Details

analyze70.0ms

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

sample25.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
0.0ms	9×	body	80	nan
0.0ms	7×	body	80	invalid

simplify65.0ms

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)))))
0.3b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.4b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

rewrite37.0ms

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

series39.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(*.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)))))
17.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
7.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify34.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5835	1498

prune121.0ms

Filtered

87 candidates to 111 candidates (-27.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	101	10	111
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	103	10	113

Merged error: 0.0b

Counts

113 → 10

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 a 1/3) 9)
0.3b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.4b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
8.4b	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

12.0ms	(*.f64 (-.f64 a 1/3) 9)
9.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
16.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))

series72.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(*.f64 (-.f64 a 1/3) 9)
24.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
9.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
32.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))

simplify37.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	4944	1594
1	4944	1594

prune115.0ms

Filtered

98 candidates to 123 candidates (-25.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	119	4	123
Fresh	6	3	9
Picked	0	1	1
Done	0	0	0
Total	125	8	133

Merged error: 0b

Counts

133 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 a 1/3))
0.0b	(+.f64 (-.f64 a 1/3) (*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9))))
0.3b	(*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9)))
0.6b	(/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

147×	`add-sqr-sqrt_binary64`
116×	`*-un-lft-identity_binary64`
110×	`times-frac_binary64`
75×	`sqrt-prod_binary64`
58×	`add-cube-cbrt_binary64`
46×	`associate-l_binary64`
29×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
22×	`associate-r_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64`
9×	`add-log-exp_binary64` `unswap-sqr_binary64`
8×	`associate-/r*_binary64`
7×	`flip3--_binary64` `flip--_binary64`
6×	`frac-add_binary64` `sqrt-div_binary64`
5×	`cbrt-undiv_binary64` `associate-/l*_binary64` `div-exp_binary64`
4×	`cbrt-unprod_binary64` `associate-/r/_binary64` `prod-exp_binary64`
3×	`associate-r/_binary64` `div-inv_binary64` `frac-times_binary64` `associate-l/_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `pow-div_binary64` `sqrt-pow1_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-+l+_binary64` `associate-+l-_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 206

Calls

4 calls:

6.0ms	(sqrt.f64 (-.f64 a 1/3))
7.0ms	(+.f64 (-.f64 a 1/3) (*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9))))
28.0ms	(*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9)))
9.0ms	(/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 a 1/3))
14.0ms	(+.f64 (-.f64 a 1/3) (*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9))))
16.0ms	(*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9)))
5.0ms	(/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3)))

simplify47.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5637	2910

prune214.0ms

Filtered

147 candidates to 218 candidates (-48.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	215	3	218
Fresh	4	2	6
Picked	1	0	1
Done	1	0	1
Total	221	5	226

Merged error: 0b

Counts

226 → 5

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
17×	`sqrt-prod_binary64`
12×	`add-cube-cbrt_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-log-exp_binary64`
8×	`associate-l_binary64`
7×	`pow1_binary64`
6×	`associate-/r*_binary64` `times-frac_binary64` `sqrt-div_binary64`
4×	`flip3--_binary64` `flip--_binary64` `associate-*l/_binary64`
3×	`associate-r_binary64` `distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `div-exp_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-+l+_binary64` `associate-+l-_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64` `-commutative_binary64`

Counts

4 → 90

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 a 1/3))
12.0ms	(+.f64 (-.f64 a 1/3) (/.f64 (*.f64 (sqrt.f64 (-.f64 a 1/3)) rand) (sqrt.f64 9)))
9.0ms	(/.f64 (*.f64 (sqrt.f64 (-.f64 a 1/3)) rand) (sqrt.f64 9))
7.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) rand)

series46.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 a 1/3))
11.0ms	(+.f64 (-.f64 a 1/3) (/.f64 (*.f64 (sqrt.f64 (-.f64 a 1/3)) rand) (sqrt.f64 9)))
16.0ms	(/.f64 (*.f64 (sqrt.f64 (-.f64 a 1/3)) rand) (sqrt.f64 9))
14.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) rand)

simplify44.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5068	1229

prune68.0ms

Filtered

78 candidates to 102 candidates (-30.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	102	5	107

Merged error: 0b

Counts

107 → 5

regimes56.0ms

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	22	12
1	22	12

end0.0ms

sample625.0ms

Algorithm

intervals

Results

454.0ms	8000×	body	80	valid
15.0ms	264×	body	80	invalid
13.0ms	260×	body	80	nan

Details

analyze70.0ms

sample25.0ms

simplify65.0ms

prune6.0ms

localize8.0ms

rewrite37.0ms

series39.0ms

simplify34.0ms

prune121.0ms

localize8.0ms

rewrite48.0ms

series72.0ms

simplify37.0ms

prune115.0ms

localize9.0ms

rewrite61.0ms

series40.0ms

simplify47.0ms

prune214.0ms

localize7.0ms

rewrite34.0ms

series46.0ms

simplify44.0ms

prune68.0ms

regimes56.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample625.0ms

Profiling