Details

analyze388.0ms (4.5%)

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

24.0ms	256×	body	128	valid
15.0ms	70×	body	128	overflowed
11.0ms	25×	body	1024	nan
7.0ms	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)

simplify207.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4908	22
1	4908	22

prune6.0ms (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 74 to 69 computations (6.8% saved)

localize13.0ms (0.1%)

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 (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`times-frac_binary64_773`
42×	`add-sqr-sqrt_binary64_789` `*-un-lft-identity_binary64_767`
33×	`add-cube-cbrt_binary64_802`
26×	`add-exp-log_binary64_805`
22×	`pow-unpow_binary64_844`
18×	`sqrt-prod_binary64_783`
14×	`pow1_binary64_828`
10×	`add-cbrt-cube_binary64_803`
9×	`prod-exp_binary64_816`
8×	`sqr-pow_binary64_739` `unpow-prod-down_binary64_846`
6×	`associate-/r*_binary64_711` `pow-exp_binary64_835` `pow-prod-down_binary64_838` `difference-of-squares_binary64_736`
5×	`associate-/l*_binary64_712` `div-exp_binary64_818`
3×	`associate-r_binary64_707` `cbrt-unprod_binary64_800` `add-log-exp_binary64_806` `distribute-lft-out--_binary64_719` `pow-pow_binary64_839`
2×	`pow-to-exp_binary64_836` `div-sub_binary64_772` `pow-sub_binary64_843` `div-inv_binary64_764`
1×	`associate-l_binary64_708` `frac-2neg_binary64_778` `associate-/l/_binary64_714` `cbrt-undiv_binary64_801` `*-commutative_binary64_698` `clear-num_binary64_766`

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)

series492.0ms (5.7%)

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))
148.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
36.0ms	(.f64 (.f64 2 PI.f64) n)

simplify63.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5400	3540

prune684.0ms (7.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	114	10	124
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	115	11	126

Merged error: 0.0b

Counts

126 → 11

Compiler

Compiled 12478 to 9901 computations (20.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
0.2b	(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
0.3b	(.f64 (.f64 2 PI.f64) n)
0.3b	(.f64 (.f64 2 PI.f64) n)

rewrite71.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

284×	`times-frac_binary64_773`
126×	`add-sqr-sqrt_binary64_789` `*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
111×	`sqrt-prod_binary64_783`
33×	`add-exp-log_binary64_805`
28×	`sqr-pow_binary64_739` `unpow-prod-down_binary64_846`
24×	`associate-/l*_binary64_712`
20×	`pow1_binary64_828`
19×	`add-cbrt-cube_binary64_803`
11×	`div-exp_binary64_818`
9×	`prod-exp_binary64_816` `pow-prod-down_binary64_838`
8×	`div-inv_binary64_764`
6×	`associate-r_binary64_707` `associate-/r*_binary64_711` `cbrt-unprod_binary64_800`
4×	`add-log-exp_binary64_806`
3×	`cbrt-undiv_binary64_801` `pow-exp_binary64_835` `sqrt-pow1_binary64_785`
2×	`associate-l_binary64_708` `*-commutative_binary64_698`
1×	`frac-2neg_binary64_778` `pow-to-exp_binary64_836` `associate-/l/_binary64_714` `pow1/2_binary64_847` `clear-num_binary64_766`

Counts

4 → 241

Calls

4 calls:

17.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
6.0ms	(.f64 (.f64 2 PI.f64) n)
6.0ms	(.f64 (.f64 2 PI.f64) n)
4.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

series559.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

438.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
43.0ms	(.f64 (.f64 2 PI.f64) n)
42.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
36.0ms	(.f64 (.f64 2 PI.f64) n)

simplify126.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5090	11746

prune652.0ms (7.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	251	2	253
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	254	10	264

Merged error: 0b

Counts

264 → 10

Compiler

Compiled 12008 to 8278 computations (31.1% saved)

localize17.0ms (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)

rewrite56.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-exp-log_binary64_805` `add-sqr-sqrt_binary64_789`
62×	`times-frac_binary64_773`
57×	`*-un-lft-identity_binary64_767`
44×	`add-cube-cbrt_binary64_802`
38×	`prod-exp_binary64_816`
25×	`sqrt-prod_binary64_783`
23×	`associate-l_binary64_708`
22×	`pow-unpow_binary64_844`
17×	`pow1_binary64_828`
16×	`add-cbrt-cube_binary64_803`
15×	`pow-exp_binary64_835`
12×	`div-exp_binary64_818`
10×	`unswap-sqr_binary64_735`
8×	`associate-r_binary64_707`
7×	`sqr-pow_binary64_739`
6×	`associate-/r*_binary64_711` `1-exp_binary64_811` `rec-exp_binary64_817` `pow-prod-down_binary64_838` `difference-of-squares_binary64_736`
5×	`pow-to-exp_binary64_836` `cbrt-unprod_binary64_800`
4×	`add-log-exp_binary64_806`
3×	`pow-flip_binary64_841` `associate-/l*_binary64_712` `distribute-lft-out--_binary64_719` `div-sub_binary64_772` `pow-sub_binary64_843` `div-inv_binary64_764` `pow-pow_binary64_839`
2×	`cbrt-undiv_binary64_801` `*-commutative_binary64_698` `unpow-prod-down_binary64_846`
1×	`frac-2neg_binary64_778` `frac-times_binary64_777` `pow1/2_binary64_847` `associate-r/_binary64_709` `associate-l/_binary64_710` `sqrt-pow1_binary64_785` `clear-num_binary64_766` `inv-pow_binary64_852`

Counts

4 → 172

Calls

4 calls:

15.0ms	(.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))
6.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(/.f64 1 (sqrt.f64 k))

series486.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

252.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
143.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
51.0ms	(/.f64 1 (sqrt.f64 k))
39.0ms	(.f64 (.f64 2 PI.f64) n)

simplify68.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5108	3852

prune278.0ms (3.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	184	10	194

Merged error: 0b

Counts

194 → 10

Compiler

Compiled 5107 to 3629 computations (28.9% saved)

localize16.0ms (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)

rewrite77.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

273×	`times-frac_binary64_773`
147×	`add-sqr-sqrt_binary64_789` `*-un-lft-identity_binary64_767`
138×	`add-cube-cbrt_binary64_802`
78×	`sqrt-prod_binary64_783`
72×	`add-exp-log_binary64_805`
40×	`associate-/r*_binary64_711`
32×	`sqr-pow_binary64_739` `unpow-prod-down_binary64_846` `div-exp_binary64_818`
22×	`pow-unpow_binary64_844`
18×	`prod-exp_binary64_816`
16×	`pow1_binary64_828` `add-cbrt-cube_binary64_803`
15×	`pow-exp_binary64_835`
9×	`associate-/l*_binary64_712`
7×	`div-inv_binary64_764`
6×	`associate-/r/_binary64_713` `1-exp_binary64_811` `rec-exp_binary64_817` `div-sub_binary64_772` `pow-prod-down_binary64_838` `pow-sub_binary64_843` `difference-of-squares_binary64_736`
5×	`pow-to-exp_binary64_836`
4×	`cbrt-undiv_binary64_801` `add-log-exp_binary64_806`
3×	`associate-r_binary64_707` `cbrt-unprod_binary64_800` `distribute-lft-out--_binary64_719` `pow-pow_binary64_839`
2×	`frac-2neg_binary64_778` `clear-num_binary64_766`
1×	`associate-l_binary64_708` `pow-flip_binary64_841` `*-commutative_binary64_698` `inv-pow_binary64_852`

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))
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)

series714.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

267.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
250.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
153.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
44.0ms	(.f64 (.f64 2 PI.f64) n)

simplify144.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

303 → 303

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4989	10793
1	4989	10793

prune632.0ms (7.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	303	0	303
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	303	10	313

Merged error: 0b

Counts

313 → 10

Compiler

Compiled 9277 to 6445 computations (30.5% saved)

regimes97.0ms (1.1%)

Compiler: Compiled 1042 to 858 computations (17.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	31
1	15	31

end0.0ms (0%)

sample2.7s (30.8%)

Algorithm

1×

intervals

Results

762.0ms	8000×	body	128	valid
635.0ms	1330×	body	1024	nan
338.0ms	2375×	body	128	overflowed
206.0ms	647×	body	512	nan
66.0ms	334×	body	256	nan
65.0ms	1045×	body	128	nan
18.0ms	184×	body	128	invalid

Compiler

Compiled 285 to 236 computations (17.2% saved)

Details

analyze388.0ms (4.5%)

sample72.0ms (0.8%)

simplify207.0ms (2.4%)

prune6.0ms (0.1%)

localize13.0ms (0.1%)

rewrite36.0ms (0.4%)

series492.0ms (5.7%)

simplify63.0ms (0.7%)

prune684.0ms (7.9%)

localize14.0ms (0.2%)

rewrite71.0ms (0.8%)

series559.0ms (6.5%)

simplify126.0ms (1.5%)

prune652.0ms (7.6%)

localize17.0ms (0.2%)

rewrite56.0ms (0.6%)

series486.0ms (5.6%)

simplify68.0ms (0.8%)

prune278.0ms (3.2%)

localize16.0ms (0.2%)

rewrite77.0ms (0.9%)

series714.0ms (8.3%)

simplify144.0ms (1.7%)

prune632.0ms (7.3%)

regimes97.0ms (1.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.7s (30.8%)

Profiling