Details

analyze401.0ms (5.5%)

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)

sample86.0ms (1.2%)

Algorithm

1×

intervals

Results

27.0ms	49×	body	1024	nan
24.0ms	256×	body	128	valid
10.0ms	75×	body	128	overflowed
8.0ms	27×	body	512	nan
2.0ms	30×	body	128	nan
1.0ms	6×	body	256	nan
0.0ms	3×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify208.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4908	22
1	4908	22

prune7.0ms (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: 0.2b

Counts

2 → 2

Compiler

Compiled 74 to 69 computations (6.8% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(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))
0.2b	(.f64 (.f64 2 PI.f64) n)

rewrite36.0ms (0.5%)

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)

series501.0ms (6.8%)

Counts

3 → 9

Calls

3 calls:

315.0ms	(/.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))
39.0ms	(.f64 (.f64 2 PI.f64) n)

simplify66.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5400	3540

prune556.0ms (7.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	117	7	124
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	118	8	126

Merged error: 0.0b

Counts

126 → 8

Compiler

Compiled 9941 to 7774 computations (21.8% saved)

localize20.0ms (0.3%)

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))))
0.2b	(.f64 (.f64 2 PI.f64) n)
0.2b	(.f64 (.f64 2 PI.f64) n)

rewrite43.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-exp-log_binary64_805`
67×	`prod-exp_binary64_816`
36×	`pow-exp_binary64_835`
30×	`div-exp_binary64_818`
20×	`pow1_binary64_828`
19×	`add-cbrt-cube_binary64_803`
15×	`add-sqr-sqrt_binary64_789` `*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
14×	`times-frac_binary64_773`
13×	`pow-unpow_binary64_844`
12×	`pow-to-exp_binary64_836`
9×	`pow-prod-down_binary64_838`
7×	`cbrt-unprod_binary64_800`
6×	`associate-r_binary64_707`
5×	`associate-/l*_binary64_712`
4×	`add-log-exp_binary64_806`
3×	`sqr-pow_binary64_739` `unpow-prod-down_binary64_846` `pow-pow_binary64_839`
2×	`associate-l_binary64_708` `cbrt-undiv_binary64_801` `*-commutative_binary64_698` `div-inv_binary64_764`
1×	`frac-2neg_binary64_778` `associate-/r*_binary64_711` `clear-num_binary64_766`

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))))
8.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
6.0ms	(.f64 (.f64 2 PI.f64) n)
6.0ms	(.f64 (.f64 2 PI.f64) n)

series713.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

424.0ms	(/.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))))
213.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
38.0ms	(.f64 (.f64 2 PI.f64) n)
37.0ms	(.f64 (.f64 2 PI.f64) n)

simplify56.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5603	2652

prune202.0ms (2.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	130	8	138

Merged error: 0.0b

Counts

138 → 8

Compiler

Compiled 3950 to 2828 computations (28.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(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)))
0.2b	(.f64 (.f64 2 PI.f64) n)
0.3b	(/.f64 1 (sqrt.f64 k))

rewrite256.0ms (3.5%)

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))

series490.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

256.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
150.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
47.0ms	(/.f64 1 (sqrt.f64 k))
36.0ms	(.f64 (.f64 2 PI.f64) n)

simplify65.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5108	3852

prune251.0ms (3.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	183	1	184
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	185	7	192

Merged error: 0b

Counts

192 → 7

Compiler

Compiled 4662 to 3285 computations (29.5% saved)

localize20.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_805`
33×	`add-sqr-sqrt_binary64_789`
30×	`prod-exp_binary64_816`
26×	`*-un-lft-identity_binary64_767`
22×	`pow-unpow_binary64_844`
18×	`times-frac_binary64_773`
17×	`pow-exp_binary64_835` `add-cube-cbrt_binary64_802`
14×	`pow1_binary64_828`
10×	`add-cbrt-cube_binary64_803`
9×	`pow-to-exp_binary64_836`
8×	`associate-l_binary64_708` `associate-r_binary64_707` `sqr-pow_binary64_739`
7×	`unpow-prod-down_binary64_846`
6×	`unswap-sqr_binary64_735` `pow-prod-down_binary64_838` `difference-of-squares_binary64_736`
4×	`cbrt-unprod_binary64_800`
3×	`add-log-exp_binary64_806` `distribute-lft-out--_binary64_719` `pow-pow_binary64_839`
2×	`*-commutative_binary64_698` `div-sub_binary64_772` `pow-sub_binary64_843`
1×	`associate-*r/_binary64_709` `div-inv_binary64_764`

Counts

3 → 100

Calls

3 calls:

11.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
9.0ms	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
6.0ms	(.f64 (.f64 2 PI.f64) n)

series437.0ms (5.9%)

Counts

3 → 9

Calls

3 calls:

245.0ms	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
154.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
37.0ms	(.f64 (.f64 2 PI.f64) n)

simplify52.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5142	2580

prune149.0ms (2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	109	7	116

Merged error: 0b

Counts

116 → 7

Compiler

Compiled 2639 to 2002 computations (24.1% saved)

regimes59.0ms (0.8%)

Compiler: Compiled 551 to 473 computations (14.2% 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%)

sample2.6s (35.6%)

Algorithm

1×

intervals

Results

754.0ms	8000×	body	128	valid
625.0ms	1321×	body	1024	nan
336.0ms	2408×	body	128	overflowed
222.0ms	670×	body	512	nan
62.0ms	346×	body	256	nan
57.0ms	1003×	body	128	nan
24.0ms	201×	body	128	invalid

Compiler

Compiled 216 to 186 computations (13.9% saved)

Details

analyze401.0ms (5.5%)

sample86.0ms (1.2%)

simplify208.0ms (2.8%)

prune7.0ms (0.1%)

localize12.0ms (0.2%)

rewrite36.0ms (0.5%)

series501.0ms (6.8%)

simplify66.0ms (0.9%)

prune556.0ms (7.6%)

localize20.0ms (0.3%)

rewrite43.0ms (0.6%)

series713.0ms (9.7%)

simplify56.0ms (0.8%)

prune202.0ms (2.7%)

localize13.0ms (0.2%)

rewrite256.0ms (3.5%)

series490.0ms (6.7%)

simplify65.0ms (0.9%)

prune251.0ms (3.4%)

localize20.0ms (0.3%)

rewrite35.0ms (0.5%)

series437.0ms (5.9%)

simplify52.0ms (0.7%)

prune149.0ms (2%)

regimes59.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.6s (35.6%)

Profiling