Details

analyze600.0ms (3.6%)

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)

sample84.0ms (0.5%)

Algorithm

1×

intervals

Results

25.0ms	43×	body	1024	nan
20.0ms	256×	body	128	valid
11.0ms	72×	body	128	overflowed
5.0ms	16×	body	512	nan
3.0ms	15×	body	256	nan
2.0ms	27×	body	128	nan
1.0ms	8×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify52.0ms (0.3%)

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

prune5.0ms (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

0.3b

Counts

2 → 2

Compiler

Compiled 44 to 41 computations (6.8% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite242.0ms (1.4%)

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×	`pow-prod-down_binary64_831` `pow-exp_binary64_828` `associate-/r*_binary64_704` `difference-of-squares_binary64_729`
5×	`div-exp_binary64_811` `associate-/l*_binary64_705`
3×	`add-log-exp_binary64_799` `cbrt-unprod_binary64_793` `associate-r_binary64_700` `distribute-lft-out--_binary64_712` `pow-pow_binary64_832`
2×	`pow-to-exp_binary64_829` `div-inv_binary64_757` `div-sub_binary64_765` `pow-sub_binary64_836`
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:

11.0ms	(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)

series639.0ms (3.8%)

Error

0.2b

Counts

3 → 18

Calls

3 calls:

315.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
256.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
41.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 1100 to 864 computations (21.5% saved)

simplify165.0ms (1%)

Algorithm

1×	egg-herbie

Rules

540×	`distribute-rgt-in_binary64_710`
536×	`distribute-lft-in_binary64_709`
199×	`associate-/l/_binary64_707`
169×	`associate-l_binary64_701`
149×	`exp-prod_binary64_812`
143×	`times-frac_binary64_766`
142×	`associate-r_binary64_700`
116×	`sqr-pow_binary64_732`
108×	`cancel-sign-sub-inv_binary64_726`
97×	`*-commutative_binary64_691`
82×	`associate-/r/_binary64_706`
78×	`log-pow_binary64_849`
74×	`log-prod_binary64_846`
56×	`associate-/l*_binary64_705`
53×	`distribute-rgt-neg-in_binary64_718` `distribute-lft-neg-in_binary64_717`
43×	`pow-sqr_binary64_733`
37×	`unswap-sqr_binary64_728`
36×	`sub-neg_binary64_753`
32×	`exp-sum_binary64_806`
22×	`exp-to-pow_binary64_822`
20×	`-rgt-identity_binary64_750` `associate-/r_binary64_704`
18×	`log-div_binary64_847` `cube-prod_binary64_788` `distribute-lft-neg-out_binary64_719`
17×	`neg-mul-1_binary64_756` `neg-sub0_binary64_755`
16×	`swap-sqr_binary64_727` `distribute-rgt-neg-out_binary64_720`
15×	`unpow3_binary64_826`
14×	`-lft-identity_binary64_749` `associate-l/_binary64_703` `associate-*r/_binary64_702` `+-commutative_binary64_690`
13×	`distribute-lft-out--_binary64_712`
11×	`cube-unmult_binary64_797`
10×	`exp-diff_binary64_808` `/-rgt-identity_binary64_751`
9×	`unpow1/2_binary64_824` `associate--l+_binary64_697`
8×	`pow-plus_binary64_823` `div-sub_binary64_765` `unsub-neg_binary64_754`
6×	`distribute-neg-frac_binary64_724`
5×	`prod-exp_binary64_809` `distribute-rgt-out_binary64_713` `associate-+l+_binary64_693`
4×	`unpow1_binary64_818` `rem-sqrt-square_binary64_773` `distribute-neg-in_binary64_721` `distribute-rgt-out--_binary64_714` `associate--r+_binary64_696`
3×	`log-rec_binary64_848` `exp-lft-sqr_binary64_815` `cube-div_binary64_789` `distribute-lft-out_binary64_711`
2×	`unpow2_binary64_825` `cube-mult_binary64_790` `count-2_binary64_708` `associate--r-_binary64_699`
1×	`1-exp_binary64_804` `exp-1-e_binary64_803` `rem-square-sqrt_binary64_772` `remove-double-neg_binary64_748` `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` `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` `exp-sqrt_binary64_813` `div-exp_binary64_811` `rec-exp_binary64_810` `exp-neg_binary64_807` `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` `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` `associate--l-_binary64_698` `associate-+l-_binary64_695` `associate-+r-_binary64_694`

Counts

133 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	3711
1	512	3530
2	1621	3389
3	4700	3385
4	4972	3385
5	4969	3385

prune187.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	111	8	119
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	113	8	121

Error

0.0b

Counts

121 → 8

Compiler

Compiled 2840 to 1780 computations (37.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
0.3b	(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
0.3b	(*.f64 n PI.f64)
0.3b	(*.f64 n PI.f64)

rewrite575.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

284×	`times-frac_binary64_766`
132×	`add-sqr-sqrt_binary64_782`
128×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
111×	`sqrt-prod_binary64_776`
28×	`unpow-prod-down_binary64_839` `sqr-pow_binary64_732`
27×	`add-exp-log_binary64_798`
24×	`associate-/l*_binary64_705`
14×	`pow1_binary64_821`
13×	`add-cbrt-cube_binary64_796`
11×	`div-exp_binary64_811`
8×	`div-inv_binary64_757`
6×	`associate-l_binary64_701` `associate-r_binary64_700` `associate-/r*_binary64_704`
5×	`pow-prod-down_binary64_831` `prod-exp_binary64_809`
4×	`add-log-exp_binary64_799`
3×	`pow-exp_binary64_828` `cbrt-undiv_binary64_794` `sqrt-pow1_binary64_778`
2×	`cbrt-unprod_binary64_793` `unswap-sqr_binary64_728` `*-commutative_binary64_691`
1×	`pow-to-exp_binary64_829` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l/_binary64_707` `pow1/2_binary64_840`

Counts

4 → 241

Calls

4 calls:

17.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
4.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
4.0ms	(*.f64 n PI.f64)
4.0ms	(*.f64 n PI.f64)

Compiler

Compiled 8806 to 4891 computations (44.5% saved)

series324.0ms (1.9%)

Error

0.0b

Counts

4 → 15

Calls

4 calls:

211.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
34.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
32.0ms	(*.f64 n PI.f64)
31.0ms	(*.f64 n PI.f64)

Compiler

Compiled 1094 to 837 computations (23.5% saved)

simplify333.0ms (2%)

Algorithm

1×	egg-herbie

Rules

832×	`associate-/l*_binary64_705`
481×	`associate-r_binary64_700`
388×	`associate-/l/_binary64_707`
262×	`associate-/r/_binary64_706`
255×	`associate-*l/_binary64_703`
230×	`associate-/r*_binary64_704`
210×	`associate-*r/_binary64_702`
129×	`distribute-rgt-in_binary64_710`
123×	`distribute-lft-in_binary64_709` `*-commutative_binary64_691`
92×	`times-frac_binary64_766`
90×	`associate-l_binary64_701`
62×	`log-prod_binary64_846`
49×	`*-rgt-identity_binary64_750`
39×	`sqr-pow_binary64_732`
37×	`exp-prod_binary64_812`
34×	`log-div_binary64_847`
32×	`distribute-neg-in_binary64_721`
29×	`sub-neg_binary64_753` `/-rgt-identity_binary64_751`
25×	`unswap-sqr_binary64_728`
24×	`exp-sum_binary64_806`
21×	`*-lft-identity_binary64_749`
16×	`neg-mul-1_binary64_756` `neg-sub0_binary64_755`
14×	`pow-sqr_binary64_733`
11×	`cancel-sign-sub-inv_binary64_726`
10×	`cube-unmult_binary64_797` `unsub-neg_binary64_754` `distribute-neg-frac_binary64_724` `+-commutative_binary64_690`
8×	`log-pow_binary64_849` `cube-prod_binary64_788`
7×	`distribute-lft-neg-out_binary64_719`
6×	`cube-div_binary64_789` `swap-sqr_binary64_727` `distribute-rgt-neg-in_binary64_718` `distribute-lft-neg-in_binary64_717`
5×	`distribute-rgt-neg-out_binary64_720` `associate-+l+_binary64_693`
4×	`rem-sqrt-square_binary64_773` `associate--l-_binary64_698`
3×	`div-sub_binary64_765` `associate--l+_binary64_697`
2×	`log-rec_binary64_848` `unpow1/2_binary64_824` `exp-to-pow_binary64_822` `rem-square-sqrt_binary64_772` `distribute-rgt-out_binary64_713` `distribute-lft-out_binary64_711` `count-2_binary64_708` `associate--r-_binary64_699` `associate-+r+_binary64_692`
1×	`1-exp_binary64_804` `exp-1-e_binary64_803` `remove-double-neg_binary64_748` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722` `associate-+l-_binary64_695`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_1023` `erf-erfc_binary64_1022` `erf-odd_binary64_1021` `if-if-and-not_binary64_1020` `if-if-and_binary64_1019` `if-if-or-not_binary64_1018` `if-if-or_binary64_1017` `if-not_binary64_1016` `if-same_binary64_1015` `if-false_binary64_1014` `if-true_binary64_1013` `not-gte_binary64_1012` `not-lte_binary64_1011` `not-gt_binary64_1010` `not-lt_binary64_1009` `gte-same_binary64_1008` `lte-same_binary64_1007` `gt-same_binary64_1006` `lt-same_binary64_1005` `sinh---cosh_binary64_952` `sinh-+-cosh_binary64_951` `sinh-cosh_binary64_950` `tanh-def-c_binary64_949` `tanh-def-b_binary64_948` `tanh-def-a_binary64_947` `cosh-def_binary64_946` `sinh-def_binary64_945` `tan-neg_binary64_892` `cos-neg_binary64_891` `sin-neg_binary64_890` `tan-0_binary64_889` `cos-0_binary64_888` `sin-0_binary64_887` `hang-m-tan_binary64_886` `hang-p-tan_binary64_885` `hang-m0-tan_binary64_884` `hang-p0-tan_binary64_883` `hang-0m-tan_binary64_882` `hang-0p-tan_binary64_881` `tan-+PI/2_binary64_880` `tan-+PI_binary64_879` `tan-PI_binary64_878` `tan-PI/3_binary64_877` `tan-PI/4_binary64_876` `tan-PI/6_binary64_875` `cos-+PI/2_binary64_874` `cos-+PI_binary64_873` `cos-PI_binary64_872` `cos-PI/2_binary64_871` `cos-PI/3_binary64_870` `cos-PI/4_binary64_869` `cos-PI/6_binary64_868` `sin-+PI/2_binary64_867` `sin-+PI_binary64_866` `sin-PI_binary64_865` `sin-PI/2_binary64_864` `sin-PI/3_binary64_863` `sin-PI/4_binary64_862` `sin-PI/6_binary64_861` `sub-1-sin_binary64_860` `sub-1-cos_binary64_859` `-1-add-sin_binary64_858` `-1-add-cos_binary64_857` `1-sub-sin_binary64_856` `1-sub-cos_binary64_855` `cos-sin-sum_binary64_854` `log-E_binary64_850` `pow-base-0_binary64_844` `unpow1/3_binary64_827` `unpow3_binary64_826` `unpow2_binary64_825` `pow-plus_binary64_823` `pow-base-1_binary64_820` `unpow0_binary64_819` `unpow1_binary64_818` `unpow-1_binary64_817` `exp-lft-cube_binary64_816` `exp-lft-sqr_binary64_815` `exp-cbrt_binary64_814` `exp-sqrt_binary64_813` `div-exp_binary64_811` `rec-exp_binary64_810` `prod-exp_binary64_809` `exp-diff_binary64_808` `exp-neg_binary64_807` `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-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `distribute-rgt-out--_binary64_714` `distribute-lft-out--_binary64_712` `associate--r+_binary64_696` `associate-+r-_binary64_694`

Counts

256 → 212

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	394	11708
1	856	11460
2	2199	11439
3	4954	11439
4	5004	11439

prune510.0ms (3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	211	1	212
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	213	7	220

Error

Counts

220 → 7

Compiler

Compiled 7794 to 4913 computations (37% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (-.f64 1 k))
0.1b	(sqrt.f64 (/.f64 1 k))
0.2b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n PI.f64))) (-.f64 1 k)))
0.3b	(*.f64 n PI.f64)

rewrite259.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

59×	`add-sqr-sqrt_binary64_782`
37×	`sqrt-prod_binary64_776`
34×	`*-un-lft-identity_binary64_760`
27×	`add-cube-cbrt_binary64_795`
26×	`times-frac_binary64_766`
19×	`associate-l_binary64_701`
15×	`pow1_binary64_821` `associate-r_binary64_700`
13×	`unswap-sqr_binary64_728`
12×	`add-exp-log_binary64_798` `unpow-prod-down_binary64_839`
8×	`add-cbrt-cube_binary64_796` `unpow-prod-up_binary64_838`
6×	`sqr-pow_binary64_732` `cancel-sign-sub-inv_binary64_726` `sqrt-pow1_binary64_778` `pow-unpow_binary64_837`
5×	`pow-pow_binary64_832`
4×	`pow-prod-down_binary64_831` `prod-exp_binary64_809` `add-log-exp_binary64_799`
3×	`pow-sub_binary64_836` `sqrt-div_binary64_777` `rem-sqrt-square_binary64_773`
2×	`cbrt-unprod_binary64_793` `*-commutative_binary64_691` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `div-inv_binary64_757` `sub-neg_binary64_753` `pow1/2_binary64_840` `difference-of-squares_binary64_729`
1×	`frac-times_binary64_770` `associate-l/_binary64_703` `associate-r/_binary64_702` `inv-pow_binary64_845` `pow-flip_binary64_834` `distribute-lft-out--_binary64_712` `sqrt-pow2_binary64_779`

Counts

4 → 132

Calls

4 calls:

21.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n PI.f64))) (-.f64 1 k)))
10.0ms	(pow.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (-.f64 1 k))
4.0ms	(*.f64 n PI.f64)
4.0ms	(sqrt.f64 (/.f64 1 k))

Compiler

Compiled 3143 to 2145 computations (31.8% saved)

series431.0ms (2.6%)

Error

Counts

4 → 21

Calls

4 calls:

178.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n PI.f64))) (-.f64 1 k)))
173.0ms	(pow.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (-.f64 1 k))
31.0ms	(*.f64 n PI.f64)
18.0ms	(sqrt.f64 (/.f64 1 k))

Compiler

Compiled 1565 to 1197 computations (23.5% saved)

simplify257.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

388×	`*-commutative_binary64_691`
317×	`exp-prod_binary64_812`
261×	`cancel-sign-sub-inv_binary64_726`
219×	`exp-sum_binary64_806` `sqr-pow_binary64_732`
210×	`distribute-rgt-in_binary64_710`
207×	`distribute-lft-in_binary64_709`
192×	`distribute-rgt-neg-in_binary64_718`
188×	`associate-r_binary64_700`
186×	`associate-l_binary64_701`
178×	`distribute-lft-neg-in_binary64_717`
138×	`unswap-sqr_binary64_728`
98×	`times-frac_binary64_766` `div-sub_binary64_765`
90×	`log-prod_binary64_846`
87×	`pow-sqr_binary64_733`
76×	`unsub-neg_binary64_754`
75×	`associate-/l*_binary64_705`
66×	`neg-mul-1_binary64_756` `neg-sub0_binary64_755`
65×	`sub-neg_binary64_753`
57×	`-lft-identity_binary64_749` `associate-/r_binary64_704`
56×	`*-rgt-identity_binary64_750`
54×	`distribute-neg-in_binary64_721`
51×	`cube-prod_binary64_788`
48×	`exp-neg_binary64_807`
42×	`exp-to-pow_binary64_822`
41×	`distribute-rgt-neg-out_binary64_720`
40×	`distribute-lft-neg-out_binary64_719` `associate-+l+_binary64_693`
35×	`exp-diff_binary64_808`
33×	`log-pow_binary64_849`
32×	`associate-+r+_binary64_692`
28×	`associate-*r/_binary64_702`
26×	`associate-/l/_binary64_707`
25×	`+-commutative_binary64_690`
24×	`rem-sqrt-square_binary64_773` `distribute-frac-neg_binary64_723`
23×	`unpow3_binary64_826`
22×	`prod-exp_binary64_809` `swap-sqr_binary64_727`
21×	`associate-/r/_binary64_706`
19×	`associate-*l/_binary64_703`
16×	`distribute-neg-frac_binary64_724`
15×	`cube-unmult_binary64_797`
14×	`unpow1/2_binary64_824`
12×	`pow-plus_binary64_823` `associate--l+_binary64_697`
10×	`associate-+l-_binary64_695`
9×	`mul0-rgt_binary64_743` `mul0-lft_binary64_742`
8×	`distribute-neg-out_binary64_722`
7×	`pow-base-1_binary64_820` `exp-sqrt_binary64_813` `rem-exp-log_binary64_800` `associate-+r-_binary64_694`
6×	`exp-lft-sqr_binary64_815` `cube-mult_binary64_790` `distribute-rgt-out--_binary64_714` `distribute-rgt-out_binary64_713` `associate--r+_binary64_696`
5×	`sub0-neg_binary64_747`
4×	`mul-1-neg_binary64_752` `/-rgt-identity_binary64_751` `+-rgt-identity_binary64_745`
3×	`unpow1_binary64_818` `distribute-rgt1-in_binary64_716`
2×	`unpow2_binary64_825` `rem-square-sqrt_binary64_772` `div0_binary64_741` `count-2_binary64_708`
1×	`log-E_binary64_850` `1-exp_binary64_804` `exp-1-e_binary64_803` `rem-log-exp_binary64_801` `cube-div_binary64_789` `rem-3cbrt-lft_binary64_785` `difference-of-sqr-1_binary64_730`
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` `log-div_binary64_847` `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` `rec-exp_binary64_810` `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` `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-lft1-in_binary64_715` `distribute-lft-out--_binary64_712` `distribute-lft-out_binary64_711` `associate--r-_binary64_699` `associate--l-_binary64_698`

Counts

153 → 113

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	208	3391
1	450	3285
2	1358	3237
3	2951	3225
4	4498	3225
5	4963	3225
6	4990	3225
7	4999	3225
8	4959	3225

prune173.0ms (1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	113	7	120

Error

Counts

120 → 7

Compiler

Compiled 2807 to 1907 computations (32.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite2.2s (13.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

768×	`sqrt-prod_binary64_776`
533×	`add-sqr-sqrt_binary64_782`
528×	`times-frac_binary64_766`
243×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
180×	`unpow-prod-down_binary64_839`
140×	`unpow-prod-up_binary64_838`
105×	`swap-sqr_binary64_727` `cancel-sign-sub-inv_binary64_726`
85×	`associate-l_binary64_701` `associate-r_binary64_700`
75×	`sqr-pow_binary64_732`
66×	`unswap-sqr_binary64_728`
35×	`sub-neg_binary64_753`
26×	`rem-sqrt-square_binary64_773`
23×	`pow1_binary64_821`
15×	`add-exp-log_binary64_798`
13×	`sqr-abs_binary64_775`
12×	`add-cbrt-cube_binary64_796` `associate-/l*_binary64_705`
8×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778`
6×	`associate-/r*_binary64_704`
5×	`pow-prod-down_binary64_831` `pow-prod-up_binary64_830` `div-inv_binary64_757`
4×	`add-log-exp_binary64_799` `sqrt-div_binary64_777`
3×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793` `pow-sqr_binary64_733` `*-commutative_binary64_691` `div-exp_binary64_811`
1×	`pow2_binary64_841` `pow-plus_binary64_823` `sqrt-unprod_binary64_780` `rem-square-sqrt_binary64_772` `frac-times_binary64_770` `associate-l/_binary64_703` `associate-r/_binary64_702` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `clear-num_binary64_759` `pow-sub_binary64_836` `associate-/l/_binary64_707`

Counts

4 → 509

Calls

4 calls:

129.0ms	(.f64 (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (-.f64 1 k)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n PI.f64))) (-.f64 1 k)) (sqrt.f64 k))))
10.0ms	(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (-.f64 1 k)) (sqrt.f64 k))
4.0ms	(*.f64 n PI.f64)
4.0ms	(*.f64 n PI.f64)

Compiler

Compiled 25734 to 14763 computations (42.6% saved)

series459.0ms (2.7%)

Error

Counts

4 → 18

Calls

4 calls:

185.0ms	(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (-.f64 1 k)) (sqrt.f64 k))
179.0ms	(.f64 (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (-.f64 1 k)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n PI.f64))) (-.f64 1 k)) (sqrt.f64 k))))
35.0ms	(*.f64 n PI.f64)
34.0ms	(*.f64 n PI.f64)

Compiler

Compiled 1796 to 1325 computations (26.2% saved)

simplify748.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

951×	`times-frac_binary64_766`
303×	`associate-l_binary64_701`
287×	`associate-r_binary64_700`
254×	`unswap-sqr_binary64_728`
169×	`log-prod_binary64_846`
136×	`associate-/l_binary64_705` `-commutative_binary64_691`
131×	`exp-prod_binary64_812`
103×	`rem-sqrt-square_binary64_773`
87×	`distribute-lft-in_binary64_709`
86×	`distribute-rgt-in_binary64_710`
84×	`*-rgt-identity_binary64_750`
83×	`rem-square-sqrt_binary64_772`
81×	`sqr-pow_binary64_732`
80×	`log-div_binary64_847`
78×	`*-lft-identity_binary64_749`
46×	`associate-/l/_binary64_707`
43×	`associate-/r*_binary64_704`
33×	`pow-sqr_binary64_733`
31×	`exp-sum_binary64_806`
25×	`log-pow_binary64_849` `unpow3_binary64_826`
21×	`cube-prod_binary64_788`
20×	`pow-plus_binary64_823`
18×	`cube-unmult_binary64_797`
17×	`exp-to-pow_binary64_822` `distribute-rgt-neg-in_binary64_718`
16×	`distribute-lft-neg-in_binary64_717`
15×	`cancel-sign-sub-inv_binary64_726`
14×	`sub-neg_binary64_753`
13×	`associate-*l/_binary64_703`
12×	`swap-sqr_binary64_727`
11×	`neg-mul-1_binary64_756` `associate-/r/_binary64_706`
10×	`prod-exp_binary64_809` `/-rgt-identity_binary64_751` `distribute-rgt-neg-out_binary64_720` `distribute-lft-neg-out_binary64_719`
9×	`neg-sub0_binary64_755`
8×	`div-sub_binary64_765` `distribute-neg-frac_binary64_724` `associate-*r/_binary64_702`
6×	`log-rec_binary64_848` `rem-exp-log_binary64_800` `cube-div_binary64_789`
4×	`pow-base-1_binary64_820` `distribute-frac-neg_binary64_723` `+-commutative_binary64_690`
3×	`unpow1/2_binary64_824` `unpow1_binary64_818`
2×	`exp-diff_binary64_808` `rem-3cbrt-lft_binary64_785`
1×	`div-exp_binary64_811` `1-exp_binary64_804` `exp-1-e_binary64_803` `rem-3cbrt-rft_binary64_786` `distribute-neg-in_binary64_721` `count-2_binary64_708` `associate-+l+_binary64_693` `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` `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-lft-sqr_binary64_815` `exp-cbrt_binary64_814` `exp-sqrt_binary64_813` `rec-exp_binary64_810` `exp-neg_binary64_807` `e-exp-1_binary64_805` `exp-0_binary64_802` `rem-log-exp_binary64_801` `cube-mult_binary64_790` `cube-neg_binary64_787` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `unsub-neg_binary64_754` `mul-1-neg_binary64_752` `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_binary64_725` `distribute-neg-out_binary64_722` `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` `associate--r-_binary64_699` `associate--l-_binary64_698` `associate--l+_binary64_697` `associate--r+_binary64_696` `associate-+l-_binary64_695` `associate-+r-_binary64_694`

Counts

527 → 395

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	496	23450
1	677	22901
2	2270	22788
3	4790	22761
4	4782	22645
5	4969	22645

prune1.1s (6.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	395	0	395
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	395	7	402

Error

Counts

402 → 7

Compiler

Compiled 14621 to 8274 computations (43.4% saved)

regimes1.4s (8.3%)

Accuracy

Total 0.4b remaining (100%)

Threshold costs 0.4b (100%)

Compiler

Compiled 15942 to 12904 computations (19.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64_691`
1×	`unpow1_binary64_818` `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` `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` `e-exp-1_binary64_805` `exp-1-e_binary64_803` `exp-0_binary64_802` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `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` `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` `+-commutative_binary64_690`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	33
1	20	33
2	19	33

end0.0ms (0%)

sample6.0s (35.9%)

Algorithm

1×

intervals

Results

817.0ms	8000×	body	128	valid
682.0ms	1343×	body	1024	nan
331.0ms	2253×	body	128	overflowed
211.0ms	646×	body	512	nan
71.0ms	350×	body	256	nan
61.0ms	994×	body	128	nan
22.0ms	223×	body	128	invalid

Compiler

Compiled 3753 to 3036 computations (19.1% saved)

Details

analyze600.0ms (3.6%)

sample84.0ms (0.5%)

simplify52.0ms (0.3%)

prune5.0ms (0%)

localize12.0ms (0.1%)

rewrite242.0ms (1.4%)

series639.0ms (3.8%)

simplify165.0ms (1%)

prune187.0ms (1.1%)

localize12.0ms (0.1%)

rewrite575.0ms (3.4%)

series324.0ms (1.9%)

simplify333.0ms (2%)

prune510.0ms (3%)

localize13.0ms (0.1%)

rewrite259.0ms (1.5%)

series431.0ms (2.6%)

simplify257.0ms (1.5%)

prune173.0ms (1%)

localize15.0ms (0.1%)

rewrite2.2s (13.2%)

series459.0ms (2.7%)

simplify748.0ms (4.4%)

prune1.1s (6.4%)

regimes1.4s (8.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.0s (35.9%)

Profiling