Details

analyze546.0ms

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
12.5%	87.4%	0.1%	6
20.3%	73.3%	6.4%	7
27.3%	66.3%	6.4%	8
38.2%	53%	8.7%	9
46%	40.6%	13.4%	10
49.9%	35.1%	15%	11
54.9%	26.9%	18.1%	12
57.4%	22%	20.6%	13
59.7%	18%	22.4%	14

sample43.0ms

Algorithm

intervals

Results

27.0ms	256×	body	80	valid
1.0ms	14×	body	80	nan
1.0ms	7×	body	80	invalid

simplify673.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (267.0ms)

Iter	Nodes	Cost
0	3270	37
1	3270	37

prune21.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 21.9b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

1.1b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))) b)
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
8×	`sqrt-prod_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `flip--_binary64` `sqrt-div_binary64`
3×	`diff-log_binary64` `distribute-lft-out--_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`associate--l-_binary64` `neg-sub0_binary64` `distribute-rgt-neg-in_binary64` `neg-log_binary64`

Counts

4 → 61

Calls

4 calls:

10.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

series87.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))
18.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))) b)
22.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
28.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

simplify78.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4874	1082
1	4874	1082

prune146.0ms

Filtered

58 candidates to 73 candidates (-25.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	65	8	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	8	74

Merged error: 10.6b

Counts

74 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

8.4b	(-.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4.0 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
8×	`add-log-exp_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`sqrt-div_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
2×	`diff-log_binary64`
1×	`sub-neg_binary64` `associate--l-_binary64` `neg-sub0_binary64` `neg-log_binary64` `difference-of-squares_binary64`

Counts

4 → 59

Calls

4 calls:

5.0ms	(-.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4.0 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

series73.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(-.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4.0 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

simplify57.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5629	983

prune137.0ms

Filtered

58 candidates to 71 candidates (-22.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	71	8	79

Merged error: 10.6b

Counts

79 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

10.5b	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4.0 a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))) b)
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
25.9b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
25.9b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `cbrt-prod_binary64`
5×	`pow1_binary64`
4×	`cbrt-div_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`sqrt-prod_binary64`
2×	`pow1/3_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 52

Calls

4 calls:

10.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4.0 a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

series112.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4.0 a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))) b)
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
26.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
32.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

simplify43.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5043	1108

prune147.0ms

Filtered

58 candidates to 64 candidates (-10.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	63	9	72

Merged error: 10.6b

Counts

72 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

1.1b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))
3.4b	(/.f64 (-.f64 (-.f64 (.f64 2.0 (/.f64 (.f64 c a) b)) b) b) (*.f64 2.0 a))
7.1b	(/.f64 (*.f64 c a) b)
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-cube-cbrt_binary64`
8×	`add-log-exp_binary64` `times-frac_binary64`
6×	`associate-/l*_binary64`
5×	`pow1_binary64`
4×	`associate-/r*_binary64` `cbrt-undiv_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `sqrt-prod_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `distribute-rgt-neg-in_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `neg-log_binary64`

Counts

4 → 81

Calls

4 calls:

10.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))
13.0ms	(/.f64 (-.f64 (-.f64 (.f64 2.0 (/.f64 (.f64 c a) b)) b) b) (*.f64 2.0 a))
5.0ms	(/.f64 (*.f64 c a) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

series64.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))))
20.0ms	(/.f64 (-.f64 (-.f64 (.f64 2.0 (/.f64 (.f64 c a) b)) b) b) (*.f64 2.0 a))
6.0ms	(/.f64 (*.f64 c a) b)
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

simplify47.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5193	1257

prune123.0ms

Filtered

68 candidates to 93 candidates (-36.8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	86	7	93
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	88	14	102

Merged error: 9.4b

Counts

102 → 14

regimes372.0ms

Accuracy

92.7% (0.9b remaining)

Error of 7.5b against oracle of 6.5b and baseline of 19.4b

bsearch60.0ms

Steps

Iters	Range		Point
9	4.133558150256362e+100	2.0370040434721257e+109	1.827145917976237e+108
9	-7.796098687113796e+132	-3.0791589294299004e+127	-3.6419385251769567e+130

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	170	123
1	170	123

end0.0ms

sample991.0ms

Algorithm

intervals

Results

697.0ms	8000×	body	80	valid
53.0ms	663×	body	80	nan
33.0ms	375×	body	80	invalid

Details

analyze546.0ms

sample43.0ms

simplify673.0ms

prune21.0ms

localize23.0ms

rewrite32.0ms

series87.0ms

simplify78.0ms

prune146.0ms

localize26.0ms

rewrite20.0ms

series73.0ms

simplify57.0ms

prune137.0ms

localize25.0ms

rewrite25.0ms

series112.0ms

simplify43.0ms

prune147.0ms

localize24.0ms

rewrite34.0ms

series64.0ms

simplify47.0ms

prune123.0ms

regimes372.0ms

bsearch60.0ms

simplify4.0ms

end0.0ms

sample991.0ms

Profiling