Details

analyze543.0ms (4.3%)

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)

sample90.0ms (0.7%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
22.0ms	36×	body	1024	nan
13.0ms	69×	body	128	overflowed
7.0ms	18×	body	512	nan
3.0ms	12×	body	256	nan
2.0ms	24×	body	128	nan
0.0ms	3×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify190.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4933	22
1	4933	22

prune4.0ms (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

Error

0.5b

Counts

2 → 2

Compiler

Compiled 44 to 41 computations (6.8% saved)

localize19.0ms (0.1%)

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

rewrite42.0ms (0.3%)

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)

series451.0ms (3.6%)

Counts

3 → 9

Calls

3 calls:

306.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
122.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
22.0ms	(.f64 (.f64 2 PI.f64) n)

simplify115.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4989	3537
1	4989	3537

prune344.0ms (2.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	113	11	124
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	114	12	126

Error

0.0b

Counts

126 → 12

Compiler

Compiled 3244 to 2221 computations (31.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 n (/.f64 (-.f64 1 k) 2))
0.2b	(/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
0.3b	(.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)))
0.6b	(pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2))

rewrite97.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

132×	`times-frac_binary64_425`
130×	`add-sqr-sqrt_binary64_441`
101×	`*-un-lft-identity_binary64_419`
83×	`add-cube-cbrt_binary64_454`
53×	`add-exp-log_binary64_457`
51×	`sqrt-prod_binary64_435`
48×	`unpow-prod-down_binary64_498`
46×	`associate-r_binary64_359`
44×	`pow-unpow_binary64_496`
27×	`sqr-pow_binary64_391`
21×	`prod-exp_binary64_468`
16×	`pow-exp_binary64_487`
15×	`div-exp_binary64_470`
14×	`unswap-sqr_binary64_387`
12×	`difference-of-squares_binary64_388`
11×	`pow-to-exp_binary64_488` `add-cbrt-cube_binary64_455`
8×	`pow1_binary64_480`
7×	`associate-/l*_binary64_364`
6×	`distribute-lft-out--_binary64_371` `associate-/r*_binary64_363`
5×	`pow-sub_binary64_495` `associate-l_binary64_360` `div-sub_binary64_424`
4×	`add-log-exp_binary64_458` `div-inv_binary64_416`
3×	`pow-pow_binary64_491`
2×	`cbrt-unprod_binary64_452` `cbrt-undiv_binary64_453`
1×	`associate-l/_binary64_362` `pow-prod-down_binary64_490` `clear-num_binary64_418` `frac-times_binary64_429` `associate-r/_binary64_361` `*-commutative_binary64_350` `frac-2neg_binary64_430` `associate-/l/_binary64_366`

Counts

4 → 238

Calls

4 calls:

27.0ms	(.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)))
13.0ms	(pow.f64 n (/.f64 (-.f64 1 k) 2))
13.0ms	(/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
8.0ms	(pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2))

series647.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

348.0ms	(.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)))
201.0ms	(/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
76.0ms	(pow.f64 n (/.f64 (-.f64 1 k) 2))
21.0ms	(pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2))

simplify166.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

250 → 250

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4953	7203
1	4953	7203

prune577.0ms (4.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	250	0	250
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	250	12	262

Error

0.0b

Counts

262 → 12

Compiler

Compiled 7819 to 5370 computations (31.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite50.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`add-exp-log_binary64_457`
67×	`prod-exp_binary64_468`
39×	`pow-exp_binary64_487`
30×	`div-exp_binary64_470`
26×	`pow-unpow_binary64_496`
23×	`times-frac_binary64_425`
21×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `pow1_binary64_480`
14×	`add-cbrt-cube_binary64_455`
13×	`pow-to-exp_binary64_488`
9×	`pow-prod-down_binary64_490`
6×	`pow-pow_binary64_491`
5×	`associate-/l*_binary64_364`
4×	`unpow-prod-down_binary64_498` `add-log-exp_binary64_458` `cbrt-unprod_binary64_452` `sqr-pow_binary64_391`
3×	`div-inv_binary64_416` `associate-r_binary64_359`
2×	`cbrt-undiv_binary64_453`
1×	`clear-num_binary64_418` `-commutative_binary64_350` `associate-l_binary64_360` `frac-2neg_binary64_430` `associate-/r_binary64_363`

Counts

4 → 129

Calls

4 calls:

11.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
8.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
7.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))
5.0ms	(.f64 (.f64 2 PI.f64) n)

series687.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

380.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
172.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
98.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))
36.0ms	(.f64 (.f64 2 PI.f64) n)

simplify91.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5089	3041

prune366.0ms (2.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	142	11	153

Error

Counts

153 → 11

Compiler

Compiled 3743 to 2600 computations (30.5% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite274.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

372×	`add-sqr-sqrt_binary64_441`
357×	`times-frac_binary64_425` `sqrt-prod_binary64_435`
160×	`*-un-lft-identity_binary64_419`
151×	`add-cube-cbrt_binary64_454`
98×	`unpow-prod-down_binary64_498`
90×	`sqr-pow_binary64_391`
86×	`add-exp-log_binary64_457`
70×	`unswap-sqr_binary64_387`
67×	`associate-r_binary64_359`
49×	`associate-l_binary64_360`
38×	`div-exp_binary64_470`
26×	`prod-exp_binary64_468`
22×	`pow-unpow_binary64_496`
20×	`add-cbrt-cube_binary64_455`
18×	`pow-exp_binary64_487` `associate-/r*_binary64_363`
12×	`pow-to-exp_binary64_488` `associate-/l*_binary64_364`
9×	`pow1_binary64_480`
6×	`difference-of-squares_binary64_388` `cbrt-undiv_binary64_453`
5×	`div-inv_binary64_416`
4×	`add-log-exp_binary64_458` `cbrt-unprod_binary64_452`
3×	`pow-sub_binary64_495` `distribute-lft-out--_binary64_371` `div-sub_binary64_424`
2×	`pow-prod-down_binary64_490` `clear-num_binary64_418` `frac-2neg_binary64_430` `pow-pow_binary64_491` `associate-/l/_binary64_366`
1×	`associate-l/_binary64_362` `frac-times_binary64_429` `associate-r/_binary64_361` `*-commutative_binary64_350`

Counts

4 → 428

Calls

4 calls:

113.0ms	(.f64 (/.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))))
15.0ms	(/.f64 (pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k)))
14.0ms	(pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2))
14.0ms	(/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k)))

series752.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

419.0ms	(.f64 (/.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))))
181.0ms	(/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k)))
126.0ms	(/.f64 (pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k)))
24.0ms	(pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2))

simplify286.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

440 → 440

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4989	19324
1	4989	19324

prune1.6s (12.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	440	0	440
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	440	11	451

Error

Counts

451 → 11

Compiler

Compiled 17368 to 10493 computations (39.6% saved)

regimes501.0ms (4%)

Accuracy

Total 0.5b remaining (98.7%)

Threshold costs 0.5b (98.7%)

Compiler

Compiled 4639 to 3908 computations (15.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	33
1	29	33

end0.0ms (0%)

sample4.7s (37.4%)

Algorithm

1×

intervals

Results

952.0ms	1298×	body	1024	nan
946.0ms	8000×	body	128	valid
483.0ms	2302×	body	128	overflowed
313.0ms	656×	body	512	nan
93.0ms	335×	body	256	nan
88.0ms	968×	body	128	nan
32.0ms	233×	body	128	invalid

Compiler

Compiled 1006 to 849 computations (15.6% saved)

Details

analyze543.0ms (4.3%)

sample90.0ms (0.7%)

simplify190.0ms (1.5%)

prune4.0ms (0%)

localize19.0ms (0.1%)

rewrite42.0ms (0.3%)

series451.0ms (3.6%)

simplify115.0ms (0.9%)

prune344.0ms (2.7%)

localize13.0ms (0.1%)

rewrite97.0ms (0.8%)

series647.0ms (5.1%)

simplify166.0ms (1.3%)

prune577.0ms (4.6%)

localize14.0ms (0.1%)

rewrite50.0ms (0.4%)

series687.0ms (5.4%)

simplify91.0ms (0.7%)

prune366.0ms (2.9%)

localize28.0ms (0.2%)

rewrite274.0ms (2.2%)

series752.0ms (5.9%)

simplify286.0ms (2.3%)

prune1.6s (12.5%)

regimes501.0ms (4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.7s (37.4%)

Profiling