Details

analyze373.0ms (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)

sample73.0ms (0.7%)

Algorithm

1×

intervals

Results

21.0ms	47×	body	1024	nan
19.0ms	256×	body	128	valid
10.0ms	75×	body	128	overflowed
7.0ms	24×	body	512	nan
2.0ms	32×	body	128	nan
2.0ms	10×	body	256	nan
1.0ms	8×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify140.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4933	22
1	4933	22

prune5.0ms (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: 0.6b

Counts

2 → 2

Compiler

Compiled 44 to 41 computations (6.8% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

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))
0.5b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))

rewrite33.0ms (0.3%)

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

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)

series287.0ms (2.8%)

Counts

3 → 9

Calls

3 calls:

171.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
83.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
33.0ms	(.f64 (.f64 2 PI.f64) n)

simplify105.0ms (1%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4989	3537
1	4989	3537

prune182.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	115	9	124
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	116	10	126

Merged error: 0.0b

Counts

126 → 10

Compiler

Compiled 3175 to 2169 computations (31.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 n (/.f64 (-.f64 1 k) 2))
0.2b	(/.f64 (.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (sqrt.f64 k))
0.3b	(.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2)))
0.6b	(pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2))

rewrite50.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`add-exp-log_binary64_798`
57×	`add-sqr-sqrt_binary64_782`
50×	`*-un-lft-identity_binary64_760`
44×	`pow-unpow_binary64_837`
42×	`times-frac_binary64_766`
32×	`add-cube-cbrt_binary64_795`
31×	`prod-exp_binary64_809`
23×	`pow-exp_binary64_828`
16×	`pow-to-exp_binary64_829`
13×	`div-exp_binary64_811`
12×	`difference-of-squares_binary64_729`
11×	`add-cbrt-cube_binary64_796`
10×	`div-sub_binary64_765` `unpow-prod-down_binary64_839` `pow-sub_binary64_836`
9×	`sqr-pow_binary64_732`
8×	`pow1_binary64_821`
7×	`associate-r_binary64_700`
6×	`unswap-sqr_binary64_728` `sqrt-prod_binary64_776` `associate-/r*_binary64_704` `distribute-lft-out--_binary64_712`
5×	`associate-l_binary64_701`
4×	`add-log-exp_binary64_799`
3×	`associate-/l/_binary64_707` `div-inv_binary64_757` `pow-pow_binary64_832`
2×	`cbrt-undiv_binary64_794` `associate-l/_binary64_703` `frac-times_binary64_770` `associate-r/_binary64_702` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831`
1×	`frac-2neg_binary64_771` `associate-/l_binary64_705` `clear-num_binary64_759` `-commutative_binary64_691`

Counts

4 → 158

Calls

4 calls:

9.0ms	(/.f64 (.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (sqrt.f64 k))
8.0ms	(.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2)))
8.0ms	(pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2))
6.0ms	(pow.f64 n (/.f64 (-.f64 1 k) 2))

series412.0ms (4%)

Counts

4 → 12

Calls

4 calls:

235.0ms	(/.f64 (.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (sqrt.f64 k))
105.0ms	(.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2)))
52.0ms	(pow.f64 n (/.f64 (-.f64 1 k) 2))
20.0ms	(pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2))

simplify90.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4974	4114
1	4974	4114

prune253.0ms (2.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	171	9	180

Merged error: 0.0b

Counts

180 → 9

Compiler

Compiled 4670 to 3333 computations (28.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (.f64 (sqrt.f64 (.f64 2 PI.f64)) (sqrt.f64 n)) (.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 k 2)) (pow.f64 n (/.f64 k 2))))
0.2b	(/.f64 (/.f64 (.f64 (sqrt.f64 (.f64 2 PI.f64)) (sqrt.f64 n)) (.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 k 2)) (pow.f64 n (/.f64 k 2)))) (sqrt.f64 k))
0.4b	(.f64 (sqrt.f64 (.f64 2 PI.f64)) (sqrt.f64 n))
1.0b	(sqrt.f64 (*.f64 2 PI.f64))

rewrite57.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

196×	`add-exp-log_binary64_798`
87×	`prod-exp_binary64_809`
79×	`div-exp_binary64_811`
40×	`pow-exp_binary64_828`
38×	`times-frac_binary64_766`
36×	`add-cbrt-cube_binary64_796`
30×	`add-sqr-sqrt_binary64_782`
28×	`pow-to-exp_binary64_829`
26×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
24×	`sqrt-prod_binary64_776`
19×	`pow1_binary64_821`
13×	`cbrt-undiv_binary64_794` `pow-prod-down_binary64_831`
10×	`sqrt-pow1_binary64_778`
9×	`div-inv_binary64_757` `cbrt-unprod_binary64_793`
7×	`associate-/r*_binary64_704`
6×	`associate-/l_binary64_705` `associate-r*_binary64_700`
5×	`pow1/2_binary64_840`
4×	`add-log-exp_binary64_799` `associate-l_binary64_701`
3×	`pow-div_binary64_835`
2×	`unswap-sqr_binary64_728` `frac-2neg_binary64_771` `clear-num_binary64_759`
1×	`associate-/l/_binary64_707` `sqrt-unprod_binary64_780` `*-commutative_binary64_691`

Counts

4 → 168

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 (sqrt.f64 (.f64 2 PI.f64)) (sqrt.f64 n)) (.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 k 2)) (pow.f64 n (/.f64 k 2)))) (sqrt.f64 k))
12.0ms	(/.f64 (.f64 (sqrt.f64 (.f64 2 PI.f64)) (sqrt.f64 n)) (.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 k 2)) (pow.f64 n (/.f64 k 2))))
7.0ms	(.f64 (sqrt.f64 (.f64 2 PI.f64)) (sqrt.f64 n))
2.0ms	(sqrt.f64 (*.f64 2 PI.f64))

series564.0ms (5.4%)

Counts

4 → 10

Calls

4 calls:

347.0ms	(/.f64 (/.f64 (.f64 (sqrt.f64 (.f64 2 PI.f64)) (sqrt.f64 n)) (.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 k 2)) (pow.f64 n (/.f64 k 2)))) (sqrt.f64 k))
185.0ms	(/.f64 (.f64 (sqrt.f64 (.f64 2 PI.f64)) (sqrt.f64 n)) (.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 k 2)) (pow.f64 n (/.f64 k 2))))
31.0ms	(.f64 (sqrt.f64 (.f64 2 PI.f64)) (sqrt.f64 n))
0.0ms	(sqrt.f64 (*.f64 2 PI.f64))

simplify105.0ms (1%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5182	7073

prune305.0ms (2.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	178	9	187

Merged error: 0b

Counts

187 → 9

Compiler

Compiled 5821 to 3765 computations (35.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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))

rewrite324.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

1246×	`times-frac_binary64_766`
734×	`add-sqr-sqrt_binary64_782`
603×	`sqrt-prod_binary64_776`
563×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
280×	`associate-r_binary64_700`
255×	`unpow-prod-down_binary64_839`
122×	`add-exp-log_binary64_798`
114×	`sqr-pow_binary64_732`
66×	`div-exp_binary64_811`
50×	`associate-/l*_binary64_705`
45×	`unswap-sqr_binary64_728`
32×	`add-cbrt-cube_binary64_796`
31×	`prod-exp_binary64_809`
24×	`associate-l_binary64_701`
18×	`pow-exp_binary64_828`
17×	`div-inv_binary64_757`
13×	`cbrt-undiv_binary64_794`
12×	`pow-to-exp_binary64_829` `pow1_binary64_821`
11×	`associate-/r*_binary64_704`
6×	`cbrt-unprod_binary64_793`
4×	`sqrt-pow1_binary64_778` `add-log-exp_binary64_799`
3×	`pow-div_binary64_835` `pow-prod-down_binary64_831`
2×	`frac-2neg_binary64_771` `pow1/2_binary64_840` `clear-num_binary64_759`
1×	`associate-l/_binary64_703` `associate-/l/_binary64_707` `frac-times_binary64_770` `associate-r/_binary64_702` `*-commutative_binary64_691`

Counts

4 → 795

Calls

4 calls:

151.0ms	(.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)))
22.0ms	(/.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))

series630.0ms (6.1%)

Counts

4 → 10

Calls

4 calls:

418.0ms	(.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)))
140.0ms	(/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 k))
72.0ms	(/.f64 (sqrt.f64 (.f64 2 PI.f64)) (pow.f64 (.f64 2 PI.f64) (/.f64 k 2)))
0.0ms	(sqrt.f64 (*.f64 2 PI.f64))

simplify306.0ms (3%)

Algorithm

1×	egg-herbie

Counts

805 → 805

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5338	33407

prune2.4s (22.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	805	0	805
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	805	9	814

Merged error: 0b

Counts

814 → 9

Compiler

Compiled 31193 to 17599 computations (43.6% saved)

regimes404.0ms (3.9%)

Compiler: Compiled 5241 to 4363 computations (16.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	41
1	22	41

end0.0ms (0%)

sample3.2s (31.3%)

Algorithm

1×

intervals

Results

620.0ms	1384×	body	1024	nan
612.0ms	8000×	body	128	valid
311.0ms	2287×	body	128	overflowed
202.0ms	675×	body	512	nan
60.0ms	982×	body	128	nan
56.0ms	322×	body	256	nan
21.0ms	242×	body	128	invalid

Compiler

Compiled 1164 to 969 computations (16.8% saved)

Details

analyze373.0ms (3.6%)

sample73.0ms (0.7%)

simplify140.0ms (1.4%)

prune5.0ms (0%)

localize10.0ms (0.1%)

rewrite33.0ms (0.3%)

series287.0ms (2.8%)

simplify105.0ms (1%)

prune182.0ms (1.8%)

localize13.0ms (0.1%)

rewrite50.0ms (0.5%)

series412.0ms (4%)

simplify90.0ms (0.9%)

prune253.0ms (2.4%)

localize16.0ms (0.2%)

rewrite57.0ms (0.5%)

series564.0ms (5.4%)

simplify105.0ms (1%)

prune305.0ms (2.9%)

localize14.0ms (0.1%)

rewrite324.0ms (3.1%)

series630.0ms (6.1%)

simplify306.0ms (3%)

prune2.4s (22.8%)

regimes404.0ms (3.9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.2s (31.3%)

Profiling