Details

analyze392.0ms

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
12.5%	37.5%	50%	5
15.6%	31.2%	53.2%	6
17.2%	26.5%	56.3%	7
18%	22.6%	59.4%	8
18.3%	19.9%	61.8%	9
18.5%	17.8%	63.7%	10
18.6%	16.3%	65.1%	11
18.7%	15.2%	66.1%	12
18.7%	14.4%	66.9%	13
18.7%	13.8%	67.4%	14

sample89.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
18.0ms	32×	body	640	nan
17.0ms	29×	body	1280	nan
11.0ms	85×	body	80	overflowed
4.0ms	15×	body	320	nan
1.0ms	23×	body	80	nan
1.0ms	7×	body	160	nan
0.0ms	4×	body	80	invalid

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5065	14

prune9.0ms

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: 0.3b

Counts

2 → 2

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
0.3b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
0.3b	(.f64 (.f64 2 PI.f64) n)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac_binary64`
42×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
33×	`add-cube-cbrt_binary64`
26×	`add-exp-log_binary64`
22×	`pow-unpow_binary64`
18×	`sqrt-prod_binary64`
14×	`pow1_binary64`
10×	`add-cbrt-cube_binary64`
9×	`prod-exp_binary64`
8×	`sqr-pow_binary64` `unpow-prod-down_binary64`
6×	`pow-prod-down_binary64` `associate-/r*_binary64` `difference-of-squares_binary64` `pow-exp_binary64`
5×	`associate-/l*_binary64` `div-exp_binary64`
3×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `pow-pow_binary64` `distribute-lft-out--_binary64`
2×	`pow-to-exp_binary64` `div-sub_binary64` `pow-sub_binary64` `div-inv_binary64`
1×	`associate-/l/_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`

Counts

3 → 115

Calls

3 calls:

10.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
7.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
5.0ms	(.f64 (.f64 2 PI.f64) n)

series71.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
46.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
5.0ms	(.f64 (.f64 2 PI.f64) n)

simplify37.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5282	2253

prune177.0ms

Filtered

81 candidates to 124 candidates (-53.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	113	11	124
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	115	11	126

Merged error: 0.0b

Counts

126 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
0.2b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
0.3b	(.f64 (.f64 2 PI.f64) n)
0.3b	(.f64 (.f64 2 PI.f64) n)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

127×	`add-exp-log_binary64`
67×	`prod-exp_binary64`
36×	`pow-exp_binary64`
30×	`div-exp_binary64`
20×	`pow1_binary64`
19×	`add-cbrt-cube_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
14×	`times-frac_binary64`
13×	`pow-unpow_binary64`
12×	`pow-to-exp_binary64`
9×	`pow-prod-down_binary64`
7×	`cbrt-unprod_binary64`
6×	`associate-r_binary64`
5×	`associate-/l*_binary64`
4×	`add-log-exp_binary64`
3×	`pow-pow_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64`
2×	`cbrt-undiv_binary64` `associate-l_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`associate-/r*_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 118

Calls

4 calls:

7.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
12.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
5.0ms	(.f64 (.f64 2 PI.f64) n)
6.0ms	(.f64 (.f64 2 PI.f64) n)

series106.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
70.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
5.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(.f64 (.f64 2 PI.f64) n)

simplify35.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5037	1629

prune129.0ms

Filtered

67 candidates to 130 candidates (-94.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	125	5	130
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	131	10	141

Merged error: 0.0b

Counts

141 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2)))))
0.2b	(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))))
0.3b	(.f64 (.f64 2 PI.f64) n)
0.3b	(.f64 (.f64 2 PI.f64) n)

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

1787×	`times-frac_binary64`
712×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
518×	`sqrt-prod_binary64`
173×	`associate-/r*_binary64`
124×	`sqr-pow_binary64` `unpow-prod-down_binary64`
100×	`add-exp-log_binary64`
58×	`div-exp_binary64`
37×	`div-inv_binary64`
28×	`add-cbrt-cube_binary64`
18×	`prod-exp_binary64`
15×	`pow1_binary64`
12×	`pow-exp_binary64`
9×	`cbrt-undiv_binary64` `associate-/l*_binary64`
7×	`1-exp_binary64` `rec-exp_binary64`
6×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `associate-/r/_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64`
2×	`associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`inv-pow_binary64` `pow-flip_binary64`

Counts

4 → 865

Calls

4 calls:

37.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2)))))
15.0ms	(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))))
5.0ms	(.f64 (.f64 2 PI.f64) n)
6.0ms	(.f64 (.f64 2 PI.f64) n)

series154.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2)))))
76.0ms	(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))))
5.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(.f64 (.f64 2 PI.f64) n)

simplify187.0ms

Algorithm

egg-herbie

Counts

877 → 877

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5630	30347

prune1.8s

Filtered

455 candidates to 877 candidates (-92.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	874	3	877
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	877	10	887

Merged error: 0b

Counts

887 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (/.f64 1 (sqrt.f64 (.f64 (.f64 2 PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))))
0.3b	(.f64 (.f64 2 PI.f64) n)
0.3b	(.f64 (.f64 2 PI.f64) n)
0.3b	(/.f64 1 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-exp-log_binary64`
62×	`prod-exp_binary64`
28×	`add-cbrt-cube_binary64`
24×	`times-frac_binary64`
23×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
18×	`associate-l_binary64`
14×	`div-exp_binary64`
12×	`cbrt-unprod_binary64` `pow-exp_binary64`
10×	`pow-prod-down_binary64`
7×	`associate-r_binary64` `1-exp_binary64` `rec-exp_binary64` `sqrt-prod_binary64`
5×	`pow-flip_binary64`
4×	`pow-to-exp_binary64` `associate-/r*_binary64` `add-log-exp_binary64`
3×	`cbrt-undiv_binary64` `sqrt-pow1_binary64` `associate-/l_binary64` `-commutative_binary64`
2×	`div-inv_binary64`
1×	`pow1/2_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `associate-*l/_binary64`

Counts

4 → 130

Calls

4 calls:

16.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 (.f64 2 PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))))
6.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(.f64 (.f64 2 PI.f64) n)
7.0ms	(/.f64 1 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)))

series84.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 (.f64 2 PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))))
5.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(.f64 (.f64 2 PI.f64) n)
21.0ms	(/.f64 1 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)))

simplify39.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5524	1915

prune114.0ms

Filtered

76 candidates to 142 candidates (-86.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	142	10	152

Merged error: 0b

Counts

152 → 10

regimes176.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	21
1	17	21

end0.0ms

sample2.4s

Algorithm

intervals

Results

705.0ms	8000×	body	80	valid
548.0ms	934×	body	1280	nan
356.0ms	832×	body	640	nan
317.0ms	2322×	body	80	overflowed
126.0ms	417×	body	320	nan
42.0ms	226×	body	160	nan
41.0ms	742×	body	80	nan
20.0ms	224×	body	80	invalid

Details

analyze392.0ms

sample89.0ms

simplify44.0ms

prune9.0ms

localize13.0ms

rewrite27.0ms

series71.0ms

simplify37.0ms

prune177.0ms

localize17.0ms

rewrite36.0ms

series106.0ms

simplify35.0ms

prune129.0ms

localize12.0ms

rewrite142.0ms

series154.0ms

simplify187.0ms

prune1.8s

localize13.0ms

rewrite40.0ms

series84.0ms

simplify39.0ms

prune114.0ms

regimes176.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.4s

Profiling