Details

analyze384.0ms (5.5%)

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)

sample82.0ms (1.2%)

Algorithm

1×

intervals

Results

26.0ms	48×	body	1024	nan
20.0ms	256×	body	128	valid
10.0ms	72×	body	128	overflowed
9.0ms	29×	body	512	nan
2.0ms	37×	body	128	nan
1.0ms	8×	body	256	nan
1.0ms	11×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify131.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

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

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

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`times-frac_binary64_1107`
42×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
33×	`add-cube-cbrt_binary64_1136`
26×	`add-exp-log_binary64_1139`
22×	`pow-unpow_binary64_1178`
18×	`sqrt-prod_binary64_1117`
14×	`pow1_binary64_1162`
10×	`add-cbrt-cube_binary64_1137`
9×	`prod-exp_binary64_1150`
8×	`unpow-prod-down_binary64_1180` `sqr-pow_binary64_1073`
6×	`pow-exp_binary64_1169` `difference-of-squares_binary64_1070` `pow-prod-down_binary64_1172` `associate-/r*_binary64_1045`
5×	`associate-/l*_binary64_1046` `div-exp_binary64_1152`
3×	`cbrt-unprod_binary64_1134` `add-log-exp_binary64_1140` `pow-pow_binary64_1173` `distribute-lft-out--_binary64_1053` `associate-r_binary64_1041`
2×	`div-inv_binary64_1098` `pow-sub_binary64_1177` `pow-to-exp_binary64_1170` `div-sub_binary64_1106`
1×	`-commutative_binary64_1032` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l/_binary64_1048` `cbrt-undiv_binary64_1135` `associate-l*_binary64_1042`

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)

series267.0ms (3.8%)

Counts

3 → 9

Calls

3 calls:

166.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
82.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
19.0ms	(.f64 (.f64 2 PI.f64) n)

simplify84.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4989	3537
1	4989	3537

prune200.0ms (2.9%)

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

Merged error: 0.0b

Counts

126 → 12

Compiler

Compiled 3318 to 2276 computations (31.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
0.3b	(.f64 (.f64 2 PI.f64) n)
0.3b	(.f64 (.f64 2 PI.f64) n)
0.3b	(/.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))))

rewrite39.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-exp-log_binary64_1139`
67×	`prod-exp_binary64_1150`
36×	`pow-exp_binary64_1169`
30×	`div-exp_binary64_1152`
20×	`pow1_binary64_1162`
19×	`add-cbrt-cube_binary64_1137`
15×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
14×	`times-frac_binary64_1107`
13×	`pow-unpow_binary64_1178`
12×	`pow-to-exp_binary64_1170`
9×	`pow-prod-down_binary64_1172`
7×	`cbrt-unprod_binary64_1134`
6×	`associate-r_binary64_1041`
5×	`associate-/l*_binary64_1046`
4×	`add-log-exp_binary64_1140`
3×	`unpow-prod-down_binary64_1180` `pow-pow_binary64_1173` `sqr-pow_binary64_1073`
2×	`-commutative_binary64_1032` `div-inv_binary64_1098` `cbrt-undiv_binary64_1135` `associate-l*_binary64_1042`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/r*_binary64_1045`

Counts

4 → 118

Calls

4 calls:

10.0ms	(/.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))
5.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(.f64 (.f64 2 PI.f64) n)

series393.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

246.0ms	(/.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))))
107.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
21.0ms	(.f64 (.f64 2 PI.f64) n)
19.0ms	(.f64 (.f64 2 PI.f64) n)

simplify57.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5259	2652

prune183.0ms (2.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	127	3	130
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	131	11	142

Merged error: 0b

Counts

142 → 11

Compiler

Compiled 3404 to 2360 computations (30.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite53.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`times-frac_binary64_1107`
46×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
45×	`add-exp-log_binary64_1139`
37×	`add-cube-cbrt_binary64_1136`
28×	`pow1_binary64_1162`
24×	`sqrt-prod_binary64_1117`
22×	`pow-unpow_binary64_1178`
21×	`prod-exp_binary64_1150`
20×	`add-cbrt-cube_binary64_1137`
15×	`pow-prod-down_binary64_1172`
12×	`associate-r_binary64_1041`
9×	`cbrt-unprod_binary64_1134`
8×	`pow-exp_binary64_1169` `unpow-prod-down_binary64_1180` `sqr-pow_binary64_1073`
6×	`difference-of-squares_binary64_1070` `div-exp_binary64_1152` `associate-/r*_binary64_1045`
5×	`associate-/l*_binary64_1046`
4×	`add-log-exp_binary64_1140` `pow-pow_binary64_1173`
3×	`distribute-lft-out--_binary64_1053`
2×	`-commutative_binary64_1032` `div-inv_binary64_1098` `pow-sub_binary64_1177` `associate-l*_binary64_1042` `pow-to-exp_binary64_1170` `div-sub_binary64_1106`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l/_binary64_1048` `cbrt-undiv_binary64_1135`

Counts

4 → 145

Calls

4 calls:

14.0ms	(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))

series326.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

172.0ms	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
105.0ms	(pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2))
26.0ms	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))
23.0ms	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))

simplify76.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5062	4348

prune217.0ms (3.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	157	11	168

Merged error: 0b

Counts

168 → 11

Compiler

Compiled 4214 to 2747 computations (34.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite52.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64_1123` `add-exp-log_binary64_1139`
62×	`times-frac_binary64_1107`
57×	`*-un-lft-identity_binary64_1101`
44×	`add-cube-cbrt_binary64_1136`
38×	`prod-exp_binary64_1150`
25×	`sqrt-prod_binary64_1117`
23×	`associate-l_binary64_1042`
22×	`pow-unpow_binary64_1178`
17×	`pow1_binary64_1162`
16×	`add-cbrt-cube_binary64_1137`
15×	`pow-exp_binary64_1169`
12×	`div-exp_binary64_1152`
10×	`unswap-sqr_binary64_1069`
8×	`associate-r_binary64_1041`
7×	`sqr-pow_binary64_1073`
6×	`1-exp_binary64_1145` `difference-of-squares_binary64_1070` `rec-exp_binary64_1151` `pow-prod-down_binary64_1172` `associate-/r*_binary64_1045`
5×	`cbrt-unprod_binary64_1134` `pow-to-exp_binary64_1170`
4×	`add-log-exp_binary64_1140`
3×	`pow-pow_binary64_1173` `distribute-lft-out--_binary64_1053` `div-inv_binary64_1098` `associate-/l*_binary64_1046` `pow-sub_binary64_1177` `pow-flip_binary64_1175` `div-sub_binary64_1106`
2×	`*-commutative_binary64_1032` `unpow-prod-down_binary64_1180` `cbrt-undiv_binary64_1135`
1×	`inv-pow_binary64_1186` `frac-times_binary64_1111` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `associate-r/_binary64_1043` `associate-l/_binary64_1044` `pow1/2_binary64_1181`

Counts

4 → 172

Calls

4 calls:

14.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
13.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
5.0ms	(.f64 (.f64 2 PI.f64) n)
4.0ms	(/.f64 1 (sqrt.f64 k))

series262.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

144.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
74.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
25.0ms	(/.f64 1 (sqrt.f64 k))
20.0ms	(.f64 (.f64 2 PI.f64) n)

simplify106.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4948	3852
1	4948	3852

prune222.0ms (3.2%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	184	11	195

Merged error: 0b

Counts

195 → 11

Compiler

Compiled 4097 to 2807 computations (31.5% saved)

regimes409.0ms (5.9%)

Compiler: Compiled 5386 to 4402 computations (18.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	35
1	53	35

end0.0ms (0%)

sample3.4s (48%)

Algorithm

1×

intervals

Results

616.0ms	8000×	body	128	valid
592.0ms	1317×	body	1024	nan
329.0ms	2341×	body	128	overflowed
204.0ms	654×	body	512	nan
58.0ms	992×	body	128	nan
58.0ms	329×	body	256	nan
19.0ms	209×	body	128	invalid

Compiler

Compiled 1373 to 1124 computations (18.1% saved)

Details

analyze384.0ms (5.5%)

sample82.0ms (1.2%)

simplify131.0ms (1.9%)

prune5.0ms (0.1%)

localize16.0ms (0.2%)

rewrite32.0ms (0.5%)

series267.0ms (3.8%)

simplify84.0ms (1.2%)

prune200.0ms (2.9%)

localize14.0ms (0.2%)

rewrite39.0ms (0.6%)

series393.0ms (5.6%)

simplify57.0ms (0.8%)

prune183.0ms (2.6%)

localize14.0ms (0.2%)

rewrite53.0ms (0.8%)

series326.0ms (4.7%)

simplify76.0ms (1.1%)

prune217.0ms (3.1%)

localize12.0ms (0.2%)

rewrite52.0ms (0.7%)

series262.0ms (3.7%)

simplify106.0ms (1.5%)

prune222.0ms (3.2%)

regimes409.0ms (5.9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.4s (48%)

Profiling