Details

analyze787.0ms

Algorithm

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

sample38.0ms

Algorithm

intervals

Results

9.0ms	194×	body	128	valid
7.0ms	256×	pre	128	true
6.0ms	24×	body	2048	valid
3.0ms	17×	body	1024	valid
2.0ms	7×	body	4096	valid
1.0ms	8×	body	512	valid
1.0ms	6×	body	256	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	37	26
1	37	26

prune3.0ms

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: 14.3b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
1.1b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
19.1b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

7.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
15.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
14.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
216.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
89.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
58.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

simplify62.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4941	1285
1	4941	1285

prune90.0ms

Filtered

55 candidates to 63 candidates (-14.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	54	9	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	9	64

Merged error: 14.0b

Counts

64 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))
0.8b	(log.f64 (exp.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))))
1.1b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
19.1b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64` `pow1_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`
5×	`log-pow_binary64` `sqrt-prod_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64` `exp-prod_binary64`
3×	`flip3-+_binary64` `log-prod_binary64` `sqrt-pow1_binary64` `flip-+_binary64`
2×	`pow1/2_binary64` `associate-*r/_binary64`
1×	`pow-prod-down_binary64` `distribute-lft-out_binary64` `rem-log-exp_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 56

Calls

4 calls:

15.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))
2.0ms	(log.f64 (exp.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))))
17.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series605.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))
255.0ms	(log.f64 (exp.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))))
86.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
49.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify107.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4868	1553
1	4868	1553

prune93.0ms

Filtered

62 candidates to 68 candidates (-9.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	68	9	77

Merged error: 14.0b

Counts

77 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

1.1b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
1.1b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
19.1b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
19.1b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
4×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64` `sqrt-div_binary64`
2×	`pow1/2_binary64` `distribute-lft-out_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 54

Calls

4 calls:

14.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
14.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
80.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
43.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
47.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify103.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4855	1308
1	4855	1308

prune112.0ms

Filtered

60 candidates to 66 candidates (-10.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	66	9	75

Merged error: 14.0b

Counts

75 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

5.2b	(log.f64 (exp.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))))))))
9.1b	(+.f64 1 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))))))
19.1b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
19.1b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
7×	`pow1_binary64` `sqrt-prod_binary64`
6×	`add-log-exp_binary64`
5×	`log-pow_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64` `exp-prod_binary64`
3×	`flip3-+_binary64` `log-prod_binary64` `flip-+_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`distribute-lft-out_binary64` `rem-log-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 58

Calls

4 calls:

2.0ms	(log.f64 (exp.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))))))))
11.0ms	(+.f64 1 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
7.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

248.0ms	(log.f64 (exp.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))))))))
91.0ms	(+.f64 1 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))))))
48.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
44.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))

simplify93.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4927	1474
1	4927	1474

prune101.0ms

Filtered

62 candidates to 70 candidates (-12.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	1	5	6
Picked	0	1	1
Done	1	1	2
Total	70	9	79

Merged error: 14.0b

Counts

79 → 9

regimes56.0ms

Accuracy

0% (0.3b remaining)

Error of 13.4b against oracle of 13.2b and baseline of 13.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	53
1	22	53

end0.0ms

sample1.1s

Algorithm

intervals

Results

298.0ms	6046×	body	128	valid
216.0ms	804×	body	2048	valid
147.0ms	8000×	pre	128	true
101.0ms	486×	body	1024	valid
96.0ms	280×	body	4096	valid
35.0ms	239×	body	512	valid
14.0ms	145×	body	256	valid

Details

analyze787.0ms

sample38.0ms

simplify9.0ms

prune3.0ms

localize11.0ms

rewrite49.0ms

series406.0ms

simplify62.0ms

prune90.0ms

localize15.0ms

rewrite45.0ms

series605.0ms

simplify107.0ms

prune93.0ms

localize17.0ms

rewrite46.0ms

series249.0ms

simplify103.0ms

prune112.0ms

localize20.0ms

rewrite35.0ms

series431.0ms

simplify93.0ms

prune101.0ms

regimes56.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling