Details

analyze268.0ms

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

sample44.0ms

Algorithm

intervals

Results

14.0ms	148×	body	160	valid
8.0ms	294×	pre	80	true
6.0ms	47×	body	320	valid
3.0ms	61×	body	80	valid
2.0ms	38×	body	80	nan

simplify252.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (249.0ms)

Iter	Nodes	Cost
0	1931	16
1	1931	16

prune9.0ms

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: 44.8b

Counts

2 → 1

localize11.0ms

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 (.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))
38.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 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 4.0 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)

series82.0ms

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))
35.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))) b) (.f64 a 2.0))
18.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)

simplify51.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4921	1309
1	4921	1309

prune100.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	5	83

Merged error: 0.2b

Counts

83 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

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

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:

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))
13.0ms	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.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))

series154.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+.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))
72.0ms	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
53.0ms	(/.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))

simplify69.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4978	3969
1	4978	3969

prune237.0ms

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	4	0	4
Picked	1	0	1
Done	0	0	0
Total	165	7	172

Merged error: 0b

Counts

172 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

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)))))
0.2b	(/.f64 a (/.f64 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))) 2.0))
0.3b	(/.f64 (/.f64 (neg.f64 (.f64 4.0 a)) 1) (/.f64 a (/.f64 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))) 2.0)))

rewrite785.0ms

Algorithm

rewrite-expression-head

Rules

17936×	`times-frac_binary64`
7690×	`*-un-lft-identity_binary64`
6368×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
661×	`distribute-lft-out_binary64`
540×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
498×	`div-inv_binary64`
465×	`associate-/r/_binary64`
241×	`associate-/r*_binary64`
220×	`flip3-+_binary64` `flip-+_binary64`
61×	`add-exp-log_binary64`
47×	`add-cbrt-cube_binary64`
45×	`div-exp_binary64`
31×	`cbrt-undiv_binary64`
28×	`associate-/l*_binary64`
6×	`add-log-exp_binary64`
4×	`pow1_binary64` `1-exp_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64`
2×	`div-sub_binary64` `distribute-frac-neg_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `neg-sub0_binary64` `flip--_binary64`

Counts

4 → 4469

Calls

4 calls:

5.0ms	(-.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)))))
28.0ms	(/.f64 a (/.f64 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))) 2.0))
112.0ms	(/.f64 (/.f64 (neg.f64 (.f64 4.0 a)) 1) (/.f64 a (/.f64 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))) 2.0)))

series184.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
57.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
63.0ms	(/.f64 a (/.f64 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))) 2.0))
53.0ms	(/.f64 (/.f64 (neg.f64 (.f64 4.0 a)) 1) (/.f64 a (/.f64 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))) 2.0)))

simplify1.5s

Algorithm

egg-herbie

Counts

4481 → 4481

Iterations

Useful iterations: 0 (174.0ms)

Iter	Nodes	Cost
0	4995	233354
1	4995	233354

prune52.3s

Filtered

2506 candidates to 4481 candidates (-78.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	4480	1	4481
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	4482	6	4488

Merged error: 0b

Counts

4488 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
0.1b	(/.f64 (neg.f64 c) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
0.2b	(/.f64 2.0 (.f64 4.0 (/.f64 (neg.f64 c) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))))))
0.3b	(/.f64 1 (/.f64 2.0 (.f64 4.0 (/.f64 (neg.f64 c) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

79×	`times-frac_binary64`
71×	`*-un-lft-identity_binary64`
49×	`add-cube-cbrt_binary64` `add-exp-log_binary64` `add-sqr-sqrt_binary64`
29×	`add-cbrt-cube_binary64`
25×	`div-exp_binary64`
16×	`associate-/l*_binary64`
15×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
13×	`associate-/r*_binary64` `cbrt-undiv_binary64`
11×	`distribute-lft-out_binary64`
8×	`associate-/r/_binary64` `prod-exp_binary64`
7×	`div-inv_binary64`
6×	`add-log-exp_binary64`
5×	`pow1_binary64` `associate-*r/_binary64` `neg-mul-1_binary64`
4×	`cbrt-unprod_binary64` `1-exp_binary64` `rec-exp_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `neg-sub0_binary64` `div-sub_binary64` `inv-pow_binary64` `distribute-frac-neg_binary64` `flip--_binary64` `pow-flip_binary64` `flip-+_binary64`

Counts

4 → 169

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
9.0ms	(/.f64 (neg.f64 c) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
14.0ms	(/.f64 2.0 (.f64 4.0 (/.f64 (neg.f64 c) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))))))
16.0ms	(/.f64 1 (/.f64 2.0 (.f64 4.0 (/.f64 (neg.f64 c) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))))))

series170.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
56.0ms	(/.f64 (neg.f64 c) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
41.0ms	(/.f64 2.0 (.f64 4.0 (/.f64 (neg.f64 c) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))))))
63.0ms	(/.f64 1 (/.f64 2.0 (.f64 4.0 (/.f64 (neg.f64 c) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))))))

simplify76.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4946	3812
1	4946	3812

prune171.0ms

Filtered

120 candidates to 181 candidates (-50.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	181	6	187

Merged error: 0b

Counts

187 → 6

regimes162.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	23
1	70	23

end0.0ms

sample1.2s

Algorithm

intervals

Results

461.0ms	4848×	body	160	valid
256.0ms	8975×	pre	80	true
189.0ms	1360×	body	320	valid
89.0ms	1792×	body	80	valid
46.0ms	975×	body	80	nan

Details

analyze268.0ms

sample44.0ms

simplify252.0ms

prune9.0ms

localize11.0ms

rewrite31.0ms

series82.0ms

simplify51.0ms

prune100.0ms

localize13.0ms

rewrite45.0ms

series154.0ms

simplify69.0ms

prune237.0ms

localize16.0ms

rewrite785.0ms

series184.0ms

simplify1.5s

prune52.3s

localize14.0ms

rewrite50.0ms

series170.0ms

simplify76.0ms

prune171.0ms

regimes162.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling