Details

analyze388.0ms (4.2%)

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)

sample72.0ms (0.8%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
16.0ms	36×	body	1024	nan
12.0ms	86×	body	128	overflowed
5.0ms	17×	body	512	nan
2.0ms	12×	body	256	nan
2.0ms	31×	body	128	nan
1.0ms	8×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify50.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4908	22
1	4908	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: 0.3b

Counts

2 → 2

Compiler

Compiled 44 to 41 computations (6.8% saved)

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite35.0ms (0.4%)

Algorithm

1×	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	(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))
6.0ms	(.f64 (.f64 2 PI.f64) n)

series486.0ms (5.3%)

Counts

3 → 9

Calls

3 calls:

308.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
142.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
36.0ms	(.f64 (.f64 2 PI.f64) n)

simplify58.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5240	3540

prune191.0ms (2.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	115	9	124
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	116	10	126

Merged error: 0.0b

Counts

126 → 10

Compiler

Compiled 3194 to 2179 computations (31.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite55.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
62×	`times-frac_binary64`
59×	`add-exp-log_binary64`
57×	`*-un-lft-identity_binary64`
44×	`add-cube-cbrt_binary64`
30×	`prod-exp_binary64`
25×	`sqrt-prod_binary64`
23×	`associate-l_binary64`
22×	`pow-unpow_binary64`
17×	`pow1_binary64`
16×	`add-cbrt-cube_binary64`
12×	`pow-exp_binary64`
10×	`unswap-sqr_binary64`
8×	`associate-r_binary64`
7×	`sqr-pow_binary64`
6×	`pow-prod-down_binary64` `associate-/r*_binary64` `difference-of-squares_binary64` `rec-exp_binary64` `div-exp_binary64`
5×	`cbrt-unprod_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64`
3×	`pow-pow_binary64` `div-sub_binary64` `pow-sub_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `pow-flip_binary64`
2×	`cbrt-undiv_binary64` `unpow-prod-down_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64`

Counts

4 → 166

Calls

4 calls:

17.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
11.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
5.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(/.f64 1 (sqrt.f64 k))

series500.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

267.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
148.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
47.0ms	(/.f64 1 (sqrt.f64 k))
37.0ms	(.f64 (.f64 2 PI.f64) n)

simplify80.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4952	3725
1	4952	3725

prune235.0ms (2.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	176	2	178
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	177	11	188

Merged error: 0.0b

Counts

188 → 11

Compiler

Compiled 4233 to 2934 computations (30.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite77.0ms (0.8%)

Algorithm

1×	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`
59×	`add-exp-log_binary64`
40×	`associate-/r*_binary64`
32×	`sqr-pow_binary64` `unpow-prod-down_binary64`
22×	`pow-unpow_binary64`
21×	`div-exp_binary64`
16×	`pow1_binary64` `add-cbrt-cube_binary64`
15×	`prod-exp_binary64`
12×	`pow-exp_binary64`
9×	`associate-/l*_binary64`
7×	`div-inv_binary64`
6×	`pow-prod-down_binary64` `associate-/r/_binary64` `div-sub_binary64` `pow-sub_binary64` `difference-of-squares_binary64` `rec-exp_binary64`
4×	`pow-to-exp_binary64` `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 → 285

Calls

4 calls:

14.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
14.0ms	(/.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)

series720.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

273.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
260.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
148.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
38.0ms	(.f64 (.f64 2 PI.f64) n)

simplify122.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

297 → 297

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5525	10553

prune544.0ms (5.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	296	1	297
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	298	10	308

Merged error: 0b

Counts

308 → 10

Compiler

Compiled 8545 to 5868 computations (31.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite180.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

954×	`times-frac_binary64` `sqrt-prod_binary64`
452×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
443×	`add-cube-cbrt_binary64`
101×	`sqr-pow_binary64` `unpow-prod-down_binary64`
54×	`associate-/l*_binary64`
46×	`add-exp-log_binary64`
22×	`pow-unpow_binary64`
18×	`associate-/r*_binary64`
16×	`add-cbrt-cube_binary64` `div-exp_binary64`
15×	`pow1_binary64`
13×	`div-inv_binary64`
12×	`prod-exp_binary64`
9×	`pow-exp_binary64`
6×	`pow-prod-down_binary64` `difference-of-squares_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64`
3×	`pow-to-exp_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `pow-pow_binary64` `distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `div-sub_binary64` `clear-num_binary64` `pow-sub_binary64` `frac-2neg_binary64`
1×	`associate-l_binary64` `*-commutative_binary64`

Counts

4 → 651

Calls

4 calls:

27.0ms	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
11.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
10.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k)))
5.0ms	(.f64 (.f64 2 PI.f64) n)

series725.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

299.0ms	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
254.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k)))
134.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
37.0ms	(.f64 (.f64 2 PI.f64) n)

simplify318.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

663 → 663

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4997	33488
1	4997	33488

prune1.6s (17%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	663	0	663
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	663	10	673

Merged error: 0b

Counts

673 → 10

Compiler

Compiled 23311 to 13185 computations (43.4% saved)

regimes97.0ms (1.1%)

Compiler: Compiled 982 to 822 computations (16.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	25
1	27	25

end0.0ms (0%)

sample2.6s (28.7%)

Algorithm

1×

intervals

Results

748.0ms	8000×	body	128	valid
629.0ms	1367×	body	1024	nan
327.0ms	2307×	body	128	overflowed
222.0ms	696×	body	512	nan
65.0ms	1041×	body	128	nan
60.0ms	334×	body	256	nan
24.0ms	238×	body	128	invalid

Compiler

Compiled 267 to 226 computations (15.4% saved)

Details

analyze388.0ms (4.2%)

sample72.0ms (0.8%)

simplify50.0ms (0.5%)

prune5.0ms (0%)

localize17.0ms (0.2%)

rewrite35.0ms (0.4%)

series486.0ms (5.3%)

simplify58.0ms (0.6%)

prune191.0ms (2.1%)

localize13.0ms (0.1%)

rewrite55.0ms (0.6%)

series500.0ms (5.4%)

simplify80.0ms (0.9%)

prune235.0ms (2.6%)

localize13.0ms (0.1%)

rewrite77.0ms (0.8%)

series720.0ms (7.8%)

simplify122.0ms (1.3%)

prune544.0ms (5.9%)

localize15.0ms (0.2%)

rewrite180.0ms (2%)

series725.0ms (7.9%)

simplify318.0ms (3.5%)

prune1.6s (17%)

regimes97.0ms (1.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.6s (28.7%)

Profiling