Details

analyze385.0ms (3.6%)

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)

sample76.0ms (0.7%)

Algorithm

1×

intervals

Results

28.0ms	256×	body	128	valid
13.0ms	29×	body	1024	nan
10.0ms	75×	body	128	overflowed
9.0ms	28×	body	512	nan
2.0ms	31×	body	128	nan
1.0ms	8×	body	256	nan
1.0ms	12×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify214.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4908	22
1	4908	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 (.f64 2 PI.f64) n)
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))

rewrite35.0ms (0.3%)

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))
5.0ms	(.f64 (.f64 2 PI.f64) n)

series512.0ms (4.8%)

Counts

3 → 9

Calls

3 calls:

330.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
143.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
38.0ms	(.f64 (.f64 2 PI.f64) n)

simplify62.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5241	3540

prune198.0ms (1.8%)

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 3240 to 2219 computations (31.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite66.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

284×	`times-frac_binary64_757`
126×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751` `add-sqr-sqrt_binary64_772`
111×	`sqrt-prod_binary64_766`
33×	`add-exp-log_binary64_786`
28×	`sqr-pow_binary64_723` `unpow-prod-down_binary64_827`
24×	`associate-/l*_binary64_698`
20×	`pow1_binary64_809`
19×	`add-cbrt-cube_binary64_784`
11×	`div-exp_binary64_799`
9×	`prod-exp_binary64_797` `pow-prod-down_binary64_819`
8×	`div-inv_binary64_748`
6×	`associate-/r_binary64_697` `associate-r*_binary64_693` `cbrt-unprod_binary64_781`
4×	`add-log-exp_binary64_787`
3×	`pow-exp_binary64_816` `cbrt-undiv_binary64_782` `sqrt-pow1_binary64_768`
2×	`-commutative_binary64_684` `associate-l*_binary64_694`
1×	`pow-to-exp_binary64_817` `associate-/l/_binary64_700` `pow1/2_binary64_828` `frac-2neg_binary64_762` `clear-num_binary64_750`

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))
5.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(.f64 (.f64 2 PI.f64) n)
4.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

series581.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

455.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
45.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
43.0ms	(.f64 (.f64 2 PI.f64) n)
38.0ms	(.f64 (.f64 2 PI.f64) n)

simplify145.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4969	11746
1	4969	11746

prune526.0ms (4.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	250	3	253
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	254	10	264

Merged error: 0b

Counts

264 → 10

Compiler

Compiled 8983 to 5824 computations (35.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
0.2b	(.f64 (.f64 2 PI.f64) n)
0.3b	(.f64 (sqrt.f64 (.f64 2 PI.f64)) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k)))
1.0b	(sqrt.f64 (*.f64 2 PI.f64))

rewrite197.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

816×	`times-frac_binary64_757`
413×	`sqrt-prod_binary64_766`
402×	`add-sqr-sqrt_binary64_772`
366×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751`
211×	`associate-r_binary64_693`
82×	`sqr-pow_binary64_723`
78×	`unpow-prod-down_binary64_827`
55×	`add-exp-log_binary64_786`
34×	`associate-/l*_binary64_698`
23×	`add-cbrt-cube_binary64_784`
22×	`div-exp_binary64_799`
16×	`prod-exp_binary64_797`
15×	`div-inv_binary64_748`
14×	`pow1_binary64_809`
11×	`unswap-sqr_binary64_719`
6×	`pow-exp_binary64_816` `associate-/r*_binary64_697` `cbrt-undiv_binary64_782` `cbrt-unprod_binary64_781`
5×	`pow-prod-down_binary64_819` `associate-l_binary64_694`
4×	`add-log-exp_binary64_787`
2×	`pow-to-exp_binary64_817` `*-commutative_binary64_684` `sqrt-pow1_binary64_768`
1×	`associate-/l/_binary64_700` `pow1/2_binary64_828` `associate-*r/_binary64_695` `frac-2neg_binary64_762` `clear-num_binary64_750`

Counts

4 → 535

Calls

4 calls:

68.0ms	(.f64 (sqrt.f64 (.f64 2 PI.f64)) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k)))
17.0ms	(/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
5.0ms	(.f64 (.f64 2 PI.f64) n)
2.0ms	(sqrt.f64 (*.f64 2 PI.f64))

series911.0ms (8.5%)

Counts

4 → 10

Calls

4 calls:

499.0ms	(.f64 (sqrt.f64 (.f64 2 PI.f64)) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k)))
373.0ms	(/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
39.0ms	(.f64 (.f64 2 PI.f64) n)
0.0ms	(sqrt.f64 (*.f64 2 PI.f64))

simplify205.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

545 → 545

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5010	22200

prune1.3s (12.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	544	1	545
Fresh	2	6	8
Picked	0	1	1
Done	1	0	1
Total	547	8	555

Merged error: 0b

Counts

555 → 8

Compiler

Compiled 19990 to 11331 computations (43.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
0.2b	(.f64 (.f64 2 PI.f64) n)
0.3b	(.f64 (.f64 (sqrt.f64 2) (sqrt.f64 PI.f64)) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k)))
1.0b	(sqrt.f64 PI.f64)

rewrite184.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

798×	`times-frac_binary64_757`
405×	`sqrt-prod_binary64_766`
367×	`add-sqr-sqrt_binary64_772`
366×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751`
211×	`associate-r_binary64_693`
89×	`add-exp-log_binary64_786`
78×	`sqr-pow_binary64_723` `unpow-prod-down_binary64_827`
35×	`add-cbrt-cube_binary64_784`
34×	`associate-/l*_binary64_698`
33×	`prod-exp_binary64_797` `div-exp_binary64_799`
15×	`pow1_binary64_809` `div-inv_binary64_748`
12×	`cbrt-unprod_binary64_781`
9×	`pow-exp_binary64_816` `cbrt-undiv_binary64_782`
6×	`associate-/r*_binary64_697` `pow-prod-down_binary64_819`
4×	`add-log-exp_binary64_787`
3×	`pow-to-exp_binary64_817`
2×	`-commutative_binary64_684` `associate-l*_binary64_694`
1×	`associate-/l/_binary64_700` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `associate-*r/_binary64_695` `frac-2neg_binary64_762` `clear-num_binary64_750` `sqrt-pow1_binary64_768`

Counts

4 → 534

Calls

4 calls:

51.0ms	(.f64 (.f64 (sqrt.f64 2) (sqrt.f64 PI.f64)) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k)))
22.0ms	(/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
6.0ms	(.f64 (.f64 2 PI.f64) n)
1.0ms	(sqrt.f64 PI.f64)

series916.0ms (8.5%)

Counts

4 → 10

Calls

4 calls:

496.0ms	(.f64 (.f64 (sqrt.f64 2) (sqrt.f64 PI.f64)) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k)))
382.0ms	(/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
38.0ms	(.f64 (.f64 2 PI.f64) n)
0.0ms	(sqrt.f64 PI.f64)

simplify203.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

544 → 544

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5333	22083

prune1.3s (11.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	544	0	544
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	544	8	552

Merged error: 0b

Counts

552 → 8

Compiler

Compiled 20025 to 10966 computations (45.2% saved)

regimes86.0ms (0.8%)

Compiler: Compiled 891 to 729 computations (18.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	35
1	21	35

end0.0ms (0%)

sample2.6s (24%)

Algorithm

1×

intervals

Results

737.0ms	8000×	body	128	valid
596.0ms	1275×	body	1024	nan
335.0ms	2377×	body	128	overflowed
223.0ms	728×	body	512	nan
60.0ms	340×	body	256	nan
59.0ms	1001×	body	128	nan
22.0ms	236×	body	128	invalid

Compiler

Compiled 265 to 219 computations (17.4% saved)

Details

analyze385.0ms (3.6%)

sample76.0ms (0.7%)

simplify214.0ms (2%)

prune4.0ms (0%)

localize12.0ms (0.1%)

rewrite35.0ms (0.3%)

series512.0ms (4.8%)

simplify62.0ms (0.6%)

prune198.0ms (1.8%)

localize14.0ms (0.1%)

rewrite66.0ms (0.6%)

series581.0ms (5.4%)

simplify145.0ms (1.4%)

prune526.0ms (4.9%)

localize13.0ms (0.1%)

rewrite197.0ms (1.8%)

series911.0ms (8.5%)

simplify205.0ms (1.9%)

prune1.3s (12.4%)

localize18.0ms (0.2%)

rewrite184.0ms (1.7%)

series916.0ms (8.5%)

simplify203.0ms (1.9%)

prune1.3s (11.9%)

regimes86.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.6s (24%)

Profiling