Details

analyze401.0ms

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

sample83.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
18.0ms	31×	body	1280	nan
13.0ms	31×	body	640	nan
10.0ms	76×	body	80	overflowed
4.0ms	12×	body	320	nan
2.0ms	31×	body	80	nan
1.0ms	8×	body	160	nan
1.0ms	8×	body	80	invalid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4987	16
1	4987	16

prune7.0ms

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: 1.0b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1.0 (sqrt.f64 k))
0.2b	(.f64 (/.f64 1.0 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2.0 PI.f64) n) (/.f64 (-.f64 1.0 k) 2.0)))
0.3b	(.f64 (.f64 2.0 PI.f64) n)
0.8b	(pow.f64 (.f64 (.f64 2.0 PI.f64) n) (/.f64 (-.f64 1.0 k) 2.0))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt_binary64`
55×	`times-frac_binary64`
49×	`*-un-lft-identity_binary64`
46×	`add-exp-log_binary64`
43×	`add-cube-cbrt_binary64`
23×	`associate-l_binary64` `sqrt-prod_binary64`
22×	`prod-exp_binary64`
19×	`pow-unpow_binary64`
16×	`add-cbrt-cube_binary64`
15×	`pow1_binary64`
9×	`pow-exp_binary64`
8×	`associate-r_binary64`
6×	`pow-prod-down_binary64` `associate-/r*_binary64` `unswap-sqr_binary64` `div-exp_binary64`
5×	`cbrt-unprod_binary64` `sqr-pow_binary64`
4×	`add-log-exp_binary64`
3×	`pow-to-exp_binary64` `pow-pow_binary64` `div-sub_binary64` `pow-sub_binary64` `difference-of-squares_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64` `div-inv_binary64`
2×	`cbrt-undiv_binary64` `unpow-prod-down_binary64` `*-commutative_binary64`
1×	`associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64`

Counts

4 → 149

Calls

4 calls:

4.0ms	(/.f64 1.0 (sqrt.f64 k))
11.0ms	(.f64 (/.f64 1.0 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2.0 PI.f64) n) (/.f64 (-.f64 1.0 k) 2.0)))
5.0ms	(.f64 (.f64 2.0 PI.f64) n)
10.0ms	(pow.f64 (.f64 (.f64 2.0 PI.f64) n) (/.f64 (-.f64 1.0 k) 2.0))

series113.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/.f64 1.0 (sqrt.f64 k))
78.0ms	(.f64 (/.f64 1.0 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2.0 PI.f64) n) (/.f64 (-.f64 1.0 k) 2.0)))
4.0ms	(.f64 (.f64 2.0 PI.f64) n)
20.0ms	(pow.f64 (.f64 (.f64 2.0 PI.f64) n) (/.f64 (-.f64 1.0 k) 2.0))

simplify66.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4978	2439
1	4978	2439

prune229.0ms

Filtered

109 candidates to 161 candidates (-47.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	150	11	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	151	11	162

Merged error: 0.0b

Counts

162 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1.0 (sqrt.f64 k))
0.2b	(.f64 (.f64 (pow.f64 (*.f64 2.0 PI.f64) (/.f64 (-.f64 1.0 k) 2.0)) (/.f64 1.0 (sqrt.f64 k))) (pow.f64 n (/.f64 (-.f64 1.0 k) 2.0)))
0.3b	(.f64 (pow.f64 (.f64 2.0 PI.f64) (/.f64 (-.f64 1.0 k) 2.0)) (/.f64 1.0 (sqrt.f64 k)))
0.6b	(pow.f64 (*.f64 2.0 PI.f64) (/.f64 (-.f64 1.0 k) 2.0))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-exp-log_binary64`
68×	`prod-exp_binary64`
63×	`add-sqr-sqrt_binary64`
55×	`times-frac_binary64`
50×	`*-un-lft-identity_binary64`
44×	`add-cube-cbrt_binary64`
29×	`associate-r_binary64`
27×	`pow-exp_binary64`
23×	`sqrt-prod_binary64`
20×	`add-cbrt-cube_binary64`
19×	`pow-unpow_binary64`
18×	`pow-to-exp_binary64`
17×	`div-exp_binary64`
11×	`div-sub_binary64` `pow-sub_binary64`
7×	`pow1_binary64` `cbrt-unprod_binary64`
6×	`associate-/r_binary64` `sqr-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64` `frac-times_binary64` `associate-l/_binary64`
5×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `associate-*r/_binary64`
3×	`cbrt-undiv_binary64` `difference-of-squares_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64` `div-inv_binary64`
2×	`pow-pow_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 180

Calls

4 calls:

4.0ms	(/.f64 1.0 (sqrt.f64 k))
12.0ms	(.f64 (.f64 (pow.f64 (*.f64 2.0 PI.f64) (/.f64 (-.f64 1.0 k) 2.0)) (/.f64 1.0 (sqrt.f64 k))) (pow.f64 n (/.f64 (-.f64 1.0 k) 2.0)))
11.0ms	(.f64 (pow.f64 (.f64 2.0 PI.f64) (/.f64 (-.f64 1.0 k) 2.0)) (/.f64 1.0 (sqrt.f64 k)))
8.0ms	(pow.f64 (*.f64 2.0 PI.f64) (/.f64 (-.f64 1.0 k) 2.0))

series180.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/.f64 1.0 (sqrt.f64 k))
129.0ms	(.f64 (.f64 (pow.f64 (*.f64 2.0 PI.f64) (/.f64 (-.f64 1.0 k) 2.0)) (/.f64 1.0 (sqrt.f64 k))) (pow.f64 n (/.f64 (-.f64 1.0 k) 2.0)))
34.0ms	(.f64 (pow.f64 (.f64 2.0 PI.f64) (/.f64 (-.f64 1.0 k) 2.0)) (/.f64 1.0 (sqrt.f64 k)))
7.0ms	(pow.f64 (*.f64 2.0 PI.f64) (/.f64 (-.f64 1.0 k) 2.0))

simplify60.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4973	3425
1	4973	3425

prune240.0ms

Filtered

115 candidates to 192 candidates (-67.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	189	3	192
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	193	10	203

Merged error: 0.0b

Counts

203 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (sqrt.f64 k) (pow.f64 n (/.f64 k 2.0)))
0.2b	(/.f64 (.f64 (.f64 1.0 (pow.f64 (.f64 2.0 PI.f64) (/.f64 (-.f64 1.0 k) 2.0))) (pow.f64 n (/.f64 1.0 2.0))) (.f64 (sqrt.f64 k) (pow.f64 n (/.f64 k 2.0))))
0.4b	(.f64 (.f64 1.0 (pow.f64 (*.f64 2.0 PI.f64) (/.f64 (-.f64 1.0 k) 2.0))) (pow.f64 n (/.f64 1.0 2.0)))
0.6b	(pow.f64 (*.f64 2.0 PI.f64) (/.f64 (-.f64 1.0 k) 2.0))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

297×	`add-exp-log_binary64`
202×	`prod-exp_binary64`
74×	`pow-exp_binary64`
64×	`div-exp_binary64`
58×	`pow-to-exp_binary64`
35×	`add-sqr-sqrt_binary64`
32×	`add-cbrt-cube_binary64`
25×	`*-un-lft-identity_binary64`
19×	`pow-unpow_binary64` `add-cube-cbrt_binary64`
16×	`times-frac_binary64`
14×	`associate-r_binary64`
13×	`cbrt-unprod_binary64`
9×	`unpow-prod-down_binary64`
7×	`pow1_binary64` `associate-l_binary64`
6×	`cbrt-undiv_binary64` `unswap-sqr_binary64` `sqrt-prod_binary64`
5×	`sqr-pow_binary64`
4×	`add-log-exp_binary64`
3×	`div-sub_binary64` `pow-sub_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
2×	`associate-r/_binary64` `pow-pow_binary64` `div-inv_binary64` `associate-l/_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `associate-/r_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 183

Calls

4 calls:

6.0ms	(*.f64 (sqrt.f64 k) (pow.f64 n (/.f64 k 2.0)))
17.0ms	(/.f64 (.f64 (.f64 1.0 (pow.f64 (.f64 2.0 PI.f64) (/.f64 (-.f64 1.0 k) 2.0))) (pow.f64 n (/.f64 1.0 2.0))) (.f64 (sqrt.f64 k) (pow.f64 n (/.f64 k 2.0))))
9.0ms	(.f64 (.f64 1.0 (pow.f64 (*.f64 2.0 PI.f64) (/.f64 (-.f64 1.0 k) 2.0))) (pow.f64 n (/.f64 1.0 2.0)))
8.0ms	(pow.f64 (*.f64 2.0 PI.f64) (/.f64 (-.f64 1.0 k) 2.0))

series272.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(*.f64 (sqrt.f64 k) (pow.f64 n (/.f64 k 2.0)))
174.0ms	(/.f64 (.f64 (.f64 1.0 (pow.f64 (.f64 2.0 PI.f64) (/.f64 (-.f64 1.0 k) 2.0))) (pow.f64 n (/.f64 1.0 2.0))) (.f64 (sqrt.f64 k) (pow.f64 n (/.f64 k 2.0))))
70.0ms	(.f64 (.f64 1.0 (pow.f64 (*.f64 2.0 PI.f64) (/.f64 (-.f64 1.0 k) 2.0))) (pow.f64 n (/.f64 1.0 2.0)))
6.0ms	(pow.f64 (*.f64 2.0 PI.f64) (/.f64 (-.f64 1.0 k) 2.0))

simplify62.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4975	4226
1	4975	4226

prune188.0ms

Filtered

83 candidates to 195 candidates (-134.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	194	1	195
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	195	10	205

Merged error: 0b

Counts

205 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (pow.f64 n (/.f64 1.0 2.0)) (pow.f64 n (/.f64 k 2.0)))
0.2b	(/.f64 (sqrt.f64 k) (/.f64 (pow.f64 n (/.f64 1.0 2.0)) (pow.f64 n (/.f64 k 2.0))))
0.3b	(/.f64 (.f64 1.0 (pow.f64 (.f64 2.0 PI.f64) (/.f64 (-.f64 1.0 k) 2.0))) (/.f64 (sqrt.f64 k) (/.f64 (pow.f64 n (/.f64 1.0 2.0)) (pow.f64 n (/.f64 k 2.0)))))
0.6b	(pow.f64 (*.f64 2.0 PI.f64) (/.f64 (-.f64 1.0 k) 2.0))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

2272×	`times-frac_binary64`
924×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
918×	`add-cube-cbrt_binary64`
847×	`unpow-prod-down_binary64`
480×	`sqrt-prod_binary64`
383×	`associate-/r*_binary64`
283×	`sqr-pow_binary64`
261×	`add-exp-log_binary64`
178×	`div-exp_binary64`
66×	`pow-exp_binary64`
56×	`prod-exp_binary64`
54×	`pow-to-exp_binary64`
32×	`add-cbrt-cube_binary64`
25×	`div-inv_binary64`
19×	`pow-unpow_binary64`
16×	`cbrt-undiv_binary64`
14×	`associate-/l*_binary64`
7×	`pow1_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64`
3×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
2×	`pow-pow_binary64` `div-sub_binary64` `pow-sub_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `pow-div_binary64` `associate-*r/_binary64`

Counts

4 → 1238

Calls

4 calls:

7.0ms	(/.f64 (pow.f64 n (/.f64 1.0 2.0)) (pow.f64 n (/.f64 k 2.0)))
17.0ms	(/.f64 (sqrt.f64 k) (/.f64 (pow.f64 n (/.f64 1.0 2.0)) (pow.f64 n (/.f64 k 2.0))))
53.0ms	(/.f64 (.f64 1.0 (pow.f64 (.f64 2.0 PI.f64) (/.f64 (-.f64 1.0 k) 2.0))) (/.f64 (sqrt.f64 k) (/.f64 (pow.f64 n (/.f64 1.0 2.0)) (pow.f64 n (/.f64 k 2.0)))))
8.0ms	(pow.f64 (*.f64 2.0 PI.f64) (/.f64 (-.f64 1.0 k) 2.0))

series321.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/.f64 (pow.f64 n (/.f64 1.0 2.0)) (pow.f64 n (/.f64 k 2.0)))
81.0ms	(/.f64 (sqrt.f64 k) (/.f64 (pow.f64 n (/.f64 1.0 2.0)) (pow.f64 n (/.f64 k 2.0))))
176.0ms	(/.f64 (.f64 1.0 (pow.f64 (.f64 2.0 PI.f64) (/.f64 (-.f64 1.0 k) 2.0))) (/.f64 (sqrt.f64 k) (/.f64 (pow.f64 n (/.f64 1.0 2.0)) (pow.f64 n (/.f64 k 2.0)))))
7.0ms	(pow.f64 (*.f64 2.0 PI.f64) (/.f64 (-.f64 1.0 k) 2.0))

simplify260.0ms

Algorithm

egg-herbie

Counts

1250 → 1250

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5365	38766

prune3.0s

Filtered

641 candidates to 1250 candidates (-95.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	1250	0	1250
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	1250	10	1260

Merged error: 0b

Counts

1260 → 10

regimes126.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	26
1	30	26

end0.0ms

sample2.6s

Algorithm

intervals

Results

699.0ms	8000×	body	80	valid
604.0ms	978×	body	1280	nan
397.0ms	891×	body	640	nan
336.0ms	2455×	body	80	overflowed
133.0ms	422×	body	320	nan
45.0ms	763×	body	80	nan
42.0ms	219×	body	160	nan
21.0ms	229×	body	80	invalid

Details

analyze401.0ms

sample83.0ms

simplify52.0ms

prune7.0ms

localize15.0ms

rewrite37.0ms

series113.0ms

simplify66.0ms

prune229.0ms

localize17.0ms

rewrite43.0ms

series180.0ms

simplify60.0ms

prune240.0ms

localize23.0ms

rewrite49.0ms

series272.0ms

simplify62.0ms

prune188.0ms

localize23.0ms

rewrite199.0ms

series321.0ms

simplify260.0ms

prune3.0s

regimes126.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.6s

Profiling