Details

analyze386.0ms (3.9%)

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)

sample82.0ms (0.8%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	80	valid
18.0ms	31×	body	1280	nan
11.0ms	81×	body	80	overflowed
10.0ms	23×	body	640	nan
3.0ms	9×	body	320	nan
1.0ms	22×	body	80	nan
1.0ms	7×	body	160	nan
1.0ms	8×	body	80	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify95.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4934	22
1	4934	22

prune4.0ms (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: 0.4b

Counts

2 → 2

Compiler

Compiled 44 to 41 computations (6.8% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite34.0ms (0.3%)

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` `insert-posit16`
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 → 118

Calls

3 calls:

13.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
9.0ms	(/.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)

series489.0ms (4.9%)

Counts

3 → 9

Calls

3 calls:

297.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
146.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
46.0ms	(.f64 (.f64 2 PI.f64) n)

simplify88.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5557	3590

prune205.0ms (2.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	117	10	127
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	119	10	129

Merged error: 0.0b

Counts

129 → 10

Compiler

Compiled 3295 to 2252 computations (31.7% 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	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
0.3b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
0.3b	(.f64 (.f64 2 PI.f64) n)

rewrite65.0ms (0.7%)

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`
72×	`add-exp-log_binary64`
40×	`associate-/r*_binary64`
32×	`sqr-pow_binary64` `unpow-prod-down_binary64` `div-exp_binary64`
22×	`pow-unpow_binary64`
18×	`prod-exp_binary64`
16×	`pow1_binary64` `add-cbrt-cube_binary64`
15×	`pow-exp_binary64`
9×	`associate-/l*_binary64`
7×	`div-inv_binary64`
6×	`pow-prod-down_binary64` `1-exp_binary64` `associate-/r/_binary64` `div-sub_binary64` `pow-sub_binary64` `difference-of-squares_binary64` `rec-exp_binary64`
5×	`pow-to-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `insert-posit16`
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 → 295

Calls

4 calls:

17.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
13.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
9.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
7.0ms	(.f64 (.f64 2 PI.f64) n)

series685.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

254.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
237.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
147.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
47.0ms	(.f64 (.f64 2 PI.f64) n)

simplify209.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	5002	10791

prune574.0ms (5.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	304	3	307
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	308	9	317

Merged error: 0.0b

Counts

317 → 9

Compiler

Compiled 8719 to 5994 computations (31.3% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite127.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

1199×	`times-frac_binary64`
519×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
510×	`add-cube-cbrt_binary64`
207×	`add-exp-log_binary64`
201×	`sqrt-prod_binary64`
138×	`div-exp_binary64`
70×	`sqr-pow_binary64` `unpow-prod-down_binary64`
47×	`div-inv_binary64`
42×	`prod-exp_binary64`
39×	`pow-exp_binary64`
37×	`1-exp_binary64` `rec-exp_binary64`
26×	`associate-/r*_binary64`
25×	`associate-/l*_binary64`
24×	`associate-/r/_binary64` `div-sub_binary64` `pow-sub_binary64`
23×	`add-cbrt-cube_binary64`
22×	`pow-unpow_binary64`
17×	`pow1_binary64`
13×	`pow-to-exp_binary64`
9×	`cbrt-undiv_binary64`
6×	`pow-prod-down_binary64` `difference-of-squares_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`cbrt-unprod_binary64` `associate-r_binary64` `pow-pow_binary64` `distribute-lft-out--_binary64` `pow-flip_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `inv-pow_binary64` `*-commutative_binary64`

Counts

4 → 668

Calls

4 calls:

27.0ms	(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
16.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
7.0ms	(.f64 (.f64 2 PI.f64) n)
6.0ms	(/.f64 1 (sqrt.f64 k))

series477.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

236.0ms	(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
141.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
55.0ms	(/.f64 1 (sqrt.f64 k))
44.0ms	(.f64 (.f64 2 PI.f64) n)

simplify282.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

680 → 680

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5124	29022

prune1.8s (18.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	679	1	680
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	679	10	689

Merged error: 0.0b

Counts

689 → 10

Compiler

Compiled 20966 to 14757 computations (29.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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)
0.4b	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

rewrite55.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

284×	`times-frac_binary64`
126×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
111×	`sqrt-prod_binary64`
33×	`add-exp-log_binary64`
28×	`sqr-pow_binary64` `unpow-prod-down_binary64`
24×	`associate-/l*_binary64`
20×	`pow1_binary64`
19×	`add-cbrt-cube_binary64`
11×	`div-exp_binary64`
9×	`pow-prod-down_binary64` `prod-exp_binary64`
8×	`div-inv_binary64`
6×	`associate-/r_binary64` `cbrt-unprod_binary64` `associate-r*_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`cbrt-undiv_binary64` `sqrt-pow1_binary64` `pow-exp_binary64`
2×	`associate-l_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `associate-/l/_binary64` `pow1/2_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 245

Calls

4 calls:

20.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
7.0ms	(.f64 (.f64 2 PI.f64) n)
6.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

series578.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

441.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
50.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
43.0ms	(.f64 (.f64 2 PI.f64) n)
43.0ms	(.f64 (.f64 2 PI.f64) n)

simplify160.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

257 → 257

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5223	11805

prune541.0ms (5.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	255	2	257
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	257	10	267

Merged error: 0b

Counts

267 → 10

Compiler

Compiled 8762 to 5642 computations (35.6% saved)

regimes79.0ms (0.8%)

Compiler: Compiled 806 to 671 computations (16.7% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	28
1	28	28

end0.0ms (0%)

sample2.8s (28.1%)

Algorithm

1×

intervals

Results

727.0ms	8000×	body	80	valid
558.0ms	954×	body	1280	nan
339.0ms	2407×	body	80	overflowed
335.0ms	778×	body	640	nan
128.0ms	426×	body	320	nan
43.0ms	740×	body	80	nan
39.0ms	220×	body	160	nan
25.0ms	233×	body	80	invalid

Compiler

Compiled 299 to 252 computations (15.7% saved)

Details

analyze386.0ms (3.9%)

sample82.0ms (0.8%)

simplify95.0ms (1%)

prune4.0ms (0%)

localize12.0ms (0.1%)

rewrite34.0ms (0.3%)

series489.0ms (4.9%)

simplify88.0ms (0.9%)

prune205.0ms (2.1%)

localize16.0ms (0.2%)

rewrite65.0ms (0.7%)

series685.0ms (6.9%)

simplify209.0ms (2.1%)

prune574.0ms (5.8%)

localize15.0ms (0.1%)

rewrite127.0ms (1.3%)

series477.0ms (4.8%)

simplify282.0ms (2.9%)

prune1.8s (18.5%)

localize11.0ms (0.1%)

rewrite55.0ms (0.6%)

series578.0ms (5.8%)

simplify160.0ms (1.6%)

prune541.0ms (5.5%)

regimes79.0ms (0.8%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample2.8s (28.1%)

Profiling