
9×	`distribute-rgt-out--_binary64_714`
8×	`cube-div_binary64_789` `distribute-rgt-out_binary64_713`
7×	`associate-+r+_binary64_692`
5×	`rem-sqrt-square_binary64_773` `distribute-rgt1-in_binary64_716` `associate-/r/_binary64_706` `associate--l+_binary64_697`
4×	`cube-mult_binary64_790`
3×	`distribute-lft-out--_binary64_712` `associate-+r-_binary64_694`
2×	`exp-lft-sqr_binary64_815` `rem-square-sqrt_binary64_772` `+-rgt-identity_binary64_745` `difference-of-sqr-1_binary64_730` `difference-of-squares_binary64_729`
1×	`unpow-1_binary64_817` `exp-diff_binary64_808` `1-exp_binary64_804` `exp-1-e_binary64_803` `cube-neg_binary64_787` `rem-3cbrt-rft_binary64_786` `sqr-neg_binary64_774` `mul-1-neg_binary64_752` `distribute-lft1-in_binary64_715` `distribute-lft-out_binary64_711` `associate-/l/_binary64_707` `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` `exp-lft-cube_binary64_816` `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-0_binary64_802` `rem-log-exp_binary64_801` `rem-exp-log_binary64_800` `rem-3cbrt-lft_binary64_785` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `div-sub_binary64_765` `/-rgt-identity_binary64_751` `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` `cancel-sign-sub_binary64_725` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722` `count-2_binary64_708` `associate--r-_binary64_699` `associate--l-_binary64_698`

Counts

142 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	240	4081
1	591	3767
2	2032	3723
3	4738	3714
4	4985	3714
5	4966	3714

prune214.0ms (0.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	98	7	105
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	98	8	106

Error

5.5b

Counts

106 → 8

Compiler

Compiled 3533 to 2690 computations (23.9% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.4b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 2)))
8.1b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 J 2) (cos.f64 (/.f64 K 2)))) 2))))
8.1b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 J 2) (cos.f64 (/.f64 K 2)))) 2))))
8.1b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 J 2) (cos.f64 (/.f64 K 2)))) 2))))

rewrite711.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

5.5b

Rules

32×	`pow1_binary64_821`
31×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
21×	`associate-r_binary64_700`
19×	`*-un-lft-identity_binary64_760`
18×	`pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793`
16×	`sqrt-prod_binary64_776`
12×	`add-sqr-sqrt_binary64_782`
11×	`add-cube-cbrt_binary64_795`
8×	`sqrt-div_binary64_777`
6×	`associate-*r/_binary64_702`
4×	`add-log-exp_binary64_799` `flip3-+_binary64_763` `flip-+_binary64_734` `distribute-lft-out_binary64_711`
3×	`associate-l_binary64_701` `*-commutative_binary64_691`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773`

Counts

4 → 97

Calls

4 calls:

18.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 J 2) (cos.f64 (/.f64 K 2)))) 2))))
16.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 J 2) (cos.f64 (/.f64 K 2)))) 2))))
15.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 J 2) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 2)))

Compiler

Compiled 9219 to 7458 computations (19.1% saved)

series4.2s (11.4%)

Error

5.5b

Counts

4 → 70

Calls

4 calls:

998.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 J 2) (cos.f64 (/.f64 K 2)))) 2))))
985.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 J 2) (cos.f64 (/.f64 K 2)))) 2))))
973.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 J 2) (cos.f64 (/.f64 K 2)))) 2))))
917.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 2)))

Compiler

Compiled 14463 to 11957 computations (17.3% saved)

simplify178.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

771×	`times-frac_binary64_766`
417×	`associate-/l*_binary64_705`
381×	`associate-/r*_binary64_704`
244×	`associate-l_binary64_701`
178×	`associate-r_binary64_700`
129×	`distribute-rgt-in_binary64_710`
127×	`distribute-lft-in_binary64_709`
126×	`*-commutative_binary64_691`
118×	`cancel-sign-sub-inv_binary64_726`
93×	`distribute-rgt-neg-in_binary64_718`
78×	`distribute-lft-neg-in_binary64_717`
69×	`unswap-sqr_binary64_728`
68×	`associate-/l/_binary64_707`
63×	`associate-/r/_binary64_706`
57×	`distribute-neg-frac_binary64_724`
47×	`cube-div_binary64_789`
45×	`log-prod_binary64_846` `exp-prod_binary64_812` `sqr-pow_binary64_732`
41×	`sub-neg_binary64_753`
32×	`cube-prod_binary64_788`
31×	`neg-sub0_binary64_755`
30×	`neg-mul-1_binary64_756` `+-commutative_binary64_690`
29×	`associate-*r/_binary64_702`
28×	`unpow3_binary64_826`
27×	`swap-sqr_binary64_727`
23×	`cube-mult_binary64_790` `associate-*l/_binary64_703`
14×	`*-lft-identity_binary64_749`
13×	`cube-unmult_binary64_797` `*-rgt-identity_binary64_750`
11×	`associate-+l+_binary64_693`
8×	`associate--r+_binary64_696`
7×	`distribute-lft-neg-out_binary64_719`
6×	`unpow1/2_binary64_824` `pow-plus_binary64_823` `unsub-neg_binary64_754` `distribute-neg-in_binary64_721`
5×	`unpow2_binary64_825` `unpow1_binary64_818` `distribute-rgt1-in_binary64_716` `distribute-rgt-out--_binary64_714` `associate-+r+_binary64_692`
4×	`associate--l+_binary64_697`
3×	`pow-sqr_binary64_733` `distribute-rgt-out_binary64_713` `associate-+r-_binary64_694`
2×	`log-pow_binary64_849` `rem-sqrt-square_binary64_773` `+-rgt-identity_binary64_745` `difference-of-sqr-1_binary64_730` `difference-of-squares_binary64_729`
1×	`1-exp_binary64_804` `exp-1-e_binary64_803` `rem-square-sqrt_binary64_772` `mul-1-neg_binary64_752` `distribute-rgt-neg-out_binary64_720` `distribute-lft1-in_binary64_715` `distribute-lft-out--_binary64_712` `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` `log-div_binary64_847` `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` `prod-exp_binary64_809` `exp-diff_binary64_808` `exp-neg_binary64_807` `exp-sum_binary64_806` `e-exp-1_binary64_805` `exp-0_binary64_802` `rem-log-exp_binary64_801` `rem-exp-log_binary64_800` `cube-neg_binary64_787` `rem-3cbrt-rft_binary64_786` `rem-3cbrt-lft_binary64_785` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `div-sub_binary64_765` `/-rgt-identity_binary64_751` `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` `cancel-sign-sub_binary64_725` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722` `distribute-lft-out_binary64_711` `count-2_binary64_708` `associate--r-_binary64_699` `associate--l-_binary64_698`

Counts

167 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	166	6246
1	440	5666
2	1602	5585
3	4899	5540
4	4980	5540

prune926.0ms (2.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	136	9	145

Error

5.5b

Counts

145 → 9

Compiler

Compiled 11962 to 9465 computations (20.9% saved)

localize39.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.1b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 J 2) (cos.f64 (/.f64 K 2)))) 2))))
8.1b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2))))
8.1b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2))))
8.1b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2))))

rewrite1.5s (3.9%)

Algorithm

1×	rewrite-expression-head

Error

5.5b

Rules

40×	`pow1_binary64_821` `add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
28×	`associate-r_binary64_700`
24×	`pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793`
20×	`*-un-lft-identity_binary64_760`
16×	`sqrt-prod_binary64_776`
12×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
8×	`sqrt-div_binary64_777` `associate-*r/_binary64_702`
4×	`add-log-exp_binary64_799` `flip3-+_binary64_763` `flip-+_binary64_734` `associate-l_binary64_701` `distribute-lft-out_binary64_711` `*-commutative_binary64_691`

Counts

4 → 108

Calls

4 calls:

20.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 J 2) (cos.f64 (/.f64 K 2)))) 2))))
16.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2))))
16.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2))))
16.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2))))

Compiler

Compiled 16056 to 12998 computations (19% saved)

series4.8s (12.9%)

Error

5.5b

Counts

4 → 64

Calls

4 calls:

1.0s	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2))))
1.0s	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 J 2) (cos.f64 (/.f64 K 2)))) 2))))
1.0s	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2))))
1.0s	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2))))

Compiler

Compiled 21816 to 17928 computations (17.8% saved)

simplify186.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

524×	`*-commutative_binary64_691`
378×	`times-frac_binary64_766`
324×	`cancel-sign-sub-inv_binary64_726`
300×	`unswap-sqr_binary64_728`
246×	`associate-l_binary64_701`
200×	`associate-/r*_binary64_704`
191×	`associate-/l*_binary64_705`
190×	`associate-*r/_binary64_702`
176×	`associate-*l/_binary64_703`
173×	`associate-r_binary64_700`
126×	`distribute-rgt-in_binary64_710`
124×	`distribute-lft-in_binary64_709`
104×	`sqr-pow_binary64_732`
96×	`cube-div_binary64_789`
94×	`cube-prod_binary64_788`
70×	`swap-sqr_binary64_727`
56×	`sub-neg_binary64_753`
54×	`neg-sub0_binary64_755`
53×	`exp-prod_binary64_812` `neg-mul-1_binary64_756`
49×	`log-prod_binary64_846`
46×	`distribute-rgt-neg-in_binary64_718`
37×	`+-commutative_binary64_690`
36×	`distribute-lft-neg-in_binary64_717`
35×	`associate-/l/_binary64_707`
33×	`associate-+l+_binary64_693`
31×	`distribute-neg-frac_binary64_724`
30×	`associate-+r+_binary64_692`
27×	`unpow3_binary64_826`
23×	`cube-mult_binary64_790`
21×	`associate-/r/_binary64_706`
18×	`*-rgt-identity_binary64_750`
17×	`*-lft-identity_binary64_749`
14×	`pow-sqr_binary64_733`
11×	`cube-unmult_binary64_797`
9×	`associate-+l-_binary64_695`
8×	`rem-sqrt-square_binary64_773`
7×	`distribute-lft-neg-out_binary64_719`
6×	`unpow2_binary64_825` `unpow1/2_binary64_824` `pow-plus_binary64_823` `associate--r+_binary64_696`
5×	`unpow1_binary64_818` `div-sub_binary64_765` `sub0-neg_binary64_747` `+-rgt-identity_binary64_745` `associate-+r-_binary64_694`
4×	`/-rgt-identity_binary64_751` `distribute-neg-in_binary64_721`
3×	`unsub-neg_binary64_754` `distribute-rgt-out--_binary64_714`
2×	`log-pow_binary64_849` `rem-square-sqrt_binary64_772`
1×	`1-exp_binary64_804` `exp-1-e_binary64_803` `mul-1-neg_binary64_752` `difference-of-sqr-1_binary64_730` `distribute-rgt-neg-out_binary64_720` `distribute-lft-out--_binary64_712`
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` `log-div_binary64_847` `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` `prod-exp_binary64_809` `exp-diff_binary64_808` `exp-neg_binary64_807` `exp-sum_binary64_806` `e-exp-1_binary64_805` `exp-0_binary64_802` `rem-log-exp_binary64_801` `rem-exp-log_binary64_800` `cube-neg_binary64_787` `rem-3cbrt-rft_binary64_786` `rem-3cbrt-lft_binary64_785` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `remove-double-neg_binary64_748` `--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-squares_binary64_729` `cancel-sign-sub_binary64_725` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `distribute-rgt-out_binary64_713` `distribute-lft-out_binary64_711` `count-2_binary64_708` `associate--r-_binary64_699` `associate--l-_binary64_698` `associate--l+_binary64_697`

Counts

172 → 111

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	6784
1	350	6040
2	1252	5948
3	3690	5948
4	5153	5948

prune1.3s (3.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	111	9	120

Error

5.5b

Counts

120 → 9

Compiler

Compiled 15231 to 12151 computations (20.2% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.7b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 6)))
8.9b	(sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
12.2b	(-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
20.1b	(/.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 6)))) (sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))))

rewrite702.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

5.5b

Rules

18×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
16×	`sqrt-prod_binary64_776`
15×	`*-un-lft-identity_binary64_760`
12×	`add-sqr-sqrt_binary64_782`
10×	`add-cube-cbrt_binary64_795`
8×	`sqrt-div_binary64_777`
7×	`times-frac_binary64_766` `associate-/r*_binary64_704`
6×	`pow1_binary64_821` `prod-exp_binary64_809` `add-log-exp_binary64_799` `cbrt-unprod_binary64_793`
4×	`div-exp_binary64_811` `cbrt-undiv_binary64_794` `distribute-lft-out_binary64_711` `flip3-+_binary64_763` `flip-+_binary64_734`
2×	`associate-*r/_binary64_702` `associate-/l/_binary64_707` `associate-/r/_binary64_706` `pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773`
1×	`frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757` `associate-/l*_binary64_705` `diff-log_binary64_852` `flip3--_binary64_764` `sub-neg_binary64_753` `flip--_binary64_735` `cancel-sign-sub-inv_binary64_726` `distribute-rgt-out--_binary64_714`

Counts

4 → 82

Calls

4 calls:

32.0ms	(/.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 6)))) (sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))))
16.0ms	(sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
16.0ms	(-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 6)))

Compiler

Compiled 8883 to 7145 computations (19.6% saved)

series10.4s (28%)

Error

0.0b

Counts

4 → 61

Calls

4 calls:

6.2s	(/.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 6)))) (sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))))
1.8s	(-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
1.5s	(sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
792.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 6)))

Compiler

Compiled 10357 to 8756 computations (15.5% saved)

simplify189.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

351×	`distribute-rgt-in_binary64_710`
268×	`associate-l_binary64_701`
247×	`cancel-sign-sub-inv_binary64_726`
215×	`associate-r_binary64_700`
203×	`associate-/l*_binary64_705`
171×	`unswap-sqr_binary64_728`
160×	`times-frac_binary64_766`
150×	`*-commutative_binary64_691`
119×	`distribute-rgt-neg-in_binary64_718`
118×	`associate-/r*_binary64_704`
105×	`sub-neg_binary64_753`
101×	`distribute-lft-neg-in_binary64_717`
85×	`associate-*r/_binary64_702`
83×	`sqr-pow_binary64_732`
77×	`associate-*l/_binary64_703`
69×	`+-commutative_binary64_690`
64×	`distribute-rgt-out_binary64_713`
58×	`cube-prod_binary64_788` `distribute-neg-frac_binary64_724`
54×	`swap-sqr_binary64_727`
45×	`div-sub_binary64_765`
43×	`cube-div_binary64_789`
42×	`neg-mul-1_binary64_756` `neg-sub0_binary64_755`
38×	`associate-/l/_binary64_707`
37×	`log-div_binary64_847`
34×	`log-prod_binary64_846` `distribute-lft-out_binary64_711`
30×	`distribute-neg-in_binary64_721`
29×	`distribute-lft-in_binary64_709` `associate-+l+_binary64_693`
28×	`exp-prod_binary64_812`
26×	`associate-/r/_binary64_706`
25×	`*-rgt-identity_binary64_750`
24×	`distribute-rgt-out--_binary64_714`
22×	`associate--l+_binary64_697`
20×	`difference-of-squares_binary64_729`
19×	`*-lft-identity_binary64_749` `distribute-lft-neg-out_binary64_719`
17×	`associate-+r+_binary64_692`
16×	`cube-unmult_binary64_797`
15×	`distribute-rgt1-in_binary64_716` `associate--r+_binary64_696`
13×	`unpow3_binary64_826` `distribute-rgt-neg-out_binary64_720`
12×	`cube-mult_binary64_790` `unsub-neg_binary64_754`
9×	`distribute-lft-out--_binary64_712`
8×	`distribute-lft1-in_binary64_715`
7×	`pow-sqr_binary64_733`
5×	`unpow2_binary64_825` `unpow1/2_binary64_824` `pow-plus_binary64_823` `unpow1_binary64_818` `associate-+r-_binary64_694`
4×	`rem-sqrt-square_binary64_773` `difference-of-sqr-1_binary64_730`
3×	`exp-sum_binary64_806` `/-rgt-identity_binary64_751` `associate--r-_binary64_699` `associate-+l-_binary64_695`
2×	`log-pow_binary64_849` `log-rec_binary64_848` `exp-diff_binary64_808` `rem-square-sqrt_binary64_772` `mul-1-neg_binary64_752` `+-rgt-identity_binary64_745` `difference-of-sqr--1_binary64_731`
1×	`div-exp_binary64_811` `1-exp_binary64_804` `exp-1-e_binary64_803` `cube-neg_binary64_787` `remove-double-neg_binary64_748` `associate--l-_binary64_698`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_1023` `erf-erfc_binary64_1022` `erf-odd_binary64_1021` `if-if-and-not_binary64_1020` `if-if-and_binary64_1019` `if-if-or-not_binary64_1018` `if-if-or_binary64_1017` `if-not_binary64_1016` `if-same_binary64_1015` `if-false_binary64_1014` `if-true_binary64_1013` `not-gte_binary64_1012` `not-lte_binary64_1011` `not-gt_binary64_1010` `not-lt_binary64_1009` `gte-same_binary64_1008` `lte-same_binary64_1007` `gt-same_binary64_1006` `lt-same_binary64_1005` `sinh---cosh_binary64_952` `sinh-+-cosh_binary64_951` `sinh-cosh_binary64_950` `tanh-def-c_binary64_949` `tanh-def-b_binary64_948` `tanh-def-a_binary64_947` `cosh-def_binary64_946` `sinh-def_binary64_945` `tan-neg_binary64_892` `cos-neg_binary64_891` `sin-neg_binary64_890` `tan-0_binary64_889` `cos-0_binary64_888` `sin-0_binary64_887` `hang-m-tan_binary64_886` `hang-p-tan_binary64_885` `hang-m0-tan_binary64_884` `hang-p0-tan_binary64_883` `hang-0m-tan_binary64_882` `hang-0p-tan_binary64_881` `tan-+PI/2_binary64_880` `tan-+PI_binary64_879` `tan-PI_binary64_878` `tan-PI/3_binary64_877` `tan-PI/4_binary64_876` `tan-PI/6_binary64_875` `cos-+PI/2_binary64_874` `cos-+PI_binary64_873` `cos-PI_binary64_872` `cos-PI/2_binary64_871` `cos-PI/3_binary64_870` `cos-PI/4_binary64_869` `cos-PI/6_binary64_868` `sin-+PI/2_binary64_867` `sin-+PI_binary64_866` `sin-PI_binary64_865` `sin-PI/2_binary64_864` `sin-PI/3_binary64_863` `sin-PI/4_binary64_862` `sin-PI/6_binary64_861` `sub-1-sin_binary64_860` `sub-1-cos_binary64_859` `-1-add-sin_binary64_858` `-1-add-cos_binary64_857` `1-sub-sin_binary64_856` `1-sub-cos_binary64_855` `cos-sin-sum_binary64_854` `log-E_binary64_850` `pow-base-0_binary64_844` `unpow1/3_binary64_827` `exp-to-pow_binary64_822` `pow-base-1_binary64_820` `unpow0_binary64_819` `unpow-1_binary64_817` `exp-lft-cube_binary64_816` `exp-lft-sqr_binary64_815` `exp-cbrt_binary64_814` `exp-sqrt_binary64_813` `rec-exp_binary64_810` `prod-exp_binary64_809` `exp-neg_binary64_807` `e-exp-1_binary64_805` `exp-0_binary64_802` `rem-log-exp_binary64_801` `rem-exp-log_binary64_800` `rem-3cbrt-rft_binary64_786` `rem-3cbrt-lft_binary64_785` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `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` `+-inverses_binary64_739` `lft-mult-inverse_binary64_738` `rgt-mult-inverse_binary64_737` `remove-double-div_binary64_736` `cancel-sign-sub_binary64_725` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722` `count-2_binary64_708`

Counts

143 → 120

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	308	8687
1	792	7658
2	3104	7590
3	5038	7590

prune597.0ms (1.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	1	4	5
Picked	1	0	1
Done	0	3	3
Total	121	8	129

Error

5.5b

Counts

129 → 8

Compiler

Compiled 8153 to 6368 computations (21.9% saved)

regimes1.4s (3.8%)

Accuracy

Total 9.2b remaining (99.8%)

Threshold costs 0b (0%)

Compiler

Compiled 14857 to 12778 computations (14% saved)

bsearch5.0ms (0%)

Compiler: Compiled 24 to 22 computations (8.3% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64_691`
2×	`+-commutative_binary64_690`
1×	`1-exp_binary64_804` `neg-mul-1_binary64_756` `neg-sub0_binary64_755` `sub-neg_binary64_753`
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` `-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-neg-in_binary64_721` `distribute-rgt-neg-out_binary64_720` `distribute-lft-neg-out_binary64_719` `distribute-rgt-neg-in_binary64_718` `distribute-lft-neg-in_binary64_717`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	125
1	37	125
2	39	125
3	40	125
4	39	125

end0.0ms (0%)

sample4.6s (12.3%)

Algorithm

1×

intervals

Results

1.1s	1971×	body	1024	valid
518.0ms	4579×	body	128	valid
385.0ms	969×	body	512	valid
122.0ms	479×	body	256	valid
2.0ms	2×	body	2048	valid
0.0ms	1×	body	512	invalid
0.0ms	3×	body	128	invalid

Compiler

Compiled 2525 to 2169 computations (14.1% saved)

Details

analyze2.0s (5.5%)

sample83.0ms (0.2%)

simplify92.0ms (0.2%)

prune8.0ms (0%)

localize15.0ms (0%)

rewrite250.0ms (0.7%)

series2.5s (6.8%)

simplify170.0ms (0.5%)

prune214.0ms (0.6%)

localize22.0ms (0.1%)

rewrite711.0ms (1.9%)

series4.2s (11.4%)

simplify178.0ms (0.5%)

prune926.0ms (2.5%)

localize39.0ms (0.1%)

rewrite1.5s (3.9%)

series4.8s (12.9%)

simplify186.0ms (0.5%)

prune1.3s (3.5%)

localize30.0ms (0.1%)

rewrite702.0ms (1.9%)

series10.4s (28%)

simplify189.0ms (0.5%)

prune597.0ms (1.6%)

regimes1.4s (3.8%)

bsearch5.0ms (0%)

simplify6.0ms (0%)

end0.0ms (0%)

sample4.6s (12.3%)

Profiling