Details

analyze5.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50.1%	13
49.9%	0%	50.1%	14

sample17.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify106.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	4859	18
1	4859	18

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.0b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6)))))
0.0b	(.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))
0.0b	(/.f64 4/3 (.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6))))))
0.2b	(.f64 (.f64 v v) 6)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`associate-*r/_binary64`
18×	`flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`pow1_binary64`
12×	`*-un-lft-identity_binary64` `frac-times_binary64`
11×	`add-cube-cbrt_binary64`
10×	`cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64`
9×	`associate-l_binary64`
8×	`associate-/r/_binary64`
7×	`pow-prod-down_binary64`
6×	`associate-*l/_binary64`
4×	`add-log-exp_binary64` `sqrt-prod_binary64`
3×	`cbrt-undiv_binary64` `unswap-sqr_binary64` `associate-/l_binary64` `times-frac_binary64` `div-exp_binary64` `-commutative_binary64`
2×	`difference-of-squares_binary64`
1×	`associate-/r*_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 108

Calls

4 calls:

12.0ms	(.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6)))))
10.0ms	(.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))
12.0ms	(/.f64 4/3 (.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6))))))
6.0ms	(.f64 (.f64 v v) 6)

series46.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6)))))
12.0ms	(.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))
19.0ms	(/.f64 4/3 (.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6))))))
3.0ms	(.f64 (.f64 v v) 6)

simplify39.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5526	2123

prune98.0ms

Filtered

88 candidates to 120 candidates (-36.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	119	3	122

Merged error: 0b

Counts

122 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (log.f64 (exp.f64 (.f64 (.f64 v v) 6))))))
0.0b	(/.f64 4/3 (.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (log.f64 (exp.f64 (.f64 (*.f64 v v) 6))))))))
0.2b	(.f64 (.f64 v v) 6)
2.5b	(log.f64 (exp.f64 (.f64 (.f64 v v) 6)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
19×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
13×	`pow1_binary64`
12×	`flip3--_binary64` `associate-r_binary64` `associate-*r/_binary64` `flip--_binary64` `sqrt-div_binary64`
11×	`add-cube-cbrt_binary64`
8×	`associate-/r/_binary64` `frac-times_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64` `sqrt-prod_binary64`
6×	`associate-l_binary64`
5×	`add-log-exp_binary64`
4×	`pow-prod-down_binary64` `log-pow_binary64` `associate-*l/_binary64`
3×	`log-prod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `div-exp_binary64`
2×	`distribute-lft-out--_binary64` `*-commutative_binary64`
1×	`associate-/r*_binary64` `rem-log-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `exp-to-pow_binary64` `exp-prod_binary64`

Counts

4 → 99

Calls

4 calls:

11.0ms	(.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (log.f64 (exp.f64 (.f64 (.f64 v v) 6))))))
16.0ms	(/.f64 4/3 (.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (log.f64 (exp.f64 (.f64 (*.f64 v v) 6))))))))
6.0ms	(.f64 (.f64 v v) 6)
2.0ms	(log.f64 (exp.f64 (.f64 (.f64 v v) 6)))

series36.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (log.f64 (exp.f64 (.f64 (.f64 v v) 6))))))
19.0ms	(/.f64 4/3 (.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (log.f64 (exp.f64 (.f64 (*.f64 v v) 6))))))))
3.0ms	(.f64 (.f64 v v) 6)
4.0ms	(log.f64 (exp.f64 (.f64 (.f64 v v) 6)))

simplify37.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5363	1711

prune83.0ms

Filtered

81 candidates to 111 candidates (-37.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	111	3	114

Merged error: 0b

Counts

114 → 3

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 v v) (*.f64 v v))
0.2b	(.f64 (.f64 v v) 6)
1.0b	(.f64 (/.f64 4/3 (.f64 PI.f64 (.f64 (-.f64 1 (pow.f64 v 6)) (sqrt.f64 (-.f64 4 (.f64 36 (pow.f64 v 4))))))) (.f64 (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 v v) (.f64 v v)) (.f64 1 (.f64 v v)))) (sqrt.f64 (+.f64 2 (.f64 (*.f64 v v) 6)))))
1.0b	(/.f64 4/3 (.f64 PI.f64 (.f64 (-.f64 1 (pow.f64 v 6)) (sqrt.f64 (-.f64 4 (*.f64 36 (pow.f64 v 4)))))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

125×	`pow1_binary64`
62×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
36×	`pow-prod-up_binary64`
32×	`cbrt-unprod_binary64` `associate-*r/_binary64` `prod-exp_binary64`
29×	`pow-prod-down_binary64`
24×	`frac-times_binary64` `sqrt-div_binary64`
22×	`pow-sqr_binary64`
18×	`pow-plus_binary64`
17×	`associate-l_binary64`
16×	`associate-/r/_binary64`
13×	`pow2_binary64`
12×	`flip3-+_binary64` `flip3--_binary64` `flip--_binary64` `flip-+_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`-un-lft-identity_binary64` `cbrt-undiv_binary64` `add-cube-cbrt_binary64` `div-exp_binary64` `associate-l/_binary64`
6×	`times-frac_binary64`
5×	`associate-r_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/l_binary64` `-commutative_binary64`
2×	`unswap-sqr_binary64` `div-inv_binary64`
1×	`associate-/r*_binary64` `swap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 172

Calls

4 calls:

9.0ms	(.f64 (.f64 v v) (*.f64 v v))
6.0ms	(.f64 (.f64 v v) 6)
36.0ms	(.f64 (/.f64 4/3 (.f64 PI.f64 (.f64 (-.f64 1 (pow.f64 v 6)) (sqrt.f64 (-.f64 4 (.f64 36 (pow.f64 v 4))))))) (.f64 (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 v v) (.f64 v v)) (.f64 1 (.f64 v v)))) (sqrt.f64 (+.f64 2 (.f64 (*.f64 v v) 6)))))
16.0ms	(/.f64 4/3 (.f64 PI.f64 (.f64 (-.f64 1 (pow.f64 v 6)) (sqrt.f64 (-.f64 4 (*.f64 36 (pow.f64 v 4)))))))

series59.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(.f64 (.f64 v v) (*.f64 v v))
3.0ms	(.f64 (.f64 v v) 6)
26.0ms	(.f64 (/.f64 4/3 (.f64 PI.f64 (.f64 (-.f64 1 (pow.f64 v 6)) (sqrt.f64 (-.f64 4 (.f64 36 (pow.f64 v 4))))))) (.f64 (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 v v) (.f64 v v)) (.f64 1 (.f64 v v)))) (sqrt.f64 (+.f64 2 (.f64 (*.f64 v v) 6)))))
25.0ms	(/.f64 4/3 (.f64 PI.f64 (.f64 (-.f64 1 (pow.f64 v 6)) (sqrt.f64 (-.f64 4 (*.f64 36 (pow.f64 v 4)))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4920	3496
1	4920	3496

prune205.0ms

Filtered

98 candidates to 184 candidates (-87.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	184	3	187

Merged error: 0b

Counts

187 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))
0.0b	(/.f64 (/.f64 4/3 PI.f64) (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))))
0.2b	(.f64 (.f64 v v) 6)
1.0b	(/.f64 4/3 PI.f64)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac_binary64`
36×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
30×	`add-cube-cbrt_binary64`
25×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`associate-/l*_binary64`
12×	`flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
11×	`pow1_binary64`
9×	`associate-r_binary64`
8×	`associate-/r/_binary64` `frac-times_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
4×	`pow-prod-down_binary64` `associate-/r_binary64` `add-log-exp_binary64` `associate-r/_binary64` `div-inv_binary64` `sqrt-prod_binary64` `associate-*l/_binary64`
3×	`unswap-sqr_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `*-commutative_binary64`
1×	`associate-/l/_binary64`

Counts

4 → 132

Calls

4 calls:

9.0ms	(.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))
12.0ms	(/.f64 (/.f64 4/3 PI.f64) (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))))
6.0ms	(.f64 (.f64 v v) 6)
3.0ms	(/.f64 4/3 PI.f64)

series34.0ms

Counts

4 → 10

Calls

4 calls:

9.0ms	(.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))
19.0ms	(/.f64 (/.f64 4/3 PI.f64) (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6)))))
6.0ms	(.f64 (.f64 v v) 6)
0.0ms	(/.f64 4/3 PI.f64)

simplify56.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5143	2232

prune100.0ms

Filtered

107 candidates to 142 candidates (-32.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	142	3	145

Merged error: 0b

Counts

145 → 3

regimes36.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	20
1	45	20

end0.0ms

sample491.0ms

Algorithm

intervals

Results

396.0ms	8000×	body	80	valid
0.0ms	1×	body	80	nan

Details

analyze5.0ms

sample17.0ms

simplify106.0ms

prune11.0ms

localize10.0ms

rewrite44.0ms

series46.0ms

simplify39.0ms

prune98.0ms

localize12.0ms

rewrite40.0ms

series36.0ms

simplify37.0ms

prune83.0ms

localize26.0ms

rewrite76.0ms

series59.0ms

simplify58.0ms

prune205.0ms

localize10.0ms

rewrite36.0ms

series34.0ms

simplify56.0ms

prune100.0ms

regimes36.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample491.0ms

Profiling