Details

analyze388.0ms (2.1%)

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)

sample73.0ms (0.4%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
17.0ms	38×	body	1024	nan
11.0ms	84×	body	128	overflowed
6.0ms	19×	body	512	nan
2.0ms	34×	body	128	nan
2.0ms	9×	body	256	nan
1.0ms	10×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify148.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4933	22
1	4933	22

prune6.0ms (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

Error

0.4b

Counts

2 → 2

Compiler

Compiled 44 to 41 computations (6.8% saved)

localize11.0ms (0.1%)

Local error

Found 6 expressions with local error:

0.3b	(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)
0.2b	(.f64 (.f64 2 PI.f64) n)
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))

rewrite33.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`times-frac_binary64_766`
42×	`*-un-lft-identity_binary64_760` `add-sqr-sqrt_binary64_782`
33×	`add-cube-cbrt_binary64_795`
26×	`add-exp-log_binary64_798`
22×	`pow-unpow_binary64_837`
18×	`sqrt-prod_binary64_776`
14×	`pow1_binary64_821`
10×	`add-cbrt-cube_binary64_796`
9×	`prod-exp_binary64_809`
8×	`sqr-pow_binary64_732` `unpow-prod-down_binary64_839`
6×	`associate-/r*_binary64_704` `pow-exp_binary64_828` `difference-of-squares_binary64_729` `pow-prod-down_binary64_831`
5×	`associate-/l*_binary64_705` `div-exp_binary64_811`
3×	`add-log-exp_binary64_799` `distribute-lft-out--_binary64_712` `associate-r_binary64_700` `cbrt-unprod_binary64_793` `pow-pow_binary64_832`
2×	`div-inv_binary64_757` `pow-to-exp_binary64_829` `div-sub_binary64_765` `pow-sub_binary64_836`
1×	`frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `associate-/l/_binary64_707` `associate-l_binary64_701` `clear-num_binary64_759` `*-commutative_binary64_691`

Counts

3 → 115

Calls

6 calls:

10.0ms	(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)
0.0ms	(.f64 (.f64 2 PI.f64) n)
0.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))

series423.0ms (2.3%)

Counts

3 → 18

Calls

3 calls:

212.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
186.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
26.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 703 to 606 computations (13.8% saved)

simplify91.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4969	3385
1	4969	3385

prune281.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	124	9	133
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	126	9	135

Error

0.0b

Counts

135 → 9

Compiler

Compiled 3107 to 2107 computations (32.2% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (.f64 2 PI.f64) n)
0.2b	(.f64 (.f64 2 PI.f64) n)
0.1b	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
0.0b	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2)))
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))

rewrite67.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

284×	`times-frac_binary64_766`
126×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
111×	`sqrt-prod_binary64_776`
33×	`add-exp-log_binary64_798`
28×	`sqr-pow_binary64_732` `unpow-prod-down_binary64_839`
24×	`associate-/l*_binary64_705`
20×	`pow1_binary64_821`
19×	`add-cbrt-cube_binary64_796`
11×	`div-exp_binary64_811`
9×	`prod-exp_binary64_809` `pow-prod-down_binary64_831`
8×	`div-inv_binary64_757`
6×	`associate-/r_binary64_704` `associate-r*_binary64_700` `cbrt-unprod_binary64_793`
4×	`add-log-exp_binary64_799`
3×	`cbrt-undiv_binary64_794` `sqrt-pow1_binary64_778` `pow-exp_binary64_828`
2×	`associate-l_binary64_701` `*-commutative_binary64_691`
1×	`frac-2neg_binary64_771` `associate-/l/_binary64_707` `pow-to-exp_binary64_829` `pow1/2_binary64_840` `clear-num_binary64_759`

Counts

4 → 241

Calls

8 calls:

16.0ms	(/.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	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
5.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(.f64 (.f64 2 PI.f64) n)
0.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2)))

series232.0ms (1.3%)

Counts

4 → 15

Calls

4 calls:

153.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
27.0ms	(.f64 (.f64 2 PI.f64) n)
26.0ms	(.f64 (.f64 2 PI.f64) n)
25.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

Compiler

Compiled 804 to 671 computations (16.5% saved)

simplify155.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5032	11499

prune573.0ms (3.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	252	4	256
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	256	9	265

Error

Counts

265 → 9

Compiler

Compiled 8762 to 5671 computations (35.3% saved)

localize12.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (.f64 2 PI.f64) n)
0.2b	(/.f64 1 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2)))))
0.1b	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
0.0b	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2)))
0.2b	(/.f64 1 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (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)
0.2b	(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))))

rewrite247.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

1787×	`times-frac_binary64_766`
712×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
518×	`sqrt-prod_binary64_776`
173×	`associate-/r*_binary64_704`
124×	`sqr-pow_binary64_732` `unpow-prod-down_binary64_839`
100×	`add-exp-log_binary64_798`
58×	`div-exp_binary64_811`
37×	`div-inv_binary64_757`
28×	`add-cbrt-cube_binary64_796`
18×	`prod-exp_binary64_809`
15×	`pow1_binary64_821`
12×	`pow-exp_binary64_828`
9×	`cbrt-undiv_binary64_794` `associate-/l*_binary64_705`
7×	`rec-exp_binary64_810` `1-exp_binary64_804`
6×	`associate-/r/_binary64_706` `associate-r_binary64_700` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831`
4×	`add-log-exp_binary64_799` `pow-to-exp_binary64_829`
2×	`frac-2neg_binary64_771` `associate-l_binary64_701` `clear-num_binary64_759` `*-commutative_binary64_691`
1×	`inv-pow_binary64_845` `pow-flip_binary64_834`

Counts

4 → 865

Calls

8 calls:

41.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2)))))
16.0ms	(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))))
8.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(.f64 (.f64 2 PI.f64) n)
0.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2)))

series569.0ms (3.1%)

Counts

4 → 18

Calls

4 calls:

238.0ms	(.f64 (.f64 2 PI.f64) n)
152.0ms	(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))))
151.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2)))))
27.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 1126 to 942 computations (16.3% saved)

simplify421.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

883 → 883

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5349	48914

prune3.5s (18.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	882	1	883
Fresh	1	6	7
Picked	0	1	1
Done	1	0	1
Total	884	8	892

Error

Counts

892 → 8

Compiler

Compiled 35033 to 23099 computations (34.1% saved)

localize14.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (.f64 2 PI.f64) n)
0.2b	(.f64 (.f64 2 PI.f64) n)
0.1b	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
0.0b	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2)))
0.2b	(.f64 (.f64 2 PI.f64) n)
0.2b	(/.f64 1 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))))
0.2b	(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2)))))
0.3b	(/.f64 1 (sqrt.f64 k))

rewrite643.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

6304×	`times-frac_binary64_766`
2364×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
1079×	`sqrt-prod_binary64_776`
337×	`add-exp-log_binary64_798`
292×	`sqr-pow_binary64_732` `unpow-prod-down_binary64_839`
251×	`div-exp_binary64_811`
177×	`div-inv_binary64_757`
107×	`associate-/r*_binary64_704`
50×	`rec-exp_binary64_810` `1-exp_binary64_804`
48×	`prod-exp_binary64_809`
45×	`pow-exp_binary64_828`
37×	`add-cbrt-cube_binary64_796`
28×	`associate-/l*_binary64_705`
25×	`associate-/r/_binary64_706`
19×	`cbrt-undiv_binary64_794`
18×	`pow1_binary64_821`
15×	`pow-to-exp_binary64_829`
8×	`pow-flip_binary64_834`
6×	`pow-prod-down_binary64_831`
4×	`pow-div_binary64_835` `sqrt-pow1_binary64_778` `add-log-exp_binary64_799`
3×	`frac-2neg_binary64_771` `associate-r_binary64_700` `cbrt-unprod_binary64_793` `clear-num_binary64_759`
2×	`inv-pow_binary64_845` `pow1/2_binary64_840`
1×	`associate-/l/_binary64_707` `associate-l_binary64_701` `*-commutative_binary64_691`

Counts

4 → 1000

Calls

8 calls:

73.0ms	(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2)))))
13.0ms	(/.f64 1 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))))
5.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(/.f64 1 (sqrt.f64 k))
0.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2)))

series408.0ms (2.2%)

Counts

4 → 21

Calls

4 calls:

208.0ms	(/.f64 1 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))))
154.0ms	(/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2)))))
26.0ms	(.f64 (.f64 2 PI.f64) n)
20.0ms	(/.f64 1 (sqrt.f64 k))

Compiler

Compiled 1241 to 1039 computations (16.3% saved)

simplify660.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1021 → 1021

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4991	73907
1	4991	73907

prune5.0s (27.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	1021	0	1021
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	1021	8	1029

Error

Counts

1029 → 8

Compiler

Compiled 46665 to 32450 computations (30.5% saved)

simplify43.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	452	2995
1	452	2995

regimes429.0ms (2.3%)

Compiler: Compiled 5459 to 4535 computations (16.9% saved)

bsearch0.0ms (0%)

regimes51.0ms (0.3%)

Compiler: Compiled 275 to 287 computations (-4.4% saved)

bsearch0.0ms (0%)

regimes26.0ms (0.1%)

Accuracy

Total 0.4b remaining (99.8%)

Threshold costs 0.4b (99.8%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch29.0ms (0.2%)

Steps

Iters	Range		Point
9	0.6400884701246073	251997334.4286402	3.531377525812489

Compiler

Compiled 41 to 41 computations (0% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	62
1	34	62

end0.0ms (0%)

sample3.9s (21.3%)

Algorithm

1×

intervals

Results

631.0ms	8000×	body	128	valid
609.0ms	1311×	body	1024	nan
322.0ms	2316×	body	128	overflowed
206.0ms	643×	body	512	nan
62.0ms	994×	body	128	nan
56.0ms	320×	body	256	nan
22.0ms	234×	body	128	invalid

Compiler

Compiled 1872 to 1562 computations (16.6% saved)

Pareto

0.5477619943783035

Details

analyze388.0ms (2.1%)

sample73.0ms (0.4%)

simplify148.0ms (0.8%)

prune6.0ms (0%)

localize11.0ms (0.1%)

rewrite33.0ms (0.2%)

series423.0ms (2.3%)

simplify91.0ms (0.5%)

prune281.0ms (1.5%)

localize11.0ms (0.1%)

rewrite67.0ms (0.4%)

series232.0ms (1.3%)

simplify155.0ms (0.8%)

prune573.0ms (3.1%)

localize12.0ms (0.1%)

rewrite247.0ms (1.3%)

series569.0ms (3.1%)

simplify421.0ms (2.3%)

prune3.5s (18.9%)

localize14.0ms (0.1%)

rewrite643.0ms (3.5%)

series408.0ms (2.2%)

simplify660.0ms (3.6%)

prune5.0s (27.2%)

simplify43.0ms (0.2%)

regimes429.0ms (2.3%)

bsearch0.0ms (0%)

regimes51.0ms (0.3%)

bsearch0.0ms (0%)

regimes26.0ms (0.1%)

bsearch29.0ms (0.2%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.9s (21.3%)

Profiling