Details

analyze1.9s (8.8%)

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
15.6%	84.3%	0.1%	8
15.6%	84.3%	0.1%	9
15.6%	84.3%	0.1%	10
30.4%	69.4%	0.1%	11
30.4%	69.4%	0.1%	12
30.4%	69.4%	0.1%	13
39.6%	60.3%	0.1%	14

Compiler

Compiled 25 to 23 computations (8% saved)

sample91.0ms (0.4%)

Algorithm

1×

intervals

Results

40.0ms	61×	body	1024	valid
16.0ms	39×	body	512	valid
15.0ms	136×	body	128	valid
5.0ms	20×	body	256	valid

Compiler

Compiled 49 to 48 computations (2% saved)

simplify180.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4871	37
1	4871	37

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

17.4b

Counts

2 → 1

Compiler

Compiled 48 to 44 computations (8.3% saved)

localize16.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))
0.1b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
0.1b	(/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))
0.0b	(+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))
0.1b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
0.2b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
5.9b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
10.4b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite49.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-exp-log_binary64_1108`
20×	`pow1_binary64_1131`
18×	`add-cbrt-cube_binary64_1106`
15×	`*-un-lft-identity_binary64_1070`
12×	`prod-exp_binary64_1119` `add-sqr-sqrt_binary64_1092`
11×	`add-cube-cbrt_binary64_1105`
10×	`associate-r_binary64_1010`
9×	`cbrt-unprod_binary64_1103` `pow-prod-down_binary64_1141`
8×	`sqrt-prod_binary64_1086`
7×	`unpow-prod-down_binary64_1149`
4×	`sqrt-div_binary64_1087` `pow-exp_binary64_1138` `add-log-exp_binary64_1109`
3×	`div-exp_binary64_1121` `times-frac_binary64_1076` `pow-unpow_binary64_1147`
2×	`-commutative_binary64_1001` `flip-+_binary64_1044` `associate-l_binary64_1011` `distribute-lft-out_binary64_1021` `associate-r/_binary64_1012` `flip3-+_binary64_1073`
1×	`pow1/2_binary64_1150` `pow-pow_binary64_1142` `sqr-pow_binary64_1042` `unpow2_binary64_1135` `pow-to-exp_binary64_1139` `rem-sqrt-square_binary64_1083` `sqrt-pow1_binary64_1088` `div-inv_binary64_1067`

Counts

4 → 86

Calls

8 calls:

15.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
12.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
7.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
5.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
0.0ms	(+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))

series1.9s (8.9%)

Counts

4 → 65

Calls

4 calls:

909.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
550.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
319.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
109.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 2895 to 2582 computations (10.8% saved)

simplify67.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4999	4307
1	4999	4307

prune353.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	143	8	151
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	144	8	152

Error

0.0b

Counts

152 → 8

Compiler

Compiled 4719 to 3651 computations (22.6% saved)

localize21.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))
0.1b	(/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))
0.0b	(+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))
0.0b	(+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))
1.7b	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
1.8b	(.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))
14.8b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
14.8b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite44.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_1070`
14×	`pow1_binary64_1131`
13×	`add-cbrt-cube_binary64_1106` `add-exp-log_binary64_1108` `cbrt-prod_binary64_1101`
11×	`add-sqr-sqrt_binary64_1092`
9×	`add-cube-cbrt_binary64_1105`
7×	`sqrt-prod_binary64_1086`
6×	`cbrt-unprod_binary64_1103` `prod-exp_binary64_1119` `pow-prod-down_binary64_1141` `cbrt-div_binary64_1102`
4×	`add-log-exp_binary64_1109`
3×	`flip-+_binary64_1044` `associate-l_binary64_1011` `distribute-lft-out_binary64_1021` `flip3-+_binary64_1073` `pow1/3_binary64_1152`
2×	`sqrt-div_binary64_1087` `rem-sqrt-square_binary64_1083` `sqrt-pow1_binary64_1088`
1×	`associate-r_binary64_1010` `*-commutative_binary64_1001` `pow1/2_binary64_1150`

Counts

4 → 70

Calls

8 calls:

10.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
7.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))
0.0ms	(+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))

series3.4s (16.3%)

Counts

4 → 76

Calls

4 calls:

1.0s	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
972.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
963.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
508.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))

Compiler

Compiled 6805 to 5963 computations (12.4% saved)

simplify76.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5042	6366

prune561.0ms (2.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	146	8	154

Error

0.0b

Counts

154 → 8

Compiler

Compiled 8279 to 6507 computations (21.4% saved)

localize23.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (.f64 J -2) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))
0.1b	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))
0.1b	(/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))
0.0b	(+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))
0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
5.9b	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
10.4b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite46.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64_1131`
29×	`add-exp-log_binary64_1108`
20×	`add-cbrt-cube_binary64_1106`
19×	`cbrt-unprod_binary64_1103` `prod-exp_binary64_1119` `pow-prod-down_binary64_1141`
13×	`*-un-lft-identity_binary64_1070`
10×	`add-sqr-sqrt_binary64_1092`
9×	`add-cube-cbrt_binary64_1105`
8×	`sqrt-prod_binary64_1086`
7×	`associate-r_binary64_1010`
6×	`cbrt-prod_binary64_1101`
4×	`sqrt-div_binary64_1087` `add-log-exp_binary64_1109`
2×	`flip-+_binary64_1044` `distribute-lft-out_binary64_1021` `associate-*r/_binary64_1012` `flip3-+_binary64_1073` `pow1/3_binary64_1152`
1×	`-commutative_binary64_1001` `pow1/2_binary64_1150` `associate-l*_binary64_1011` `rem-sqrt-square_binary64_1083` `sqrt-pow1_binary64_1088`

Counts

4 → 74

Calls

8 calls:

24.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
0.0ms	(+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))

series1.7s (8%)

Counts

4 → 57

Calls

4 calls:

936.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
599.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
79.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
76.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 2998 to 2635 computations (12.1% saved)

simplify64.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5498	3933

prune319.0ms (1.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	130	9	139

Error

0.0b

Counts

139 → 9

Compiler

Compiled 5097 to 4042 computations (20.7% saved)

localize26.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b	(exp.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))
0.1b	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))
0.1b	(/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))
0.0b	(+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))
0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
5.9b	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (log.f64 (exp.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
10.4b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite48.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64_1131`
29×	`add-exp-log_binary64_1108`
25×	`add-cbrt-cube_binary64_1106`
19×	`cbrt-unprod_binary64_1103` `prod-exp_binary64_1119` `pow-prod-down_binary64_1141`
13×	`*-un-lft-identity_binary64_1070`
10×	`add-sqr-sqrt_binary64_1092`
9×	`add-cube-cbrt_binary64_1105`
8×	`sqrt-prod_binary64_1086`
7×	`associate-r_binary64_1010`
6×	`cbrt-prod_binary64_1101`
4×	`sqrt-div_binary64_1087` `add-log-exp_binary64_1109`
2×	`flip-+_binary64_1044` `distribute-lft-out_binary64_1021` `associate-*r/_binary64_1012` `flip3-+_binary64_1073` `pow1/3_binary64_1152`
1×	`-commutative_binary64_1001` `pow1/2_binary64_1150` `associate-l*_binary64_1011` `rem-sqrt-square_binary64_1083` `sqrt-pow1_binary64_1088`

Counts

4 → 74

Calls

8 calls:

26.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (log.f64 (exp.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
0.0ms	(+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))

series2.9s (13.9%)

Counts

4 → 57

Calls

4 calls:

2.2s	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (log.f64 (exp.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
599.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
84.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
74.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 3960 to 3521 computations (11.1% saved)

simplify132.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4947	4755
1	4947	4755

prune349.0ms (1.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	131	9	140

Error

0.0b

Counts

140 → 9

Compiler

Compiled 5519 to 4427 computations (19.8% saved)

simplify20.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	242	1354
1	242	1354

regimes515.0ms (2.4%)

Accuracy

Total 17.2b remaining (99.8%)

Threshold costs 0b (0%)

Compiler

Compiled 4375 to 3980 computations (9% saved)

bsearch264.0ms (1.2%)

Steps

Iters	Range		Point
5	2.9461380309665427e-112	6.169392266300259e-112	3.5351986706589427e-112
7	1.3729597641581034e-183	1.1329834833202832e-181	8.15590711171135e-182
5	5.423475145520907e-218	1.5092211457541319e-217	1.2804491241499647e-217
4	3.775843826874276e-263	5.508271825316319e-263	5.129303200657122e-263
8	-2.9412156428288794e-286	-1.7232264100762818e-290	-3.407987670226901e-287
9	-2.552390171360266e-102	-2.0654314670595655e-111	-2.1144643127566853e-111

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	73	197
1	73	197

end0.0ms (0%)

sample6.0s (28.6%)

Algorithm

1×

intervals

Results

1.4s	2028×	body	1024	valid
524.0ms	4464×	body	128	valid
422.0ms	1013×	body	512	valid
134.0ms	491×	body	256	valid
3.0ms	4×	body	2048	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 2898 to 2588 computations (10.7% saved)

Pareto

0.43970361836762833

Details

analyze1.9s (8.8%)

sample91.0ms (0.4%)

simplify180.0ms (0.9%)

prune4.0ms (0%)

localize16.0ms (0.1%)

rewrite49.0ms (0.2%)

series1.9s (8.9%)

simplify67.0ms (0.3%)

prune353.0ms (1.7%)

localize21.0ms (0.1%)

rewrite44.0ms (0.2%)

series3.4s (16.3%)

simplify76.0ms (0.4%)

prune561.0ms (2.7%)

localize23.0ms (0.1%)

rewrite46.0ms (0.2%)

series1.7s (8%)

simplify64.0ms (0.3%)

prune319.0ms (1.5%)

localize26.0ms (0.1%)

rewrite48.0ms (0.2%)

series2.9s (13.9%)

simplify132.0ms (0.6%)

prune349.0ms (1.7%)

simplify20.0ms (0.1%)

regimes515.0ms (2.4%)

bsearch264.0ms (1.2%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.0s (28.6%)

Profiling