Details

analyze128.0ms

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

sample37.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
1.0ms	7×	body	80	nan
0.0ms	5×	body	80	invalid

simplify254.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (250.0ms)

Iter	Nodes	Cost
0	4908	20
1	4908	20

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.1b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 a (/.f64 1.0 3.0)) (+.f64 1.0 (.f64 (/.f64 1.0 (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))) rand)))
0.2b	(.f64 (/.f64 1.0 (sqrt.f64 (.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))) rand)
0.3b	(/.f64 1.0 (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0)))))
0.4b	(sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

14.0ms	(.f64 (-.f64 a (/.f64 1.0 3.0)) (+.f64 1.0 (.f64 (/.f64 1.0 (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))) rand)))
15.0ms	(.f64 (/.f64 1.0 (sqrt.f64 (.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))) rand)
11.0ms	(/.f64 1.0 (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0)))))
8.0ms	(sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))

series61.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(.f64 (-.f64 a (/.f64 1.0 3.0)) (+.f64 1.0 (.f64 (/.f64 1.0 (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))) rand)))
24.0ms	(.f64 (/.f64 1.0 (sqrt.f64 (.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))) rand)
12.0ms	(/.f64 1.0 (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0)))))
8.0ms	(sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))

simplify63.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4974	2418
1	4974	2418

prune314.0ms

Filtered

105 candidates to 126 candidates (-20.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	118	8	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	8	127

Merged error: 0.0b

Counts

127 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 9.0 (-.f64 a (/.f64 1.0 3.0)))
0.1b	(.f64 (-.f64 a (/.f64 1.0 3.0)) (+.f64 1.0 (.f64 1.0 (/.f64 rand (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))))))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0)))))
0.4b	(sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

10.0ms	(*.f64 9.0 (-.f64 a (/.f64 1.0 3.0)))
12.0ms	(.f64 (-.f64 a (/.f64 1.0 3.0)) (+.f64 1.0 (.f64 1.0 (/.f64 rand (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))))))
10.0ms	(/.f64 rand (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0)))))
8.0ms	(sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))

series49.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(*.f64 9.0 (-.f64 a (/.f64 1.0 3.0)))
18.0ms	(.f64 (-.f64 a (/.f64 1.0 3.0)) (+.f64 1.0 (.f64 1.0 (/.f64 rand (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))))))
18.0ms	(/.f64 rand (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0)))))
7.0ms	(sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))

simplify39.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5053	2006

prune180.0ms

Filtered

91 candidates to 114 candidates (-25.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	115	7	122

Merged error: 0.0b

Counts

122 → 7

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b

(sqrt.f64 (-.f64 a (/.f64 1.0 3.0)))

0.1b

(*.f64 (-.f64 a (/.f64 1.0 3.0)) (+.f64 1.0 (*.f64 1.0 (/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0)))))))

0.3b

(/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

403×	`times-frac_binary64`
310×	`add-sqr-sqrt_binary64`
234×	`sqrt-prod_binary64`
232×	`*-un-lft-identity_binary64`
182×	`add-cube-cbrt_binary64`
50×	`difference-of-squares_binary64`
25×	`distribute-lft-out--_binary64`
22×	`associate-/l*_binary64`
11×	`div-inv_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-/r*_binary64`
6×	`pow1_binary64` `associate-l_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`frac-times_binary64` `sqrt-div_binary64`
3×	`flip3-+_binary64` `add-log-exp_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip-+_binary64`
2×	`associate-r/_binary64` `associate-/r/_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `*-commutative_binary64`

Counts

3 → 295

Calls

3 calls:

9.0ms

(sqrt.f64 (-.f64 a (/.f64 1.0 3.0)))

12.0ms

(*.f64 (-.f64 a (/.f64 1.0 3.0)) (+.f64 1.0 (*.f64 1.0 (/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0)))))))

18.0ms

(/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))))

series45.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms

(sqrt.f64 (-.f64 a (/.f64 1.0 3.0)))

19.0ms

(*.f64 (-.f64 a (/.f64 1.0 3.0)) (+.f64 1.0 (*.f64 1.0 (/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0)))))))

21.0ms

(/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))))

simplify86.0ms

Algorithm

egg-herbie

Counts

304 → 304

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4985	7011
1	4985	7011

prune406.0ms

Filtered

171 candidates to 304 candidates (-77.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	302	2	304
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	306	5	311

Merged error: 0b

Counts

311 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 a (/.f64 1.0 3.0)))
0.1b	(.f64 (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))) (+.f64 1.0 (.f64 1.0 (/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0)))))))
0.3b	(/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))))
0.4b	(.f64 (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))) (.f64 (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))) (+.f64 1.0 (*.f64 1.0 (/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))))))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

404×	`times-frac_binary64`
321×	`add-sqr-sqrt_binary64`
247×	`sqrt-prod_binary64`
238×	`*-un-lft-identity_binary64`
186×	`add-cube-cbrt_binary64`
52×	`difference-of-squares_binary64`
46×	`sqrt-div_binary64`
32×	`frac-times_binary64`
26×	`distribute-lft-out--_binary64`
23×	`flip3--_binary64` `flip--_binary64`
22×	`associate-/l*_binary64`
18×	`associate-l_binary64`
16×	`associate-*r/_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`flip3-+_binary64` `pow1_binary64` `flip-+_binary64`
11×	`div-inv_binary64`
10×	`associate-*l/_binary64`
9×	`associate-/r*_binary64`
5×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64`
3×	`cbrt-undiv_binary64` `div-exp_binary64`
2×	`associate-/r/_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 353

Calls

4 calls:

10.0ms	(sqrt.f64 (-.f64 a (/.f64 1.0 3.0)))
13.0ms	(.f64 (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))) (+.f64 1.0 (.f64 1.0 (/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0)))))))
18.0ms	(/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))))
22.0ms	(.f64 (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))) (.f64 (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))) (+.f64 1.0 (*.f64 1.0 (/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))))))))

series91.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 a (/.f64 1.0 3.0)))
37.0ms	(.f64 (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))) (+.f64 1.0 (.f64 1.0 (/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0)))))))
26.0ms	(/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))))
22.0ms	(.f64 (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))) (.f64 (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))) (+.f64 1.0 (*.f64 1.0 (/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))))))))

simplify74.0ms

Algorithm

egg-herbie

Counts

365 → 365

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5058	9323

prune681.0ms

Filtered

214 candidates to 365 candidates (-70.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	365	0	365
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	365	5	370

Merged error: 0b

Counts

370 → 5

regimes127.0ms

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	34	21
1	34	21

end0.0ms

sample668.0ms

Algorithm

intervals

Results

480.0ms	8000×	body	80	valid
16.0ms	267×	body	80	invalid
14.0ms	257×	body	80	nan

Details

analyze128.0ms

sample37.0ms

simplify254.0ms

prune5.0ms

localize10.0ms

rewrite51.0ms

series61.0ms

simplify63.0ms

prune314.0ms

localize10.0ms

rewrite45.0ms

series49.0ms

simplify39.0ms

prune180.0ms

localize11.0ms

rewrite58.0ms

series45.0ms

simplify86.0ms

prune406.0ms

localize12.0ms

rewrite87.0ms

series91.0ms

simplify74.0ms

prune681.0ms

regimes127.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample668.0ms

Profiling