Details

analyze382.0ms (2.9%)

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)

sample75.0ms (0.6%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
19.0ms	43×	body	1024	nan
9.0ms	70×	body	128	overflowed
9.0ms	29×	body	512	nan
2.0ms	35×	body	128	nan
1.0ms	14×	body	128	invalid
1.0ms	7×	body	256	nan

Compiler

Compiled 33 to 33 computations (0% saved)

simplify142.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

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

rewrite35.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`times-frac_binary64_743`
42×	`add-sqr-sqrt_binary64_759` `*-un-lft-identity_binary64_737`
33×	`add-cube-cbrt_binary64_772`
26×	`add-exp-log_binary64_775`
22×	`pow-unpow_binary64_814`
18×	`sqrt-prod_binary64_753`
14×	`pow1_binary64_798`
10×	`add-cbrt-cube_binary64_773`
9×	`prod-exp_binary64_786`
8×	`unpow-prod-down_binary64_816` `sqr-pow_binary64_709`
6×	`pow-exp_binary64_805` `associate-/r*_binary64_681` `pow-prod-down_binary64_808` `difference-of-squares_binary64_706`
5×	`associate-/l*_binary64_682` `div-exp_binary64_788`
3×	`add-log-exp_binary64_776` `cbrt-unprod_binary64_770` `distribute-lft-out--_binary64_689` `pow-pow_binary64_809` `associate-r_binary64_677`
2×	`div-sub_binary64_742` `div-inv_binary64_734` `pow-to-exp_binary64_806` `pow-sub_binary64_813`
1×	`frac-2neg_binary64_748` `clear-num_binary64_736` `cbrt-undiv_binary64_771` `associate-/l/_binary64_684` `associate-l_binary64_678` `*-commutative_binary64_668`

Counts

3 → 115

Calls

6 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)
0.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
0.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))

series423.0ms (3.2%)

Counts

3 → 18

Calls

3 calls:

214.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
178.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
31.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 703 to 606 computations (13.8% saved)

simplify92.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4969	3385
1	4969	3385

prune270.0ms (2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	121	12	133
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	123	12	135

Error

0.0b

Counts

135 → 12

Compiler

Compiled 3135 to 2130 computations (32.1% saved)

localize12.0ms (0.1%)

Local error

Found 8 expressions with local error:

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

rewrite65.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

284×	`times-frac_binary64_743`
126×	`add-cube-cbrt_binary64_772` `add-sqr-sqrt_binary64_759` `*-un-lft-identity_binary64_737`
111×	`sqrt-prod_binary64_753`
33×	`add-exp-log_binary64_775`
28×	`unpow-prod-down_binary64_816` `sqr-pow_binary64_709`
24×	`associate-/l*_binary64_682`
20×	`pow1_binary64_798`
19×	`add-cbrt-cube_binary64_773`
11×	`div-exp_binary64_788`
9×	`prod-exp_binary64_786` `pow-prod-down_binary64_808`
8×	`div-inv_binary64_734`
6×	`cbrt-unprod_binary64_770` `associate-/r_binary64_681` `associate-r*_binary64_677`
4×	`add-log-exp_binary64_776`
3×	`pow-exp_binary64_805` `cbrt-undiv_binary64_771` `sqrt-pow1_binary64_755`
2×	`associate-l_binary64_678` `*-commutative_binary64_668`
1×	`frac-2neg_binary64_748` `clear-num_binary64_736` `pow1/2_binary64_817` `pow-to-exp_binary64_806` `associate-/l/_binary64_684`

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))
7.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(.f64 (.f64 2 PI.f64) n)
4.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
0.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2)))

series234.0ms (1.8%)

Counts

4 → 15

Calls

4 calls:

150.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
33.0ms	(.f64 (.f64 2 PI.f64) n)
28.0ms	(.f64 (.f64 2 PI.f64) n)
23.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

Compiler

Compiled 804 to 671 computations (16.5% saved)

simplify150.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5032	11499

prune485.0ms (3.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	253	3	256
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	257	11	268

Error

Counts

268 → 11

Compiler

Compiled 8814 to 5718 computations (35.1% saved)

localize12.0ms (0.1%)

Local error

Found 8 expressions with local error:

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

rewrite32.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-exp-log_binary64_775`
20×	`pow1_binary64_798`
19×	`add-cbrt-cube_binary64_773`
14×	`prod-exp_binary64_786`
9×	`pow-prod-down_binary64_808`
8×	`add-cube-cbrt_binary64_772` `add-sqr-sqrt_binary64_759` `*-un-lft-identity_binary64_737`
7×	`cbrt-unprod_binary64_770`
6×	`div-exp_binary64_788` `associate-r_binary64_677`
4×	`add-log-exp_binary64_776` `associate-/l*_binary64_682` `times-frac_binary64_743`
3×	`pow-exp_binary64_805` `sqrt-pow1_binary64_755` `sqrt-prod_binary64_753`
2×	`cbrt-undiv_binary64_771` `associate-l_binary64_678` `*-commutative_binary64_668`
1×	`frac-2neg_binary64_748` `clear-num_binary64_736` `pow1/2_binary64_817` `associate-/r*_binary64_681` `div-inv_binary64_734` `pow-to-exp_binary64_806`

Counts

4 → 75

Calls

8 calls:

11.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
6.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(.f64 (.f64 2 PI.f64) n)
4.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
0.0ms	(.f64 (sqrt.f64 k) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))

series228.0ms (1.7%)

Counts

4 → 15

Calls

4 calls:

151.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
28.0ms	(.f64 (.f64 2 PI.f64) n)
27.0ms	(.f64 (.f64 2 PI.f64) n)
22.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

Compiler

Compiled 804 to 671 computations (16.5% saved)

simplify53.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4967	1641
1	4967	1641

prune103.0ms (0.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	90	11	101

Error

Counts

101 → 11

Compiler

Compiled 2239 to 1512 computations (32.5% saved)

localize16.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 k))
0.0b	(/.f64 (sqrt.f64 (.f64 2 PI.f64)) (pow.f64 (.f64 2 PI.f64) (/.f64 k 2)))
0.0b	(/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2)))
0.0b	(pow.f64 (*.f64 2 PI.f64) (/.f64 k 2))
0.0b	(/.f64 (sqrt.f64 (.f64 2 PI.f64)) (pow.f64 (.f64 2 PI.f64) (/.f64 k 2)))
0.2b	(/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 k))
0.3b	(.f64 (/.f64 (sqrt.f64 (.f64 2 PI.f64)) (pow.f64 (*.f64 2 PI.f64) (/.f64 k 2))) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 k)))
1.0b	(sqrt.f64 (*.f64 2 PI.f64))

rewrite345.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

1246×	`times-frac_binary64_743`
734×	`add-sqr-sqrt_binary64_759`
603×	`sqrt-prod_binary64_753`
563×	`add-cube-cbrt_binary64_772` `*-un-lft-identity_binary64_737`
280×	`associate-r_binary64_677`
255×	`unpow-prod-down_binary64_816`
122×	`add-exp-log_binary64_775`
114×	`sqr-pow_binary64_709`
66×	`div-exp_binary64_788`
50×	`associate-/l*_binary64_682`
45×	`unswap-sqr_binary64_705`
32×	`add-cbrt-cube_binary64_773`
31×	`prod-exp_binary64_786`
24×	`associate-l_binary64_678`
18×	`pow-exp_binary64_805`
17×	`div-inv_binary64_734`
13×	`cbrt-undiv_binary64_771`
12×	`pow1_binary64_798` `pow-to-exp_binary64_806`
11×	`associate-/r*_binary64_681`
6×	`cbrt-unprod_binary64_770`
4×	`add-log-exp_binary64_776` `sqrt-pow1_binary64_755`
3×	`pow-div_binary64_812` `pow-prod-down_binary64_808`
2×	`frac-2neg_binary64_748` `clear-num_binary64_736` `pow1/2_binary64_817`
1×	`frac-times_binary64_747` `associate-l/_binary64_680` `associate-/l/_binary64_684` `-commutative_binary64_668` `associate-*r/_binary64_679`

Counts

4 → 795

Calls

8 calls:

163.0ms	(.f64 (/.f64 (sqrt.f64 (.f64 2 PI.f64)) (pow.f64 (*.f64 2 PI.f64) (/.f64 k 2))) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 k)))
19.0ms	(/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 k))
6.0ms	(/.f64 (sqrt.f64 (.f64 2 PI.f64)) (pow.f64 (.f64 2 PI.f64) (/.f64 k 2)))
2.0ms	(sqrt.f64 (*.f64 2 PI.f64))
0.0ms	(pow.f64 (*.f64 2 PI.f64) (/.f64 k 2))

series413.0ms (3.1%)

Counts

4 → 18

Calls

4 calls:

205.0ms	(.f64 (/.f64 (sqrt.f64 (.f64 2 PI.f64)) (pow.f64 (*.f64 2 PI.f64) (/.f64 k 2))) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 k)))
106.0ms	(/.f64 (sqrt.f64 (.f64 2 PI.f64)) (pow.f64 (.f64 2 PI.f64) (/.f64 k 2)))
102.0ms	(/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 k))
0.0ms	(sqrt.f64 (*.f64 2 PI.f64))

Compiler

Compiled 1235 to 1017 computations (17.7% saved)

simplify305.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

813 → 813

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5002	33259

prune2.3s (17.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	812	1	813
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	814	10	824

Error

Counts

824 → 10

Compiler

Compiled 31177 to 17575 computations (43.6% saved)

simplify27.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	260	2085
1	260	2085

regimes425.0ms (3.2%)

Accuracy

Total 0.4b remaining (99.5%)

Threshold costs 0.4b (99.5%)

Compiler

Compiled 5125 to 4264 computations (16.8% 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%)

sample6.6s (49.6%)

Algorithm

1×

intervals

Results

629.0ms	8000×	body	128	valid
595.0ms	1298×	body	1024	nan
323.0ms	2363×	body	128	overflowed
185.0ms	610×	body	512	nan
68.0ms	1010×	body	128	nan
59.0ms	337×	body	256	nan
22.0ms	245×	body	128	invalid

Compiler

Compiled 3788 to 3138 computations (17.2% saved)

Pareto

0.8103098440246215

Details

analyze382.0ms (2.9%)

sample75.0ms (0.6%)

simplify142.0ms (1.1%)

prune6.0ms (0%)

localize11.0ms (0.1%)

rewrite35.0ms (0.3%)

series423.0ms (3.2%)

simplify92.0ms (0.7%)

prune270.0ms (2%)

localize12.0ms (0.1%)

rewrite65.0ms (0.5%)

series234.0ms (1.8%)

simplify150.0ms (1.1%)

prune485.0ms (3.7%)

localize12.0ms (0.1%)

rewrite32.0ms (0.2%)

series228.0ms (1.7%)

simplify53.0ms (0.4%)

prune103.0ms (0.8%)

localize16.0ms (0.1%)

rewrite345.0ms (2.6%)

series413.0ms (3.1%)

simplify305.0ms (2.3%)

prune2.3s (17.6%)

simplify27.0ms (0.2%)

regimes425.0ms (3.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample6.6s (49.6%)

Profiling