Details

analyze99.0ms

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

sample23.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
0.0ms	9×	body	80	invalid
0.0ms	9×	body	80	nan

simplify189.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (186.0ms)

Iter	Nodes	Cost
0	4908	20
1	4908	20

prune6.0ms

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: 0.2b

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)))))
1.3b	(sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))

rewrite52.0ms

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:

12.0ms	(.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)))
17.0ms	(.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))))

series68.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(.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)))
26.0ms	(.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))))

simplify56.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4974	2418
1	4974	2418

prune268.0ms

Filtered

105 candidates to 126 candidates (-20.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	116	10	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	10	127

Merged error: 0.0b

Counts

127 → 10

localize12.0ms

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)))))
1.3b	(sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))

rewrite43.0ms

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)))
11.0ms	(.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))))))))
11.0ms	(/.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))))

series52.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(*.f64 9.0 (-.f64 a (/.f64 1.0 3.0)))
21.0ms	(.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))))))))
19.0ms	(/.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))))

simplify38.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5053	2006

prune185.0ms

Filtered

91 candidates to 114 candidates (-25.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	115	9	124

Merged error: 0.0b

Counts

124 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

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)))))
1.3b	(sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))
8.7b	(.f64 (-.f64 a (/.f64 1.0 3.0)) (.f64 (/.f64 1.0 (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))) rand))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

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))))
21.0ms	(.f64 (-.f64 a (/.f64 1.0 3.0)) (.f64 (/.f64 1.0 (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))) rand))

series72.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(.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)))))
7.0ms	(sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))
27.0ms	(.f64 (-.f64 a (/.f64 1.0 3.0)) (.f64 (/.f64 1.0 (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))) rand))

simplify51.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5182	2263

prune254.0ms

Filtered

105 candidates to 123 candidates (-17.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	123	9	132

Merged error: 0.0b

Counts

132 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (-.f64 a (/.f64 1.0 3.0)) (/.f64 1.0 (sqrt.f64 (*.f64 (-.f64 a (/.f64 1.0 3.0)) 9.0)))) rand)
0.3b	(.f64 (-.f64 a (/.f64 1.0 3.0)) (/.f64 1.0 (sqrt.f64 (.f64 (-.f64 a (/.f64 1.0 3.0)) 9.0))))
0.3b	(/.f64 1.0 (sqrt.f64 (*.f64 (-.f64 a (/.f64 1.0 3.0)) 9.0)))
1.3b	(sqrt.f64 (*.f64 (-.f64 a (/.f64 1.0 3.0)) 9.0))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

22.0ms	(.f64 (.f64 (-.f64 a (/.f64 1.0 3.0)) (/.f64 1.0 (sqrt.f64 (*.f64 (-.f64 a (/.f64 1.0 3.0)) 9.0)))) rand)
22.0ms	(.f64 (-.f64 a (/.f64 1.0 3.0)) (/.f64 1.0 (sqrt.f64 (.f64 (-.f64 a (/.f64 1.0 3.0)) 9.0))))
11.0ms	(/.f64 1.0 (sqrt.f64 (*.f64 (-.f64 a (/.f64 1.0 3.0)) 9.0)))
8.0ms	(sqrt.f64 (*.f64 (-.f64 a (/.f64 1.0 3.0)) 9.0))

series57.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(.f64 (.f64 (-.f64 a (/.f64 1.0 3.0)) (/.f64 1.0 (sqrt.f64 (*.f64 (-.f64 a (/.f64 1.0 3.0)) 9.0)))) rand)
12.0ms	(.f64 (-.f64 a (/.f64 1.0 3.0)) (/.f64 1.0 (sqrt.f64 (.f64 (-.f64 a (/.f64 1.0 3.0)) 9.0))))
12.0ms	(/.f64 1.0 (sqrt.f64 (*.f64 (-.f64 a (/.f64 1.0 3.0)) 9.0)))
8.0ms	(sqrt.f64 (*.f64 (-.f64 a (/.f64 1.0 3.0)) 9.0))

simplify40.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5545	2434

prune213.0ms

Filtered

102 candidates to 127 candidates (-24.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	2	4	6
Picked	0	1	1
Done	1	1	2
Total	129	7	136

Merged error: 0.0b

Counts

136 → 7

regimes331.0ms

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	36	26
1	36	26

end0.0ms

sample614.0ms

Algorithm

intervals

Results

446.0ms	8000×	body	80	valid
17.0ms	283×	body	80	invalid
12.0ms	245×	body	80	nan

Details

analyze99.0ms

sample23.0ms

simplify189.0ms

prune6.0ms

localize10.0ms

rewrite52.0ms

series68.0ms

simplify56.0ms

prune268.0ms

localize12.0ms

rewrite43.0ms

series52.0ms

simplify38.0ms

prune185.0ms

localize11.0ms

rewrite58.0ms

series72.0ms

simplify51.0ms

prune254.0ms

localize11.0ms

rewrite67.0ms

series57.0ms

simplify40.0ms

prune213.0ms

regimes331.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample614.0ms

Profiling