Details

analyze80.0ms

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	8×	body	80	nan
0.0ms	5×	body	80	invalid

simplify97.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	1050	21
1	1050	21

prune7.0ms

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

localize9.0ms

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)))
0.6b	(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))

series143.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(*.f64 (-.f64 a 1/3) 9)
42.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
60.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
21.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify83.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4930	2229
1	4930	2229

prune139.0ms

Filtered

87 candidates to 111 candidates (-27.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	104	7	111
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	106	7	113

Merged error: 0b

Counts

113 → 7

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 a 1/3) 9)
0.2b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.6b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
7.7b	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))

rewrite41.0ms

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:

7.0ms	(*.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))
18.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))

series158.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(*.f64 (-.f64 a 1/3) 9)
58.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
17.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
60.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))

simplify58.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4994	2381
1	4994	2381

prune147.0ms

Filtered

98 candidates to 123 candidates (-25.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	123	7	130

Merged error: 0b

Counts

130 → 7

localize17.0ms

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

rewrite116.0ms

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:

3.0ms	(sqrt.f64 (-.f64 a 1/3))
54.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
26.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
12.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))

series179.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(sqrt.f64 (-.f64 a 1/3))
39.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
72.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
54.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))

simplify127.0ms

Algorithm

egg-herbie

Counts

340 → 340

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5127	8870

prune329.0ms

Filtered

198 candidates to 340 candidates (-71.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	340	0	340
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	340	7	347

Merged error: 0b

Counts

347 → 7

localize10.0ms

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)
0.6b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.9b	(/.f64 1 (/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand))

rewrite63.0ms

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:

24.0ms	(.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)
7.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
10.0ms	(/.f64 1 (/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand))

series213.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)) rand))))
74.0ms	(/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand)
24.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
69.0ms	(/.f64 1 (/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand))

simplify87.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5512	4290

prune183.0ms

Filtered

129 candidates to 178 candidates (-38.0%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	178	7	185

Merged error: 0b

Counts

185 → 7

regimes35.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	24
1	24	24

end0.0ms

sample614.0ms

Algorithm

intervals

Results

443.0ms	8000×	body	80	valid
13.0ms	261×	body	80	nan
13.0ms	237×	body	80	invalid

Details

analyze80.0ms

sample22.0ms

simplify97.0ms

prune7.0ms

localize9.0ms

rewrite37.0ms

series143.0ms

simplify83.0ms

prune139.0ms

localize8.0ms

rewrite41.0ms

series158.0ms

simplify58.0ms

prune147.0ms

localize17.0ms

rewrite116.0ms

series179.0ms

simplify127.0ms

prune329.0ms

localize10.0ms

rewrite63.0ms

series213.0ms

simplify87.0ms

prune183.0ms

regimes35.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample614.0ms

Profiling