Details

analyze266.0ms

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

sample40.0ms

Algorithm

intervals

Results

13.0ms	139×	body	160	valid
10.0ms	295×	pre	80	true
6.0ms	117×	body	80	valid
2.0ms	39×	body	80	nan

simplify315.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (307.0ms)

Iter	Nodes	Cost
0	1835	24
1	1835	24

prune4.0ms

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: 27.6b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
27.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite31.0ms

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:

4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

series273.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
33.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
104.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
69.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

simplify85.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4988	1963
1	4988	1963

prune85.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	7	83

Merged error: 0.4b

Counts

83 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.2b	(/.f64 (/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.4b	(/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`associate-/l*_binary64`
10×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
6×	`associate-/r/_binary64`
5×	`associate-/r*_binary64` `distribute-lft-out_binary64`
4×	`flip3-+_binary64` `pow1_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`clear-num_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 → 98

Calls

4 calls:

4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
15.0ms	(/.f64 (/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

series458.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
62.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
154.0ms	(/.f64 (/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
205.0ms	(/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

simplify71.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5150	3003

prune128.0ms

Filtered

76 candidates to 110 candidates (-44.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	100	10	110
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	107	10	117

Merged error: 0b

Counts

117 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.3b	(/.f64 1 (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (/.f64 2 (*.f64 c -4))))
0.4b	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (/.f64 2 (*.f64 c -4)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-exp-log_binary64`
27×	`add-cbrt-cube_binary64`
16×	`prod-exp_binary64` `div-exp_binary64`
13×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`pow1_binary64` `add-cube-cbrt_binary64`
8×	`add-log-exp_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64`
7×	`associate-r_binary64`
6×	`times-frac_binary64`
5×	`flip3-+_binary64` `associate-/r/_binary64` `flip-+_binary64`
4×	`1-exp_binary64` `associate-l_binary64` `rec-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
3×	`associate-/l*_binary64`
2×	`pow-prod-down_binary64` `distribute-lft-out_binary64` `associate-*r/_binary64` `div-inv_binary64` `pow-flip_binary64`
1×	`associate-/r_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `unswap-sqr_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 96

Calls

4 calls:

4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
16.0ms	(/.f64 1 (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (/.f64 2 (*.f64 c -4))))
13.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (/.f64 2 (*.f64 c -4)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
63.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
127.0ms	(/.f64 1 (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (/.f64 2 (*.f64 c -4))))
79.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (/.f64 2 (*.f64 c -4)))

simplify61.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5030	2571

prune106.0ms

Filtered

74 candidates to 108 candidates (-45.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	109	9	118

Merged error: 0b

Counts

118 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
0.2b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))

rewrite25.0ms

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 c (*.f64 a 4))))
8.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))

series330.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
174.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
35.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
62.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))

simplify116.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4897	1965
1	4897	1965

prune78.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	84	8	92

Merged error: 0b

Counts

92 → 8

regimes59.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	69	36
1	69	36

end0.0ms

sample1.1s

Algorithm

intervals

Results

422.0ms	4431×	body	160	valid
259.0ms	8831×	pre	80	true
176.0ms	3568×	body	80	valid
39.0ms	831×	body	80	nan
0.0ms	1×	body	320	valid

Details

analyze266.0ms

sample40.0ms

simplify315.0ms

prune4.0ms

localize10.0ms

rewrite31.0ms

series273.0ms

simplify85.0ms

prune85.0ms

localize14.0ms

rewrite41.0ms

series458.0ms

simplify71.0ms

prune128.0ms

localize13.0ms

rewrite43.0ms

series302.0ms

simplify61.0ms

prune106.0ms

localize12.0ms

rewrite25.0ms

series330.0ms

simplify116.0ms

prune78.0ms

regimes59.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample1.1s

Profiling