Details

analyze390.0ms (5.7%)

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)

sample84.0ms (1.2%)

Algorithm

1×

intervals

Results

28.0ms	51×	body	1024	nan
19.0ms	256×	body	128	valid
10.0ms	70×	body	128	overflowed
9.0ms	32×	body	512	nan
3.0ms	16×	body	256	nan
2.0ms	32×	body	128	nan
1.0ms	11×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify144.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4933	22
1	4933	22

prune5.0ms (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

0.3b

Counts

2 → 2

Compiler

Compiled 44 to 41 computations (6.8% saved)

localize16.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite33.0ms (0.5%)

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)

series409.0ms (5.9%)

Counts

3 → 18

Calls

3 calls:

201.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
180.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
28.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 703 to 606 computations (13.8% saved)

simplify91.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4969	3385
1	4969	3385

prune189.0ms (2.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	122	11	133
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	124	11	135

Error

0.0b

Counts

135 → 11

Compiler

Compiled 3100 to 2101 computations (32.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (-.f64 1 k))
0.2b	(.f64 (.f64 2 PI.f64) n)
0.3b	(.f64 (pow.f64 (sqrt.f64 (.f64 (*.f64 2 PI.f64) n)) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
0.4b	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64_782`
25×	`*-un-lft-identity_binary64_760` `sqrt-prod_binary64_776`
22×	`pow1_binary64_821`
19×	`add-cube-cbrt_binary64_795` `associate-r_binary64_700`
15×	`add-exp-log_binary64_798` `times-frac_binary64_766`
13×	`associate-l_binary64_701`
12×	`unswap-sqr_binary64_728` `unpow-prod-down_binary64_839`
11×	`add-cbrt-cube_binary64_796`
9×	`pow-prod-down_binary64_831`
8×	`unpow-prod-up_binary64_838`
6×	`prod-exp_binary64_809` `cancel-sign-sub-inv_binary64_726` `sqrt-pow1_binary64_778` `sqr-pow_binary64_732` `pow-unpow_binary64_837`
5×	`pow-pow_binary64_832`
4×	`add-log-exp_binary64_799` `cbrt-unprod_binary64_793`
3×	`pow-sub_binary64_836`
2×	`pow-exp_binary64_828` `difference-of-squares_binary64_729` `sqrt-div_binary64_777` `pow-to-exp_binary64_829` `pow1/2_binary64_840` `sub-neg_binary64_753` `*-commutative_binary64_691`
1×	`associate-l/_binary64_703` `div-inv_binary64_757` `distribute-lft-out--_binary64_712` `frac-times_binary64_770` `associate-r/_binary64_702` `sqrt-pow2_binary64_779`

Counts

4 → 116

Calls

4 calls:

14.0ms	(.f64 (pow.f64 (sqrt.f64 (.f64 (*.f64 2 PI.f64) n)) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
8.0ms	(pow.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (-.f64 1 k))
5.0ms	(.f64 (.f64 2 PI.f64) n)
4.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

series293.0ms (4.3%)

Counts

4 → 21

Calls

4 calls:

130.0ms	(.f64 (pow.f64 (sqrt.f64 (.f64 (*.f64 2 PI.f64) n)) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
114.0ms	(pow.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (-.f64 1 k))
25.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
24.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 1123 to 915 computations (18.5% saved)

simplify122.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4934	3140
1	4934	3140

prune179.0ms (2.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	134	3	137
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	138	10	148

Error

Counts

148 → 10

Compiler

Compiled 3197 to 2350 computations (26.5% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite54.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 145

Calls

4 calls:

15.0ms	(pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2))
10.0ms	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
8.0ms	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
6.0ms	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))

series377.0ms (5.5%)

Counts

4 → 21

Calls

4 calls:

167.0ms	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
155.0ms	(pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2))
32.0ms	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
22.0ms	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))

Compiler

Compiled 949 to 815 computations (14.1% saved)

simplify85.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5397	3839

prune199.0ms (2.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	166	10	176

Error

Counts

176 → 10

Compiler

Compiled 3842 to 2478 computations (35.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 2 PI.f64) n)
0.3b	(.f64 (.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (neg.f64 k))) (sqrt.f64 (/.f64 1 k)))
0.4b	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
0.4b	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`pow1_binary64_821`
19×	`add-exp-log_binary64_798` `associate-r_binary64_700`
15×	`sqrt-prod_binary64_776`
14×	`add-cbrt-cube_binary64_796`
13×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
10×	`prod-exp_binary64_809` `pow-prod-down_binary64_831`
9×	`times-frac_binary64_766`
6×	`sqrt-pow1_binary64_778` `cbrt-unprod_binary64_793`
5×	`associate-*r/_binary64_702`
4×	`add-log-exp_binary64_799` `sqrt-div_binary64_777` `pow-neg_binary64_833`
3×	`associate-*l/_binary64_703` `frac-times_binary64_770`
2×	`neg-sub0_binary64_755` `associate-l_binary64_701` `pow1/2_binary64_840` `un-div-inv_binary64_758` `*-commutative_binary64_691` `pow-sub_binary64_836`
1×	`pow-exp_binary64_828` `div-inv_binary64_757` `pow-to-exp_binary64_829`

Counts

4 → 81

Calls

4 calls:

16.0ms	(.f64 (.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (neg.f64 k))) (sqrt.f64 (/.f64 1 k)))
5.0ms	(.f64 (.f64 2 PI.f64) n)
4.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
4.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

series270.0ms (3.9%)

Counts

4 → 15

Calls

4 calls:

189.0ms	(.f64 (.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (neg.f64 k))) (sqrt.f64 (/.f64 1 k)))
29.0ms	(.f64 (.f64 2 PI.f64) n)
27.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
24.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

Compiler

Compiled 966 to 792 computations (18% saved)

simplify74.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5014	1613

prune107.0ms (1.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	96	10	106

Error

Counts

106 → 10

Compiler

Compiled 2117 to 1472 computations (30.5% saved)

regimes333.0ms (4.8%)

Accuracy

Total 0.5b remaining (99%)

Threshold costs 0.5b (99%)

Compiler

Compiled 3910 to 3374 computations (13.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	22
1	26	22

end0.0ms (0%)

sample3.3s (48.2%)

Algorithm

1×

intervals

Results

811.0ms	8000×	body	128	valid
598.0ms	1328×	body	1024	nan
315.0ms	2316×	body	128	overflowed
194.0ms	654×	body	512	nan
57.0ms	321×	body	256	nan
55.0ms	1010×	body	128	nan
27.0ms	262×	body	128	invalid

Compiler

Compiled 997 to 862 computations (13.5% saved)

Details

analyze390.0ms (5.7%)

sample84.0ms (1.2%)

simplify144.0ms (2.1%)

prune5.0ms (0.1%)

localize16.0ms (0.2%)

rewrite33.0ms (0.5%)

series409.0ms (5.9%)

simplify91.0ms (1.3%)

prune189.0ms (2.7%)

localize10.0ms (0.2%)

rewrite41.0ms (0.6%)

series293.0ms (4.3%)

simplify122.0ms (1.8%)

prune179.0ms (2.6%)

localize15.0ms (0.2%)

rewrite54.0ms (0.8%)

series377.0ms (5.5%)

simplify85.0ms (1.2%)

prune199.0ms (2.9%)

localize12.0ms (0.2%)

rewrite37.0ms (0.5%)

series270.0ms (3.9%)

simplify74.0ms (1.1%)

prune107.0ms (1.6%)

regimes333.0ms (4.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.3s (48.2%)

Profiling