Details

analyze578.0ms (0.4%)

Algorithm

1×

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

Compiler

Compiled 17 to 16 computations (5.9% saved)

sample92.0ms (0.1%)

Algorithm

1×

intervals

Results

34.0ms	45×	body	1024	nan
22.0ms	256×	body	128	valid
11.0ms	72×	body	128	overflowed
6.0ms	17×	body	512	nan
2.0ms	9×	body	256	nan
1.0ms	21×	body	128	nan
1.0ms	6×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify173.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4933	22
1	4933	22

prune5.0ms (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

Compiler

Compiled 44 to 41 computations (6.8% saved)

localize15.0ms (0%)

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))
0.3b	(.f64 (.f64 2 PI.f64) n)
0.5b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))

rewrite34.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`times-frac_binary64_425`
42×	`*-un-lft-identity_binary64_419` `add-sqr-sqrt_binary64_441`
33×	`add-cube-cbrt_binary64_454`
26×	`add-exp-log_binary64_457`
22×	`pow-unpow_binary64_496`
18×	`sqrt-prod_binary64_435`
14×	`pow1_binary64_480`
10×	`add-cbrt-cube_binary64_455`
9×	`prod-exp_binary64_468`
8×	`unpow-prod-down_binary64_498` `sqr-pow_binary64_391`
6×	`pow-prod-down_binary64_490` `difference-of-squares_binary64_388` `pow-exp_binary64_487` `associate-/r*_binary64_363`
5×	`div-exp_binary64_470` `associate-/l*_binary64_364`
3×	`add-log-exp_binary64_458` `associate-r_binary64_359` `cbrt-unprod_binary64_452` `distribute-lft-out--_binary64_371` `pow-pow_binary64_491`
2×	`pow-sub_binary64_495` `div-inv_binary64_416` `pow-to-exp_binary64_488` `div-sub_binary64_424`
1×	`clear-num_binary64_418` `-commutative_binary64_350` `associate-l*_binary64_360` `frac-2neg_binary64_430` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`

Counts

3 → 115

Calls

3 calls:

11.0ms	(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)

series334.0ms (0.2%)

Counts

3 → 9

Calls

3 calls:

200.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
108.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
25.0ms	(.f64 (.f64 2 PI.f64) n)

simplify122.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4989	3537
1	4989	3537

prune676.0ms (0.4%)

Pruning

63 alts after pruning (62 fresh and 1 done)

	Pruned	Kept	Total
New	62	62	124
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	63	63	126

Merged error: 0.0b

Counts

126 → 63

Compiler

Compiled 4727 to 3431 computations (27.4% saved)

localize24.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (sqrt.f64 k))
0.2b	(pow.f64 n (/.f64 (-.f64 1 k) 2))
0.3b	(.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2)))
0.6b	(pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2))

rewrite62.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`add-exp-log_binary64_457`
57×	`add-sqr-sqrt_binary64_441`
50×	`*-un-lft-identity_binary64_419`
44×	`pow-unpow_binary64_496`
42×	`times-frac_binary64_425`
32×	`add-cube-cbrt_binary64_454`
31×	`prod-exp_binary64_468`
23×	`pow-exp_binary64_487`
16×	`pow-to-exp_binary64_488`
13×	`div-exp_binary64_470`
12×	`difference-of-squares_binary64_388`
11×	`add-cbrt-cube_binary64_455`
10×	`unpow-prod-down_binary64_498` `pow-sub_binary64_495` `div-sub_binary64_424`
9×	`sqr-pow_binary64_391`
8×	`pow1_binary64_480`
7×	`associate-r_binary64_359`
6×	`unswap-sqr_binary64_387` `distribute-lft-out--_binary64_371` `sqrt-prod_binary64_435` `associate-/r*_binary64_363`
5×	`associate-l_binary64_360`
4×	`add-log-exp_binary64_458`
3×	`div-inv_binary64_416` `pow-pow_binary64_491` `associate-/l/_binary64_366`
2×	`associate-l/_binary64_362` `pow-prod-down_binary64_490` `frac-times_binary64_429` `cbrt-unprod_binary64_452` `associate-r/_binary64_361` `cbrt-undiv_binary64_453`
1×	`clear-num_binary64_418` `-commutative_binary64_350` `frac-2neg_binary64_430` `associate-/l_binary64_364`

Counts

4 → 158

Calls

4 calls:

13.0ms	(/.f64 (.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (sqrt.f64 k))
11.0ms	(pow.f64 n (/.f64 (-.f64 1 k) 2))
9.0ms	(.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2)))
8.0ms	(pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2))

series581.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

329.0ms	(/.f64 (.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (sqrt.f64 k))
134.0ms	(.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2)))
92.0ms	(pow.f64 n (/.f64 (-.f64 1 k) 2))
26.0ms	(pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2))

simplify119.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4974	4114
1	4974	4114

prune1.7s (1.1%)

Pruning

122 alts after pruning (120 fresh and 2 done)

	Pruned	Kept	Total
New	103	67	170
Fresh	8	53	61
Picked	0	1	1
Done	0	1	1
Total	111	122	233

Merged error: 0b

Counts

233 → 122

Compiler

Compiled 8131 to 6218 computations (23.5% saved)

localize24.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (.f64 (pow.f64 2 (/.f64 (-.f64 1 k) 2)) (.f64 (pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2)))) (sqrt.f64 k))
0.2b	(pow.f64 n (/.f64 (-.f64 1 k) 2))
0.3b	(.f64 (pow.f64 2 (/.f64 (-.f64 1 k) 2)) (.f64 (pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2))))
0.6b	(pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2))

rewrite76.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`add-exp-log_binary64_457`
114×	`prod-exp_binary64_468`
58×	`pow-exp_binary64_487` `pow-to-exp_binary64_488`
50×	`*-un-lft-identity_binary64_419` `add-sqr-sqrt_binary64_441`
44×	`pow-unpow_binary64_496`
42×	`times-frac_binary64_425`
32×	`add-cube-cbrt_binary64_454`
31×	`div-exp_binary64_470`
26×	`pow-sub_binary64_495` `div-sub_binary64_424`
18×	`add-cbrt-cube_binary64_455`
12×	`difference-of-squares_binary64_388`
10×	`frac-times_binary64_429` `associate-*r/_binary64_361`
9×	`unpow-prod-down_binary64_498`
7×	`associate-l_binary64_360` `associate-/l/_binary64_366`
6×	`associate-l/_binary64_362` `cbrt-unprod_binary64_452` `distribute-lft-out--_binary64_371` `sqrt-prod_binary64_435` `associate-/r_binary64_363` `pow1_binary64_480`
4×	`add-log-exp_binary64_458`
3×	`div-inv_binary64_416` `sqr-pow_binary64_391` `cbrt-undiv_binary64_453`
2×	`pow-prod-down_binary64_490` `pow-pow_binary64_491`
1×	`clear-num_binary64_418` `associate-r_binary64_359` `-commutative_binary64_350` `frac-2neg_binary64_430` `associate-/l_binary64_364`

Counts

4 → 194

Calls

4 calls:

24.0ms	(/.f64 (.f64 (pow.f64 2 (/.f64 (-.f64 1 k) 2)) (.f64 (pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2)))) (sqrt.f64 k))
11.0ms	(.f64 (pow.f64 2 (/.f64 (-.f64 1 k) 2)) (.f64 (pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2))))
7.0ms	(pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2))
7.0ms	(pow.f64 n (/.f64 (-.f64 1 k) 2))

series830.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

536.0ms	(/.f64 (.f64 (pow.f64 2 (/.f64 (-.f64 1 k) 2)) (.f64 (pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2)))) (sqrt.f64 k))
190.0ms	(.f64 (pow.f64 2 (/.f64 (-.f64 1 k) 2)) (.f64 (pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2))))
81.0ms	(pow.f64 n (/.f64 (-.f64 1 k) 2))
22.0ms	(pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2))

simplify121.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5550	5410

prune3.2s (2%)

Pruning

181 alts after pruning (179 fresh and 2 done)

	Pruned	Kept	Total
New	140	66	206
Fresh	6	113	119
Picked	1	0	1
Done	0	2	2
Total	147	181	328

Merged error: 0b

Counts

328 → 181

Compiler

Compiled 11914 to 9133 computations (23.3% saved)

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 n (/.f64 (-.f64 1 k) 2))
0.2b	(/.f64 (*.f64 (pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (sqrt.f64 k))
0.3b	(.f64 (pow.f64 2 (/.f64 (-.f64 1 k) 2)) (/.f64 (.f64 (pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (sqrt.f64 k)))
0.6b	(pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2))

rewrite73.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

123×	`add-exp-log_binary64_457`
69×	`prod-exp_binary64_468`
58×	`add-sqr-sqrt_binary64_441`
53×	`*-un-lft-identity_binary64_419`
48×	`times-frac_binary64_425`
44×	`pow-unpow_binary64_496`
40×	`div-exp_binary64_470`
37×	`pow-exp_binary64_487` `pow-to-exp_binary64_488`
35×	`add-cube-cbrt_binary64_454`
18×	`add-cbrt-cube_binary64_455`
12×	`difference-of-squares_binary64_388`
10×	`unpow-prod-down_binary64_498` `associate-r_binary64_359`
9×	`sqrt-prod_binary64_435`
8×	`pow-sub_binary64_495` `div-sub_binary64_424`
7×	`associate-l_binary64_360`
6×	`distribute-lft-out--_binary64_371` `associate-/r*_binary64_363` `pow1_binary64_480`
5×	`cbrt-unprod_binary64_452`
4×	`add-log-exp_binary64_458` `div-inv_binary64_416` `sqr-pow_binary64_391` `cbrt-undiv_binary64_453`
3×	`unswap-sqr_binary64_387` `associate-/l/_binary64_366`
2×	`associate-l/_binary64_362` `frac-times_binary64_429` `associate-r/_binary64_361` `pow-pow_binary64_491`
1×	`clear-num_binary64_418` `-commutative_binary64_350` `frac-2neg_binary64_430` `associate-/l_binary64_364`

Counts

4 → 179

Calls

4 calls:

21.0ms	(.f64 (pow.f64 2 (/.f64 (-.f64 1 k) 2)) (/.f64 (.f64 (pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (sqrt.f64 k)))
15.0ms	(/.f64 (*.f64 (pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (sqrt.f64 k))
9.0ms	(pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2))
7.0ms	(pow.f64 n (/.f64 (-.f64 1 k) 2))

series827.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

478.0ms	(.f64 (pow.f64 2 (/.f64 (-.f64 1 k) 2)) (/.f64 (.f64 (pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (sqrt.f64 k)))
269.0ms	(/.f64 (*.f64 (pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (sqrt.f64 k))
56.0ms	(pow.f64 n (/.f64 (-.f64 1 k) 2))
24.0ms	(pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2))

simplify140.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5113	5272

prune4.2s (2.7%)

Pruning

209 alts after pruning (207 fresh and 2 done)

	Pruned	Kept	Total
New	137	54	191
Fresh	25	153	178
Picked	1	0	1
Done	0	2	2
Total	163	209	372

Merged error: 0b

Counts

372 → 209

Compiler

Compiled 6014 to 4235 computations (29.6% saved)

regimes6.4s (4%)

Compiler: Compiled 55157 to 46973 computations (14.8% saved)

bsearch1.9min (71%)

simplify21.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	40
1	27	40

end0.0ms (0%)

sample25.4s (16.1%)

Algorithm

1×

intervals

Results

853.0ms	8000×	body	128	valid
832.0ms	1331×	body	1024	nan
445.0ms	2389×	body	128	overflowed
290.0ms	644×	body	512	nan
97.0ms	359×	body	256	nan
70.0ms	938×	body	128	nan
27.0ms	220×	body	128	invalid

Compiler

Compiled 13924 to 11846 computations (14.9% saved)

Pareto

7.09396918735538e-05

Details

analyze578.0ms (0.4%)

sample92.0ms (0.1%)

simplify173.0ms (0.1%)

prune5.0ms (0%)

localize15.0ms (0%)

rewrite34.0ms (0%)

series334.0ms (0.2%)

simplify122.0ms (0.1%)

prune676.0ms (0.4%)

localize24.0ms (0%)

rewrite62.0ms (0%)

series581.0ms (0.4%)

simplify119.0ms (0.1%)

prune1.7s (1.1%)

localize24.0ms (0%)

rewrite76.0ms (0%)

series830.0ms (0.5%)

simplify121.0ms (0.1%)

prune3.2s (2%)

localize15.0ms (0%)

rewrite73.0ms (0%)

series827.0ms (0.5%)

simplify140.0ms (0.1%)

prune4.2s (2.7%)

regimes6.4s (4%)

bsearch1.9min (71%)

simplify21.0ms (0%)

end0.0ms (0%)

sample25.4s (16.1%)

Profiling