Details

analyze578.0ms (5%)

Algorithm

1×	search
2×	egg-herbie

Rules

570×	`neg-mul-1_binary64_756`
442×	`div-sub_binary64_765`
428×	`unswap-sqr_binary64_728`
418×	`associate-/l*_binary64_705`
306×	`associate-l_binary64_701`
304×	`distribute-rgt-in_binary64_710`
286×	`associate-/r*_binary64_704`
278×	`distribute-frac-neg_binary64_723`
228×	`associate-/l/_binary64_707`
210×	`associate-r_binary64_700`
205×	`*-commutative_binary64_691`
188×	`distribute-rgt-neg-out_binary64_720`
154×	`associate-/r/_binary64_706`
134×	`associate-*r/_binary64_702`
116×	`distribute-lft-neg-out_binary64_719`
106×	`associate-*l/_binary64_703`
70×	`sub-neg_binary64_753`
64×	`distribute-lft-in_binary64_709`
56×	`neg-sub0_binary64_755`
50×	`sqr-pow_binary64_732`
36×	`cube-prod_binary64_788`
30×	`*-lft-identity_binary64_749` `pow-sqr_binary64_733` `distribute-neg-frac_binary64_724`
24×	`+-commutative_binary64_690`
22×	`/-rgt-identity_binary64_751`
20×	`pow-plus_binary64_823`
18×	`distribute-lft-neg-in_binary64_717`
14×	`unsub-neg_binary64_754` `distribute-rgt-neg-in_binary64_718`
12×	`*-rgt-identity_binary64_750` `sub0-neg_binary64_747`
10×	`cube-unmult_binary64_797` `associate-+l-_binary64_695`
8×	`unpow3_binary64_826`
4×	`unpow2_binary64_825` `cube-mult_binary64_790` `--rgt-identity_binary64_746` `associate-+l+_binary64_693`
2×	`unpow1_binary64_818` `remove-double-div_binary64_736` `associate--r+_binary64_696` `associate-+r+_binary64_692`
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` `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` `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-sqrt-square_binary64_773` `rem-square-sqrt_binary64_772` `times-frac_binary64_766` `mul-1-neg_binary64_752` `remove-double-neg_binary64_748` `+-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` `difference-of-sqr--1_binary64_731` `difference-of-sqr-1_binary64_730` `difference-of-squares_binary64_729` `swap-sqr_binary64_727` `cancel-sign-sub-inv_binary64_726` `cancel-sign-sub_binary64_725` `distribute-neg-out_binary64_722` `distribute-neg-in_binary64_721` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `distribute-rgt-out--_binary64_714` `distribute-rgt-out_binary64_713` `distribute-lft-out--_binary64_712` `distribute-lft-out_binary64_711` `count-2_binary64_708` `associate--r-_binary64_699` `associate--l-_binary64_698` `associate--l+_binary64_697` `associate-+r-_binary64_694`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	50
1	52	44
2	113	44
3	232	44
4	507	44
5	1156	44
6	2424	44
7	4691	44
8	4942	44
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
12.5%	37.5%	50%	5
15.6%	31.2%	53.2%	6
17.2%	26.5%	56.3%	7
18%	22.6%	59.4%	8
18.3%	19.9%	61.8%	9
18.5%	17.8%	63.7%	10
18.6%	16.3%	65.1%	11
18.7%	15.2%	66.1%	12
18.7%	14.4%	66.9%	13
18.7%	13.8%	67.4%	14

Compiler

Compiled 17 to 16 computations (5.9% saved)

sample77.0ms (0.7%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
19.0ms	42×	body	1024	nan
9.0ms	29×	body	512	nan
8.0ms	59×	body	128	overflowed
2.0ms	12×	body	256	nan
1.0ms	26×	body	128	nan
1.0ms	13×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify55.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

788×	`neg-mul-1_binary64_756`
672×	`associate-/l*_binary64_705`
625×	`associate-/r*_binary64_704`
480×	`div-sub_binary64_765`
445×	`distribute-frac-neg_binary64_723`
288×	`distribute-rgt-neg-out_binary64_720`
267×	`associate-*r/_binary64_702`
257×	`associate-*l/_binary64_703`
235×	`distribute-lft-neg-out_binary64_719`
214×	`unswap-sqr_binary64_728`
164×	`*-commutative_binary64_691`
153×	`associate-l_binary64_701`
150×	`distribute-rgt-in_binary64_710`
125×	`distribute-lft-in_binary64_709`
115×	`associate-/l/_binary64_707`
105×	`associate-r_binary64_700`
77×	`associate-/r/_binary64_706`
76×	`sub-neg_binary64_753`
68×	`neg-sub0_binary64_755`
40×	`*-lft-identity_binary64_749`
38×	`sqr-pow_binary64_732`
27×	`cube-prod_binary64_788`
25×	`*-rgt-identity_binary64_750`
21×	`pow-sqr_binary64_733`
20×	`unsub-neg_binary64_754`
18×	`/-rgt-identity_binary64_751`
17×	`+-commutative_binary64_690`
15×	`pow-plus_binary64_823` `distribute-neg-frac_binary64_724`
12×	`associate-+l-_binary64_695`
9×	`unpow3_binary64_826` `distribute-lft-neg-in_binary64_717`
7×	`sub0-neg_binary64_747` `distribute-rgt-neg-in_binary64_718`
6×	`cube-unmult_binary64_797` `cube-mult_binary64_790`
4×	`unpow2_binary64_825`
3×	`--rgt-identity_binary64_746` `remove-double-div_binary64_736` `associate--r+_binary64_696` `associate-+l+_binary64_693`
2×	`unpow1_binary64_818`
1×	`unpow1/2_binary64_824` `1-exp_binary64_804` `associate-+r+_binary64_692`
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-sqrt-square_binary64_773` `rem-square-sqrt_binary64_772` `times-frac_binary64_766` `mul-1-neg_binary64_752` `remove-double-neg_binary64_748` `+-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` `difference-of-sqr--1_binary64_731` `difference-of-sqr-1_binary64_730` `difference-of-squares_binary64_729` `swap-sqr_binary64_727` `cancel-sign-sub-inv_binary64_726` `cancel-sign-sub_binary64_725` `distribute-neg-out_binary64_722` `distribute-neg-in_binary64_721` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `distribute-rgt-out--_binary64_714` `distribute-rgt-out_binary64_713` `distribute-lft-out--_binary64_712` `distribute-lft-out_binary64_711` `count-2_binary64_708` `associate--r-_binary64_699` `associate--l-_binary64_698` `associate--l+_binary64_697` `associate-+r-_binary64_694`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	32	22
2	65	22
3	128	22
4	277	22
5	623	22
6	1296	22
7	3024	22
8	4691	22
9	4933	22

prune6.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.4b

Counts

2 → 2

Compiler

Compiled 44 to 41 computations (6.8% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
0.2b	(.f64 (.f64 2 PI.f64) n)
0.3b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))

rewrite242.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

48×	`times-frac_binary64_766`
42×	`add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
33×	`add-cube-cbrt_binary64_795`
26×	`add-exp-log_binary64_798`
22×	`pow-unpow_binary64_837`
18×	`sqrt-prod_binary64_776`
14×	`pow1_binary64_821`
10×	`add-cbrt-cube_binary64_796`
9×	`prod-exp_binary64_809`
8×	`unpow-prod-down_binary64_839` `sqr-pow_binary64_732`
6×	`difference-of-squares_binary64_729` `pow-prod-down_binary64_831` `pow-exp_binary64_828` `associate-/r*_binary64_704`
5×	`div-exp_binary64_811` `associate-/l*_binary64_705`
3×	`distribute-lft-out--_binary64_712` `pow-pow_binary64_832` `add-log-exp_binary64_799` `cbrt-unprod_binary64_793` `associate-r_binary64_700`
2×	`div-inv_binary64_757` `div-sub_binary64_765` `pow-sub_binary64_836` `pow-to-exp_binary64_829`
1×	`associate-l_binary64_701` `*-commutative_binary64_691` `cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l/_binary64_707`

Counts

3 → 115

Calls

3 calls:

17.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
7.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
6.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 2834 to 1916 computations (32.4% saved)

series637.0ms (5.5%)

Error

0.1b

Counts

3 → 17

Calls

3 calls:

301.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
272.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
41.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 1025 to 819 computations (20.1% saved)

simplify131.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

434×	`*-commutative_binary64_691`
416×	`distribute-rgt-in_binary64_710`
414×	`distribute-lft-in_binary64_709`
304×	`exp-sum_binary64_806`
208×	`associate-/l*_binary64_705`
199×	`associate-/l/_binary64_707`
146×	`associate-l_binary64_701`
143×	`exp-prod_binary64_812` `times-frac_binary64_766`
137×	`associate-/r*_binary64_704`
121×	`associate-r_binary64_700`
110×	`sqr-pow_binary64_732`
101×	`associate-*r/_binary64_702`
82×	`associate-/r/_binary64_706`
75×	`associate-*l/_binary64_703`
68×	`log-prod_binary64_846`
50×	`cancel-sign-sub-inv_binary64_726`
42×	`pow-sqr_binary64_733`
32×	`log-div_binary64_847`
31×	`unswap-sqr_binary64_728`
29×	`distribute-lft-neg-in_binary64_717`
27×	`sub-neg_binary64_753` `distribute-rgt-neg-in_binary64_718`
26×	`associate--l+_binary64_697`
23×	`associate-+l+_binary64_693`
22×	`exp-to-pow_binary64_822`
21×	`log-pow_binary64_849`
20×	`*-rgt-identity_binary64_750`
19×	`exp-diff_binary64_808`
18×	`exp-neg_binary64_807`
17×	`associate-+r+_binary64_692`
16×	`swap-sqr_binary64_727` `associate-+r-_binary64_694`
15×	`cube-prod_binary64_788` `distribute-rgt-neg-out_binary64_720` `distribute-lft-neg-out_binary64_719`
14×	`*-lft-identity_binary64_749`
13×	`neg-mul-1_binary64_756` `neg-sub0_binary64_755`
12×	`pow-plus_binary64_823` `associate--r-_binary64_699`
11×	`cube-unmult_binary64_797` `associate-+l-_binary64_695` `+-commutative_binary64_690`
10×	`/-rgt-identity_binary64_751`
9×	`unpow1/2_binary64_824`
8×	`div-sub_binary64_765`
6×	`unpow3_binary64_826` `exp-sqrt_binary64_813` `distribute-neg-frac_binary64_724`
5×	`prod-exp_binary64_809` `unsub-neg_binary64_754` `associate--r+_binary64_696`
4×	`unpow1_binary64_818` `rem-sqrt-square_binary64_773`
3×	`log-rec_binary64_848` `exp-lft-sqr_binary64_815` `cube-div_binary64_789` `distribute-rgt-out_binary64_713` `distribute-lft-out_binary64_711`
2×	`unpow2_binary64_825` `rec-exp_binary64_810` `distribute-neg-in_binary64_721` `distribute-rgt-out--_binary64_714` `distribute-lft-out--_binary64_712` `count-2_binary64_708` `associate--l-_binary64_698`
1×	`1-exp_binary64_804` `exp-1-e_binary64_803` `rem-square-sqrt_binary64_772` `remove-double-neg_binary64_748`
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` `pow-base-1_binary64_820` `unpow0_binary64_819` `unpow-1_binary64_817` `exp-lft-cube_binary64_816` `exp-cbrt_binary64_814` `div-exp_binary64_811` `e-exp-1_binary64_805` `exp-0_binary64_802` `rem-log-exp_binary64_801` `rem-exp-log_binary64_800` `cube-mult_binary64_790` `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` `mul-1-neg_binary64_752` `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_binary64_725` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715`

Counts

132 → 121

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	228	3591
1	476	3428
2	1456	3296
3	4202	3277
4	4964	3277

prune196.0ms (1.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	111	10	121
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	113	10	123

Error

0.0b

Counts

123 → 10

Compiler

Compiled 2855 to 1933 computations (32.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))
0.2b	(.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
0.2b	(.f64 n (.f64 2 PI.f64))
0.6b	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

rewrite223.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

45×	`add-sqr-sqrt_binary64_782`
25×	`sqrt-prod_binary64_776` `*-un-lft-identity_binary64_760`
22×	`pow1_binary64_821`
19×	`add-cube-cbrt_binary64_795`
17×	`associate-r_binary64_700`
15×	`add-exp-log_binary64_798` `associate-l_binary64_701` `times-frac_binary64_766`
12×	`unpow-prod-down_binary64_839` `unswap-sqr_binary64_728`
11×	`add-cbrt-cube_binary64_796`
9×	`pow-prod-down_binary64_831`
8×	`unpow-prod-up_binary64_838`
6×	`sqrt-pow1_binary64_778` `prod-exp_binary64_809` `sqr-pow_binary64_732` `cancel-sign-sub-inv_binary64_726` `pow-unpow_binary64_837`
5×	`pow-pow_binary64_832`
4×	`add-log-exp_binary64_799` `cbrt-unprod_binary64_793`
3×	`pow-sub_binary64_836`
2×	`pow1/2_binary64_840` `*-commutative_binary64_691` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `sqrt-div_binary64_777` `sub-neg_binary64_753` `difference-of-squares_binary64_729`
1×	`frac-times_binary64_770` `associate-l/_binary64_703` `associate-r/_binary64_702` `div-inv_binary64_757` `distribute-lft-out--_binary64_712` `sqrt-pow2_binary64_779`

Counts

4 → 116

Calls

4 calls:

15.0ms	(.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
11.0ms	(pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))
5.0ms	(.f64 n (.f64 2 PI.f64))
4.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 2812 to 2087 computations (25.8% saved)

series449.0ms (3.9%)

Error

0.0b

Counts

4 → 20

Calls

4 calls:

186.0ms	(.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
166.0ms	(pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))
41.0ms	(.f64 n (.f64 2 PI.f64))
34.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 1500 to 1167 computations (22.2% saved)

simplify178.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

963×	`times-frac_binary64_766`
481×	`*-commutative_binary64_691`
272×	`exp-prod_binary64_812`
232×	`sqr-pow_binary64_732`
201×	`associate-l_binary64_701`
199×	`associate-r_binary64_700`
166×	`exp-sum_binary64_806`
161×	`unswap-sqr_binary64_728`
160×	`distribute-rgt-in_binary64_710`
159×	`distribute-lft-in_binary64_709`
109×	`log-prod_binary64_846`
90×	`pow-sqr_binary64_733`
74×	`associate-/l*_binary64_705`
66×	`unsub-neg_binary64_754`
51×	`associate-/r*_binary64_704`
48×	`*-rgt-identity_binary64_750`
45×	`*-lft-identity_binary64_749`
44×	`neg-mul-1_binary64_756`
42×	`neg-sub0_binary64_755`
40×	`div-sub_binary64_765`
39×	`log-pow_binary64_849`
38×	`cube-prod_binary64_788`
35×	`sub-neg_binary64_753`
33×	`exp-to-pow_binary64_822` `associate-*r/_binary64_702`
31×	`associate-+l+_binary64_693`
30×	`exp-diff_binary64_808`
29×	`prod-exp_binary64_809` `swap-sqr_binary64_727`
28×	`cancel-sign-sub-inv_binary64_726`
26×	`distribute-rgt-neg-in_binary64_718` `associate-/l/_binary64_707`
25×	`associate-+r+_binary64_692`
23×	`distribute-lft-neg-in_binary64_717` `associate-/r/_binary64_706` `+-commutative_binary64_690`
18×	`pow-plus_binary64_823`
17×	`associate-*l/_binary64_703`
15×	`cube-unmult_binary64_797`
14×	`unpow1/2_binary64_824`
13×	`distribute-lft-neg-out_binary64_719`
12×	`unpow3_binary64_826`
11×	`distribute-rgt-neg-out_binary64_720`
10×	`exp-neg_binary64_807`
9×	`rem-sqrt-square_binary64_773` `mul0-rgt_binary64_743` `mul0-lft_binary64_742`
7×	`exp-lft-sqr_binary64_815` `rem-exp-log_binary64_800`
6×	`unpow1_binary64_818` `distribute-frac-neg_binary64_723`
5×	`pow-base-1_binary64_820` `rec-exp_binary64_810` `cube-mult_binary64_790` `/-rgt-identity_binary64_751`
4×	`log-div_binary64_847` `exp-sqrt_binary64_813` `distribute-neg-in_binary64_721` `distribute-rgt-out--_binary64_714` `associate-+l-_binary64_695`
3×	`rem-square-sqrt_binary64_772` `sub0-neg_binary64_747` `+-rgt-identity_binary64_745` `distribute-neg-frac_binary64_724` `distribute-rgt1-in_binary64_716` `distribute-rgt-out_binary64_713` `associate-+r-_binary64_694`
2×	`unpow2_binary64_825` `mul-1-neg_binary64_752` `div0_binary64_741` `count-2_binary64_708` `associate--l+_binary64_697`
1×	`log-E_binary64_850` `1-exp_binary64_804` `exp-1-e_binary64_803` `rem-3cbrt-lft_binary64_785` `difference-of-sqr-1_binary64_730` `distribute-lft-out_binary64_711`
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-rec_binary64_848` `pow-base-0_binary64_844` `unpow1/3_binary64_827` `unpow0_binary64_819` `unpow-1_binary64_817` `exp-lft-cube_binary64_816` `exp-cbrt_binary64_814` `div-exp_binary64_811` `e-exp-1_binary64_805` `exp-0_binary64_802` `rem-log-exp_binary64_801` `cube-div_binary64_789` `cube-neg_binary64_787` `rem-3cbrt-rft_binary64_786` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `remove-double-neg_binary64_748` `--rgt-identity_binary64_746` `+-lft-identity_binary64_744` `*-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-neg-out_binary64_722` `distribute-lft1-in_binary64_715` `distribute-lft-out--_binary64_712` `associate--r-_binary64_699` `associate--l-_binary64_698` `associate--r+_binary64_696`

Counts

136 → 116

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	3202
1	444	3072
2	1383	3049
3	2782	3037
4	4730	3037
5	4963	3037
6	4921	3037

prune181.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	112	4	116
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	117	9	126

Error

Counts

126 → 9

Compiler

Compiled 2782 to 1921 computations (30.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))
0.2b	(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 (sqrt.f64 k)))
0.2b	(.f64 n (.f64 2 PI.f64))
0.6b	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

rewrite388.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

129×	`sqrt-prod_binary64_776`
108×	`times-frac_binary64_766`
80×	`add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
77×	`add-cube-cbrt_binary64_795`
44×	`unpow-prod-down_binary64_839` `unpow-prod-up_binary64_838`
33×	`cancel-sign-sub-inv_binary64_726`
22×	`pow1_binary64_821`
15×	`add-exp-log_binary64_798`
12×	`associate-/l*_binary64_705`
11×	`add-cbrt-cube_binary64_796` `sub-neg_binary64_753` `sqr-pow_binary64_732`
9×	`pow-prod-down_binary64_831` `associate-/r*_binary64_704`
6×	`sqrt-pow1_binary64_778` `pow-unpow_binary64_837`
5×	`pow-pow_binary64_832`
4×	`add-log-exp_binary64_799`
3×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793` `associate-l_binary64_701` `div-exp_binary64_811`
2×	`pow1/2_binary64_840` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `pow-sub_binary64_836` `difference-of-squares_binary64_729`
1×	`associate-r_binary64_700` `*-commutative_binary64_691` `cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757` `associate-/l/_binary64_707` `distribute-lft-out--_binary64_712` `sqrt-pow2_binary64_779`

Counts

4 → 205

Calls

4 calls:

12.0ms	(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 (sqrt.f64 k)))
8.0ms	(pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))
6.0ms	(.f64 n (.f64 2 PI.f64))
4.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 6410 to 3446 computations (46.2% saved)

series579.0ms (5%)

Error

Counts

4 → 22

Calls

4 calls:

307.0ms	(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 (sqrt.f64 k)))
163.0ms	(pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))
43.0ms	(.f64 n (.f64 2 PI.f64))
34.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 1987 to 1404 computations (29.3% saved)

simplify333.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

445×	`*-commutative_binary64_691`
325×	`associate-/l*_binary64_705`
217×	`exp-prod_binary64_812`
194×	`associate-/r*_binary64_704`
188×	`distribute-rgt-in_binary64_710`
187×	`distribute-lft-in_binary64_709`
184×	`exp-sum_binary64_806`
181×	`associate-/l/_binary64_707`
163×	`times-frac_binary64_766`
161×	`associate-r_binary64_700`
146×	`associate-l_binary64_701`
116×	`sqr-pow_binary64_732`
113×	`associate-/r/_binary64_706`
95×	`associate-*l/_binary64_703`
88×	`pow-sqr_binary64_733`
85×	`log-prod_binary64_846`
84×	`log-div_binary64_847`
79×	`cube-div_binary64_789` `unsub-neg_binary64_754` `sub-neg_binary64_753` `associate-*r/_binary64_702`
74×	`cancel-sign-sub-inv_binary64_726`
70×	`unswap-sqr_binary64_728`
60×	`cube-prod_binary64_788` `neg-mul-1_binary64_756`
56×	`neg-sub0_binary64_755`
52×	`unpow3_binary64_826`
40×	`*-rgt-identity_binary64_750` `distribute-rgt-neg-in_binary64_718`
39×	`*-lft-identity_binary64_749`
37×	`cube-mult_binary64_790`
35×	`distribute-lft-neg-in_binary64_717`
33×	`exp-diff_binary64_808`
32×	`log-pow_binary64_849`
31×	`exp-to-pow_binary64_822`
29×	`+-commutative_binary64_690`
27×	`div-sub_binary64_765`
23×	`swap-sqr_binary64_727` `associate-+l+_binary64_693`
22×	`associate-+r+_binary64_692`
20×	`pow-plus_binary64_823`
17×	`prod-exp_binary64_809` `/-rgt-identity_binary64_751` `distribute-lft-neg-out_binary64_719`
16×	`cube-unmult_binary64_797`
14×	`log-rec_binary64_848`
12×	`distribute-rgt-neg-out_binary64_720`
11×	`exp-neg_binary64_807` `associate-+l-_binary64_695`
10×	`mul0-rgt_binary64_743` `mul0-lft_binary64_742` `distribute-rgt-out_binary64_713` `associate--l+_binary64_697`
9×	`rem-sqrt-square_binary64_773` `distribute-rgt-out--_binary64_714`
8×	`associate-+r-_binary64_694`
7×	`rem-exp-log_binary64_800` `+-rgt-identity_binary64_745`
6×	`sub0-neg_binary64_747` `distribute-frac-neg_binary64_723` `distribute-neg-in_binary64_721`
4×	`unpow1/2_binary64_824` `pow-base-1_binary64_820` `unpow1_binary64_818` `exp-lft-sqr_binary64_815` `rec-exp_binary64_810` `distribute-neg-frac_binary64_724`
3×	`rem-square-sqrt_binary64_772` `distribute-rgt1-in_binary64_716` `associate--l-_binary64_698`
2×	`unpow2_binary64_825` `exp-sqrt_binary64_813` `div0_binary64_741` `count-2_binary64_708` `associate--r+_binary64_696`
1×	`log-E_binary64_850` `1-exp_binary64_804` `exp-1-e_binary64_803` `rem-log-exp_binary64_801` `rem-3cbrt-lft_binary64_785` `distribute-lft-out_binary64_711`
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` `pow-base-0_binary64_844` `unpow1/3_binary64_827` `unpow0_binary64_819` `unpow-1_binary64_817` `exp-lft-cube_binary64_816` `exp-cbrt_binary64_814` `div-exp_binary64_811` `e-exp-1_binary64_805` `exp-0_binary64_802` `cube-neg_binary64_787` `rem-3cbrt-rft_binary64_786` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `mul-1-neg_binary64_752` `remove-double-neg_binary64_748` `--rgt-identity_binary64_746` `+-lft-identity_binary64_744` `*-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_binary64_725` `distribute-neg-out_binary64_722` `distribute-lft1-in_binary64_715` `distribute-lft-out--_binary64_712` `associate--r-_binary64_699`

Counts

227 → 207

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	293	7537
1	547	7348
2	1624	7325
3	4090	7313
4	4629	7313
5	4973	7313
6	4893	7313

prune356.0ms (3.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	207	9	216

Error

Counts

216 → 9

Compiler

Compiled 6088 to 2997 computations (50.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 n (.f64 2 PI.f64))
0.3b	(/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
0.6b	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))
0.6b	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

rewrite478.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

141×	`sqrt-prod_binary64_776`
90×	`times-frac_binary64_766`
65×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
28×	`unpow-prod-down_binary64_839` `unpow-prod-up_binary64_838`
21×	`pow1_binary64_821` `cancel-sign-sub-inv_binary64_726`
15×	`associate-/l*_binary64_705`
11×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
9×	`pow-prod-down_binary64_831`
7×	`sub-neg_binary64_753` `sqr-pow_binary64_732`
6×	`sqrt-pow1_binary64_778` `associate-/r*_binary64_704`
4×	`add-log-exp_binary64_799`
3×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793` `associate-l_binary64_701`
2×	`pow1/2_binary64_840`
1×	`div-exp_binary64_811` `cbrt-undiv_binary64_794` `sqrt-undiv_binary64_781` `frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757` `pow-sub_binary64_836` `sqrt-div_binary64_777` `associate-/l/_binary64_707` `associate-r_binary64_700` `*-commutative_binary64_691`

Counts

4 → 167

Calls

4 calls:

14.0ms	(/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
5.0ms	(.f64 n (.f64 2 PI.f64))
4.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))
4.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 6604 to 4452 computations (32.6% saved)

series342.0ms (3%)

Error

Counts

4 → 15

Calls

4 calls:

199.0ms	(/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
45.0ms	(.f64 n (.f64 2 PI.f64))
38.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))
36.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 1483 to 1161 computations (21.7% saved)

simplify189.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

709×	`associate-l_binary64_701`
500×	`associate-r_binary64_700`
411×	`distribute-rgt-in_binary64_710`
390×	`distribute-lft-in_binary64_709`
174×	`*-commutative_binary64_691`
163×	`exp-prod_binary64_812`
155×	`sqr-pow_binary64_732`
148×	`unswap-sqr_binary64_728`
147×	`exp-sum_binary64_806`
144×	`associate-/l*_binary64_705`
121×	`times-frac_binary64_766`
119×	`associate-/r*_binary64_704`
95×	`associate-/l/_binary64_707`
62×	`pow-sqr_binary64_733`
49×	`distribute-rgt-neg-out_binary64_720`
45×	`swap-sqr_binary64_727`
44×	`log-prod_binary64_846` `distribute-lft-neg-out_binary64_719`
43×	`unsub-neg_binary64_754`
39×	`associate-*r/_binary64_702`
37×	`associate-/r/_binary64_706`
36×	`associate-*l/_binary64_703`
26×	`sub-neg_binary64_753`
25×	`distribute-rgt-out_binary64_713`
24×	`cube-unmult_binary64_797` `rem-sqrt-square_binary64_773`
23×	`div-sub_binary64_765`
22×	`*-rgt-identity_binary64_750`
19×	`cube-prod_binary64_788`
18×	`neg-sub0_binary64_755` `/-rgt-identity_binary64_751` `*-lft-identity_binary64_749` `distribute-lft-out_binary64_711`
17×	`exp-to-pow_binary64_822` `associate-+l+_binary64_693` `+-commutative_binary64_690`
16×	`neg-mul-1_binary64_756`
15×	`associate-+r+_binary64_692`
13×	`prod-exp_binary64_809`
10×	`exp-neg_binary64_807` `distribute-frac-neg_binary64_723`
9×	`log-div_binary64_847` `pow-plus_binary64_823`
8×	`distribute-neg-out_binary64_722` `distribute-lft-neg-in_binary64_717`
7×	`rem-exp-log_binary64_800` `mul0-rgt_binary64_743` `mul0-lft_binary64_742`
6×	`log-pow_binary64_849` `exp-diff_binary64_808`
5×	`mul-1-neg_binary64_752` `cancel-sign-sub-inv_binary64_726`
4×	`pow-base-1_binary64_820` `cube-div_binary64_789` `distribute-rgt-neg-in_binary64_718`
3×	`unpow3_binary64_826` `exp-lft-sqr_binary64_815` `rem-square-sqrt_binary64_772` `distribute-neg-frac_binary64_724` `associate-+l-_binary64_695`
2×	`unpow1_binary64_818` `sub0-neg_binary64_747` `div0_binary64_741` `associate--l-_binary64_698` `associate-+r-_binary64_694`
1×	`unpow1/2_binary64_824` `rec-exp_binary64_810` `1-exp_binary64_804` `exp-1-e_binary64_803` `cube-mult_binary64_790` `rem-3cbrt-lft_binary64_785` `+-rgt-identity_binary64_745` `difference-of-sqr-1_binary64_730` `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` `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` `unpow2_binary64_825` `unpow0_binary64_819` `unpow-1_binary64_817` `exp-lft-cube_binary64_816` `exp-cbrt_binary64_814` `exp-sqrt_binary64_813` `div-exp_binary64_811` `e-exp-1_binary64_805` `exp-0_binary64_802` `rem-log-exp_binary64_801` `cube-neg_binary64_787` `rem-3cbrt-rft_binary64_786` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `remove-double-neg_binary64_748` `--rgt-identity_binary64_746` `+-lft-identity_binary64_744` `*-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-neg-in_binary64_721` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `distribute-rgt-out--_binary64_714` `distribute-lft-out--_binary64_712` `associate--r-_binary64_699` `associate--l+_binary64_697` `associate--r+_binary64_696`

Counts

182 → 159

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	259	5811
1	421	5658
2	1040	5658
3	3069	5652
4	4967	5652

prune370.0ms (3.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	159	9	168

Error

Counts

168 → 9

Compiler

Compiled 5868 to 3735 computations (36.3% saved)

regimes835.0ms (7.3%)

Accuracy

Total 0.4b remaining (99.5%)

Threshold costs 0.4b (99.5%)

Compiler

Compiled 9538 to 7810 computations (18.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64_691`
2×	`sub-neg_binary64_753` `+-commutative_binary64_690`
1×	`1-exp_binary64_804` `neg-mul-1_binary64_756` `neg-sub0_binary64_755`
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	13	22
1	19	22
2	23	22
3	25	22
4	26	22
5	25	22

end0.0ms (0%)

sample4.6s (40.2%)

Algorithm

1×

intervals

Results

617.0ms	8000×	body	128	valid
609.0ms	1311×	body	1024	nan
405.0ms	662×	body	512	nan
299.0ms	2203×	body	128	overflowed
58.0ms	333×	body	256	nan
50.0ms	935×	body	128	nan
20.0ms	215×	body	128	invalid

Compiler

Compiled 2404 to 1971 computations (18% saved)

Details

analyze578.0ms (5%)

sample77.0ms (0.7%)

simplify55.0ms (0.5%)

prune6.0ms (0%)

localize11.0ms (0.1%)

rewrite242.0ms (2.1%)

series637.0ms (5.5%)

simplify131.0ms (1.1%)

prune196.0ms (1.7%)

localize10.0ms (0.1%)

rewrite223.0ms (1.9%)

series449.0ms (3.9%)

simplify178.0ms (1.6%)

prune181.0ms (1.6%)

localize13.0ms (0.1%)

rewrite388.0ms (3.4%)

series579.0ms (5%)

simplify333.0ms (2.9%)

prune356.0ms (3.1%)

localize12.0ms (0.1%)

rewrite478.0ms (4.2%)

series342.0ms (3%)

simplify189.0ms (1.6%)

prune370.0ms (3.2%)

regimes835.0ms (7.3%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.6s (40.2%)

Profiling