Details

analyze390.0ms (5.1%)

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)

sample71.0ms (0.9%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
14.0ms	70×	body	128	overflowed
12.0ms	25×	body	1024	nan
6.0ms	20×	body	512	nan
2.0ms	31×	body	128	nan
2.0ms	9×	body	256	nan
1.0ms	6×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify202.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

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)

localize16.0ms (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)

rewrite36.0ms (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))
8.0ms	(/.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)

series499.0ms (6.6%)

Counts

3 → 9

Calls

3 calls:

322.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
139.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
38.0ms	(.f64 (.f64 2 PI.f64) n)

simplify63.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5241	3540

prune185.0ms (2.4%)

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 3167 to 2159 computations (31.8% 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:

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))))
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)

series715.0ms (9.4%)

Counts

4 → 12

Calls

4 calls:

428.0ms	(/.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))))
208.0ms	(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)

simplify57.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5437	2652

prune177.0ms (2.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	130	10	140

Merged error: 0b

Counts

140 → 10

Compiler

Compiled 3344 to 2317 computations (30.7% 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 (sqrt.f64 k))
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)

rewrite55.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-exp-log_binary64_786` `add-sqr-sqrt_binary64_772`
62×	`times-frac_binary64_757`
57×	`*-un-lft-identity_binary64_751`
44×	`add-cube-cbrt_binary64_783`
38×	`prod-exp_binary64_797`
25×	`sqrt-prod_binary64_766`
23×	`associate-l_binary64_694`
22×	`pow-unpow_binary64_825`
17×	`pow1_binary64_809`
16×	`add-cbrt-cube_binary64_784`
15×	`pow-exp_binary64_816`
12×	`div-exp_binary64_799`
10×	`unswap-sqr_binary64_719`
8×	`associate-r_binary64_693`
7×	`sqr-pow_binary64_723`
6×	`1-exp_binary64_792` `rec-exp_binary64_798` `associate-/r*_binary64_697` `pow-prod-down_binary64_819` `difference-of-squares_binary64_720`
5×	`pow-to-exp_binary64_817` `cbrt-unprod_binary64_781`
4×	`add-log-exp_binary64_787`
3×	`distribute-lft-out--_binary64_705` `div-sub_binary64_756` `pow-pow_binary64_820` `div-inv_binary64_748` `associate-/l*_binary64_698` `pow-sub_binary64_824` `pow-flip_binary64_822`
2×	`unpow-prod-down_binary64_827` `*-commutative_binary64_684` `cbrt-undiv_binary64_782`
1×	`frac-times_binary64_761` `pow1/2_binary64_828` `inv-pow_binary64_833` `associate-r/_binary64_695` `frac-2neg_binary64_762` `clear-num_binary64_750` `associate-l/_binary64_696` `sqrt-pow1_binary64_768`

Counts

4 → 172

Calls

4 calls:

16.0ms	(.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)
4.0ms	(/.f64 1 (sqrt.f64 k))

series504.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

263.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
149.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
54.0ms	(/.f64 1 (sqrt.f64 k))
37.0ms	(.f64 (.f64 2 PI.f64) n)

simplify83.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4955	3852
1	4955	3852

prune238.0ms (3.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	184	10	194

Merged error: 0b

Counts

194 → 10

Compiler

Compiled 4309 to 2982 computations (30.8% saved)

localize14.0ms (0.2%)

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)

rewrite79.0ms (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:

14.0ms	(/.f64 1 (/.f64 (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))
8.0ms	(.f64 (.f64 2 PI.f64) n)
7.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))

series741.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

280.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
271.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
151.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
38.0ms	(.f64 (.f64 2 PI.f64) n)

simplify136.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

303 → 303

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5528	10697

prune543.0ms (7.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

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

Merged error: 0b

Counts

313 → 10

Compiler

Compiled 8423 to 5756 computations (31.7% saved)

regimes94.0ms (1.2%)

Compiler: Compiled 958 to 806 computations (15.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (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 (34.6%)

Algorithm

1×

intervals

Results

748.0ms	8000×	body	128	valid
628.0ms	1330×	body	1024	nan
356.0ms	2375×	body	128	overflowed
215.0ms	647×	body	512	nan
64.0ms	334×	body	256	nan
60.0ms	1045×	body	128	nan
18.0ms	184×	body	128	invalid

Compiler

Compiled 261 to 222 computations (14.9% saved)

Details

analyze390.0ms (5.1%)

sample71.0ms (0.9%)

simplify202.0ms (2.7%)

prune4.0ms (0.1%)

localize16.0ms (0.2%)

rewrite36.0ms (0.5%)

series499.0ms (6.6%)

simplify63.0ms (0.8%)

prune185.0ms (2.4%)

localize17.0ms (0.2%)

rewrite45.0ms (0.6%)

series715.0ms (9.4%)

simplify57.0ms (0.7%)

prune177.0ms (2.3%)

localize13.0ms (0.2%)

rewrite55.0ms (0.7%)

series504.0ms (6.6%)

simplify83.0ms (1.1%)

prune238.0ms (3.1%)

localize14.0ms (0.2%)

rewrite79.0ms (1%)

series741.0ms (9.7%)

simplify136.0ms (1.8%)

prune543.0ms (7.1%)

regimes94.0ms (1.2%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.6s (34.6%)

Profiling