Details

analyze382.0ms (4.4%)

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)

sample65.0ms (0.7%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
16.0ms	36×	body	1024	nan
9.0ms	69×	body	128	overflowed
5.0ms	18×	body	512	nan
2.0ms	12×	body	256	nan
1.0ms	24×	body	128	nan
0.0ms	3×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify145.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4933	22
1	4933	22

prune4.0ms (0.1%)

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

0.5b

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))
0.4b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))

rewrite32.0ms (0.4%)

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:

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)

series264.0ms (3%)

Counts

3 → 9

Calls

3 calls:

158.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
84.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
21.0ms	(.f64 (.f64 2 PI.f64) n)

simplify82.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4989	3537
1	4989	3537

prune188.0ms (2.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	113	11	124
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	114	12	126

Error

0.0b

Counts

126 → 12

Compiler

Compiled 3244 to 2221 computations (31.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 n (/.f64 (-.f64 1 k) 2))
0.2b	(/.f64 (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)) (/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)))
0.6b	(pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2))

rewrite72.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

132×	`times-frac_binary64_766`
130×	`add-sqr-sqrt_binary64_782`
101×	`*-un-lft-identity_binary64_760`
83×	`add-cube-cbrt_binary64_795`
53×	`add-exp-log_binary64_798`
51×	`sqrt-prod_binary64_776`
48×	`unpow-prod-down_binary64_839`
46×	`associate-r_binary64_700`
44×	`pow-unpow_binary64_837`
27×	`sqr-pow_binary64_732`
21×	`prod-exp_binary64_809`
16×	`pow-exp_binary64_828`
15×	`div-exp_binary64_811`
14×	`unswap-sqr_binary64_728`
12×	`difference-of-squares_binary64_729`
11×	`add-cbrt-cube_binary64_796` `pow-to-exp_binary64_829`
8×	`pow1_binary64_821`
7×	`associate-/l*_binary64_705`
6×	`associate-/r*_binary64_704` `distribute-lft-out--_binary64_712`
5×	`associate-l_binary64_701` `div-sub_binary64_765` `pow-sub_binary64_836`
4×	`add-log-exp_binary64_799` `div-inv_binary64_757`
3×	`pow-pow_binary64_832`
2×	`cbrt-undiv_binary64_794` `cbrt-unprod_binary64_793`
1×	`frac-2neg_binary64_771` `associate-l/_binary64_703` `associate-/l/_binary64_707` `frac-times_binary64_770` `associate-r/_binary64_702` `clear-num_binary64_759` `pow-prod-down_binary64_831` `*-commutative_binary64_691`

Counts

4 → 238

Calls

4 calls:

20.0ms	(.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)))
8.0ms	(pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2))
6.0ms	(/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
6.0ms	(pow.f64 n (/.f64 (-.f64 1 k) 2))

series401.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

220.0ms	(.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)))
109.0ms	(/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
50.0ms	(pow.f64 n (/.f64 (-.f64 1 k) 2))
22.0ms	(pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2))

simplify116.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

250 → 250

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4953	7203
1	4953	7203

prune483.0ms (5.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	250	0	250
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	250	12	262

Error

0.0b

Counts

262 → 12

Compiler

Compiled 7819 to 5370 computations (31.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 2 PI.f64) n)
0.2b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
0.2b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))
0.4b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`add-exp-log_binary64_798`
67×	`prod-exp_binary64_809`
39×	`pow-exp_binary64_828`
30×	`div-exp_binary64_811`
26×	`pow-unpow_binary64_837`
23×	`times-frac_binary64_766`
21×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `pow1_binary64_821` `add-sqr-sqrt_binary64_782`
14×	`add-cbrt-cube_binary64_796`
13×	`pow-to-exp_binary64_829`
9×	`pow-prod-down_binary64_831`
6×	`pow-pow_binary64_832`
5×	`associate-/l*_binary64_705`
4×	`add-log-exp_binary64_799` `sqr-pow_binary64_732` `cbrt-unprod_binary64_793` `unpow-prod-down_binary64_839`
3×	`div-inv_binary64_757` `associate-r_binary64_700`
2×	`cbrt-undiv_binary64_794`
1×	`frac-2neg_binary64_771` `associate-/r_binary64_704` `associate-l_binary64_701` `clear-num_binary64_759` `-commutative_binary64_691`

Counts

4 → 129

Calls

4 calls:

9.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
7.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
7.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))
5.0ms	(.f64 (.f64 2 PI.f64) n)

series415.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

235.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
104.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
58.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))
18.0ms	(.f64 (.f64 2 PI.f64) n)

simplify62.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5089	3041

prune198.0ms (2.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	142	11	153

Error

Counts

153 → 11

Compiler

Compiled 3743 to 2600 computations (30.5% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite161.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

372×	`add-sqr-sqrt_binary64_782`
357×	`sqrt-prod_binary64_776` `times-frac_binary64_766`
160×	`*-un-lft-identity_binary64_760`
151×	`add-cube-cbrt_binary64_795`
98×	`unpow-prod-down_binary64_839`
90×	`sqr-pow_binary64_732`
86×	`add-exp-log_binary64_798`
70×	`unswap-sqr_binary64_728`
67×	`associate-r_binary64_700`
49×	`associate-l_binary64_701`
38×	`div-exp_binary64_811`
26×	`prod-exp_binary64_809`
22×	`pow-unpow_binary64_837`
20×	`add-cbrt-cube_binary64_796`
18×	`associate-/r*_binary64_704` `pow-exp_binary64_828`
12×	`associate-/l*_binary64_705` `pow-to-exp_binary64_829`
9×	`pow1_binary64_821`
6×	`cbrt-undiv_binary64_794` `difference-of-squares_binary64_729`
5×	`div-inv_binary64_757`
4×	`add-log-exp_binary64_799` `cbrt-unprod_binary64_793`
3×	`distribute-lft-out--_binary64_712` `div-sub_binary64_765` `pow-sub_binary64_836`
2×	`frac-2neg_binary64_771` `associate-/l/_binary64_707` `clear-num_binary64_759` `pow-prod-down_binary64_831` `pow-pow_binary64_832`
1×	`associate-l/_binary64_703` `frac-times_binary64_770` `associate-r/_binary64_702` `*-commutative_binary64_691`

Counts

4 → 428

Calls

4 calls:

66.0ms	(.f64 (/.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))))
8.0ms	(pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2))
7.0ms	(/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k)))
7.0ms	(/.f64 (pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k)))

series425.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

226.0ms	(.f64 (/.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))))
109.0ms	(/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k)))
70.0ms	(/.f64 (pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k)))
19.0ms	(pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2))

simplify214.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

440 → 440

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4989	19324
1	4989	19324

prune1.5s (17.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	440	0	440
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	440	11	451

Error

Counts

451 → 11

Compiler

Compiled 17368 to 10493 computations (39.6% saved)

regimes373.0ms (4.3%)

Accuracy

Total 0.5b remaining (98.7%)

Threshold costs 0.5b (98.7%)

Compiler

Compiled 4639 to 3908 computations (15.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	33
1	29	33

end0.0ms (0%)

sample3.1s (35.1%)

Algorithm

1×

intervals

Results

619.0ms	8000×	body	128	valid
579.0ms	1298×	body	1024	nan
316.0ms	2302×	body	128	overflowed
197.0ms	656×	body	512	nan
59.0ms	968×	body	128	nan
57.0ms	335×	body	256	nan
21.0ms	233×	body	128	invalid

Compiler

Compiled 1006 to 849 computations (15.6% saved)

Details

analyze382.0ms (4.4%)

sample65.0ms (0.7%)

simplify145.0ms (1.7%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

rewrite32.0ms (0.4%)

series264.0ms (3%)

simplify82.0ms (0.9%)

prune188.0ms (2.2%)

localize13.0ms (0.1%)

rewrite72.0ms (0.8%)

series401.0ms (4.6%)

simplify116.0ms (1.3%)

prune483.0ms (5.5%)

localize14.0ms (0.2%)

rewrite44.0ms (0.5%)

series415.0ms (4.7%)

simplify62.0ms (0.7%)

prune198.0ms (2.3%)

localize16.0ms (0.2%)

rewrite161.0ms (1.8%)

series425.0ms (4.8%)

simplify214.0ms (2.4%)

prune1.5s (17.1%)

regimes373.0ms (4.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.1s (35.1%)

Profiling