Details

analyze396.0ms

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

sample87.0ms

Algorithm

intervals

Results

25.0ms	36×	body	1280	nan
21.0ms	256×	body	80	valid
12.0ms	28×	body	640	nan
9.0ms	68×	body	80	overflowed
4.0ms	15×	body	320	nan
2.0ms	11×	body	160	nan
1.0ms	7×	body	80	invalid
1.0ms	21×	body	80	nan

simplify43.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5065	14

prune7.0ms

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 (.f64 2 PI.f64) n)
0.2b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
0.5b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))

rewrite28.0ms

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:

6.0ms	(.f64 (.f64 2 PI.f64) n)
7.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
11.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))

series60.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(.f64 (.f64 2 PI.f64) n)
39.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
18.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))

simplify38.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5282	2253

prune122.0ms

Filtered

83 candidates to 124 candidates (-49.4%)

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

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

128×	`add-exp-log_binary64`
67×	`prod-exp_binary64`
39×	`pow-exp_binary64`
30×	`div-exp_binary64`
26×	`pow-unpow_binary64`
23×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
14×	`add-cbrt-cube_binary64`
13×	`pow-to-exp_binary64`
9×	`pow-prod-down_binary64`
6×	`pow-pow_binary64`
5×	`associate-/l*_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64`
3×	`associate-l_binary64` `div-inv_binary64`
2×	`cbrt-undiv_binary64`
1×	`associate-/r_binary64` `associate-r_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 129

Calls

4 calls:

5.0ms	(.f64 n (.f64 2 PI.f64))
10.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (pow.f64 (.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)) (sqrt.f64 k)))
7.0ms	(pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))
7.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))

series98.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(.f64 n (.f64 2 PI.f64))
59.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (pow.f64 (.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)) (sqrt.f64 k)))
15.0ms	(pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))
21.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))

simplify52.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5000	1881

prune301.0ms

Filtered

80 candidates to 141 candidates (-76.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	141	9	150

Merged error: 0b

Counts

150 → 9

localize30.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt.f64 2)
1.0b	(cbrt.f64 2)
1.0b	(/.f64 1 (*.f64 (cbrt.f64 2) (cbrt.f64 2)))
4.7b	(pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 1 (*.f64 (cbrt.f64 2) (cbrt.f64 2))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log_binary64`
18×	`pow1_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`pow-flip_binary64`
8×	`pow1/3_binary64`
7×	`pow-unpow_binary64` `add-cbrt-cube_binary64`
6×	`prod-exp_binary64` `times-frac_binary64` `cbrt-prod_binary64`
5×	`pow-prod-down_binary64`
4×	`add-log-exp_binary64` `div-exp_binary64`
3×	`pow-pow_binary64` `associate-/l*_binary64` `pow-exp_binary64`
2×	`pow-prod-up_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `div-inv_binary64` `pow-sqr_binary64`
1×	`pow-to-exp_binary64` `associate-/r*_binary64` `cbrt-unprod_binary64` `sqr-pow_binary64` `pow-plus_binary64` `clear-num_binary64` `inv-pow_binary64` `unpow-prod-down_binary64` `frac-2neg_binary64` `pow2_binary64`

Counts

4 → 80

Calls

4 calls:

1.0ms	(cbrt.f64 2)
1.0ms	(cbrt.f64 2)
7.0ms	(/.f64 1 (*.f64 (cbrt.f64 2) (cbrt.f64 2)))
8.0ms	(pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 1 (*.f64 (cbrt.f64 2) (cbrt.f64 2))))

series38.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt.f64 2)
0.0ms	(cbrt.f64 2)
0.0ms	(/.f64 1 (*.f64 (cbrt.f64 2) (cbrt.f64 2)))
38.0ms	(pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 1 (*.f64 (cbrt.f64 2) (cbrt.f64 2))))

simplify46.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4885	591
1	4885	591

prune89.0ms

Filtered

54 candidates to 86 candidates (-59.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	86	9	95

Merged error: 0b

Counts

95 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log_binary64`
26×	`pow-unpow_binary64`
23×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
20×	`prod-exp_binary64`
14×	`add-cbrt-cube_binary64`
12×	`pow-exp_binary64`
10×	`div-exp_binary64`
9×	`pow-prod-down_binary64`
6×	`pow-pow_binary64`
5×	`associate-/l*_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64`
3×	`associate-l_binary64` `div-inv_binary64`
2×	`cbrt-undiv_binary64`
1×	`associate-/r_binary64` `associate-r_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 109

Calls

4 calls:

5.0ms	(.f64 n (.f64 2 PI.f64))
9.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (log.f64 (exp.f64 (pow.f64 (.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) (sqrt.f64 k)))
7.0ms	(pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))
9.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))

series99.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(.f64 n (.f64 2 PI.f64))
60.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (log.f64 (exp.f64 (pow.f64 (.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) (sqrt.f64 k)))
14.0ms	(pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))
21.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))

simplify52.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5007	1561

prune84.0ms

Filtered

80 candidates to 121 candidates (-51.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	121	9	130

Merged error: 0b

Counts

130 → 9

regimes84.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	29
1	22	29

end0.0ms

sample2.5s

Algorithm

intervals

Results

696.0ms	8000×	body	80	valid
612.0ms	1020×	body	1280	nan
359.0ms	845×	body	640	nan
310.0ms	2385×	body	80	overflowed
126.0ms	415×	body	320	nan
43.0ms	741×	body	80	nan
35.0ms	205×	body	160	nan
19.0ms	222×	body	80	invalid

Details

analyze396.0ms

sample87.0ms

simplify43.0ms

prune7.0ms

localize12.0ms

rewrite28.0ms

series60.0ms

simplify38.0ms

prune122.0ms

localize18.0ms

rewrite37.0ms

series98.0ms

simplify52.0ms

prune301.0ms

localize30.0ms

rewrite20.0ms

series38.0ms

simplify46.0ms

prune89.0ms

localize21.0ms

rewrite35.0ms

series99.0ms

simplify52.0ms

prune84.0ms

regimes84.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.5s

Profiling