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

sample104.0ms

Algorithm

intervals

Results

33.0ms	41×	body	1280	valid
25.0ms	45×	body	640	valid
18.0ms	33×	body	320	valid
14.0ms	127×	body	80	valid
3.0ms	10×	body	160	valid

simplify69.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5501	24

prune8.0ms

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: 20.7b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0)))
0.2b	(pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)
8.9b	(.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))) (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (*.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
10.3b	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))

rewrite42.0ms

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` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`

Counts

4 → 85

Calls

4 calls:

6.0ms	(.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0)))
7.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)
18.0ms	(.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))) (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (*.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
8.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))

series153.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0)))
39.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)
60.0ms	(.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))) (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (*.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
45.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))

simplify85.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4983	1601
1	4983	1601

prune169.0ms

Filtered

66 candidates to 97 candidates (-47.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	89	8	97
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	89	9	98

Merged error: 14.7b

Counts

98 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

9.0b	(sqrt.f64 (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
9.0b	(sqrt.f64 (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
10.3b	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))
10.3b	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-prod_binary64`
18×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`sqrt-div_binary64`
10×	`pow1_binary64` `add-cube-cbrt_binary64` `sqrt-pow1_binary64`
6×	`pow1/2_binary64` `rem-sqrt-square_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`

Counts

4 → 76

Calls

4 calls:

9.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
8.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
8.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))
8.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
81.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
46.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))
45.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))

simplify71.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4904	1580
1	4904	1580

prune178.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	88	9	97

Merged error: 14.7b

Counts

97 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2.0)))
0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2.0)))
8.9b	(.f64 (.f64 (.f64 (.f64 J -2.0) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2.0))) (cbrt.f64 (cos.f64 (/.f64 K 2.0))))) (cbrt.f64 (cos.f64 (/.f64 K 2.0)))) (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (*.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
10.3b	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2.0)))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2.0)))
24.0ms	(.f64 (.f64 (.f64 (.f64 J -2.0) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2.0))) (cbrt.f64 (cos.f64 (/.f64 K 2.0))))) (cbrt.f64 (cos.f64 (/.f64 K 2.0)))) (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (*.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
8.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))

series143.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2.0)))
20.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2.0)))
57.0ms	(.f64 (.f64 (.f64 (.f64 J -2.0) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2.0))) (cbrt.f64 (cos.f64 (/.f64 K 2.0))))) (cbrt.f64 (cos.f64 (/.f64 K 2.0)))) (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (*.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
48.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))

simplify51.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5405	1435

prune142.0ms

Filtered

53 candidates to 86 candidates (-62.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	84	11	95

Merged error: 14.6b

Counts

95 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2.0)))
0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2.0)))
8.9b	(.f64 (.f64 (.f64 (.f64 J -2.0) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2.0))) (cbrt.f64 (cos.f64 (/.f64 K 2.0))))) (log.f64 (exp.f64 (cbrt.f64 (cos.f64 (/.f64 K 2.0)))))) (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (*.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
10.3b	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2.0)))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2.0)))
25.0ms	(.f64 (.f64 (.f64 (.f64 J -2.0) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2.0))) (cbrt.f64 (cos.f64 (/.f64 K 2.0))))) (log.f64 (exp.f64 (cbrt.f64 (cos.f64 (/.f64 K 2.0)))))) (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (*.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
8.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))

series142.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2.0)))
20.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2.0)))
57.0ms	(.f64 (.f64 (.f64 (.f64 J -2.0) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2.0))) (cbrt.f64 (cos.f64 (/.f64 K 2.0))))) (log.f64 (exp.f64 (cbrt.f64 (cos.f64 (/.f64 K 2.0)))))) (sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (*.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
48.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))

simplify52.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5559	1435

prune116.0ms

Filtered

53 candidates to 86 candidates (-62.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	7	7
Picked	1	0	1
Done	0	3	3
Total	86	11	97

Merged error: 14.6b

Counts

97 → 11

regimes538.0ms

Accuracy

90.3% (0.5b remaining)

Error of 13.3b against oracle of 12.7b and baseline of 18.3b

bsearch1.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	99
1	45	99

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.2s	1461×	body	1280	valid
717.0ms	1268×	body	640	valid
495.0ms	4311×	body	80	valid
258.0ms	645×	body	320	valid
89.0ms	315×	body	160	valid
0.0ms	1×	body	80	invalid

Details

analyze1.9s

sample104.0ms

simplify69.0ms

prune8.0ms

localize16.0ms

rewrite42.0ms

series153.0ms

simplify85.0ms

prune169.0ms

localize19.0ms

rewrite37.0ms

series252.0ms

simplify71.0ms

prune178.0ms

localize19.0ms

rewrite37.0ms

series143.0ms

simplify51.0ms

prune142.0ms

localize23.0ms

rewrite39.0ms

series142.0ms

simplify52.0ms

prune116.0ms

regimes538.0ms

bsearch1.0ms

simplify3.0ms

end0.0ms

sample3.0s

Profiling