Details

analyze2.1s (2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
1.6%	98.3%	0.1%	8
2.3%	97.5%	0.1%	9
7.4%	90.9%	1.7%	10
9.2%	87.4%	3.5%	11
11.7%	83.5%	4.8%	12
15.2%	76%	8.8%	13
16.4%	72%	11.6%	14

Compiler

Compiled 26 to 22 computations (15.4% saved)

sample113.0ms (0.1%)

Algorithm

1×

intervals

Results

49.0ms	94×	body	1024	valid
17.0ms	101×	body	128	valid
16.0ms	42×	body	512	valid
5.0ms	19×	body	256	valid
5.0ms	38×	body	128	invalid
3.0ms	5×	body	1024	invalid
2.0ms	6×	body	512	invalid
1.0ms	3×	body	256	invalid

Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify219.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

701×	`distribute-rgt-in_binary64_710`
559×	`times-frac_binary64_766`
480×	`associate-/r/_binary64_706`
421×	`associate-/r*_binary64_704`
393×	`distribute-rgt-out_binary64_713`
373×	`associate-/l*_binary64_705`
317×	`distribute-lft-in_binary64_709`
234×	`*-commutative_binary64_691`
145×	`distribute-lft-out_binary64_711`
122×	`associate-/l/_binary64_707`
101×	`associate-*l/_binary64_703`
94×	`associate-l_binary64_701`
90×	`associate-r_binary64_700`
78×	`associate-*r/_binary64_702`
45×	`/-rgt-identity_binary64_751`
26×	`*-lft-identity_binary64_749`
25×	`unswap-sqr_binary64_728`
18×	`*-rgt-identity_binary64_750`
17×	`sqr-pow_binary64_732`
16×	`distribute-rgt1-in_binary64_716`
11×	`pow-sqr_binary64_733`
7×	`remove-double-div_binary64_736` `associate-+l+_binary64_693`
6×	`cube-unmult_binary64_797` `swap-sqr_binary64_727` `distribute-lft1-in_binary64_715` `associate-+r+_binary64_692`
5×	`pow-plus_binary64_823`
4×	`div-exp_binary64_811` `prod-exp_binary64_809`
2×	`rec-exp_binary64_810`
1×	`unpow3_binary64_826` `unpow2_binary64_825` `unpow1_binary64_818` `1-exp_binary64_804` `cube-mult_binary64_790` `+-rgt-identity_binary64_745` `*-inverses_binary64_740` `count-2_binary64_708` `+-commutative_binary64_690`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_1023` `erf-erfc_binary64_1022` `erf-odd_binary64_1021` `if-if-and-not_binary64_1020` `if-if-and_binary64_1019` `if-if-or-not_binary64_1018` `if-if-or_binary64_1017` `if-not_binary64_1016` `if-same_binary64_1015` `if-false_binary64_1014` `if-true_binary64_1013` `not-gte_binary64_1012` `not-lte_binary64_1011` `not-gt_binary64_1010` `not-lt_binary64_1009` `gte-same_binary64_1008` `lte-same_binary64_1007` `gt-same_binary64_1006` `lt-same_binary64_1005` `sinh---cosh_binary64_952` `sinh-+-cosh_binary64_951` `sinh-cosh_binary64_950` `tanh-def-c_binary64_949` `tanh-def-b_binary64_948` `tanh-def-a_binary64_947` `cosh-def_binary64_946` `sinh-def_binary64_945` `tan-neg_binary64_892` `cos-neg_binary64_891` `sin-neg_binary64_890` `tan-0_binary64_889` `cos-0_binary64_888` `sin-0_binary64_887` `hang-m-tan_binary64_886` `hang-p-tan_binary64_885` `hang-m0-tan_binary64_884` `hang-p0-tan_binary64_883` `hang-0m-tan_binary64_882` `hang-0p-tan_binary64_881` `tan-+PI/2_binary64_880` `tan-+PI_binary64_879` `tan-PI_binary64_878` `tan-PI/3_binary64_877` `tan-PI/4_binary64_876` `tan-PI/6_binary64_875` `cos-+PI/2_binary64_874` `cos-+PI_binary64_873` `cos-PI_binary64_872` `cos-PI/2_binary64_871` `cos-PI/3_binary64_870` `cos-PI/4_binary64_869` `cos-PI/6_binary64_868` `sin-+PI/2_binary64_867` `sin-+PI_binary64_866` `sin-PI_binary64_865` `sin-PI/2_binary64_864` `sin-PI/3_binary64_863` `sin-PI/4_binary64_862` `sin-PI/6_binary64_861` `sub-1-sin_binary64_860` `sub-1-cos_binary64_859` `-1-add-sin_binary64_858` `-1-add-cos_binary64_857` `1-sub-sin_binary64_856` `1-sub-cos_binary64_855` `cos-sin-sum_binary64_854` `log-E_binary64_850` `log-pow_binary64_849` `log-rec_binary64_848` `log-div_binary64_847` `log-prod_binary64_846` `pow-base-0_binary64_844` `unpow1/3_binary64_827` `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` `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-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` `rem-sqrt-square_binary64_773` `rem-square-sqrt_binary64_772` `div-sub_binary64_765` `neg-mul-1_binary64_756` `neg-sub0_binary64_755` `unsub-neg_binary64_754` `sub-neg_binary64_753` `mul-1-neg_binary64_752` `remove-double-neg_binary64_748` `sub0-neg_binary64_747` `--rgt-identity_binary64_746` `+-lft-identity_binary64_744` `mul0-rgt_binary64_743` `mul0-lft_binary64_742` `div0_binary64_741` `+-inverses_binary64_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` `cancel-sign-sub-inv_binary64_726` `cancel-sign-sub_binary64_725` `distribute-neg-frac_binary64_724` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722` `distribute-neg-in_binary64_721` `distribute-rgt-neg-out_binary64_720` `distribute-lft-neg-out_binary64_719` `distribute-rgt-neg-in_binary64_718` `distribute-lft-neg-in_binary64_717` `distribute-rgt-out--_binary64_714` `distribute-lft-out--_binary64_712` `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

1 → 4

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	38
1	53	38
2	178	35
3	882	35
4	3773	35

prune19.0ms (0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Kept	Total
New	4	4
Fresh	1	1
Picked	0	0
Done	0	0
Total	5	5

Error

29.7b

Counts

5 → 5

Compiler

Compiled 217 to 160 computations (26.3% saved)

localize25.0ms (0%)

Local error

Found 4 expressions with local error:

6.7b	(.f64 (pow.f64 t 3) (.f64 (sin.f64 k) (tan.f64 k)))
7.2b	(.f64 (/.f64 (/.f64 2 (+.f64 2 (pow.f64 (/.f64 k t) 2))) (.f64 (pow.f64 t 3) (*.f64 (sin.f64 k) (tan.f64 k)))) l)
7.3b	(.f64 l (.f64 (/.f64 (/.f64 2 (+.f64 2 (pow.f64 (/.f64 k t) 2))) (.f64 (pow.f64 t 3) (.f64 (sin.f64 k) (tan.f64 k)))) l))
15.6b	(/.f64 (/.f64 2 (+.f64 2 (pow.f64 (/.f64 k t) 2))) (.f64 (pow.f64 t 3) (.f64 (sin.f64 k) (tan.f64 k))))

rewrite564.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

23.3b

Rules

213×	`add-exp-log_binary64_798`
109×	`prod-exp_binary64_809`
97×	`add-cbrt-cube_binary64_796`
72×	`times-frac_binary64_766`
63×	`div-exp_binary64_811`
52×	`*-un-lft-identity_binary64_760`
43×	`cbrt-unprod_binary64_793`
38×	`associate-l_binary64_701`
36×	`add-sqr-sqrt_binary64_782`
34×	`add-cube-cbrt_binary64_795`
27×	`cbrt-undiv_binary64_794`
18×	`associate-/l*_binary64_705`
14×	`pow-to-exp_binary64_829` `pow-exp_binary64_828`
11×	`pow1_binary64_821`
9×	`distribute-lft-out_binary64_711`
8×	`associate-/r/_binary64_706`
7×	`associate-*r/_binary64_702`
5×	`div-inv_binary64_757` `associate-r_binary64_700`
4×	`add-log-exp_binary64_799` `pow-prod-down_binary64_831`
3×	`flip3-+_binary64_763` `flip-+_binary64_734` `tan-quot_binary64_919` `*-commutative_binary64_691` `unpow-prod-down_binary64_839` `cube-prod_binary64_788`
2×	`associate-*l/_binary64_703`
1×	`frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l/_binary64_707` `associate-/r*_binary64_704` `unswap-sqr_binary64_728` `unpow3_binary64_826` `cube-mult_binary64_790` `sqr-pow_binary64_732`

Counts

4 → 197

Calls

4 calls:

27.0ms	(.f64 (/.f64 (/.f64 2 (+.f64 2 (pow.f64 (/.f64 k t) 2))) (.f64 (pow.f64 t 3) (*.f64 (sin.f64 k) (tan.f64 k)))) l)
25.0ms	(.f64 l (.f64 (/.f64 (/.f64 2 (+.f64 2 (pow.f64 (/.f64 k t) 2))) (.f64 (pow.f64 t 3) (.f64 (sin.f64 k) (tan.f64 k)))) l))
21.0ms	(/.f64 (/.f64 2 (+.f64 2 (pow.f64 (/.f64 k t) 2))) (.f64 (pow.f64 t 3) (.f64 (sin.f64 k) (tan.f64 k))))
14.0ms	(.f64 (pow.f64 t 3) (.f64 (sin.f64 k) (tan.f64 k)))

Compiler

Compiled 7149 to 3932 computations (45% saved)

series2.5s (2.4%)

Error

18.2b

Counts

4 → 33

Calls

4 calls:

983.0ms	(.f64 (/.f64 (/.f64 2 (+.f64 2 (pow.f64 (/.f64 k t) 2))) (.f64 (pow.f64 t 3) (*.f64 (sin.f64 k) (tan.f64 k)))) l)
821.0ms	(.f64 l (.f64 (/.f64 (/.f64 2 (+.f64 2 (pow.f64 (/.f64 k t) 2))) (.f64 (pow.f64 t 3) (.f64 (sin.f64 k) (tan.f64 k)))) l))
335.0ms	(.f64 (pow.f64 t 3) (.f64 (sin.f64 k) (tan.f64 k)))
307.0ms	(/.f64 (/.f64 2 (+.f64 2 (pow.f64 (/.f64 k t) 2))) (.f64 (pow.f64 t 3) (.f64 (sin.f64 k) (tan.f64 k))))

Compiler

Compiled 2474 to 1889 computations (23.6% saved)

simplify1.5s (1.4%)

Algorithm

1×	egg-herbie

Rules

370×	`associate-/r*_binary64_704`
341×	`associate-l_binary64_701`
303×	`associate-r_binary64_700`
279×	`times-frac_binary64_766`
264×	`associate-/l*_binary64_705`
238×	`unswap-sqr_binary64_728`
187×	`associate-*l/_binary64_703`
153×	`*-commutative_binary64_691`
140×	`associate-*r/_binary64_702`
112×	`associate-/l/_binary64_707`
103×	`cancel-sign-sub-inv_binary64_726`
99×	`log-prod_binary64_846`
78×	`exp-prod_binary64_812` `sqr-pow_binary64_732`
72×	`sub-neg_binary64_753` `associate-/r/_binary64_706`
65×	`distribute-neg-frac_binary64_724`
62×	`swap-sqr_binary64_727`
52×	`log-div_binary64_847`
51×	`cube-prod_binary64_788`
45×	`neg-mul-1_binary64_756`
44×	`neg-sub0_binary64_755`
41×	`pow-sqr_binary64_733`
40×	`cube-div_binary64_789` `distribute-rgt-in_binary64_710`
36×	`distribute-lft-in_binary64_709`
27×	`*-rgt-identity_binary64_750`
24×	`+-commutative_binary64_690`
23×	`div-sub_binary64_765`
20×	`pow-plus_binary64_823`
17×	`cube-unmult_binary64_797`
13×	`distribute-rgt-neg-in_binary64_718`
12×	`associate--r+_binary64_696`
11×	`log-pow_binary64_849` `distribute-lft-neg-in_binary64_717`
10×	`unsub-neg_binary64_754` `associate-+r+_binary64_692`
9×	`unpow3_binary64_826` `div-exp_binary64_811` `prod-exp_binary64_809` `distribute-neg-in_binary64_721`
8×	`*-lft-identity_binary64_749`
7×	`associate-+l-_binary64_695`
6×	`/-rgt-identity_binary64_751` `associate--l+_binary64_697` `associate-+l+_binary64_693`
5×	`unpow2_binary64_825` `unpow1_binary64_818` `cube-mult_binary64_790` `associate-+r-_binary64_694`
4×	`rem-sqrt-square_binary64_773` `associate--l-_binary64_698`
3×	`rec-exp_binary64_810`
2×	`difference-of-squares_binary64_729` `distribute-lft-neg-out_binary64_719`
1×	`log-rec_binary64_848` `exp-sqrt_binary64_813` `1-exp_binary64_804` `exp-1-e_binary64_803` `rem-log-exp_binary64_801` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `rem-square-sqrt_binary64_772` `*-inverses_binary64_740` `distribute-rgt-out--_binary64_714`
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` `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-diff_binary64_808` `exp-neg_binary64_807` `exp-sum_binary64_806` `e-exp-1_binary64_805` `exp-0_binary64_802` `rem-exp-log_binary64_800` `cube-neg_binary64_787` `rem-3cbrt-rft_binary64_786` `rem-3cbrt-lft_binary64_785` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `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_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` `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_713` `distribute-lft-out--_binary64_712` `distribute-lft-out_binary64_711` `count-2_binary64_708` `associate--r-_binary64_699`

Counts

230 → 480

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	328	8681
1	877	7013
2	3924	7013

prune1.3s (1.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	466	14	480
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	470	15	485

Error

10.7b

Counts

485 → 15

Compiler

Compiled 16687 to 9532 computations (42.9% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

0.7b	(/.f64 (cos.f64 k) (/.f64 (*.f64 k k) l))
4.8b	(/.f64 (/.f64 (/.f64 (cos.f64 k) (/.f64 (*.f64 k k) l)) (pow.f64 (sin.f64 k) 2)) t)
7.0b	(.f64 l (.f64 2 (/.f64 (/.f64 (/.f64 (cos.f64 k) (/.f64 (*.f64 k k) l)) (pow.f64 (sin.f64 k) 2)) t)))
8.9b	(/.f64 (*.f64 k k) l)

rewrite2.5s (2.4%)

Algorithm

1×	rewrite-expression-head

Error

7.1b

Rules

2464×	`times-frac_binary64_766`
896×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
312×	`unpow-prod-down_binary64_839`
216×	`associate-/l*_binary64_705`
153×	`add-exp-log_binary64_798`
139×	`div-inv_binary64_757`
104×	`unpow2_binary64_825` `sqr-pow_binary64_732`
87×	`div-exp_binary64_811`
73×	`add-cbrt-cube_binary64_796`
37×	`prod-exp_binary64_809`
35×	`cbrt-undiv_binary64_794`
33×	`associate-/r/_binary64_706`
17×	`cbrt-unprod_binary64_793`
13×	`associate-/r*_binary64_704`
9×	`pow1_binary64_821`
8×	`pow-to-exp_binary64_829` `pow-exp_binary64_828`
4×	`add-log-exp_binary64_799`
3×	`frac-2neg_binary64_771` `clear-num_binary64_759` `pow-prod-down_binary64_831` `associate-l_binary64_701`
2×	`associate-*r/_binary64_702`
1×	`associate-r_binary64_700` `*-commutative_binary64_691` `associate-/l/_binary64_707`

Counts

4 → 986

Calls

4 calls:

77.0ms	(.f64 l (.f64 2 (/.f64 (/.f64 (/.f64 (cos.f64 k) (/.f64 (*.f64 k k) l)) (pow.f64 (sin.f64 k) 2)) t)))
63.0ms	(/.f64 (/.f64 (/.f64 (cos.f64 k) (/.f64 (*.f64 k k) l)) (pow.f64 (sin.f64 k) 2)) t)
12.0ms	(/.f64 (cos.f64 k) (/.f64 (*.f64 k k) l))
5.0ms	(/.f64 (*.f64 k k) l)

Compiler

Compiled 37284 to 13664 computations (63.4% saved)

series1.9s (1.8%)

Error

10.7b

Counts

4 → 33

Calls

4 calls:

834.0ms	(.f64 l (.f64 2 (/.f64 (/.f64 (/.f64 (cos.f64 k) (/.f64 (*.f64 k k) l)) (pow.f64 (sin.f64 k) 2)) t)))
713.0ms	(/.f64 (/.f64 (/.f64 (cos.f64 k) (/.f64 (*.f64 k k) l)) (pow.f64 (sin.f64 k) 2)) t)
181.0ms	(/.f64 (cos.f64 k) (/.f64 (*.f64 k k) l))
109.0ms	(/.f64 (*.f64 k k) l)

Compiler

Compiled 1829 to 1406 computations (23.1% saved)

simplify4.5s (4.2%)

Algorithm

1×	egg-herbie

Rules

573×	`associate-/r/_binary64_706`
346×	`associate-/l*_binary64_705`
267×	`times-frac_binary64_766`
258×	`associate-*l/_binary64_703`
230×	`associate-/r*_binary64_704`
208×	`*-commutative_binary64_691`
206×	`/-rgt-identity_binary64_751`
204×	`associate-r_binary64_700`
131×	`associate-l_binary64_701`
110×	`associate-*r/_binary64_702`
62×	`sub-neg_binary64_753`
51×	`log-prod_binary64_846`
37×	`log-div_binary64_847`
33×	`neg-mul-1_binary64_756`
31×	`neg-sub0_binary64_755`
30×	`cube-prod_binary64_788`
26×	`pow-plus_binary64_823`
24×	`exp-prod_binary64_812`
19×	`sqr-pow_binary64_732`
18×	`cube-unmult_binary64_797`
16×	`div-exp_binary64_811` `prod-exp_binary64_809` `+-commutative_binary64_690`
15×	`log-pow_binary64_849`
14×	`cube-div_binary64_789`
13×	`pow-sqr_binary64_733` `distribute-neg-frac_binary64_724`
10×	`div-sub_binary64_765` `distribute-rgt-neg-in_binary64_718`
9×	`cancel-sign-sub-inv_binary64_726`
8×	`associate-+r-_binary64_694` `associate-+l+_binary64_693`
7×	`unpow2_binary64_825` `associate-+l-_binary64_695`
6×	`unpow1_binary64_818` `swap-sqr_binary64_727` `distribute-lft-neg-in_binary64_717` `associate--l-_binary64_698` `associate--l+_binary64_697`
5×	`exp-lft-sqr_binary64_815` `unsub-neg_binary64_754` `associate-+r+_binary64_692`
4×	`rec-exp_binary64_810` `rem-sqrt-square_binary64_773` `unswap-sqr_binary64_728` `distribute-lft-neg-out_binary64_719`
3×	`pow-base-1_binary64_820` `associate--r+_binary64_696`
2×	`log-rec_binary64_848` `distribute-neg-in_binary64_721`
1×	`1-exp_binary64_804` `rem-log-exp_binary64_801` `rem-3cbrt-rft_binary64_786` `rem-3cbrt-lft_binary64_785` `rem-square-sqrt_binary64_772` `*-inverses_binary64_740` `count-2_binary64_708` `associate--r-_binary64_699`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_1023` `erf-erfc_binary64_1022` `erf-odd_binary64_1021` `if-if-and-not_binary64_1020` `if-if-and_binary64_1019` `if-if-or-not_binary64_1018` `if-if-or_binary64_1017` `if-not_binary64_1016` `if-same_binary64_1015` `if-false_binary64_1014` `if-true_binary64_1013` `not-gte_binary64_1012` `not-lte_binary64_1011` `not-gt_binary64_1010` `not-lt_binary64_1009` `gte-same_binary64_1008` `lte-same_binary64_1007` `gt-same_binary64_1006` `lt-same_binary64_1005` `sinh---cosh_binary64_952` `sinh-+-cosh_binary64_951` `sinh-cosh_binary64_950` `tanh-def-c_binary64_949` `tanh-def-b_binary64_948` `tanh-def-a_binary64_947` `cosh-def_binary64_946` `sinh-def_binary64_945` `tan-neg_binary64_892` `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` `unpow1/2_binary64_824` `exp-to-pow_binary64_822` `unpow0_binary64_819` `unpow-1_binary64_817` `exp-lft-cube_binary64_816` `exp-cbrt_binary64_814` `exp-sqrt_binary64_813` `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-exp-log_binary64_800` `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` `mul-1-neg_binary64_752` `-rgt-identity_binary64_750` `-lft-identity_binary64_749` `remove-double-neg_binary64_748` `sub0-neg_binary64_747` `--rgt-identity_binary64_746` `+-rgt-identity_binary64_745` `+-lft-identity_binary64_744` `mul0-rgt_binary64_743` `mul0-lft_binary64_742` `div0_binary64_741` `+-inverses_binary64_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-rgt-neg-out_binary64_720` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `distribute-rgt-out--_binary64_714` `distribute-rgt-out_binary64_713` `distribute-lft-out--_binary64_712` `distribute-lft-out_binary64_711` `distribute-rgt-in_binary64_710` `distribute-lft-in_binary64_709` `associate-/l/_binary64_707`

Counts

1019 → 5033

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1972	44227
1	2742	39929
2	4706	39851

prune14.1s (13.4%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	5022	11	5033
Fresh	6	8	14
Picked	1	0	1
Done	0	0	0
Total	5029	19	5048

Error

7.2b

Counts

5048 → 19

Compiler

Compiled 189858 to 58666 computations (69.1% saved)

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 (cos.f64 k) (/.f64 k l))
0.9b	(/.f64 (/.f64 (cos.f64 k) (/.f64 k l)) (pow.f64 (sin.f64 k) 2))
7.0b	(.f64 l (.f64 2 (*.f64 (/.f64 1 k) (/.f64 (/.f64 (/.f64 (cos.f64 k) (/.f64 k l)) (pow.f64 (sin.f64 k) 2)) t))))
9.3b	(/.f64 (/.f64 (/.f64 (cos.f64 k) (/.f64 k l)) (pow.f64 (sin.f64 k) 2)) t)

rewrite7.4s (7.1%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

5609×	`times-frac_binary64_766`
2285×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
663×	`unpow-prod-down_binary64_839`
403×	`associate-/l*_binary64_705`
360×	`add-exp-log_binary64_798`
221×	`unpow2_binary64_825` `sqr-pow_binary64_732`
183×	`div-exp_binary64_811`
175×	`div-inv_binary64_757`
135×	`prod-exp_binary64_809`
102×	`add-cbrt-cube_binary64_796`
44×	`cbrt-undiv_binary64_794`
42×	`associate-/r/_binary64_706`
33×	`cbrt-unprod_binary64_793`
24×	`associate-/r*_binary64_704`
18×	`pow-to-exp_binary64_829` `pow-exp_binary64_828`
13×	`pow1_binary64_821`
11×	`1-exp_binary64_804` `rec-exp_binary64_810`
7×	`associate-*r/_binary64_702`
6×	`pow-prod-down_binary64_831`
4×	`add-log-exp_binary64_799`
3×	`frac-2neg_binary64_771` `clear-num_binary64_759` `associate-l_binary64_701`
2×	`associate-/l/_binary64_707`
1×	`frac-times_binary64_770` `associate-l/_binary64_703` `associate-r_binary64_700` `-commutative_binary64_691`

Counts

4 → 2025

Calls

4 calls:

136.0ms	(.f64 l (.f64 2 (*.f64 (/.f64 1 k) (/.f64 (/.f64 (/.f64 (cos.f64 k) (/.f64 k l)) (pow.f64 (sin.f64 k) 2)) t))))
93.0ms	(/.f64 (/.f64 (/.f64 (cos.f64 k) (/.f64 k l)) (pow.f64 (sin.f64 k) 2)) t)
24.0ms	(/.f64 (/.f64 (cos.f64 k) (/.f64 k l)) (pow.f64 (sin.f64 k) 2))
8.0ms	(/.f64 (cos.f64 k) (/.f64 k l))

Compiler

Compiled 83394 to 34773 computations (58.3% saved)

series2.1s (2%)

Error

7.2b

Counts

4 → 34

Calls

4 calls:

837.0ms	(.f64 l (.f64 2 (*.f64 (/.f64 1 k) (/.f64 (/.f64 (/.f64 (cos.f64 k) (/.f64 k l)) (pow.f64 (sin.f64 k) 2)) t))))
703.0ms	(/.f64 (/.f64 (/.f64 (cos.f64 k) (/.f64 k l)) (pow.f64 (sin.f64 k) 2)) t)
339.0ms	(/.f64 (/.f64 (cos.f64 k) (/.f64 k l)) (pow.f64 (sin.f64 k) 2))
169.0ms	(/.f64 (cos.f64 k) (/.f64 k l))

Compiler

Compiled 2011 to 1499 computations (25.5% saved)

simplify6.2s (5.9%)

Algorithm

1×	egg-herbie

Rules

701×	`associate-/l*_binary64_705`
500×	`times-frac_binary64_766`
446×	`associate-*l/_binary64_703`
383×	`associate-/r/_binary64_706`
359×	`/-rgt-identity_binary64_751`
349×	`associate-/r*_binary64_704`
67×	`*-commutative_binary64_691`
44×	`associate-l_binary64_701` `associate-r_binary64_700`
27×	`associate-*r/_binary64_702`
24×	`sub-neg_binary64_753`
21×	`sqr-pow_binary64_732`
20×	`neg-mul-1_binary64_756` `neg-sub0_binary64_755`
17×	`log-div_binary64_847` `cancel-sign-sub-inv_binary64_726` `distribute-rgt-neg-in_binary64_718`
16×	`log-prod_binary64_846`
15×	`swap-sqr_binary64_727`
14×	`cube-unmult_binary64_797`
12×	`distribute-neg-frac_binary64_724` `distribute-lft-neg-in_binary64_717`
9×	`exp-prod_binary64_812`
7×	`unpow2_binary64_825`
6×	`unpow1_binary64_818` `pow-sqr_binary64_733`
5×	`*-lft-identity_binary64_749` `unswap-sqr_binary64_728` `distribute-lft-neg-out_binary64_719`
4×	`associate--l-_binary64_698` `associate-+l-_binary64_695` `associate-+r+_binary64_692`
3×	`pow-plus_binary64_823` `*-rgt-identity_binary64_750` `+-commutative_binary64_690`
2×	`log-pow_binary64_849` `log-rec_binary64_848` `pow-base-1_binary64_820` `div-sub_binary64_765` `remove-double-div_binary64_736` `associate-+r-_binary64_694`
1×	`unpow3_binary64_826` `div-exp_binary64_811` `rec-exp_binary64_810` `prod-exp_binary64_809` `1-exp_binary64_804` `rem-log-exp_binary64_801` `cube-mult_binary64_790` `rem-sqrt-square_binary64_773` `rem-square-sqrt_binary64_772` `unsub-neg_binary64_754` `sub0-neg_binary64_747` `*-inverses_binary64_740` `distribute-neg-in_binary64_721` `associate--r-_binary64_699`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_1023` `erf-erfc_binary64_1022` `erf-odd_binary64_1021` `if-if-and-not_binary64_1020` `if-if-and_binary64_1019` `if-if-or-not_binary64_1018` `if-if-or_binary64_1017` `if-not_binary64_1016` `if-same_binary64_1015` `if-false_binary64_1014` `if-true_binary64_1013` `not-gte_binary64_1012` `not-lte_binary64_1011` `not-gt_binary64_1010` `not-lt_binary64_1009` `gte-same_binary64_1008` `lte-same_binary64_1007` `gt-same_binary64_1006` `lt-same_binary64_1005` `sinh---cosh_binary64_952` `sinh-+-cosh_binary64_951` `sinh-cosh_binary64_950` `tanh-def-c_binary64_949` `tanh-def-b_binary64_948` `tanh-def-a_binary64_947` `cosh-def_binary64_946` `sinh-def_binary64_945` `tan-neg_binary64_892` `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` `unpow1/2_binary64_824` `exp-to-pow_binary64_822` `unpow0_binary64_819` `unpow-1_binary64_817` `exp-lft-cube_binary64_816` `exp-lft-sqr_binary64_815` `exp-cbrt_binary64_814` `exp-sqrt_binary64_813` `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-exp-log_binary64_800` `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` `mul-1-neg_binary64_752` `remove-double-neg_binary64_748` `--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` `rgt-mult-inverse_binary64_737` `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` `distribute-rgt-out_binary64_713` `distribute-lft-out--_binary64_712` `distribute-lft-out_binary64_711` `distribute-rgt-in_binary64_710` `distribute-lft-in_binary64_709` `count-2_binary64_708` `associate-/l/_binary64_707` `associate--l+_binary64_697` `associate--r+_binary64_696` `associate-+l+_binary64_693`

Counts

2059 → 7233

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	3279	89539
1	4405	80711

prune31.6s (30%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	7226	7	7233
Fresh	6	12	18
Picked	0	1	1
Done	0	0	0
Total	7232	20	7252

Error

4.8b

Counts

7252 → 20

Compiler

Compiled 284288 to 102283 computations (64% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

2.2b	(/.f64 (.f64 (.f64 l 2) (/.f64 (*.f64 (/.f64 (cos.f64 k) k) (/.f64 l (pow.f64 (sin.f64 k) 2))) t)) k)
3.3b	(.f64 (.f64 l 2) (/.f64 (*.f64 (/.f64 (cos.f64 k) k) (/.f64 l (pow.f64 (sin.f64 k) 2))) t))
3.6b	(/.f64 l (pow.f64 (sin.f64 k) 2))
9.3b	(/.f64 (*.f64 (/.f64 (cos.f64 k) k) (/.f64 l (pow.f64 (sin.f64 k) 2))) t)

rewrite352.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

265×	`add-exp-log_binary64_798`
150×	`add-cbrt-cube_binary64_796`
119×	`div-exp_binary64_811`
100×	`prod-exp_binary64_809`
59×	`cbrt-undiv_binary64_794`
56×	`cbrt-unprod_binary64_793`
33×	`times-frac_binary64_766`
27×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
14×	`associate-/r*_binary64_704`
12×	`unpow-prod-down_binary64_839`
11×	`pow-to-exp_binary64_829` `pow-exp_binary64_828`
9×	`pow1_binary64_821`
7×	`associate-r_binary64_700`
5×	`associate-/l*_binary64_705`
4×	`add-log-exp_binary64_799` `div-inv_binary64_757` `associate-/l/_binary64_707` `unpow2_binary64_825` `sqr-pow_binary64_732`
3×	`frac-2neg_binary64_771` `clear-num_binary64_759` `associate-*r/_binary64_702` `pow-prod-down_binary64_831`
1×	`frac-times_binary64_770` `associate-l/_binary64_703` `associate-l_binary64_701` `-commutative_binary64_691`

Counts

4 → 186

Calls

4 calls:

18.0ms	(/.f64 (.f64 (.f64 l 2) (/.f64 (*.f64 (/.f64 (cos.f64 k) k) (/.f64 l (pow.f64 (sin.f64 k) 2))) t)) k)
16.0ms	(.f64 (.f64 l 2) (/.f64 (*.f64 (/.f64 (cos.f64 k) k) (/.f64 l (pow.f64 (sin.f64 k) 2))) t))
12.0ms	(/.f64 (*.f64 (/.f64 (cos.f64 k) k) (/.f64 l (pow.f64 (sin.f64 k) 2))) t)
6.0ms	(/.f64 l (pow.f64 (sin.f64 k) 2))

Compiler

Compiled 5818 to 2679 computations (54% saved)

series2.6s (2.4%)

Error

4.8b

Counts

4 → 37

Calls

4 calls:

813.0ms	(/.f64 (.f64 (.f64 l 2) (/.f64 (*.f64 (/.f64 (cos.f64 k) k) (/.f64 l (pow.f64 (sin.f64 k) 2))) t)) k)
782.0ms	(.f64 (.f64 l 2) (/.f64 (*.f64 (/.f64 (cos.f64 k) k) (/.f64 l (pow.f64 (sin.f64 k) 2))) t))
711.0ms	(/.f64 (*.f64 (/.f64 (cos.f64 k) k) (/.f64 l (pow.f64 (sin.f64 k) 2))) t)
212.0ms	(/.f64 l (pow.f64 (sin.f64 k) 2))

Compiler

Compiled 2064 to 1533 computations (25.7% saved)

simplify1.7s (1.6%)

Algorithm

1×	egg-herbie

Rules

419×	`times-frac_binary64_766`
302×	`associate-/l*_binary64_705`
230×	`associate-l_binary64_701`
221×	`log-div_binary64_847`
220×	`associate-*r/_binary64_702`
195×	`associate-/r*_binary64_704`
187×	`associate-*l/_binary64_703`
177×	`associate-/l/_binary64_707`
163×	`associate-r_binary64_700`
119×	`associate-+l+_binary64_693`
116×	`associate-+l-_binary64_695`
105×	`distribute-neg-frac_binary64_724`
99×	`associate--l+_binary64_697` `associate-+r+_binary64_692`
98×	`*-commutative_binary64_691`
94×	`associate-/r/_binary64_706`
87×	`distribute-rgt-neg-in_binary64_718`
86×	`log-prod_binary64_846`
83×	`distribute-lft-neg-in_binary64_717`
82×	`associate-+r-_binary64_694`
75×	`cube-div_binary64_789`
67×	`cancel-sign-sub-inv_binary64_726`
66×	`unswap-sqr_binary64_728`
65×	`sub-neg_binary64_753`
61×	`associate--l-_binary64_698`
60×	`+-commutative_binary64_690`
54×	`sqr-pow_binary64_732`
48×	`cube-prod_binary64_788`
44×	`exp-prod_binary64_812` `swap-sqr_binary64_727`
43×	`*-rgt-identity_binary64_750`
35×	`neg-mul-1_binary64_756`
33×	`neg-sub0_binary64_755`
31×	`log-pow_binary64_849`
26×	`/-rgt-identity_binary64_751`
19×	`*-lft-identity_binary64_749`
18×	`pow-plus_binary64_823`
17×	`log-rec_binary64_848` `prod-exp_binary64_809`
16×	`div-exp_binary64_811` `cube-unmult_binary64_797`
14×	`pow-sqr_binary64_733` `associate--r-_binary64_699` `associate--r+_binary64_696`
12×	`distribute-lft-neg-out_binary64_719`
11×	`div-sub_binary64_765`
9×	`exp-lft-sqr_binary64_815`
7×	`unpow2_binary64_825`
6×	`unpow1_binary64_818`
5×	`rem-sqrt-square_binary64_773` `distribute-neg-in_binary64_721`
4×	`rec-exp_binary64_810`
3×	`pow-base-1_binary64_820` `exp-sqrt_binary64_813` `unsub-neg_binary64_754` `distribute-rgt-neg-out_binary64_720` `distribute-rgt-in_binary64_710`
2×	`distribute-rgt-out--_binary64_714` `distribute-rgt-out_binary64_713`
1×	`unpow3_binary64_826` `1-exp_binary64_804` `exp-1-e_binary64_803` `rem-log-exp_binary64_801` `cube-mult_binary64_790` `rem-3cbrt-rft_binary64_786` `rem-3cbrt-lft_binary64_785` `rem-square-sqrt_binary64_772` `*-inverses_binary64_740` `rgt-mult-inverse_binary64_737` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715`
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` `unpow1/2_binary64_824` `exp-to-pow_binary64_822` `unpow0_binary64_819` `unpow-1_binary64_817` `exp-lft-cube_binary64_816` `exp-cbrt_binary64_814` `exp-diff_binary64_808` `exp-neg_binary64_807` `exp-sum_binary64_806` `e-exp-1_binary64_805` `exp-0_binary64_802` `rem-exp-log_binary64_800` `cube-neg_binary64_787` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `mul-1-neg_binary64_752` `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_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-lft-out--_binary64_712` `distribute-lft-out_binary64_711` `distribute-lft-in_binary64_709` `count-2_binary64_708`

Counts

223 → 495

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	309	7176
1	781	5251
2	3043	5229
3	4969	5229

prune811.0ms (0.8%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	489	6	495
Fresh	6	12	18
Picked	0	1	1
Done	0	1	1
Total	495	20	515

Error

4.8b

Counts

515 → 20

Compiler

Compiled 13534 to 6155 computations (54.5% saved)

regimes8.4s (8%)

Accuracy

Total 7.3b remaining (58.3%)

Threshold costs 0b (0%)

Compiler

Compiled 69958 to 48149 computations (31.2% saved)

bsearch288.0ms (0.3%)

Steps

Iters	Range		Point
10	8.856294352433011e+70	1.5533381578236447e+86	1.0275830431192084e+73
6	6.494322418222212e+66	6.577715337346823e+67	6.439006299831887e+67
6	3.408944378237824e-83	2.2612485244434277e-82	8.924049272980926e-83
5	-5.673888236475523e-09	-1.6625812997540152e-09	-3.5362665831654716e-09

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify13.0ms (0%)

Algorithm

1×	egg-herbie

Rules

19×	`*-commutative_binary64_691`
1×	`+-commutative_binary64_690`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `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` `1-exp_binary64_804` `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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	274
1	91	274

Proof

(if real (<= f64 h0 -2137541988714571/604462909807314587353088) (* f64 h1 (=> (* f64 (/ f64 (/ f64 2 (+ f64 2 (pow f64 (/ f64 h2 h0) 2))) (* f64 h0 (* f64 (sin f64 h2) (* f64 (tan f64 h2) (* f64 h0 h0))))) h1))) (if real (<= f64 h0 3049864568801069/34175792574734561318320347298712833833643272357706444319152665725155515612490248800367393390985216) (* f64 (/ f64 (* f64 h1 2) (* f64 (cbrt f64 h2) (cbrt f64 h2))) (/ f64 (/ f64 (* f64 (/ f64 (cos f64 h2) h2) (/ f64 h1 (pow f64 (sin f64 h2) 2))) h0) (cbrt f64 h2))) (if real (<= f64 h0 64390062998318865313378124977189265318776997723003709669165253001216) (* f64 h1 (* f64 (/ f64 (* f64 (cbrt f64 (/ f64 2 (+ f64 2 (pow f64 (/ f64 h2 h0) 2)))) (cbrt f64 (/ f64 2 (+ f64 2 (pow f64 (/ f64 h2 h0) 2))))) (pow f64 h0 3)) (* f64 (/ f64 (cbrt f64 (/ f64 2 (+ f64 2 (pow f64 (/ f64 h2 h0) 2)))) (sin f64 h2)) (/ f64 h1 (tan f64 h2))))) (if real (<= f64 h0 10275830431192083531347455722316101648639645393848034099015047297579876352) (* f64 h1 (* f64 2 (/ f64 (/ f64 (/ f64 (cos f64 h2) (* f64 (* f64 (cbrt f64 (/ f64 h2 (/ f64 h1 h2))) (cbrt f64 (/ f64 h2 (/ f64 h1 h2)))) (cbrt f64 (/ f64 h2 (/ f64 h1 h2))))) (pow f64 (sin f64 h2) 2)) h0))) (* f64 h1 (* f64 (/ f64 (/ f64 2 (+ f64 2 (pow f64 (/ f64 h2 h0) 2))) (* f64 (pow f64 h0 (/ f64 3 2)) (* f64 (tan f64 h2) (* f64 (sin f64 h2) (pow f64 h0 (/ f64 3 2)))))) h1))))))
*-commutative_binary64_691 =>
(if real (<= f64 h0 -2137541988714571/604462909807314587353088) (* f64 h1 (* f64 h1 (/ f64 (/ f64 2 (+ f64 2 (pow f64 (/ f64 h2 h0) 2))) (* f64 h0 (* f64 (sin f64 h2) (* f64 (tan f64 h2) (* f64 h0 h0))))))) (if real (<= f64 h0 3049864568801069/34175792574734561318320347298712833833643272357706444319152665725155515612490248800367393390985216) (* f64 (/ f64 (* f64 h1 2) (* f64 (cbrt f64 h2) (cbrt f64 h2))) (/ f64 (/ f64 (* f64 (/ f64 (cos f64 h2) h2) (/ f64 h1 (pow f64 (sin f64 h2) 2))) h0) (cbrt f64 h2))) (if real (<= f64 h0 64390062998318865313378124977189265318776997723003709669165253001216) (* f64 h1 (* f64 (/ f64 (* f64 (cbrt f64 (/ f64 2 (+ f64 2 (pow f64 (/ f64 h2 h0) 2)))) (cbrt f64 (/ f64 2 (+ f64 2 (pow f64 (/ f64 h2 h0) 2))))) (pow f64 h0 3)) (* f64 (/ f64 (cbrt f64 (/ f64 2 (+ f64 2 (pow f64 (/ f64 h2 h0) 2)))) (sin f64 h2)) (/ f64 h1 (tan f64 h2))))) (if real (<= f64 h0 10275830431192083531347455722316101648639645393848034099015047297579876352) (* f64 h1 (* f64 2 (/ f64 (/ f64 (/ f64 (cos f64 h2) (* f64 (* f64 (cbrt f64 (/ f64 h2 (/ f64 h1 h2))) (cbrt f64 (/ f64 h2 (/ f64 h1 h2)))) (cbrt f64 (/ f64 h2 (/ f64 h1 h2))))) (pow f64 (sin f64 h2) 2)) h0))) (* f64 h1 (=> (* f64 (/ f64 (/ f64 2 (+ f64 2 (pow f64 (/ f64 h2 h0) 2))) (* f64 (pow f64 h0 (/ f64 3 2)) (* f64 (tan f64 h2) (* f64 (sin f64 h2) (pow f64 h0 (/ f64 3 2)))))) h1)))))))
*-commutative_binary64_691 =>
(if real (<= f64 h0 -2137541988714571/604462909807314587353088) (* f64 h1 (* f64 h1 (/ f64 (/ f64 2 (+ f64 2 (pow f64 (/ f64 h2 h0) 2))) (* f64 h0 (* f64 (sin f64 h2) (* f64 (tan f64 h2) (* f64 h0 h0))))))) (if real (<= f64 h0 3049864568801069/34175792574734561318320347298712833833643272357706444319152665725155515612490248800367393390985216) (* f64 (/ f64 (* f64 h1 2) (* f64 (cbrt f64 h2) (cbrt f64 h2))) (/ f64 (/ f64 (* f64 (/ f64 (cos f64 h2) h2) (/ f64 h1 (pow f64 (sin f64 h2) 2))) h0) (cbrt f64 h2))) (if real (<= f64 h0 64390062998318865313378124977189265318776997723003709669165253001216) (* f64 h1 (* f64 (/ f64 (* f64 (cbrt f64 (/ f64 2 (+ f64 2 (pow f64 (/ f64 h2 h0) 2)))) (cbrt f64 (/ f64 2 (+ f64 2 (pow f64 (/ f64 h2 h0) 2))))) (pow f64 h0 3)) (* f64 (/ f64 (cbrt f64 (/ f64 2 (+ f64 2 (pow f64 (/ f64 h2 h0) 2)))) (sin f64 h2)) (/ f64 h1 (tan f64 h2))))) (if real (<= f64 h0 10275830431192083531347455722316101648639645393848034099015047297579876352) (* f64 h1 (* f64 2 (/ f64 (/ f64 (/ f64 (cos f64 h2) (=> (* f64 (* f64 (cbrt f64 (/ f64 h2 (/ f64 h1 h2))) (cbrt f64 (/ f64 h2 (/ f64 h1 h2)))) (cbrt f64 (/ f64 h2 (/ f64 h1 h2)))))) (pow f64 (sin f64 h2) 2)) h0))) (* f64 h1 (* f64 h1 (/ f64 (/ f64 2 (+ f64 2 (pow f64 (/ f64 h2 h0) 2))) (* f64 (pow f64 h0 (/ f64 3 2)) (* f64 (tan f64 h2) (* f64 (sin f64 h2) (pow f64 h0 (/ f64 3 2))))))))))))
*-commutative_binary64_691 =>
(if real (<= f64 h0 -2137541988714571/604462909807314587353088) (* f64 h1 (* f64 h1 (/ f64 (/ f64 2 (+ f64 2 (pow f64 (/ f64 h2 h0) 2))) (* f64 h0 (* f64 (sin f64 h2) (* f64 (tan f64 h2) (* f64 h0 h0))))))) (if real (<= f64 h0 3049864568801069/34175792574734561318320347298712833833643272357706444319152665725155515612490248800367393390985216) (* f64 (/ f64 (* f64 h1 2) (* f64 (cbrt f64 h2) (cbrt f64 h2))) (/ f64 (/ f64 (* f64 (/ f64 (cos f64 h2) h2) (/ f64 h1 (pow f64 (sin f64 h2) 2))) h0) (cbrt f64 h2))) (if real (<= f64 h0 64390062998318865313378124977189265318776997723003709669165253001216) (* f64 h1 (* f64 (/ f64 (* f64 (cbrt f64 (/ f64 2 (+ f64 2 (pow f64 (/ f64 h2 h0) 2)))) (cbrt f64 (/ f64 2 (+ f64 2 (pow f64 (/ f64 h2 h0) 2))))) (pow f64 h0 3)) (* f64 (/ f64 (cbrt f64 (/ f64 2 (+ f64 2 (pow f64 (/ f64 h2 h0) 2)))) (sin f64 h2)) (/ f64 h1 (tan f64 h2))))) (if real (<= f64 h0 10275830431192083531347455722316101648639645393848034099015047297579876352) (* f64 h1 (* f64 2 (/ f64 (/ f64 (/ f64 (cos f64 h2) (* f64 (cbrt f64 (/ f64 h2 (/ f64 h1 h2))) (* f64 (cbrt f64 (/ f64 h2 (/ f64 h1 h2))) (cbrt f64 (/ f64 h2 (/ f64 h1 h2)))))) (pow f64 (sin f64 h2) 2)) h0))) (* f64 h1 (* f64 h1 (/ f64 (/ f64 2 (+ f64 2 (pow f64 (/ f64 h2 h0) 2))) (* f64 (pow f64 h0 (/ f64 3 2)) (* f64 (tan f64 h2) (* f64 (sin f64 h2) (pow f64 h0 (/ f64 3 2))))))))))))

end0.0ms (0%)

sample12.3s (11.7%)

Algorithm

1×

intervals

Results

1.4s	2671×	body	1024	valid
493.0ms	1229×	body	512	valid
449.0ms	3489×	body	128	valid
203.0ms	1523×	body	128	invalid
155.0ms	604×	body	256	valid
54.0ms	133×	body	512	invalid
35.0ms	120×	body	256	invalid
33.0ms	56×	body	1024	invalid
5.0ms	7×	body	2048	valid

Compiler

Compiled 11805 to 8106 computations (31.3% saved)

Details

analyze2.1s (2%)

sample113.0ms (0.1%)

simplify219.0ms (0.2%)

prune19.0ms (0%)

localize25.0ms (0%)

rewrite564.0ms (0.5%)

series2.5s (2.4%)

simplify1.5s (1.4%)

prune1.3s (1.3%)

localize16.0ms (0%)

rewrite2.5s (2.4%)

series1.9s (1.8%)

simplify4.5s (4.2%)

prune14.1s (13.4%)

localize15.0ms (0%)

rewrite7.4s (7.1%)

series2.1s (2%)

simplify6.2s (5.9%)

prune31.6s (30%)

localize18.0ms (0%)

rewrite352.0ms (0.3%)

series2.6s (2.4%)

simplify1.7s (1.6%)

prune811.0ms (0.8%)

regimes8.4s (8%)

bsearch288.0ms (0.3%)

simplify13.0ms (0%)

end0.0ms (0%)

sample12.3s (11.7%)

Profiling