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

sample111.0ms

Algorithm

intervals

Results

38.0ms	45×	body	1280	valid
28.0ms	49×	body	640	valid
15.0ms	129×	body	80	valid
8.0ms	18×	body	320	valid
5.0ms	15×	body	160	valid

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5501	24

prune7.0ms

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: 17.1b

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)
7.1b	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))
9.0b	(.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))))

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

Counts

4 → 85

Calls

4 calls:

5.0ms	(.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)
7.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))
15.0ms	(.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))))

series154.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0)))
40.0ms	(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)))
58.0ms	(.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))))

simplify82.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4983	1601
1	4983	1601

prune149.0ms

Filtered

66 candidates to 97 candidates (-47.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	90	7	97
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	90	8	98

Merged error: 12.7b

Counts

98 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

2.4b	(sqrt.f64 (cbrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
2.5b	(.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))) (fabs.f64 (cbrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2.0)) (*.f64 J 2.0))) 2.0)))))
13.8b	(cbrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))
13.8b	(cbrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2.0)) (.f64 J 2.0))) 2.0)))

rewrite35.0ms

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:

8.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
7.0ms	(.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))) (fabs.f64 (cbrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2.0)) (*.f64 J 2.0))) 2.0)))))
7.0ms	(cbrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))
10.0ms	(cbrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2.0)) (.f64 J 2.0))) 2.0)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0))))
48.0ms	(.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))) (fabs.f64 (cbrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2.0)) (*.f64 J 2.0))) 2.0)))))
81.0ms	(cbrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))
87.0ms	(cbrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2.0)) (.f64 J 2.0))) 2.0)))

simplify65.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5083	1785

prune185.0ms

Filtered

65 candidates to 82 candidates (-26.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	82	8	90

Merged error: 12.7b

Counts

90 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))))
0.6b	(cbrt.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))))
7.1b	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))
9.0b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0)))) (cbrt.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))))) (cbrt.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))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

4.0ms	(cbrt.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))))
4.0ms	(cbrt.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))))
7.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))
22.0ms	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0)))) (cbrt.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))))) (cbrt.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))))

series180.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(cbrt.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))))
35.0ms	(cbrt.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))))
44.0ms	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))
67.0ms	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0)))) (cbrt.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))))) (cbrt.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))))

simplify84.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5413	1256

prune141.0ms

Filtered

50 candidates to 73 candidates (-46.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	71	10	81

Merged error: 12.7b

Counts

81 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))))
0.6b	(cbrt.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))))
7.1b	(sqrt.f64 (+.f64 1.0 (pow.f64 (/.f64 U (.f64 (.f64 2.0 J) (cos.f64 (/.f64 K 2.0)))) 2.0)))
9.0b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0)))) (.f64 (cbrt.f64 (.f64 -2.0 J)) (cbrt.f64 (cos.f64 (/.f64 K 2.0))))) (cbrt.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))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

4.0ms	(cbrt.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))))
4.0ms	(cbrt.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 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)))
22.0ms	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0)))) (.f64 (cbrt.f64 (.f64 -2.0 J)) (cbrt.f64 (cos.f64 (/.f64 K 2.0))))) (cbrt.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))))

series182.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(cbrt.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0))))
34.0ms	(cbrt.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 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)))
68.0ms	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 -2.0 J) (cos.f64 (/.f64 K 2.0)))) (.f64 (cbrt.f64 (.f64 -2.0 J)) (cbrt.f64 (cos.f64 (/.f64 K 2.0))))) (cbrt.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))))

simplify63.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5025	1329

prune115.0ms

Filtered

50 candidates to 76 candidates (-52.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	76	10	86

Merged error: 12.7b

Counts

86 → 10

regimes465.0ms

Accuracy

92.6% (0.4b remaining)

Error of 12.8b against oracle of 12.4b and baseline of 17.7b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	99
1	45	99

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.3s	1521×	body	1280	valid
714.0ms	1229×	body	640	valid
510.0ms	4321×	body	80	valid
260.0ms	631×	body	320	valid
79.0ms	298×	body	160	valid
1.0ms	1×	body	1280	invalid

Details

analyze1.9s

sample111.0ms

simplify68.0ms

prune7.0ms

localize16.0ms

rewrite38.0ms

series154.0ms

simplify82.0ms

prune149.0ms

localize27.0ms

rewrite35.0ms

series297.0ms

simplify65.0ms

prune185.0ms

localize20.0ms

rewrite39.0ms

series180.0ms

simplify84.0ms

prune141.0ms

localize25.0ms

rewrite41.0ms

series182.0ms

simplify63.0ms

prune115.0ms

regimes465.0ms

bsearch3.0ms

simplify2.0ms

end0.0ms

sample3.1s

Profiling