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

sample121.0ms

Algorithm

intervals

Results

46.0ms	50×	body	1280	valid
29.0ms	49×	body	640	valid
16.0ms	126×	body	80	valid
8.0ms	19×	body	320	valid
3.0ms	12×	body	160	valid
0.0ms	1×	body	80	invalid

simplify121.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	6460	37

prune15.0ms

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: 16.7b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))
0.3b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
7.5b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0b	(.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))))

rewrite38.0ms

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)))
7.0ms	(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)))
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))))

series481.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))
112.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
154.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
179.0ms	(.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))))

simplify74.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4940	2394
1	4940	2394

prune420.0ms

Filtered

67 candidates to 98 candidates (-46.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	90	8	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	90	9	99

Merged error: 12.0b

Counts

99 → 9

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
0.3b	(pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)
7.5b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))
8.1b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))

rewrite39.0ms

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-l*_binary64` `sqrt-prod_binary64` `pow-exp_binary64` `sqrt-div_binary64`
3×	`pow-unpow_binary64` `times-frac_binary64` `div-exp_binary64`
2×	`flip3-+_binary64` `associate-r_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 (cos.f64 (/.f64 K 2)) (.f64 J 2))
8.0ms	(pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))
15.0ms	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))

series472.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
114.0ms	(pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)
140.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))
179.0ms	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))

simplify73.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5103	2337

prune368.0ms

Filtered

58 candidates to 95 candidates (-63.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	93	11	104

Merged error: 12.0b

Counts

104 → 11

localize50.0ms

Local error

Found 4 expressions with local error:

2.2b	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
2.3b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))
13.5b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))
13.5b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite34.0ms

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` `associate-r_binary64` `pow1/3_binary64` `flip-+_binary64`
2×	`sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate-l_binary64` `*-commutative_binary64`

Counts

4 → 70

Calls

4 calls:

9.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
7.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))
8.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))
8.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

293.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
159.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))
304.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))
297.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify69.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5498	2771

prune483.0ms

Filtered

66 candidates to 82 candidates (-24.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	1	7	8
Picked	1	0	1
Done	0	2	2
Total	82	11	93

Merged error: 12.0b

Counts

93 → 11

localize45.0ms

Local error

Found 4 expressions with local error:

2.3b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))
7.5b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.3b	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
13.5b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))

rewrite38.0ms

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-r_binary64` `flip-+_binary64`
2×	`pow1/3_binary64`
1×	`pow1/2_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `*-commutative_binary64`

Counts

4 → 68

Calls

4 calls:

7.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))
9.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
12.0ms	(cbrt.f64 (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 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))

series913.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))
149.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
296.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
311.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))

simplify71.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5777	2763

prune402.0ms

Filtered

63 candidates to 80 candidates (-27.0%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	80	11	91

Merged error: 12.0b

Counts

91 → 11

regimes1.1s

Accuracy

91% (0.5b remaining)

Error of 13.1b against oracle of 12.7b and baseline of 17.8b

bsearch1.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	179
1	46	179

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.3s	1486×	body	1280	valid
781.0ms	1284×	body	640	valid
522.0ms	4310×	body	80	valid
262.0ms	622×	body	320	valid
81.0ms	298×	body	160	valid
1.0ms	1×	body	640	invalid
0.0ms	2×	body	80	invalid

Details

analyze1.9s

sample121.0ms

simplify121.0ms

prune15.0ms

localize25.0ms

rewrite38.0ms

series481.0ms

simplify74.0ms

prune420.0ms

localize32.0ms

rewrite39.0ms

series472.0ms

simplify73.0ms

prune368.0ms

localize50.0ms

rewrite34.0ms

series1.1s

simplify69.0ms

prune483.0ms

localize45.0ms

rewrite38.0ms

series913.0ms

simplify71.0ms

prune402.0ms

regimes1.1s

bsearch1.0ms

simplify4.0ms

end0.0ms

sample3.2s

Profiling