Details

analyze264.0ms

Algorithm

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

sample43.0ms

Algorithm

intervals

Results

14.0ms	154×	body	160	valid
8.0ms	290×	pre	80	true
5.0ms	40×	body	320	valid
3.0ms	62×	body	80	valid
2.0ms	34×	body	80	nan

simplify258.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (255.0ms)

Iter	Nodes	Cost
0	1931	16
1	1931	16

prune7.0ms

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: 42.3b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))) b) (.f64 a 2.0))
37.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))) b) (.f64 a 2.0))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)

series87.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
37.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))) b) (.f64 a 2.0))
20.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)

simplify50.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4921	1309
1	4921	1309

prune94.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	3	83

Merged error: 0.2b

Counts

83 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
0.2b	(/.f64 (/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))) (.f64 a 2.0))
0.3b	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac_binary64`
78×	`*-un-lft-identity_binary64`
38×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
36×	`associate-/l*_binary64`
20×	`distribute-lft-out_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
8×	`add-log-exp_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`associate-/r/_binary64`
5×	`associate-/r*_binary64`
4×	`flip3-+_binary64` `pow1_binary64` `div-inv_binary64` `flip-+_binary64`
3×	`div-sub_binary64` `distribute-frac-neg_binary64`
2×	`cbrt-unprod_binary64` `neg-sub0_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 155

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
15.0ms	(/.f64 (/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))) (.f64 a 2.0))
10.0ms	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))

series164.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
20.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
58.0ms	(/.f64 (/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))) (.f64 a 2.0))
74.0ms	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4978	3969
1	4978	3969

prune242.0ms

Filtered

124 candidates to 167 candidates (-34.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	160	7	167
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	163	7	170

Merged error: 0b

Counts

170 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/r*_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 71

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
8.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))

series113.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
60.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
22.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))

simplify69.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4930	1299
1	4930	1299

prune107.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	84	6	90

Merged error: 0b

Counts

90 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))) (*.f64 a 2.0))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
0.3b	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))) (*.f64 a 2.0)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`*-un-lft-identity_binary64`
9×	`pow1_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`cbrt-unprod_binary64` `prod-exp_binary64` `associate-/l*_binary64` `times-frac_binary64`
4×	`associate-l_binary64` `associate-*l/_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip-+_binary64`
2×	`distribute-lft-out_binary64` `neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `associate-/r/_binary64` `distribute-rgt-neg-in_binary64`
1×	`associate-/r_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-r_binary64` `neg-sub0_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `+-commutative_binary64` `distribute-frac-neg_binary64` `flip--_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 77

Calls

4 calls:

13.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))) (*.f64 a 2.0))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
13.0ms	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))) (*.f64 a 2.0)))

series113.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))) (*.f64 a 2.0))
13.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
19.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
56.0ms	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))) (*.f64 a 2.0)))

simplify50.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5093	1567

prune87.0ms

Filtered

67 candidates to 89 candidates (-32.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	89	6	95

Merged error: 0b

Counts

95 → 6

regimes155.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	68	23
1	68	23

end0.0ms

sample1.2s

Algorithm

intervals

Results

453.0ms	4853×	body	160	valid
255.0ms	8888×	pre	80	true
189.0ms	1371×	body	320	valid
89.0ms	1776×	body	80	valid
41.0ms	888×	body	80	nan

Details

analyze264.0ms

sample43.0ms

simplify258.0ms

prune7.0ms

localize13.0ms

rewrite32.0ms

series87.0ms

simplify50.0ms

prune94.0ms

localize13.0ms

rewrite45.0ms

series164.0ms

simplify64.0ms

prune242.0ms

localize12.0ms

rewrite26.0ms

series113.0ms

simplify69.0ms

prune107.0ms

localize12.0ms

rewrite39.0ms

series113.0ms

simplify50.0ms

prune87.0ms

regimes155.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling