Details

analyze78.0ms

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

sample22.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
0.0ms	9×	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

prune8.0ms

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)))))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.4b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

rewrite41.0ms

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)
17.0ms	(.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))

series36.0ms

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)))))
14.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify37.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5835	1498

prune166.0ms

Filtered

87 candidates to 111 candidates (-27.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	102	9	111
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	104	9	113

Merged error: 0b

Counts

113 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)) rand))))
0.2b	(/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand)
0.4b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.8b	(/.f64 1 (/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac_binary64`
69×	`*-un-lft-identity_binary64`
68×	`add-sqr-sqrt_binary64`
64×	`add-cube-cbrt_binary64`
19×	`associate-/r*_binary64` `add-exp-log_binary64`
17×	`sqrt-prod_binary64`
13×	`add-cbrt-cube_binary64`
10×	`pow1_binary64`
8×	`div-exp_binary64`
7×	`associate-/l*_binary64` `div-inv_binary64`
6×	`associate-*l/_binary64`
5×	`flip3--_binary64` `associate-r_binary64` `associate-l_binary64` `flip--_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `frac-times_binary64` `sqrt-div_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `distribute-lft-out_binary64` `1-exp_binary64` `associate-*r/_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`pow1/2_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `associate-/r/_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `inv-pow_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 166

Calls

4 calls:

21.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)) rand))))
8.0ms	(/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand)
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
10.0ms	(/.f64 1 (/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand))

series60.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)) rand))))
22.0ms	(/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand)
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
20.0ms	(/.f64 1 (/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand))

simplify51.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5424	2806

prune215.0ms

Filtered

126 candidates to 178 candidates (-41.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	178	9	187

Merged error: 0b

Counts

187 → 9

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 (sqrt.f64 (-.f64 a 1/3)) 3))))
0.2b	(*.f64 (sqrt.f64 (-.f64 a 1/3)) 3)
0.2b	(/.f64 rand (*.f64 (sqrt.f64 (-.f64 a 1/3)) 3))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 a 1/3))
12.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (.f64 (sqrt.f64 (-.f64 a 1/3)) 3))))
8.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) 3)
8.0ms	(/.f64 rand (*.f64 (sqrt.f64 (-.f64 a 1/3)) 3))

series38.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt.f64 (-.f64 a 1/3))
12.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (.f64 (sqrt.f64 (-.f64 a 1/3)) 3))))
6.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) 3)
14.0ms	(/.f64 rand (*.f64 (sqrt.f64 (-.f64 a 1/3)) 3))

simplify35.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5110	1456

prune139.0ms

Filtered

86 candidates to 109 candidates (-26.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	110	8	118

Merged error: 0b

Counts

118 → 8

localize10.0ms

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))) 3)))
0.2b	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
0.3b	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) 3)

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

210×	`times-frac_binary64`
154×	`add-sqr-sqrt_binary64`
153×	`*-un-lft-identity_binary64`
115×	`add-cube-cbrt_binary64`
85×	`sqrt-prod_binary64`
33×	`associate-/l*_binary64`
18×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`sqrt-div_binary64`
11×	`associate-/r*_binary64`
10×	`associate-/r/_binary64`
9×	`flip3--_binary64` `flip--_binary64`
7×	`pow1_binary64`
6×	`div-inv_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 → 235

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 a 1/3))
32.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) 3)))
7.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
12.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) 3)

series42.0ms

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 rand (sqrt.f64 (-.f64 a 1/3))) 3)))
12.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
14.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) 3)

simplify78.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4930	3856
1	4930	3856

prune265.0ms

Filtered

175 candidates to 247 candidates (-41.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	247	0	247
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	247	8	255

Merged error: 0b

Counts

255 → 8

regimes100.0ms

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	25	16
1	25	16

end0.0ms

sample605.0ms

Algorithm

intervals

Results

442.0ms	8000×	body	80	valid
15.0ms	287×	body	80	invalid
13.0ms	263×	body	80	nan

Details

analyze78.0ms

sample22.0ms

simplify66.0ms

prune8.0ms

localize8.0ms

rewrite41.0ms

series36.0ms

simplify37.0ms

prune166.0ms

localize9.0ms

rewrite53.0ms

series60.0ms

simplify51.0ms

prune215.0ms

localize8.0ms

rewrite34.0ms

series38.0ms

simplify35.0ms

prune139.0ms

localize10.0ms

rewrite69.0ms

series42.0ms

simplify78.0ms

prune265.0ms

regimes100.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample605.0ms

Profiling