Details

analyze1.9s

Algorithm

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

sample90.0ms

Algorithm

intervals

Results

45.0ms	68×	body	1024	valid
17.0ms	143×	body	128	valid
13.0ms	30×	body	512	valid
4.0ms	15×	body	256	valid

simplify87.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4870	37
1	4870	37

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

Merged error: 17.2b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

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)
7.6b	(.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))))
8.5b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log_binary64`
20×	`pow1_binary64`
18×	`add-cbrt-cube_binary64`
15×	`*-un-lft-identity_binary64`
12×	`prod-exp_binary64` `add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
10×	`associate-r_binary64`
9×	`pow-prod-down_binary64` `cbrt-unprod_binary64`
8×	`sqrt-prod_binary64`
7×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `pow-exp_binary64` `sqrt-div_binary64`
3×	`pow-unpow_binary64` `times-frac_binary64` `div-exp_binary64`
2×	`flip3-+_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `associate-l_binary64` `flip-+_binary64` `-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`

Counts

4 → 86

Calls

4 calls:

6.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
8.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
17.0ms	(.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))))
9.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series857.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
218.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
307.0ms	(.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))))
268.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify78.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5137	2394

prune132.0ms

Filtered

64 candidates to 98 candidates (-53.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	89	9	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	89	10	99

Merged error: 11.7b

Counts

99 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

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)
7.6b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
8.5b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log_binary64`
23×	`pow1_binary64`
21×	`add-cbrt-cube_binary64`
14×	`prod-exp_binary64`
11×	`pow-prod-down_binary64` `*-un-lft-identity_binary64` `cbrt-unprod_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
7×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `associate-r_binary64` `associate-*r/_binary64` `sqrt-prod_binary64` `pow-exp_binary64` `sqrt-div_binary64`
3×	`pow-unpow_binary64` `times-frac_binary64` `div-exp_binary64`
2×	`flip3-+_binary64` `associate-l_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `distribute-lft-out_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`

Counts

4 → 83

Calls

4 calls:

6.0ms	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))
8.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
15.0ms	(.f64 (.f64 -2 J) (.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)))

series815.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))
197.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
303.0ms	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
251.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify61.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5228	2306

prune116.0ms

Filtered

58 candidates to 95 candidates (-63.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	94	11	105

Merged error: 11.7b

Counts

105 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
1.2b	(.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)))
15.2b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
15.2b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
14×	`pow1_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `cbrt-prod_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
7×	`sqrt-prod_binary64`
6×	`cbrt-div_binary64` `pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64`
3×	`flip3-+_binary64` `distribute-lft-out_binary64` `pow1/3_binary64` `associate-l_binary64` `flip-+_binary64`
2×	`sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate-r_binary64` `*-commutative_binary64`

Counts

4 → 70

Calls

4 calls:

13.0ms	(sqrt.f64 (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)))
9.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series1.8s

Counts

4 → 12

Calls

4 calls:

491.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
307.0ms	(.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)))
491.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
490.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify92.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4961	2721
1	4961	2721

prune198.0ms

Filtered

60 candidates to 82 candidates (-36.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	80	13	93

Merged error: 11.7b

Counts

93 → 13

localize22.0ms

Local error

Found 4 expressions with local error:

1.2b	(.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)))
7.9b	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.5b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
15.2b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
14×	`pow1_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`cbrt-prod_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
8×	`sqrt-prod_binary64`
6×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`cbrt-div_binary64` `add-log-exp_binary64` `sqrt-div_binary64`
3×	`flip3-+_binary64` `distribute-lft-out_binary64` `associate-l_binary64` `flip-+_binary64`
2×	`pow1/3_binary64`
1×	`pow1/2_binary64` `associate-r_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `*-commutative_binary64`

Counts

4 → 68

Calls

4 calls:

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)))
9.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.0ms	(sqrt.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)))

series1.5s

Counts

4 → 12

Calls

4 calls:

304.0ms	(.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)))
494.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
251.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
492.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify94.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4944	2741
1	4944	2741

prune166.0ms

Filtered

58 candidates to 80 candidates (-37.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	80	13	93

Merged error: 11.7b

Counts

93 → 13

regimes265.0ms

Accuracy

85.4% (0.7b remaining)

Error of 12.9b against oracle of 12.2b and baseline of 17.3b

bsearch2.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	152
1	45	152

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.2s	1921×	body	1024	valid
578.0ms	4642×	body	128	valid
405.0ms	936×	body	512	valid
136.0ms	501×	body	256	valid
0.0ms	2×	body	128	invalid

Details

analyze1.9s

sample90.0ms

simplify87.0ms

prune4.0ms

localize21.0ms

rewrite49.0ms

series857.0ms

simplify78.0ms

prune132.0ms

localize19.0ms

rewrite47.0ms

series815.0ms

simplify61.0ms

prune116.0ms

localize20.0ms

rewrite48.0ms

series1.8s

simplify92.0ms

prune198.0ms

localize22.0ms

rewrite45.0ms

series1.5s

simplify94.0ms

prune166.0ms

regimes265.0ms

bsearch2.0ms

simplify3.0ms

end0.0ms

sample2.6s

Profiling