Details

analyze581.0ms

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

sample90.0ms

Algorithm

intervals

Results

25.0ms	41×	body	1280	nan
23.0ms	256×	body	80	valid
11.0ms	25×	body	640	nan
11.0ms	77×	body	80	overflowed
5.0ms	18×	body	320	nan
2.0ms	30×	body	80	nan
1.0ms	6×	body	160	nan
1.0ms	6×	body	80	invalid

simplify71.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4934	22
1	4934	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: 0.3b

Counts

2 → 2

localize12.0ms

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

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:

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))

series266.0ms

Counts

3 → 9

Calls

3 calls:

169.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
19.0ms	(.f64 (.f64 2 PI.f64) n)
79.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))

simplify67.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5612	3511

prune143.0ms

Filtered

81 candidates to 124 candidates (-53.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	115	9	124
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	117	9	126

Merged error: 0.0b

Counts

126 → 9

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)

rewrite47.0ms

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))
18.0ms	(/.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)

series305.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
236.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
23.0ms	(.f64 (.f64 2 PI.f64) n)
23.0ms	(.f64 (.f64 2 PI.f64) n)

simplify160.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5004	11742

prune342.0ms

Filtered

164 candidates to 253 candidates (-54.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	249	4	253
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	252	10	262

Merged error: 0b

Counts

262 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

4.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
11.0ms	(/.f64 (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)

series292.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
227.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
18.0ms	(.f64 (.f64 2 PI.f64) n)
24.0ms	(.f64 (.f64 2 PI.f64) n)

simplify57.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5249	1884

prune83.0ms

Filtered

55 candidates to 87 candidates (-58.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	88	9	97

Merged error: 0b

Counts

97 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac_binary64`
23×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `sqrt-prod_binary64`
20×	`pow1_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow-prod-down_binary64`
6×	`associate-/r_binary64` `cbrt-unprod_binary64` `associate-r*_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `associate-/l*_binary64`
3×	`sqrt-pow1_binary64`
2×	`associate-l_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 95

Calls

4 calls:

4.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
5.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(.f64 (.f64 2 PI.f64) n)
14.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (sqrt.f64 k))

series159.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
22.0ms	(.f64 (.f64 2 PI.f64) n)
19.0ms	(.f64 (.f64 2 PI.f64) n)
91.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (sqrt.f64 k))

simplify72.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5077	1956

prune87.0ms

Filtered

69 candidates to 107 candidates (-55.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	6	7
Picked	0	1	1
Done	1	0	1
Total	108	8	116

Merged error: 0b

Counts

116 → 8

regimes60.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	31
1	15	31

end0.0ms

sample2.5s

Algorithm

intervals

Results

694.0ms	8000×	body	80	valid
601.0ms	1015×	body	1280	nan
336.0ms	790×	body	640	nan
327.0ms	2463×	body	80	overflowed
118.0ms	391×	body	320	nan
44.0ms	747×	body	80	nan
38.0ms	213×	body	160	nan
19.0ms	214×	body	80	invalid

Details

analyze581.0ms

sample90.0ms

simplify71.0ms

prune4.0ms

localize12.0ms

rewrite27.0ms

series266.0ms

simplify67.0ms

prune143.0ms

localize11.0ms

rewrite47.0ms

series305.0ms

simplify160.0ms

prune342.0ms

localize11.0ms

rewrite27.0ms

series292.0ms

simplify57.0ms

prune83.0ms

localize19.0ms

rewrite31.0ms

series159.0ms

simplify72.0ms

prune87.0ms

regimes60.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample2.5s

Profiling