Details

analyze2.1s

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
31.2%	68.7%	0.1%	7
34.3%	65.6%	0.1%	8
37.5%	59.3%	3.2%	9
42.9%	53.5%	3.6%	10
44.5%	50%	5.6%	11
47.8%	45.8%	6.4%	12
48.7%	43.7%	7.6%	13
50.5%	41.3%	8.2%	14

sample141.0ms

Algorithm

intervals

Results

47.0ms	217×	body	80	valid
46.0ms	190×	body	80	invalid
14.0ms	16×	body	640	valid
9.0ms	8×	body	1280	valid
7.0ms	10×	body	320	valid
2.0ms	5×	body	160	valid

simplify484.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5001	105

prune16.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.4b

Counts

2 → 2

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) (+.f64 (.f64 x1 (+.f64 -6 (.f64 2 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))))) (.f64 4 (*.f64 x1 x1))))
0.2b	(.f64 (.f64 x1 x1) -6)
2.7b	(+.f64 (.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) (+.f64 (.f64 x1 (+.f64 -6 (.f64 2 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))))) (.f64 4 (.f64 x1 x1)))) (.f64 (*.f64 x1 x1) -6))
4.0b	(+.f64 -6 (.f64 2 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
22×	`associate-l_binary64`
21×	`*-un-lft-identity_binary64`
16×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`pow1_binary64`
8×	`add-log-exp_binary64`
6×	`associate-r_binary64`
5×	`flip3-+_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `flip-+_binary64`
4×	`pow-prod-down_binary64`
3×	`unswap-sqr_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
2×	`associate-r/_binary64` `associate-+l+_binary64` `distribute-lft-in_binary64` `associate-/r/_binary64` `distribute-rgt-in_binary64` `+-commutative_binary64` `frac-times_binary64` `sum-log_binary64` `-commutative_binary64`
1×	`cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `associate-*l/_binary64`

Counts

4 → 89

Calls

4 calls:

24.0ms	(.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) (+.f64 (.f64 x1 (+.f64 -6 (.f64 2 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))))) (.f64 4 (*.f64 x1 x1))))
6.0ms	(.f64 (.f64 x1 x1) -6)
24.0ms	(+.f64 (.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) (+.f64 (.f64 x1 (+.f64 -6 (.f64 2 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))))) (.f64 4 (.f64 x1 x1)))) (.f64 (*.f64 x1 x1) -6))
10.0ms	(+.f64 -6 (.f64 2 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))))

series143.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) (+.f64 (.f64 x1 (+.f64 -6 (.f64 2 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))))) (.f64 4 (*.f64 x1 x1))))
3.0ms	(.f64 (.f64 x1 x1) -6)
72.0ms	(+.f64 (.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) (+.f64 (.f64 x1 (+.f64 -6 (.f64 2 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))))) (.f64 4 (.f64 x1 x1)))) (.f64 (*.f64 x1 x1) -6))
32.0ms	(+.f64 -6 (.f64 2 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))))

simplify50.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4948	3748
1	4948	3748

prune429.0ms

Filtered

78 candidates to 101 candidates (-29.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	95	6	101
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	96	7	103

Merged error: 0.4b

Counts

103 → 7

localize41.0ms

Local error

Found 4 expressions with local error:

2.7b	(+.f64 (.f64 (.f64 (.f64 2 x1) (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 (.f64 x1 x1) (-.f64 (.f64 4 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) 6)))
4.0b	(-.f64 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3)
6.3b	(.f64 (.f64 (.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))
6.4b	(.f64 (.f64 x1 x1) (-.f64 (.f64 4 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) 6))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
26×	`add-sqr-sqrt_binary64`
24×	`associate-r_binary64`
23×	`associate-*r/_binary64`
22×	`*-un-lft-identity_binary64`
18×	`pow1_binary64`
16×	`times-frac_binary64`
15×	`cbrt-unprod_binary64` `prod-exp_binary64`
14×	`add-cube-cbrt_binary64`
11×	`flip3--_binary64` `flip--_binary64`
10×	`frac-add_binary64`
9×	`pow-prod-down_binary64`
8×	`add-log-exp_binary64`
7×	`sub-neg_binary64`
5×	`difference-of-squares_binary64`
4×	`distribute-lft-out--_binary64` `frac-times_binary64`
3×	`cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-exp_binary64`
2×	`flip3-+_binary64` `associate-+l+_binary64` `associate-/r/_binary64` `associate-l_binary64` `flip-+_binary64` `associate-+r+_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`associate--l-_binary64` `diff-log_binary64` `unswap-sqr_binary64` `div-sub_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 109

Calls

4 calls:

45.0ms	(+.f64 (.f64 (.f64 (.f64 2 x1) (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 (.f64 x1 x1) (-.f64 (.f64 4 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) 6)))
20.0ms	(-.f64 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3)
20.0ms	(.f64 (.f64 (.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))
22.0ms	(.f64 (.f64 x1 x1) (-.f64 (.f64 4 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) 6))

series120.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(+.f64 (.f64 (.f64 (.f64 2 x1) (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 (.f64 x1 x1) (-.f64 (.f64 4 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) 6)))
15.0ms	(-.f64 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3)
11.0ms	(.f64 (.f64 (.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))
17.0ms	(.f64 (.f64 x1 x1) (-.f64 (.f64 4 (/.f64 (-.f64 (+.f64 (.f64 (.f64 3 x1) x1) (.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) 6))

simplify87.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4950	5851
1	4950	5851

prune597.0ms

Filtered

90 candidates to 121 candidates (-34.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	118	10	128

Merged error: 0.3b

Counts

128 → 10

localize43.0ms

Local error

Found 4 expressions with local error:

6.3b	(+.f64 (.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) (+.f64 (.f64 x1 (+.f64 -6 (.f64 2 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))))) (.f64 4 (.f64 x1 x1)))) (.f64 (.f64 (cbrt.f64 (.f64 -6 (.f64 x1 x1))) (cbrt.f64 (.f64 -6 (.f64 x1 x1)))) (cbrt.f64 (.f64 -6 (*.f64 x1 x1)))))
28.0b	(cbrt.f64 (.f64 -6 (.f64 x1 x1)))
28.0b	(cbrt.f64 (.f64 -6 (.f64 x1 x1)))
28.0b	(cbrt.f64 (.f64 -6 (.f64 x1 x1)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
3×	`pow1/3_binary64` `cbrt-prod_binary64`
2×	`associate-+l+_binary64`
1×	`flip3-+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 40

Calls

4 calls:

27.0ms	(+.f64 (.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) (+.f64 (.f64 x1 (+.f64 -6 (.f64 2 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))))) (.f64 4 (.f64 x1 x1)))) (.f64 (.f64 (cbrt.f64 (.f64 -6 (.f64 x1 x1))) (cbrt.f64 (.f64 -6 (.f64 x1 x1)))) (cbrt.f64 (.f64 -6 (*.f64 x1 x1)))))
5.0ms	(cbrt.f64 (.f64 -6 (.f64 x1 x1)))
5.0ms	(cbrt.f64 (.f64 -6 (.f64 x1 x1)))
5.0ms	(cbrt.f64 (.f64 -6 (.f64 x1 x1)))

series146.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(+.f64 (.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) (+.f64 (.f64 x1 (+.f64 -6 (.f64 2 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))))) (.f64 4 (.f64 x1 x1)))) (.f64 (.f64 (cbrt.f64 (.f64 -6 (.f64 x1 x1))) (cbrt.f64 (.f64 -6 (.f64 x1 x1)))) (cbrt.f64 (.f64 -6 (*.f64 x1 x1)))))
23.0ms	(cbrt.f64 (.f64 -6 (.f64 x1 x1)))
21.0ms	(cbrt.f64 (.f64 -6 (.f64 x1 x1)))
23.0ms	(cbrt.f64 (.f64 -6 (.f64 x1 x1)))

simplify49.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5008	1117

prune181.0ms

Filtered

38 candidates to 52 candidates (-36.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	52	10	62

Merged error: 0.3b

Counts

62 → 10

localize44.0ms

Local error

Found 4 expressions with local error:

5.2b	(+.f64 (.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) (+.f64 (.f64 x1 (+.f64 -6 (.f64 2 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))))) (.f64 4 (.f64 x1 x1)))) (.f64 (.f64 (cbrt.f64 (.f64 -6 (.f64 x1 x1))) (.f64 (cbrt.f64 -6) (cbrt.f64 (.f64 x1 x1)))) (cbrt.f64 (.f64 -6 (*.f64 x1 x1)))))
28.0b	(cbrt.f64 (.f64 -6 (.f64 x1 x1)))
28.0b	(cbrt.f64 (.f64 -6 (.f64 x1 x1)))
28.2b	(cbrt.f64 (*.f64 x1 x1))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
3×	`pow1/3_binary64` `cbrt-prod_binary64`
2×	`associate-+l+_binary64`
1×	`flip3-+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 40

Calls

4 calls:

28.0ms	(+.f64 (.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) (+.f64 (.f64 x1 (+.f64 -6 (.f64 2 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))))) (.f64 4 (.f64 x1 x1)))) (.f64 (.f64 (cbrt.f64 (.f64 -6 (.f64 x1 x1))) (.f64 (cbrt.f64 -6) (cbrt.f64 (.f64 x1 x1)))) (cbrt.f64 (.f64 -6 (*.f64 x1 x1)))))
5.0ms	(cbrt.f64 (.f64 -6 (.f64 x1 x1)))
5.0ms	(cbrt.f64 (.f64 -6 (.f64 x1 x1)))
5.0ms	(cbrt.f64 (*.f64 x1 x1))

series137.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(+.f64 (.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) (+.f64 (.f64 x1 (+.f64 -6 (.f64 2 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))))) (.f64 4 (.f64 x1 x1)))) (.f64 (.f64 (cbrt.f64 (.f64 -6 (.f64 x1 x1))) (.f64 (cbrt.f64 -6) (cbrt.f64 (.f64 x1 x1)))) (cbrt.f64 (.f64 -6 (*.f64 x1 x1)))))
21.0ms	(cbrt.f64 (.f64 -6 (.f64 x1 x1)))
21.0ms	(cbrt.f64 (.f64 -6 (.f64 x1 x1)))
14.0ms	(cbrt.f64 (*.f64 x1 x1))

simplify41.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4966	1379
1	4966	1379

prune182.0ms

Filtered

45 candidates to 52 candidates (-15.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	52	10	62

Merged error: 0.3b

Counts

62 → 10

regimes403.0ms

Accuracy

0% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	107	127
1	107	127

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.5s	6987×	body	80	valid
1.2s	5755×	body	80	invalid
350.0ms	401×	body	640	valid
199.0ms	183×	body	1280	valid
170.0ms	270×	body	320	valid
70.0ms	159×	body	160	valid

Details

analyze2.1s

sample141.0ms

simplify484.0ms

prune16.0ms

localize51.0ms

rewrite68.0ms

series143.0ms

simplify50.0ms

prune429.0ms

localize41.0ms

rewrite111.0ms

series120.0ms

simplify87.0ms

prune597.0ms

localize43.0ms

rewrite42.0ms

series146.0ms

simplify49.0ms

prune181.0ms

localize44.0ms

rewrite43.0ms

series137.0ms

simplify41.0ms

prune182.0ms

regimes403.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample3.8s

Profiling