Details

analyze522.0ms

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

sample71.0ms

Algorithm

intervals

Results

23.0ms	256×	body	128	valid
18.0ms	40×	body	1024	nan
8.0ms	56×	body	128	overflowed
7.0ms	21×	body	512	nan
1.0ms	8×	body	256	nan
1.0ms	22×	body	128	nan
0.0ms	5×	body	128	invalid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4933	22
1	4933	22

prune5.0ms

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: 0.6b

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)
0.4b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))

rewrite39.0ms

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	(/.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))

series511.0ms

Counts

3 → 9

Calls

3 calls:

319.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
40.0ms	(.f64 (.f64 2 PI.f64) n)
152.0ms	(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 (28.0ms)

Iter	Nodes	Cost
0	5551	3537

prune150.0ms

Filtered

81 candidates to 124 candidates (-53.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	114	10	124
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	116	10	126

Merged error: 0.0b

Counts

126 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
0.3b	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))
0.4b	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
0.4b	(pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac_binary64`
46×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
45×	`add-exp-log_binary64`
37×	`add-cube-cbrt_binary64`
28×	`pow1_binary64`
24×	`sqrt-prod_binary64`
22×	`pow-unpow_binary64`
21×	`prod-exp_binary64`
20×	`add-cbrt-cube_binary64`
15×	`pow-prod-down_binary64`
12×	`associate-r_binary64`
9×	`cbrt-unprod_binary64`
8×	`sqr-pow_binary64` `unpow-prod-down_binary64` `pow-exp_binary64`
6×	`associate-/r*_binary64` `difference-of-squares_binary64` `div-exp_binary64`
5×	`associate-/l*_binary64`
4×	`add-log-exp_binary64` `pow-pow_binary64`
3×	`distribute-lft-out--_binary64`
2×	`pow-to-exp_binary64` `associate-l_binary64` `div-sub_binary64` `pow-sub_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`associate-/l/_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 145

Calls

4 calls:

9.0ms	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
7.0ms	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))
10.0ms	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
15.0ms	(pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2))

series600.0ms

Counts

4 → 12

Calls

4 calls:

326.0ms	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
36.0ms	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))
42.0ms	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
195.0ms	(pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2))

simplify123.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4950	4348
1	4950	4348

prune148.0ms

Filtered

95 candidates to 157 candidates (-65.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	155	2	157
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	157	10	167

Merged error: 0b

Counts

167 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))
0.4b	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
0.4b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
0.4b	(pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
44×	`pow-unpow_binary64`
36×	`times-frac_binary64`
34×	`pow1_binary64` `add-exp-log_binary64`
28×	`add-cube-cbrt_binary64`
18×	`pow-prod-down_binary64` `add-cbrt-cube_binary64` `prod-exp_binary64`
12×	`associate-r_binary64` `difference-of-squares_binary64`
9×	`cbrt-unprod_binary64`
7×	`pow-pow_binary64` `pow-exp_binary64`
6×	`distribute-lft-out--_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64`
2×	`pow-to-exp_binary64` `sqr-pow_binary64` `associate-l_binary64` `div-sub_binary64` `pow-sub_binary64` `unpow-prod-down_binary64` `div-inv_binary64` `*-commutative_binary64`

Counts

4 → 125

Calls

4 calls:

7.0ms	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))
10.0ms	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
11.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
15.0ms	(pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2))

series395.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))
41.0ms	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
143.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
178.0ms	(pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2))

simplify56.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5140	2611

prune192.0ms

Filtered

89 candidates to 137 candidates (-53.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	137	10	147

Merged error: 0b

Counts

147 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 2 PI.f64) n)
0.3b	(.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (-.f64 1/4 (/.f64 k 4))) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (-.f64 1/4 (/.f64 k 4))))
0.4b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (-.f64 1/4 (/.f64 k 4)))
0.4b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (-.f64 1/4 (/.f64 k 4)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-exp-log_binary64`
64×	`prod-exp_binary64`
36×	`pow-exp_binary64`
25×	`add-sqr-sqrt_binary64`
21×	`pow1_binary64`
15×	`*-un-lft-identity_binary64`
12×	`pow-to-exp_binary64` `pow-unpow_binary64`
11×	`add-cube-cbrt_binary64` `add-cbrt-cube_binary64`
10×	`pow-prod-down_binary64` `sqr-pow_binary64`
9×	`associate-r_binary64`
7×	`associate-l_binary64`
6×	`sub-neg_binary64` `swap-sqr_binary64` `pow-pow_binary64` `unpow-prod-up_binary64` `pow-sub_binary64` `unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64`
2×	`distribute-lft-out--_binary64` `times-frac_binary64` `*-commutative_binary64`
1×	`pow-prod-up_binary64` `associate-r/_binary64` `pow-sqr_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64`

Counts

4 → 129

Calls

4 calls:

5.0ms	(.f64 (.f64 2 PI.f64) n)
11.0ms	(.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (-.f64 1/4 (/.f64 k 4))) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (-.f64 1/4 (/.f64 k 4))))
12.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (-.f64 1/4 (/.f64 k 4)))
13.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (-.f64 1/4 (/.f64 k 4)))

series622.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(.f64 (.f64 2 PI.f64) n)
287.0ms	(.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (-.f64 1/4 (/.f64 k 4))) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (-.f64 1/4 (/.f64 k 4))))
142.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (-.f64 1/4 (/.f64 k 4)))
154.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (-.f64 1/4 (/.f64 k 4)))

simplify78.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5047	3197

prune129.0ms

Filtered

77 candidates to 141 candidates (-83.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	141	10	151

Merged error: 0b

Counts

151 → 10

regimes92.0ms

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	34	52
1	34	52

end0.0ms

sample2.3s

Algorithm

intervals

Results

741.0ms	8000×	body	128	valid
614.0ms	1300×	body	1024	nan
311.0ms	2197×	body	128	overflowed
212.0ms	659×	body	512	nan
66.0ms	369×	body	256	nan
55.0ms	996×	body	128	nan
20.0ms	218×	body	128	invalid

Details

analyze522.0ms

sample71.0ms

simplify52.0ms

prune5.0ms

localize12.0ms

rewrite39.0ms

series511.0ms

simplify61.0ms

prune150.0ms

localize18.0ms

rewrite57.0ms

series600.0ms

simplify123.0ms

prune148.0ms

localize23.0ms

rewrite65.0ms

series395.0ms

simplify56.0ms

prune192.0ms

localize14.0ms

rewrite55.0ms

series622.0ms

simplify78.0ms

prune129.0ms

regimes92.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.3s

Profiling