Details

analyze82.0ms

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

sample24.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
0.0ms	7×	body	80	nan
0.0ms	5×	body	80	invalid

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	1048	14
1	1048	14

prune19.0ms

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

localize15.0ms

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))

rewrite64.0ms

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:

12.0ms	(*.f64 (-.f64 a 1/3) 9)
25.0ms	(.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)))
9.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series58.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(*.f64 (-.f64 a 1/3) 9)
16.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
27.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
11.0ms	(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

prune161.0ms

Filtered

87 candidates to 111 candidates (-27.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	107	6	113

Merged error: 0.0b

Counts

113 → 6

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

rewrite99.0ms

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))))
10.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
15.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))

series49.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 a 1/3))
14.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
14.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
17.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))

simplify77.0ms

Algorithm

egg-herbie

Counts

340 → 340

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5034	5658

prune374.0ms

Filtered

198 candidates to 340 candidates (-71.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	338	2	340
Fresh	2	2	4
Picked	0	1	1
Done	1	0	1
Total	341	5	346

Merged error: 0b

Counts

346 → 5

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

rewrite39.0ms

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`
35×	`associate-l_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`
6×	`flip3--_binary64` `associate-r_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` `prod-exp_binary64` `associate-/l_binary64` `flip-+_binary64` `associate-l/_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `div-inv_binary64` `div-exp_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 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) 1/3)))
7.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
12.0ms	(*.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) 1/3)

series48.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 a 1/3))
13.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) 1/3)))
14.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
16.0ms	(*.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) 1/3)

simplify40.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5513	2088

prune193.0ms

Filtered

120 candidates to 158 candidates (-31.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	158	5	163

Merged error: 0b

Counts

163 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

210×	`times-frac_binary64`
157×	`add-sqr-sqrt_binary64`
155×	`*-un-lft-identity_binary64`
117×	`add-cube-cbrt_binary64`
91×	`sqrt-prod_binary64`
52×	`sqrt-div_binary64`
33×	`associate-/l*_binary64`
32×	`frac-times_binary64`
26×	`flip3--_binary64` `flip--_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
16×	`associate-r/_binary64` `associate-l*_binary64`
12×	`flip3-+_binary64` `flip-+_binary64`
11×	`associate-/r*_binary64` `pow1_binary64`
10×	`associate-/r/_binary64` `associate-*l/_binary64`
6×	`div-inv_binary64`
5×	`associate-r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
2×	`unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`associate-/l/_binary64` `distribute-lft-out_binary64`

Counts

4 → 275

Calls

4 calls:

44.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) 3) 1))
7.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
12.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) 3)
48.0ms	(.f64 (sqrt.f64 (-.f64 a 1/3)) (.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) 3) 1)))

series81.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) 3) 1))
14.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
17.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) 3)
16.0ms	(.f64 (sqrt.f64 (-.f64 a 1/3)) (.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) 3) 1)))

simplify66.0ms

Algorithm

egg-herbie

Counts

287 → 287

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5317	5212

prune429.0ms

Filtered

201 candidates to 287 candidates (-42.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	287	0	287
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	287	5	292

Merged error: 0b

Counts

292 → 5

regimes93.0ms

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

sample703.0ms

Algorithm

intervals

Results

516.0ms	8000×	body	80	valid
17.0ms	267×	body	80	invalid
15.0ms	257×	body	80	nan

Details

analyze82.0ms

sample24.0ms

simplify68.0ms

prune19.0ms

localize15.0ms

rewrite64.0ms

series58.0ms

simplify34.0ms

prune161.0ms

localize10.0ms

rewrite99.0ms

series49.0ms

simplify77.0ms

prune374.0ms

localize8.0ms

rewrite39.0ms

series48.0ms

simplify40.0ms

prune193.0ms

localize10.0ms

rewrite127.0ms

series81.0ms

simplify66.0ms

prune429.0ms

regimes93.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample703.0ms

Profiling