Details

analyze507.0ms

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
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

sample38.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
2.0ms	27×	body	80	nan
1.0ms	11×	body	80	invalid

simplify272.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (269.0ms)

Iter	Nodes	Cost
0	3532	37
1	3532	37

prune8.0ms

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: 20.1b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

1.5b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

rewrite28.0ms

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:

9.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
18.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
21.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

simplify79.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4879	1082
1	4879	1082

prune144.0ms

Filtered

58 candidates to 73 candidates (-25.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	66	7	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	7	74

Merged error: 6.9b

Counts

74 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

10.3b	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))) b)
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `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`
1×	`sub-neg_binary64` `diff-log_binary64` `difference-of-squares_binary64`

Counts

4 → 57

Calls

4 calls:

17.0ms	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))) b)
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
20.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5004	935

prune130.0ms

Filtered

58 candidates to 69 candidates (-19.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	69	7	76

Merged error: 6.9b

Counts

76 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

5.2b	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
18.5b	(-.f64 (neg.f64 b) (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))))
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
10×	`sqrt-prod_binary64`
9×	`add-cube-cbrt_binary64`
8×	`add-log-exp_binary64` `pow1_binary64` `log-prod_binary64` `exp-sum_binary64`
6×	`sqrt-div_binary64` `exp-prod_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`pow1/2_binary64` `log-pow_binary64` `sqrt-pow1_binary64` `difference-of-squares_binary64`
2×	`diff-log_binary64` `exp-diff_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `log-div_binary64`
1×	`sub-neg_binary64` `associate--l-_binary64` `neg-sub0_binary64` `rem-exp-log_binary64` `distribute-rgt-neg-in_binary64` `neg-log_binary64`

Counts

4 → 70

Calls

4 calls:

7.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
16.0ms	(-.f64 (neg.f64 b) (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
20.0ms	(-.f64 (neg.f64 b) (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

simplify81.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4900	1140
1	4900	1140

prune130.0ms

Filtered

61 candidates to 82 candidates (-34.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	81	8	89

Merged error: 6.9b

Counts

89 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

1.5b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
2.2b	(/.f64 (.f64 c 2.0) (-.f64 (-.f64 (.f64 2.0 (/.f64 (*.f64 a c) b)) b) b))
5.6b	(/.f64 (*.f64 a c) b)
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

rewrite33.0ms

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×	`associate-/r*_binary64` `add-log-exp_binary64` `times-frac_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `sqrt-prod_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`diff-log_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_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` `rem-sqrt-square_binary64` `neg-log_binary64`

Counts

4 → 80

Calls

4 calls:

9.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
13.0ms	(/.f64 (.f64 c 2.0) (-.f64 (-.f64 (.f64 2.0 (/.f64 (*.f64 a c) b)) b) b))
5.0ms	(/.f64 (*.f64 a c) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
26.0ms	(/.f64 (.f64 c 2.0) (-.f64 (-.f64 (.f64 2.0 (/.f64 (*.f64 a c) b)) b) b))
6.0ms	(/.f64 (*.f64 a c) b)
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5243	1214

prune110.0ms

Filtered

67 candidates to 92 candidates (-37.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	92	8	100

Merged error: 6.1b

Counts

100 → 8

regimes243.0ms

Accuracy

92% (1.0b remaining)

Error of 7.8b against oracle of 6.8b and baseline of 19.9b

bsearch45.0ms

Steps

Iters	Range		Point
5	9.803037244659017e+91	3.4843437681471106e+92	2.485959951540932e+92
9	-1.3495067265639191e+126	-3.595720007866579e+117	-4.250178820340957e+119

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	151	129
1	151	129

end0.0ms

sample994.0ms

Algorithm

intervals

Results

698.0ms	8000×	body	80	valid
58.0ms	687×	body	80	nan
36.0ms	421×	body	80	invalid

Details

analyze507.0ms

sample38.0ms

simplify272.0ms

prune8.0ms

localize21.0ms

rewrite28.0ms

series77.0ms

simplify79.0ms

prune144.0ms

localize24.0ms

rewrite32.0ms

series76.0ms

simplify48.0ms

prune130.0ms

localize25.0ms

rewrite34.0ms

series75.0ms

simplify81.0ms

prune130.0ms

localize28.0ms

rewrite33.0ms

series70.0ms

simplify47.0ms

prune110.0ms

regimes243.0ms

bsearch45.0ms

simplify3.0ms

end0.0ms

sample994.0ms

Profiling