Details

analyze552.0ms

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

sample37.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
1.0ms	14×	body	80	nan
1.0ms	11×	body	80	invalid

simplify913.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (393.0ms)

Iter	Nodes	Cost
0	2978	54
1	2978	54

prune8.0ms

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: 24.0b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
26.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
26.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `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×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 52

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
22.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series207.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
37.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
77.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify118.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	4907	1222
1	4907	1222

prune109.0ms

Filtered

50 candidates to 64 candidates (-28.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	58	6	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	6	65

Merged error: 8.6b

Counts

65 → 6

localize27.0ms

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
3.2b	(/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (-.f64 b (.f64 2 (/.f64 (*.f64 a c) b)))))
4.9b	(/.f64 (*.f64 a c) b)
26.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
11.0ms	(/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (-.f64 b (.f64 2 (/.f64 (*.f64 a c) b)))))
5.0ms	(/.f64 (*.f64 a c) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series224.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
114.0ms	(/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (-.f64 b (.f64 2 (/.f64 (*.f64 a c) b)))))
17.0ms	(/.f64 (*.f64 a c) b)
60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify114.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4940	1598
1	4940	1598

prune129.0ms

Filtered

63 candidates to 88 candidates (-39.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	87	7	94

Merged error: 7.7b

Counts

94 → 7

localize30.0ms

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
2.8b	(.f64 (/.f64 a (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 c (cbrt.f64 b)))
3.2b	(/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (-.f64 b (.f64 2 (.f64 (/.f64 a (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 c (cbrt.f64 b)))))))
26.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
34×	`times-frac_binary64`
30×	`*-un-lft-identity_binary64` `add-exp-log_binary64`
23×	`add-cbrt-cube_binary64`
22×	`associate-r_binary64` `add-cube-cbrt_binary64`
11×	`cbrt-prod_binary64`
9×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
7×	`pow1_binary64` `associate-l_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `unswap-sqr_binary64`
4×	`distribute-lft-out--_binary64`
3×	`flip3--_binary64` `div-inv_binary64` `flip--_binary64` `sqrt-prod_binary64`
2×	`associate-/r/_binary64` `distribute-rgt-neg-in_binary64` `difference-of-squares_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `frac-times_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 114

Calls

4 calls:

4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
18.0ms	(.f64 (/.f64 a (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 c (cbrt.f64 b)))
11.0ms	(/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (-.f64 b (.f64 2 (.f64 (/.f64 a (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 c (cbrt.f64 b)))))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
38.0ms	(.f64 (/.f64 a (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 c (cbrt.f64 b)))
141.0ms	(/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (-.f64 b (.f64 2 (.f64 (/.f64 a (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 c (cbrt.f64 b)))))))
64.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify88.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5036	2497

prune190.0ms

Filtered

93 candidates to 126 candidates (-35.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	124	9	133

Merged error: 7.2b

Counts

133 → 9

localize35.0ms

Local error

Found 4 expressions with local error:

7.3b	(cbrt.f64 (/.f64 a (*.f64 (cbrt.f64 b) (cbrt.f64 b))))
7.3b	(cbrt.f64 (/.f64 a (*.f64 (cbrt.f64 b) (cbrt.f64 b))))
7.3b	(cbrt.f64 (/.f64 a (*.f64 (cbrt.f64 b) (cbrt.f64 b))))
26.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`cbrt-div_binary64` `pow1/3_binary64` `div-inv_binary64` `sqrt-prod_binary64`
2×	`sqrt-div_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`

Counts

4 → 63

Calls

4 calls:

5.0ms	(cbrt.f64 (/.f64 a (*.f64 (cbrt.f64 b) (cbrt.f64 b))))
7.0ms	(cbrt.f64 (/.f64 a (*.f64 (cbrt.f64 b) (cbrt.f64 b))))
5.0ms	(cbrt.f64 (/.f64 a (*.f64 (cbrt.f64 b) (cbrt.f64 b))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(cbrt.f64 (/.f64 a (*.f64 (cbrt.f64 b) (cbrt.f64 b))))
116.0ms	(cbrt.f64 (/.f64 a (*.f64 (cbrt.f64 b) (cbrt.f64 b))))
110.0ms	(cbrt.f64 (/.f64 a (*.f64 (cbrt.f64 b) (cbrt.f64 b))))
60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5006	1392

prune130.0ms

Filtered

66 candidates to 75 candidates (-13.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	75	9	84

Merged error: 7.2b

Counts

84 → 9

regimes178.0ms

Accuracy

92.4% (1.2b remaining)

Error of 6.6b against oracle of 5.5b and baseline of 20.8b

bsearch90.0ms

Steps

Iters	Range		Point
8	2.5370093648000586e+35	7.898821145874956e+37	7.829617407859173e+37
9	-9.790520146599943e+156	-1.0920483647301425e+151	-1.1277279800686637e+154

simplify25.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	780	247
1	780	247

end0.0ms

sample979.0ms

Algorithm

intervals

Results

692.0ms	8000×	body	80	valid
51.0ms	643×	body	80	nan
31.0ms	373×	body	80	invalid

Details

analyze552.0ms

sample37.0ms

simplify913.0ms

prune8.0ms

localize25.0ms

rewrite38.0ms

series207.0ms

simplify118.0ms

prune109.0ms

localize27.0ms

rewrite26.0ms

series224.0ms

simplify114.0ms

prune129.0ms

localize30.0ms

rewrite43.0ms

series278.0ms

simplify88.0ms

prune190.0ms

localize35.0ms

rewrite24.0ms

series397.0ms

simplify67.0ms

prune130.0ms

regimes178.0ms

bsearch90.0ms

simplify25.0ms

end0.0ms

sample979.0ms

Profiling