Details

analyze75.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
6.2%	43.7%	50%	5
9.4%	28.1%	62.5%	6
12.5%	25%	62.5%	7
15.6%	15.6%	68.8%	8
16.8%	14.4%	68.8%	9
18.5%	8.8%	72.7%	10
19.2%	7.7%	73.1%	11
20.1%	4.6%	75.2%	12
20.5%	4%	75.5%	13
21%	2.4%	76.6%	14

sample26.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
1.0ms	13×	body	80	invalid
0.0ms	9×	body	80	nan

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	1048	14
1	1048	14

prune6.0ms

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: 0.1b

Counts

2 → 2

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 a 1/3) 9)
0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
0.1b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.3b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
11×	`pow1_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
8×	`associate-*l/_binary64`
7×	`associate-r_binary64`
6×	`flip3--_binary64` `flip--_binary64`
5×	`sqrt-prod_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `frac-times_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`cbrt-unprod_binary64` `associate-r/_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `-commutative_binary64`
1×	`pow1/2_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 99

Calls

4 calls:

7.0ms	(*.f64 (-.f64 a 1/3) 9)
14.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
8.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(*.f64 (-.f64 a 1/3) 9)
12.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
17.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))

simplify35.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5835	1498

prune119.0ms

Filtered

89 candidates to 111 candidates (-24.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	105	6	111
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	107	6	113

Merged error: 0.0b

Counts

113 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 a 1/3))
0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
0.2b	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
0.3b	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

372×	`times-frac_binary64`
248×	`add-sqr-sqrt_binary64`
247×	`*-un-lft-identity_binary64`
223×	`sqrt-prod_binary64`
191×	`add-cube-cbrt_binary64`
33×	`associate-/l*_binary64`
27×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
18×	`sqrt-div_binary64`
16×	`associate-/r/_binary64`
14×	`associate-/r*_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`flip3--_binary64` `flip--_binary64`
9×	`div-inv_binary64`
7×	`pow1_binary64`
5×	`associate-l_binary64`
4×	`add-log-exp_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `frac-times_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 328

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 a 1/3))
48.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
7.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
14.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))

series44.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 a 1/3))
13.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
12.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
15.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))

simplify73.0ms

Algorithm

egg-herbie

Counts

340 → 340

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5034	5658

prune262.0ms

Filtered

198 candidates to 340 candidates (-71.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	338	2	340
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	340	6	346

Merged error: 0.0b

Counts

346 → 6

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 a 1/3))
0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))))
0.2b	(*.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))
0.3b	(/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt_binary64`
58×	`*-un-lft-identity_binary64`
50×	`times-frac_binary64`
41×	`sqrt-prod_binary64`
40×	`add-cube-cbrt_binary64`
33×	`associate-r_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow1_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`associate-/r_binary64` `associate-l*_binary64`
6×	`flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `frac-times_binary64`
3×	`flip3-+_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `prod-exp_binary64` `associate-/l_binary64` `flip-+_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 146

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 a 1/3))
9.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))))
15.0ms	(*.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))
7.0ms	(/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 a 1/3))
12.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))))
14.0ms	(*.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))
7.0ms	(/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))

simplify48.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5582	2073

prune132.0ms

Filtered

116 candidates to 158 candidates (-36.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	156	2	158
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	157	7	164

Merged error: 0.0b

Counts

164 → 7

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 a 1/3))
0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (.f64 1/3 rand) (sqrt.f64 (-.f64 a 1/3)))))
0.3b	(/.f64 (*.f64 1/3 rand) (sqrt.f64 (-.f64 a 1/3)))
0.4b	(*.f64 1/3 rand)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
15×	`sqrt-prod_binary64`
13×	`add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow1_binary64`
8×	`associate-/r_binary64` `associate-l*_binary64` `times-frac_binary64`
7×	`associate-r_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `frac-times_binary64` `sqrt-div_binary64`
3×	`flip3-+_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `flip-+_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `div-exp_binary64` `associate-l/_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 99

Calls

4 calls:

3.0ms	(sqrt.f64 (-.f64 a 1/3))
17.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (.f64 1/3 rand) (sqrt.f64 (-.f64 a 1/3)))))
8.0ms	(/.f64 (*.f64 1/3 rand) (sqrt.f64 (-.f64 a 1/3)))
4.0ms	(*.f64 1/3 rand)

series33.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 a 1/3))
12.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (.f64 1/3 rand) (sqrt.f64 (-.f64 a 1/3)))))
14.0ms	(/.f64 (*.f64 1/3 rand) (sqrt.f64 (-.f64 a 1/3)))
2.0ms	(*.f64 1/3 rand)

simplify47.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4962	1355
1	4962	1355

prune74.0ms

Filtered

80 candidates to 111 candidates (-38.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	111	7	118

Merged error: 0.0b

Counts

118 → 7

regimes67.0ms

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	24	14
1	24	14

end0.0ms

sample643.0ms

Algorithm

intervals

Results

467.0ms	8000×	body	80	valid
17.0ms	255×	body	80	invalid
15.0ms	281×	body	80	nan

Details

analyze75.0ms

sample26.0ms

simplify66.0ms

prune6.0ms

localize8.0ms

rewrite36.0ms

series38.0ms

simplify35.0ms

prune119.0ms

localize9.0ms

rewrite96.0ms

series44.0ms

simplify73.0ms

prune262.0ms

localize8.0ms

rewrite40.0ms

series38.0ms

simplify48.0ms

prune132.0ms

localize8.0ms

rewrite35.0ms

series33.0ms

simplify47.0ms

prune74.0ms

regimes67.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample643.0ms

Profiling