Details

analyze533.0ms

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

sample92.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
23.0ms	37×	body	1280	nan
18.0ms	94×	body	80	overflowed
9.0ms	21×	body	640	nan
4.0ms	14×	body	320	nan
2.0ms	9×	body	160	nan
2.0ms	28×	body	80	nan
1.0ms	6×	body	80	invalid

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

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:

0.1b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
0.2b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
0.3b	(.f64 (.f64 2 PI.f64) n)

rewrite26.0ms

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:

10.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
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)

series259.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
160.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
20.0ms	(.f64 (.f64 2 PI.f64) n)

simplify70.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5612	3511

prune146.0ms

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

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
0.2b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
0.2b	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
0.3b	(.f64 (.f64 2 PI.f64) n)

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

273×	`times-frac_binary64`
147×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
138×	`add-cube-cbrt_binary64`
78×	`sqrt-prod_binary64`
72×	`add-exp-log_binary64`
40×	`associate-/r*_binary64`
32×	`sqr-pow_binary64` `unpow-prod-down_binary64` `div-exp_binary64`
22×	`pow-unpow_binary64`
18×	`prod-exp_binary64`
16×	`pow1_binary64` `add-cbrt-cube_binary64`
15×	`pow-exp_binary64`
9×	`associate-/l*_binary64`
7×	`div-inv_binary64`
6×	`pow-prod-down_binary64` `1-exp_binary64` `associate-/r/_binary64` `div-sub_binary64` `pow-sub_binary64` `difference-of-squares_binary64` `rec-exp_binary64`
5×	`pow-to-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64`
3×	`cbrt-unprod_binary64` `associate-r_binary64` `pow-pow_binary64` `distribute-lft-out--_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`associate-l_binary64` `inv-pow_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 291

Calls

4 calls:

10.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
16.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
7.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
6.0ms	(.f64 (.f64 2 PI.f64) n)

series381.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
128.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
149.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
23.0ms	(.f64 (.f64 2 PI.f64) n)

simplify164.0ms

Algorithm

egg-herbie

Counts

303 → 303

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4988	10776
1	4988	10776

prune302.0ms

Filtered

162 candidates to 303 candidates (-87.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	301	2	303
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	303	10	313

Merged error: 0.0b

Counts

313 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

330×	`sqrt-prod_binary64`
221×	`add-sqr-sqrt_binary64`
218×	`times-frac_binary64`
101×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
59×	`sqr-pow_binary64`
49×	`swap-sqr_binary64`
43×	`associate-r_binary64`
39×	`associate-l_binary64`
36×	`unswap-sqr_binary64`
35×	`unpow-prod-down_binary64`
29×	`pow1_binary64`
28×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`
10×	`prod-exp_binary64`
9×	`pow-prod-down_binary64`
8×	`pow1/2_binary64` `sqrt-pow1_binary64`
7×	`cbrt-unprod_binary64`
6×	`associate-/r*_binary64`
5×	`pow-prod-up_binary64` `associate-/l*_binary64` `div-inv_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`pow-sqr_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `associate-/l/_binary64` `cbrt-undiv_binary64` `rem-square-sqrt_binary64` `associate-r/_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `div-sub_binary64` `clear-num_binary64` `pow-sub_binary64` `frac-2neg_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64`

Counts

4 → 281

Calls

4 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)
5.0ms	(.f64 (.f64 2 PI.f64) n)
37.0ms	(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))))

series370.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
22.0ms	(.f64 (.f64 2 PI.f64) n)
23.0ms	(.f64 (.f64 2 PI.f64) n)
170.0ms	(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))))

simplify176.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5309	12542

prune404.0ms

Filtered

153 candidates to 293 candidates (-91.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	292	1	293
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	294	9	303

Merged error: 0.0b

Counts

303 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

255×	`times-frac_binary64`
131×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
96×	`add-exp-log_binary64`
84×	`sqrt-prod_binary64`
40×	`associate-/r*_binary64`
38×	`div-exp_binary64`
33×	`prod-exp_binary64`
31×	`sqr-pow_binary64` `unpow-prod-down_binary64`
25×	`add-cbrt-cube_binary64`
19×	`pow1_binary64`
16×	`pow-exp_binary64`
12×	`associate-r_binary64`
9×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-/l*_binary64`
7×	`1-exp_binary64` `rec-exp_binary64`
6×	`associate-/r/_binary64` `div-inv_binary64`
5×	`div-sub_binary64` `pow-sub_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64`
2×	`associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`inv-pow_binary64` `pow-flip_binary64`

Counts

4 → 283

Calls

4 calls:

18.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2))))
8.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2)))
6.0ms	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))
10.0ms	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))

series332.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2))))
149.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2)))
22.0ms	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))
26.0ms	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))

simplify197.0ms

Algorithm

egg-herbie

Counts

295 → 295

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4956	10710
1	4956	10710

prune248.0ms

Filtered

154 candidates to 295 candidates (-91.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	294	1	295
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	295	9	304

Merged error: 0.0b

Counts

304 → 9

regimes66.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	50
1	28	50

end0.0ms

sample2.6s

Algorithm

intervals

Results

734.0ms	8000×	body	80	valid
607.0ms	985×	body	1280	nan
370.0ms	793×	body	640	nan
356.0ms	2475×	body	80	overflowed
139.0ms	416×	body	320	nan
44.0ms	238×	body	160	nan
42.0ms	710×	body	80	nan
22.0ms	229×	body	80	invalid

Details

analyze533.0ms

sample92.0ms

simplify66.0ms

prune4.0ms

localize12.0ms

rewrite26.0ms

series259.0ms

simplify70.0ms

prune146.0ms

localize14.0ms

rewrite54.0ms

series381.0ms

simplify164.0ms

prune302.0ms

localize16.0ms

rewrite73.0ms

series370.0ms

simplify176.0ms

prune404.0ms

localize16.0ms

rewrite57.0ms

series332.0ms

simplify197.0ms

prune248.0ms

regimes66.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample2.6s

Profiling