Details

analyze386.0ms (1.4%)

Algorithm

1×

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)

sample82.0ms (0.3%)

Algorithm

1×

intervals

Results

22.0ms	41×	body	1024	nan
19.0ms	256×	body	128	valid
12.0ms	90×	body	128	overflowed
8.0ms	26×	body	512	nan
2.0ms	34×	body	128	nan
1.0ms	8×	body	256	nan
0.0ms	6×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify6.7s (24.3%)

Algorithm

1×	egg-herbie

Rules

670×	`div-sub_binary64_765`
274×	`distribute-frac-neg_binary64_723`
248×	`distribute-rgt-in_binary64_710` `associate-/l*_binary64_705`
219×	`unswap-sqr_binary64_728` `distribute-lft-in_binary64_709`
163×	`distribute-rgt-neg-out_binary64_720`
159×	`unsub-neg_binary64_754`
150×	`associate-/l/_binary64_707` `associate-l_binary64_701`
148×	`associate-/r*_binary64_704`
137×	`distribute-lft-neg-out_binary64_719`
120×	`associate-r_binary64_700`
98×	`*-commutative_binary64_691`
79×	`times-frac_binary64_766`
78×	`associate-*r/_binary64_702`
65×	`associate-/r/_binary64_706`
64×	`associate-*l/_binary64_703`
63×	`sub-neg_binary64_753`
55×	`neg-mul-1_binary64_756`
48×	`neg-sub0_binary64_755`
34×	`sqr-pow_binary64_732`
33×	`distribute-neg-frac_binary64_724`
28×	`*-lft-identity_binary64_749`
26×	`cancel-sign-sub-inv_binary64_726`
24×	`distribute-rgt-neg-in_binary64_718`
23×	`pow-sqr_binary64_733`
22×	`distribute-lft-neg-in_binary64_717`
20×	`/-rgt-identity_binary64_751`
19×	`*-rgt-identity_binary64_750` `+-commutative_binary64_690`
13×	`distribute-neg-in_binary64_721`
10×	`pow-plus_binary64_823` `cube-prod_binary64_788` `cancel-sign-sub_binary64_725`
9×	`associate-+l-_binary64_695`
8×	`associate-+r-_binary64_694`
7×	`+-rgt-identity_binary64_745` `div0_binary64_741` `associate-+r+_binary64_692`
6×	`cube-unmult_binary64_797` `swap-sqr_binary64_727` `associate--r+_binary64_696`
5×	`sub0-neg_binary64_747`
4×	`--rgt-identity_binary64_746` `mul0-lft_binary64_742` `remove-double-div_binary64_736`
3×	`mul0-rgt_binary64_743` `associate-+l+_binary64_693`
2×	`unpow3_binary64_826` `remove-double-neg_binary64_748` `+-lft-identity_binary64_744` `distribute-neg-out_binary64_722` `associate--l+_binary64_697`
1×	`pow-base-1_binary64_820` `1-exp_binary64_804` `cube-mult_binary64_790` `mul-1-neg_binary64_752` `*-inverses_binary64_740` `lft-mult-inverse_binary64_738` `rgt-mult-inverse_binary64_737` `distribute-lft-out--_binary64_712` `count-2_binary64_708` `associate--r-_binary64_699` `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` `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` `unpow2_binary64_825` `unpow1/2_binary64_824` `exp-to-pow_binary64_822` `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` `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` `+-inverses_binary64_739` `difference-of-sqr--1_binary64_731` `difference-of-sqr-1_binary64_730` `difference-of-squares_binary64_729` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `distribute-rgt-out--_binary64_714` `distribute-rgt-out_binary64_713` `distribute-lft-out_binary64_711`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	31	22
2	62	22
3	126	22
4	277	22
5	649	22
6	1569	22

prune5.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.4b

Counts

3 → 2

Compiler

Compiled 60 to 51 computations (15% saved)

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite200.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

48×	`times-frac_binary64_766`
45×	`add-sqr-sqrt_binary64_782`
43×	`*-un-lft-identity_binary64_760`
34×	`add-cube-cbrt_binary64_795`
23×	`add-exp-log_binary64_798`
22×	`pow-unpow_binary64_837`
18×	`sqrt-prod_binary64_776`
11×	`pow1_binary64_821`
8×	`unpow-prod-down_binary64_839` `sqr-pow_binary64_732`
7×	`prod-exp_binary64_809` `add-cbrt-cube_binary64_796`
6×	`difference-of-squares_binary64_729` `pow-exp_binary64_828` `associate-/r*_binary64_704`
5×	`div-exp_binary64_811` `associate-/l*_binary64_705`
4×	`pow-prod-down_binary64_831`
3×	`distribute-lft-out--_binary64_712` `pow-pow_binary64_832` `add-log-exp_binary64_799` `associate-l_binary64_701` `associate-r_binary64_700`
2×	`div-inv_binary64_757` `div-sub_binary64_765` `pow-sub_binary64_836` `pow-to-exp_binary64_829`
1×	`cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l/_binary64_707` `cbrt-unprod_binary64_793` `unswap-sqr_binary64_728` `*-commutative_binary64_691`

Counts

3 → 115

Calls

3 calls:

10.0ms	(pow.f64 (.f64 2 (.f64 PI.f64 n)) (/.f64 (-.f64 1 k) 2))
7.0ms	(/.f64 (pow.f64 (.f64 2 (.f64 PI.f64 n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
4.0ms	(*.f64 PI.f64 n)

Compiler

Compiled 2822 to 1742 computations (38.3% saved)

series429.0ms (1.6%)

Error

0.2b

Counts

3 → 18

Calls

3 calls:

206.0ms	(/.f64 (pow.f64 (.f64 2 (.f64 PI.f64 n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
180.0ms	(pow.f64 (.f64 2 (.f64 PI.f64 n)) (/.f64 (-.f64 1 k) 2))
20.0ms	(*.f64 PI.f64 n)

Compiler

Compiled 1100 to 864 computations (21.5% saved)

simplify234.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

599×	`distribute-rgt-in_binary64_710`
595×	`distribute-lft-in_binary64_709`
243×	`associate-/l/_binary64_707`
168×	`times-frac_binary64_766`
131×	`sqr-pow_binary64_732`
125×	`associate-l_binary64_701`
115×	`associate-r_binary64_700`
107×	`cancel-sign-sub-inv_binary64_726`
85×	`*-commutative_binary64_691`
61×	`associate-/l*_binary64_705`
59×	`pow-sqr_binary64_733`
53×	`distribute-rgt-neg-in_binary64_718`
49×	`distribute-lft-neg-in_binary64_717`
41×	`exp-prod_binary64_812`
38×	`exp-sum_binary64_806`
37×	`log-prod_binary64_846` `sub-neg_binary64_753`
31×	`unswap-sqr_binary64_728`
25×	`*-rgt-identity_binary64_750`
23×	`distribute-lft-neg-out_binary64_719`
21×	`associate-/r*_binary64_704`
19×	`neg-mul-1_binary64_756` `neg-sub0_binary64_755`
17×	`*-lft-identity_binary64_749`
16×	`distribute-rgt-neg-out_binary64_720` `+-commutative_binary64_690`
15×	`associate-*r/_binary64_702`
14×	`associate-/r/_binary64_706` `associate-*l/_binary64_703`
13×	`/-rgt-identity_binary64_751` `distribute-lft-out--_binary64_712`
12×	`cube-prod_binary64_788`
11×	`log-div_binary64_847`
10×	`cube-unmult_binary64_797` `div-sub_binary64_765`
8×	`log-pow_binary64_849` `unsub-neg_binary64_754` `associate--l+_binary64_697`
7×	`pow-plus_binary64_823`
6×	`distribute-neg-frac_binary64_724`
5×	`cube-div_binary64_789` `swap-sqr_binary64_727` `distribute-rgt-out_binary64_713`
4×	`distribute-neg-in_binary64_721` `distribute-rgt-out--_binary64_714` `associate--r+_binary64_696` `associate-+l+_binary64_693`
3×	`exp-to-pow_binary64_822` `unpow1_binary64_818` `rem-sqrt-square_binary64_773` `distribute-lft-out_binary64_711` `associate-+r+_binary64_692`
2×	`unpow3_binary64_826` `unpow2_binary64_825` `unpow1/2_binary64_824` `cube-mult_binary64_790` `count-2_binary64_708` `associate--r-_binary64_699`
1×	`log-rec_binary64_848` `1-exp_binary64_804` `exp-1-e_binary64_803` `rem-square-sqrt_binary64_772` `remove-double-neg_binary64_748` `*-inverses_binary64_740` `rgt-mult-inverse_binary64_737`
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-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-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_739` `lft-mult-inverse_binary64_738` `remove-double-div_binary64_736` `difference-of-sqr--1_binary64_731` `difference-of-sqr-1_binary64_730` `difference-of-squares_binary64_729` `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 → 389

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	250	3724
1	513	3563
2	1568	3503

prune844.0ms (3.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	379	10	389
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	380	11	391

Error

0.0b

Counts

391 → 11

Compiler

Compiled 11627 to 7490 computations (35.6% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite959.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

358×	`times-frac_binary64_766`
156×	`add-sqr-sqrt_binary64_782`
152×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
111×	`add-exp-log_binary64_798`
90×	`sqrt-prod_binary64_776`
71×	`unpow-prod-down_binary64_839` `sqr-pow_binary64_732`
51×	`div-exp_binary64_811`
35×	`prod-exp_binary64_809`
33×	`pow-exp_binary64_828`
29×	`associate-/l*_binary64_705`
14×	`pow1_binary64_821`
13×	`add-cbrt-cube_binary64_796` `pow-unpow_binary64_837`
11×	`pow-to-exp_binary64_829`
9×	`div-inv_binary64_757`
6×	`associate-/r_binary64_704` `associate-l_binary64_701` `associate-r*_binary64_700`
5×	`pow-prod-down_binary64_831`
4×	`add-log-exp_binary64_799`
3×	`cbrt-undiv_binary64_794` `pow-pow_binary64_832`
2×	`cbrt-unprod_binary64_793` `unswap-sqr_binary64_728` `*-commutative_binary64_691`
1×	`frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l/_binary64_707`

Counts

4 → 313

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 PI.f64 n)) (/.f64 1 2)) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
7.0ms	(pow.f64 (.f64 2 (.f64 PI.f64 n)) (/.f64 1 2))
4.0ms	(*.f64 n PI.f64)
4.0ms	(*.f64 PI.f64 n)

Compiler

Compiled 12903 to 8010 computations (37.9% saved)

series305.0ms (1.1%)

Error

0.0b

Counts

4 → 15

Calls

4 calls:

145.0ms	(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 PI.f64 n)) (/.f64 1 2)) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
99.0ms	(pow.f64 (.f64 2 (.f64 PI.f64 n)) (/.f64 1 2))
23.0ms	(*.f64 n PI.f64)
23.0ms	(*.f64 PI.f64 n)

Compiler

Compiled 1161 to 917 computations (21% saved)

simplify1.0s (3.8%)

Algorithm

1×	egg-herbie

Rules

568×	`associate-/r/_binary64_706`
309×	`associate-/r*_binary64_704`
252×	`associate-/l*_binary64_705`
232×	`associate-/l/_binary64_707`
224×	`times-frac_binary64_766`
204×	`distribute-rgt-in_binary64_710`
195×	`distribute-lft-in_binary64_709`
155×	`associate-r_binary64_700`
141×	`*-commutative_binary64_691`
129×	`associate-l_binary64_701`
106×	`sqr-pow_binary64_732`
68×	`associate-*l/_binary64_703`
54×	`sub-neg_binary64_753`
52×	`log-prod_binary64_846`
51×	`exp-prod_binary64_812` `exp-sum_binary64_806`
48×	`unswap-sqr_binary64_728`
47×	`pow-sqr_binary64_733`
45×	`/-rgt-identity_binary64_751`
40×	`distribute-neg-in_binary64_721`
38×	`associate-*r/_binary64_702`
26×	`cancel-sign-sub-inv_binary64_726`
22×	`log-div_binary64_847`
19×	`-rgt-identity_binary64_750` `-lft-identity_binary64_749`
18×	`neg-mul-1_binary64_756` `neg-sub0_binary64_755`
16×	`cube-prod_binary64_788` `associate--l-_binary64_698`
14×	`distribute-neg-frac_binary64_724` `distribute-rgt-neg-in_binary64_718` `distribute-lft-neg-in_binary64_717`
12×	`cube-unmult_binary64_797` `unsub-neg_binary64_754` `+-commutative_binary64_690`
11×	`swap-sqr_binary64_727` `distribute-lft-neg-out_binary64_719`
10×	`log-pow_binary64_849`
9×	`cube-div_binary64_789` `distribute-rgt-neg-out_binary64_720`
8×	`div-sub_binary64_765`
6×	`exp-to-pow_binary64_822` `distribute-rgt-out_binary64_713`
5×	`unpow1/2_binary64_824` `rem-sqrt-square_binary64_773`
4×	`pow-plus_binary64_823` `associate-+l+_binary64_693`
3×	`count-2_binary64_708` `associate--l+_binary64_697` `associate-+r+_binary64_692`
2×	`exp-diff_binary64_808` `distribute-lft-out_binary64_711` `associate--r-_binary64_699`
1×	`log-rec_binary64_848` `unpow1_binary64_818` `1-exp_binary64_804` `exp-1-e_binary64_803` `rem-square-sqrt_binary64_772` `remove-double-neg_binary64_748` `rgt-mult-inverse_binary64_737` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `distribute-rgt-out--_binary64_714` `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-base-1_binary64_820` `unpow0_binary64_819` `unpow-1_binary64_817` `exp-lft-cube_binary64_816` `exp-lft-sqr_binary64_815` `exp-cbrt_binary64_814` `exp-sqrt_binary64_813` `div-exp_binary64_811` `rec-exp_binary64_810` `prod-exp_binary64_809` `exp-neg_binary64_807` `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` `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-lft-out--_binary64_712` `associate--r+_binary64_696` `associate-+r-_binary64_694`

Counts

328 → 1920

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	565	17055
1	1144	16548
2	3022	16524

prune11.4s (41.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	1918	2	1920
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	1922	9	1931

Error

0.0b

Counts

1931 → 9

Compiler

Compiled 90303 to 59018 computations (34.6% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite3.6s (13.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

2038×	`add-exp-log_binary64_798`
1238×	`div-exp_binary64_811`
993×	`prod-exp_binary64_809`
648×	`pow-exp_binary64_828`
450×	`pow-to-exp_binary64_829`
354×	`times-frac_binary64_766`
215×	`add-sqr-sqrt_binary64_782`
210×	`1-exp_binary64_804`
169×	`associate-l_binary64_701`
163×	`*-un-lft-identity_binary64_760`
153×	`add-cube-cbrt_binary64_795`
141×	`unpow-prod-down_binary64_839`
57×	`sqr-pow_binary64_732`
49×	`add-cbrt-cube_binary64_796`
23×	`unswap-sqr_binary64_728`
17×	`cbrt-undiv_binary64_794`
15×	`cbrt-unprod_binary64_793` `associate-r_binary64_700`
10×	`pow1_binary64_821`
6×	`div-inv_binary64_757`
5×	`associate-/l*_binary64_705`
4×	`add-log-exp_binary64_799`
3×	`pow-prod-down_binary64_831` `*-commutative_binary64_691`
1×	`frac-times_binary64_770` `associate-l/_binary64_703` `associate-r/_binary64_702` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/r*_binary64_704`

Counts

4 → 734

Calls

4 calls:

70.0ms	(.f64 (/.f64 (/.f64 (pow.f64 2 (/.f64 1 2)) (pow.f64 2 (/.f64 k 2))) 1) (/.f64 (pow.f64 (.f64 n PI.f64) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n PI.f64) (/.f64 k 2)))))
8.0ms	(/.f64 (pow.f64 (.f64 n PI.f64) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (*.f64 n PI.f64) (/.f64 k 2))))
4.0ms	(*.f64 n PI.f64)
4.0ms	(*.f64 n PI.f64)

Compiler

Compiled 32029 to 22702 computations (29.1% saved)

series394.0ms (1.4%)

Error

0.0b

Counts

4 → 18

Calls

4 calls:

201.0ms	(.f64 (/.f64 (/.f64 (pow.f64 2 (/.f64 1 2)) (pow.f64 2 (/.f64 k 2))) 1) (/.f64 (pow.f64 (.f64 n PI.f64) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n PI.f64) (/.f64 k 2)))))
122.0ms	(/.f64 (pow.f64 (.f64 n PI.f64) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (*.f64 n PI.f64) (/.f64 k 2))))
25.0ms	(*.f64 n PI.f64)
24.0ms	(*.f64 n PI.f64)

Compiler

Compiled 1963 to 1547 computations (21.2% saved)

simplify830.0ms (3%)

Algorithm

1×	egg-herbie

Rules

892×	`times-frac_binary64_766`
712×	`associate-/r*_binary64_704`
638×	`associate-/l*_binary64_705`
375×	`associate-/l/_binary64_707`
214×	`*-commutative_binary64_691`
160×	`associate-*l/_binary64_703`
143×	`associate-*r/_binary64_702`
130×	`associate-+l-_binary64_695`
60×	`associate-+r-_binary64_694`
44×	`/-rgt-identity_binary64_751`
42×	`sub-neg_binary64_753`
37×	`+-commutative_binary64_690`
31×	`sqr-pow_binary64_732`
30×	`associate-r_binary64_700`
21×	`exp-prod_binary64_812` `associate-l_binary64_701`
19×	`pow-sqr_binary64_733`
17×	`associate-/r/_binary64_706`
16×	`log-prod_binary64_846`
14×	`distribute-rgt-in_binary64_710`
13×	`neg-sub0_binary64_755`
12×	`cube-unmult_binary64_797` `neg-mul-1_binary64_756` `swap-sqr_binary64_727` `distribute-lft-in_binary64_709`
11×	`*-lft-identity_binary64_749` `unswap-sqr_binary64_728`
10×	`log-div_binary64_847`
9×	`cancel-sign-sub-inv_binary64_726` `associate--r+_binary64_696`
8×	`distribute-rgt-neg-in_binary64_718` `associate--l-_binary64_698`
7×	`*-rgt-identity_binary64_750` `distribute-lft-neg-in_binary64_717`
6×	`prod-exp_binary64_809`
4×	`log-pow_binary64_849` `rem-sqrt-square_binary64_773` `--rgt-identity_binary64_746`
3×	`distribute-rgt-out_binary64_713` `distribute-lft-out_binary64_711`
2×	`distribute-neg-in_binary64_721`
1×	`log-rec_binary64_848` `rec-exp_binary64_810` `1-exp_binary64_804` `rem-square-sqrt_binary64_772` `mul-1-neg_binary64_752` `remove-double-neg_binary64_748` `sub0-neg_binary64_747` `+-rgt-identity_binary64_745` `rgt-mult-inverse_binary64_737` `distribute-neg-frac_binary64_724` `distribute-lft-neg-out_binary64_719` `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` `pow-base-0_binary64_844` `unpow1/3_binary64_827` `unpow3_binary64_826` `unpow2_binary64_825` `unpow1/2_binary64_824` `pow-plus_binary64_823` `exp-to-pow_binary64_822` `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` `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-mult_binary64_790` `cube-div_binary64_789` `cube-prod_binary64_788` `cube-neg_binary64_787` `rem-3cbrt-rft_binary64_786` `rem-3cbrt-lft_binary64_785` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `div-sub_binary64_765` `unsub-neg_binary64_754` `+-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` `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-rgt-neg-out_binary64_720` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `distribute-rgt-out--_binary64_714` `count-2_binary64_708` `associate--r-_binary64_699` `associate--l+_binary64_697` `associate-+l+_binary64_693` `associate-+r+_binary64_692`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	693	36669
1	1517	35162

Details

analyze386.0ms (1.4%)

sample82.0ms (0.3%)

simplify6.7s (24.3%)

prune5.0ms (0%)

localize15.0ms (0.1%)

rewrite200.0ms (0.7%)

series429.0ms (1.6%)

simplify234.0ms (0.9%)

prune844.0ms (3.1%)

localize18.0ms (0.1%)

rewrite959.0ms (3.5%)

series305.0ms (1.1%)

simplify1.0s (3.8%)

prune11.4s (41.6%)

localize22.0ms (0.1%)

rewrite3.6s (13.1%)

series394.0ms (1.4%)

simplify830.0ms (3%)

end0.0ms (0%)

Profiling