Details

analyze394.0ms (5.4%)

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)

sample85.0ms (1.2%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
24.0ms	51×	body	1024	nan
11.0ms	74×	body	128	overflowed
10.0ms	33×	body	512	nan
2.0ms	29×	body	128	nan
2.0ms	9×	body	256	nan
1.0ms	8×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify205.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4908	22
1	4908	22

prune4.0ms (0.1%)

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)

localize12.0ms (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))
0.2b	(/.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)

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`times-frac_binary64_757`
42×	`*-un-lft-identity_binary64_751` `add-sqr-sqrt_binary64_772`
33×	`add-cube-cbrt_binary64_783`
26×	`add-exp-log_binary64_786`
22×	`pow-unpow_binary64_825`
18×	`sqrt-prod_binary64_766`
14×	`pow1_binary64_809`
10×	`add-cbrt-cube_binary64_784`
9×	`prod-exp_binary64_797`
8×	`sqr-pow_binary64_723` `unpow-prod-down_binary64_827`
6×	`pow-exp_binary64_816` `associate-/r*_binary64_697` `pow-prod-down_binary64_819` `difference-of-squares_binary64_720`
5×	`associate-/l*_binary64_698` `div-exp_binary64_799`
3×	`distribute-lft-out--_binary64_705` `add-log-exp_binary64_787` `pow-pow_binary64_820` `associate-r_binary64_693` `cbrt-unprod_binary64_781`
2×	`pow-to-exp_binary64_817` `div-sub_binary64_756` `div-inv_binary64_748` `pow-sub_binary64_824`
1×	`associate-/l/_binary64_700` `-commutative_binary64_684` `cbrt-undiv_binary64_782` `frac-2neg_binary64_762` `associate-l*_binary64_694` `clear-num_binary64_750`

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)

series494.0ms (6.8%)

Counts

3 → 9

Calls

3 calls:

314.0ms	(/.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))
37.0ms	(.f64 (.f64 2 PI.f64) n)

simplify60.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5241	3540

prune192.0ms (2.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	112	12	124
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	114	12	126

Merged error: 0.0b

Counts

126 → 12

Compiler

Compiled 3270 to 2237 computations (31.6% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
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))))
0.3b	(.f64 (.f64 2 PI.f64) n)
0.3b	(.f64 (.f64 2 PI.f64) n)

rewrite45.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-exp-log_binary64_786`
67×	`prod-exp_binary64_797`
36×	`pow-exp_binary64_816`
30×	`div-exp_binary64_799`
20×	`pow1_binary64_809`
19×	`add-cbrt-cube_binary64_784`
15×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751` `add-sqr-sqrt_binary64_772`
14×	`times-frac_binary64_757`
13×	`pow-unpow_binary64_825`
12×	`pow-to-exp_binary64_817`
9×	`pow-prod-down_binary64_819`
7×	`cbrt-unprod_binary64_781`
6×	`associate-r_binary64_693`
5×	`associate-/l*_binary64_698`
4×	`add-log-exp_binary64_787`
3×	`sqr-pow_binary64_723` `unpow-prod-down_binary64_827` `pow-pow_binary64_820`
2×	`-commutative_binary64_684` `div-inv_binary64_748` `cbrt-undiv_binary64_782` `associate-l*_binary64_694`
1×	`associate-/r*_binary64_697` `frac-2neg_binary64_762` `clear-num_binary64_750`

Counts

4 → 118

Calls

4 calls:

10.0ms	(/.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))))
7.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
6.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(.f64 (.f64 2 PI.f64) n)

series707.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

430.0ms	(/.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))))
198.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
40.0ms	(.f64 (.f64 2 PI.f64) n)
39.0ms	(.f64 (.f64 2 PI.f64) n)

simplify58.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5437	2652

prune181.0ms (2.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	129	13	142

Merged error: 0.0b

Counts

142 → 13

Compiler

Compiled 3444 to 2392 computations (30.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
0.3b	(.f64 (.f64 2 PI.f64) n)
0.3b	(.f64 (.f64 2 PI.f64) n)
0.3b	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (sqrt.f64 k))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64_757`
23×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751` `sqrt-prod_binary64_766` `add-sqr-sqrt_binary64_772`
20×	`pow1_binary64_809`
16×	`add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
9×	`pow-prod-down_binary64_819`
6×	`prod-exp_binary64_797` `associate-/r_binary64_697` `associate-r*_binary64_693` `cbrt-unprod_binary64_781`
4×	`add-log-exp_binary64_787` `associate-/l*_binary64_698`
3×	`sqrt-pow1_binary64_768`
2×	`-commutative_binary64_684` `associate-l*_binary64_694`
1×	`pow1/2_binary64_828` `sqrt-undiv_binary64_771` `div-inv_binary64_748` `cbrt-undiv_binary64_782` `frac-2neg_binary64_762` `clear-num_binary64_750` `div-exp_binary64_799`

Counts

4 → 95

Calls

4 calls:

8.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (sqrt.f64 k))
6.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(.f64 (.f64 2 PI.f64) n)
4.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

series290.0ms (4%)

Counts

4 → 12

Calls

4 calls:

161.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (sqrt.f64 k))
45.0ms	(.f64 (.f64 2 PI.f64) n)
43.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
41.0ms	(.f64 (.f64 2 PI.f64) n)

simplify68.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4957	1953
1	4957	1953

prune142.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	5	6	11
Picked	1	0	1
Done	0	1	1
Total	111	9	120

Merged error: 0.0b

Counts

120 → 9

Compiler

Compiled 2914 to 1891 computations (35.1% saved)

localize13.0ms (0.2%)

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

rewrite78.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

273×	`times-frac_binary64_757`
147×	`*-un-lft-identity_binary64_751` `add-sqr-sqrt_binary64_772`
138×	`add-cube-cbrt_binary64_783`
78×	`sqrt-prod_binary64_766`
72×	`add-exp-log_binary64_786`
40×	`associate-/r*_binary64_697`
32×	`sqr-pow_binary64_723` `unpow-prod-down_binary64_827` `div-exp_binary64_799`
22×	`pow-unpow_binary64_825`
18×	`prod-exp_binary64_797`
16×	`pow1_binary64_809` `add-cbrt-cube_binary64_784`
15×	`pow-exp_binary64_816`
9×	`associate-/l*_binary64_698`
7×	`div-inv_binary64_748`
6×	`1-exp_binary64_792` `div-sub_binary64_756` `rec-exp_binary64_798` `pow-prod-down_binary64_819` `associate-/r/_binary64_699` `pow-sub_binary64_824` `difference-of-squares_binary64_720`
5×	`pow-to-exp_binary64_817`
4×	`add-log-exp_binary64_787` `cbrt-undiv_binary64_782`
3×	`distribute-lft-out--_binary64_705` `pow-pow_binary64_820` `associate-r_binary64_693` `cbrt-unprod_binary64_781`
2×	`frac-2neg_binary64_762` `clear-num_binary64_750`
1×	`inv-pow_binary64_833` `-commutative_binary64_684` `associate-l*_binary64_694` `pow-flip_binary64_822`

Counts

4 → 291

Calls

4 calls:

13.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
12.0ms	(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)))
5.0ms	(.f64 (.f64 2 PI.f64) n)

series700.0ms (9.6%)

Counts

4 → 12

Calls

4 calls:

274.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
249.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
139.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
38.0ms	(.f64 (.f64 2 PI.f64) n)

simplify126.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

303 → 303

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5528	10697

prune548.0ms (7.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	301	2	303
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	303	9	312

Merged error: 0b

Counts

312 → 9

Compiler

Compiled 8423 to 5756 computations (31.7% saved)

regimes71.0ms (1%)

Compiler: Compiled 830 to 674 computations (18.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	32
1	19	32

end0.0ms (0%)

sample2.7s (37.1%)

Algorithm

1×

intervals

Results

763.0ms	8000×	body	128	valid
643.0ms	1333×	body	1024	nan
337.0ms	2325×	body	128	overflowed
226.0ms	699×	body	512	nan
68.0ms	369×	body	256	nan
61.0ms	981×	body	128	nan
26.0ms	263×	body	128	invalid

Compiler

Compiled 309 to 253 computations (18.1% saved)

Details

analyze394.0ms (5.4%)

sample85.0ms (1.2%)

simplify205.0ms (2.8%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

rewrite39.0ms (0.5%)

series494.0ms (6.8%)

simplify60.0ms (0.8%)

prune192.0ms (2.6%)

localize17.0ms (0.2%)

rewrite45.0ms (0.6%)

series707.0ms (9.7%)

simplify58.0ms (0.8%)

prune181.0ms (2.5%)

localize11.0ms (0.2%)

rewrite31.0ms (0.4%)

series290.0ms (4%)

simplify68.0ms (0.9%)

prune142.0ms (2%)

localize13.0ms (0.2%)

rewrite78.0ms (1.1%)

series700.0ms (9.6%)

simplify126.0ms (1.7%)

prune548.0ms (7.5%)

regimes71.0ms (1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.7s (37.1%)

Profiling