Details

analyze389.0ms

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

sample74.0ms

Algorithm

intervals

Results

23.0ms	256×	body	128	valid
18.0ms	40×	body	1024	nan
9.0ms	65×	body	128	overflowed
9.0ms	28×	body	512	nan
2.0ms	12×	body	256	nan
1.0ms	27×	body	128	nan
1.0ms	6×	body	128	invalid

simplify55.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4933	22
1	4933	22

prune4.0ms

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: 0.4b

Counts

2 → 2

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite35.0ms

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:

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)
11.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))

series514.0ms

Counts

3 → 9

Calls

3 calls:

317.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
41.0ms	(.f64 (.f64 2 PI.f64) n)
156.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))

simplify61.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5551	3537

prune155.0ms

Filtered

81 candidates to 124 candidates (-53.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	115	9	124
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	116	10	126

Merged error: 0.0b

Counts

126 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

284×	`times-frac_binary64`
126×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
111×	`sqrt-prod_binary64`
33×	`add-exp-log_binary64`
28×	`sqr-pow_binary64` `unpow-prod-down_binary64`
24×	`associate-/l*_binary64`
20×	`pow1_binary64`
19×	`add-cbrt-cube_binary64`
11×	`div-exp_binary64`
9×	`pow-prod-down_binary64` `prod-exp_binary64`
8×	`div-inv_binary64`
6×	`associate-/r_binary64` `cbrt-unprod_binary64` `associate-r*_binary64`
4×	`add-log-exp_binary64`
3×	`cbrt-undiv_binary64` `sqrt-pow1_binary64` `pow-exp_binary64`
2×	`associate-l_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `associate-/l/_binary64` `pow1/2_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 241

Calls

4 calls:

4.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
17.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
5.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(.f64 (.f64 2 PI.f64) n)

series573.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
450.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
39.0ms	(.f64 (.f64 2 PI.f64) n)
39.0ms	(.f64 (.f64 2 PI.f64) n)

simplify129.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5217	11740

prune335.0ms

Filtered

164 candidates to 253 candidates (-54.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	249	4	253
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	255	8	263

Merged error: 0b

Counts

263 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

284×	`times-frac_binary64`
129×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
116×	`sqrt-prod_binary64`
42×	`add-exp-log_binary64`
28×	`sqr-pow_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64`
24×	`associate-/l*_binary64`
23×	`pow1_binary64`
15×	`associate-r_binary64` `prod-exp_binary64`
12×	`pow-prod-down_binary64` `cbrt-unprod_binary64`
11×	`div-exp_binary64`
8×	`div-inv_binary64`
6×	`associate-/r*_binary64`
4×	`add-log-exp_binary64`
3×	`cbrt-undiv_binary64` `associate-l_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 256

Calls

4 calls:

20.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
5.0ms	(.f64 (.f64 2 PI.f64) n)
7.0ms	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))
11.0ms	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))

series593.0ms

Counts

4 → 12

Calls

4 calls:

477.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
39.0ms	(.f64 (.f64 2 PI.f64) n)
37.0ms	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))
40.0ms	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))

simplify192.0ms

Algorithm

egg-herbie

Counts

268 → 268

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4959	12268
1	4959	12268

prune353.0ms

Filtered

171 candidates to 268 candidates (-56.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	267	1	268
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	268	8	276

Merged error: 0b

Counts

276 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

85×	`add-sqr-sqrt_binary64`
80×	`add-exp-log_binary64`
78×	`times-frac_binary64`
50×	`*-un-lft-identity_binary64`
44×	`add-cube-cbrt_binary64`
33×	`prod-exp_binary64`
32×	`sqrt-prod_binary64`
28×	`associate-r_binary64` `add-cbrt-cube_binary64`
26×	`associate-l_binary64`
22×	`div-exp_binary64`
18×	`pow1_binary64`
15×	`unswap-sqr_binary64`
10×	`cbrt-unprod_binary64`
9×	`sqr-pow_binary64` `pow-exp_binary64`
7×	`pow-prod-down_binary64` `rec-exp_binary64`
6×	`associate-/r*_binary64`
5×	`cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `unpow-prod-down_binary64`
3×	`pow-to-exp_binary64` `associate-/l_binary64` `div-inv_binary64` `pow-flip_binary64` `-commutative_binary64`
1×	`pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `frac-times_binary64` `associate-l/_binary64`

Counts

4 → 176

Calls

4 calls:

6.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(.f64 (.f64 2 PI.f64) n)
33.0ms	(.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (/.f64 1 (sqrt.f64 k)))
5.0ms	(/.f64 1 (sqrt.f64 k))

series580.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(.f64 (.f64 2 PI.f64) n)
39.0ms	(.f64 (.f64 2 PI.f64) n)
451.0ms	(.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (/.f64 1 (sqrt.f64 k)))
52.0ms	(/.f64 1 (sqrt.f64 k))

simplify91.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4976	4889
1	4976	4889

prune156.0ms

Filtered

104 candidates to 188 candidates (-80.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	188	8	196

Merged error: 0b

Counts

196 → 8

regimes75.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	38
1	20	38

end0.0ms

sample2.3s

Algorithm

intervals

Results

738.0ms	8000×	body	128	valid
622.0ms	1350×	body	1024	nan
320.0ms	2289×	body	128	overflowed
222.0ms	692×	body	512	nan
63.0ms	338×	body	256	nan
53.0ms	991×	body	128	nan
26.0ms	236×	body	128	invalid

Details

analyze389.0ms

sample74.0ms

simplify55.0ms

prune4.0ms

localize13.0ms

rewrite35.0ms

series514.0ms

simplify61.0ms

prune155.0ms

localize11.0ms

rewrite70.0ms

series573.0ms

simplify129.0ms

prune335.0ms

localize15.0ms

rewrite86.0ms

series593.0ms

simplify192.0ms

prune353.0ms

localize13.0ms

rewrite70.0ms

series580.0ms

simplify91.0ms

prune156.0ms

regimes75.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.3s

Profiling