Details

analyze260.0ms

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

sample51.0ms

Algorithm

intervals

Results

17.0ms	108×	body	320	valid
9.0ms	93×	body	160	valid
8.0ms	284×	pre	80	true
4.0ms	20×	body	640	valid
2.0ms	35×	body	80	valid
1.0ms	28×	body	80	nan

simplify249.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (247.0ms)

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: 51.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))) b) (.f64 a 2.0))
24.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)

rewrite34.0ms

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:

7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
12.0ms	(/.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)

series81.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
33.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))) b) (.f64 a 2.0))
19.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)

simplify54.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4921	1309
1	4921	1309

prune98.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	4	83

Merged error: 0.1b

Counts

83 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
0.1b	(-.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))
0.2b	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))

rewrite43.0ms

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:

6.0ms	(+.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))
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))
11.0ms	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))

series167.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+.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))
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))
78.0ms	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4978	3969
1	4978	3969

prune244.0ms

Filtered

124 candidates to 167 candidates (-34.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	161	6	167
Fresh	2	0	2
Picked	1	0	1
Done	1	0	1
Total	165	6	171

Merged error: 0b

Counts

171 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
0.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
0.1b	(-.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)))))

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:

5.0ms	(sqrt.f64 (-.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))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
9.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))

series112.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(sqrt.f64 (-.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))))
14.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
61.0ms	(/.f64 c (+.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 (60.0ms)

Iter	Nodes	Cost
0	4930	1299
1	4930	1299

prune111.0ms

Filtered

68 candidates to 83 candidates (-22.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	83	6	89

Merged error: 0b

Counts

89 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
0.0b	(/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))
0.3b	(.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4.0 a)))))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
31×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`
17×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
8×	`pow1_binary64`
7×	`distribute-lft-out_binary64`
6×	`add-log-exp_binary64`
4×	`associate-/r*_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64`
3×	`associate-l_binary64` `unswap-sqr_binary64` `associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `div-inv_binary64` `flip--_binary64` `flip-+_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` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `pow-flip_binary64` `-commutative_binary64`

Counts

4 → 104

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
9.0ms	(/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))
13.0ms	(.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4.0 a)))))))

series125.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
33.0ms	(/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))))
11.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))
62.0ms	(.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4.0 a)))))))

simplify75.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4911	1733
1	4911	1733

prune110.0ms

Filtered

77 candidates to 116 candidates (-50.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	116	6	122

Merged error: 0b

Counts

122 → 6

regimes169.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	84	19
1	84	19

end0.0ms

sample1.4s

Algorithm

intervals

Results

493.0ms	3575×	body	320	valid
283.0ms	3024×	body	160	valid
253.0ms	8840×	pre	80	true
92.0ms	501×	body	640	valid
44.0ms	900×	body	80	valid
42.0ms	840×	body	80	nan

Details

analyze260.0ms

sample51.0ms

simplify249.0ms

prune7.0ms

localize10.0ms

rewrite34.0ms

series81.0ms

simplify54.0ms

prune98.0ms

localize13.0ms

rewrite43.0ms

series167.0ms

simplify62.0ms

prune244.0ms

localize15.0ms

rewrite26.0ms

series112.0ms

simplify69.0ms

prune111.0ms

localize13.0ms

rewrite35.0ms

series125.0ms

simplify75.0ms

prune110.0ms

regimes169.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling