Details

analyze398.0ms

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

sample91.0ms

Algorithm

intervals

Results

24.0ms	40×	body	1280	nan
22.0ms	256×	body	80	valid
15.0ms	35×	body	640	nan
10.0ms	76×	body	80	overflowed
5.0ms	16×	body	320	nan
1.0ms	26×	body	80	nan
1.0ms	9×	body	80	invalid
1.0ms	3×	body	160	nan

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5065	14

prune10.0ms

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

localize12.0ms

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

rewrite29.0ms

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:

11.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
5.0ms	(.f64 (.f64 2 PI.f64) n)
8.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))

series62.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
4.0ms	(.f64 (.f64 2 PI.f64) n)
37.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))

simplify39.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5282	2253

prune120.0ms

Filtered

83 candidates to 124 candidates (-49.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	117	7	124
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	118	8	126

Merged error: 0.0b

Counts

126 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

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-l*_binary64`
4×	`add-log-exp_binary64`
3×	`cbrt-undiv_binary64` `sqrt-pow1_binary64` `pow-exp_binary64`
2×	`associate-r_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 n (.f64 2 PI.f64)))
5.0ms	(.f64 n (.f64 2 PI.f64))
5.0ms	(.f64 n (.f64 2 PI.f64))
16.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))

series83.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))
4.0ms	(.f64 n (.f64 2 PI.f64))
4.0ms	(.f64 n (.f64 2 PI.f64))
68.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))

simplify84.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5122	7121

prune261.0ms

Filtered

164 candidates to 253 candidates (-54.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	246	7	253
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	251	10	261

Merged error: 0b

Counts

261 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite177.0ms

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-l_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64`
2×	`associate-r_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`inv-pow_binary64` `pow-flip_binary64`

Counts

4 → 865

Calls

4 calls:

44.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2)))))
15.0ms	(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))))
7.0ms	(.f64 n (.f64 2 PI.f64))
6.0ms	(.f64 n (.f64 2 PI.f64))

series140.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2)))))
64.0ms	(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))))
4.0ms	(.f64 n (.f64 2 PI.f64))
11.0ms	(.f64 n (.f64 2 PI.f64))

simplify196.0ms

Algorithm

egg-herbie

Counts

877 → 877

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5578	30219

prune1.4s

Filtered

457 candidates to 877 candidates (-91.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	877	0	877
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	877	10	887

Merged error: 0b

Counts

887 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

441×	`times-frac_binary64`
235×	`add-sqr-sqrt_binary64`
207×	`*-un-lft-identity_binary64`
203×	`add-cube-cbrt_binary64`
123×	`sqrt-prod_binary64`
120×	`associate-r_binary64`
118×	`add-exp-log_binary64`
52×	`div-exp_binary64`
43×	`sqr-pow_binary64`
41×	`prod-exp_binary64`
39×	`unpow-prod-down_binary64`
28×	`add-cbrt-cube_binary64`
19×	`associate-/l*_binary64`
18×	`pow-exp_binary64`
16×	`pow1_binary64`
15×	`div-inv_binary64`
11×	`unswap-sqr_binary64`
10×	`1-exp_binary64` `associate-l_binary64` `rec-exp_binary64`
9×	`cbrt-unprod_binary64`
7×	`pow-prod-down_binary64`
6×	`pow-to-exp_binary64` `associate-/r*_binary64` `cbrt-undiv_binary64`
4×	`add-log-exp_binary64`
3×	`*-commutative_binary64`
1×	`associate-/l/_binary64` `associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 367

Calls

4 calls:

12.0ms	(/.f64 (/.f64 1 (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
5.0ms	(.f64 n (.f64 2 PI.f64))
6.0ms	(.f64 n (.f64 2 PI.f64))
40.0ms	(.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (/.f64 (/.f64 1 (pow.f64 (.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k)))

series117.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/.f64 (/.f64 1 (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
4.0ms	(.f64 n (.f64 2 PI.f64))
4.0ms	(.f64 n (.f64 2 PI.f64))
67.0ms	(.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (/.f64 (/.f64 1 (pow.f64 (.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k)))

simplify110.0ms

Algorithm

egg-herbie

Counts

379 → 379

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4972	8391
1	4972	8391

prune292.0ms

Filtered

192 candidates to 379 candidates (-97.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	379	0	379
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	379	10	389

Merged error: 0b

Counts

389 → 10

regimes86.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	19
1	14	19

end0.0ms

sample2.6s

Algorithm

intervals

Results

709.0ms	8000×	body	80	valid
596.0ms	969×	body	1280	nan
380.0ms	847×	body	640	nan
343.0ms	2501×	body	80	overflowed
139.0ms	441×	body	320	nan
49.0ms	783×	body	80	nan
39.0ms	199×	body	160	nan
23.0ms	249×	body	80	invalid

Details

analyze398.0ms

sample91.0ms

simplify41.0ms

prune10.0ms

localize12.0ms

rewrite29.0ms

series62.0ms

simplify39.0ms

prune120.0ms

localize11.0ms

rewrite46.0ms

series83.0ms

simplify84.0ms

prune261.0ms

localize12.0ms

rewrite177.0ms

series140.0ms

simplify196.0ms

prune1.4s

localize15.0ms

rewrite92.0ms

series117.0ms

simplify110.0ms

prune292.0ms

regimes86.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.6s

Profiling