Details

analyze395.0ms (0.1%)

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)

sample77.0ms (0%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
19.0ms	40×	body	1024	nan
10.0ms	71×	body	128	overflowed
7.0ms	23×	body	512	nan
6.0ms	28×	body	128	nan
1.0ms	6×	body	256	nan
1.0ms	8×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify146.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4933	22
1	4933	22

prune3.0ms (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 14 to 13 computations (7.1% saved)

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite55.0ms (0%)

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

8 calls:

15.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
13.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (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))
0.0ms	(/.f64 1 (sqrt.f64 k))

series474.0ms (0.2%)

Counts

4 → 21

Calls

4 calls:

231.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
196.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
30.0ms	(.f64 (.f64 2 PI.f64) n)
15.0ms	(/.f64 1 (sqrt.f64 k))

Compiler

Compiled 847 to 742 computations (12.4% saved)

simplify99.0ms (0%)

Algorithm

1×	egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4954	3852
1	4954	3852

localize11.0ms (0%)

Local error

Found 6 expressions with local error:

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

rewrite36.0ms (0%)

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

6 calls:

13.0ms	(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)
0.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
0.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))

series423.0ms (0.1%)

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))
180.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
29.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 703 to 606 computations (13.8% saved)

simplify98.0ms (0%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4969	3385
1	4969	3385

prune2.2s (0.7%)

Pruning

148 alts after pruning (146 fresh and 2 done)

	Pruned	Kept	Total
New	180	146	326
Fresh	0	0	0
Picked	0	0	0
Done	0	2	2
Total	180	148	328

Error

0.0b

Counts

328 → 148

Compiler

Compiled 8114 to 6135 computations (24.4% saved)

localize12.0ms (0%)

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)

rewrite70.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

284×	`times-frac_binary64_1107`
126×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
111×	`sqrt-prod_binary64_1117`
33×	`add-exp-log_binary64_1139`
28×	`unpow-prod-down_binary64_1180` `sqr-pow_binary64_1073`
24×	`associate-/l*_binary64_1046`
20×	`pow1_binary64_1162`
19×	`add-cbrt-cube_binary64_1137`
11×	`div-exp_binary64_1152`
9×	`prod-exp_binary64_1150` `pow-prod-down_binary64_1172`
8×	`div-inv_binary64_1098`
6×	`cbrt-unprod_binary64_1134` `associate-r_binary64_1041` `associate-/r*_binary64_1045`
4×	`add-log-exp_binary64_1140`
3×	`pow-exp_binary64_1169` `sqrt-pow1_binary64_1119` `cbrt-undiv_binary64_1135`
2×	`-commutative_binary64_1032` `associate-l*_binary64_1042`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l/_binary64_1048` `pow-to-exp_binary64_1170` `pow1/2_binary64_1181`

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))
5.0ms	(.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)))

series241.0ms (0.1%)

Counts

4 → 15

Calls

4 calls:

158.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
31.0ms	(.f64 (.f64 2 PI.f64) n)
28.0ms	(.f64 (.f64 2 PI.f64) n)
25.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

Compiler

Compiled 804 to 671 computations (16.5% saved)

simplify170.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5032	11499

localize14.0ms (0%)

Local error

Found 6 expressions with local error:

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

rewrite37.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_1139`
33×	`add-sqr-sqrt_binary64_1123`
30×	`prod-exp_binary64_1150`
26×	`*-un-lft-identity_binary64_1101`
22×	`pow-unpow_binary64_1178`
18×	`times-frac_binary64_1107`
17×	`pow-exp_binary64_1169` `add-cube-cbrt_binary64_1136`
14×	`pow1_binary64_1162`
10×	`add-cbrt-cube_binary64_1137`
9×	`pow-to-exp_binary64_1170`
8×	`associate-r_binary64_1041` `associate-l_binary64_1042` `sqr-pow_binary64_1073`
7×	`unpow-prod-down_binary64_1180`
6×	`difference-of-squares_binary64_1070` `pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069`
4×	`cbrt-unprod_binary64_1134`
3×	`add-log-exp_binary64_1140` `pow-pow_binary64_1173` `distribute-lft-out--_binary64_1053`
2×	`*-commutative_binary64_1032` `pow-sub_binary64_1177` `div-sub_binary64_1106`
1×	`associate-*r/_binary64_1043` `div-inv_binary64_1098`

Counts

3 → 100

Calls

6 calls:

11.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
10.0ms	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
6.0ms	(.f64 (.f64 2 PI.f64) n)
0.0ms	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
0.0ms	(.f64 (.f64 2 PI.f64) n)

series434.0ms (0.1%)

Counts

3 → 18

Calls

3 calls:

211.0ms	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
192.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
30.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 733 to 634 computations (13.5% saved)

simplify78.0ms (0%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5030	2566

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.7b	(log.f64 (/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)))
0.3b	(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))
0.3b	(.f64 (.f64 2 PI.f64) n)
0.3b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
0.7b	(log.f64 (/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)))
3.3b	(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))))

rewrite52.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`times-frac_binary64_1107`
68×	`log-prod_binary64_1187`
59×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
50×	`add-cube-cbrt_binary64_1136`
34×	`exp-sum_binary64_1147`
30×	`sqrt-prod_binary64_1117`
28×	`add-exp-log_binary64_1139`
22×	`pow-unpow_binary64_1178`
17×	`pow1_binary64_1162`
13×	`unpow-prod-down_binary64_1180` `sqr-pow_binary64_1073`
9×	`prod-exp_binary64_1150` `add-cbrt-cube_binary64_1137`
6×	`pow-exp_binary64_1169` `difference-of-squares_binary64_1070` `rem-log-exp_binary64_1142` `pow-prod-down_binary64_1172`
5×	`div-exp_binary64_1152`
4×	`add-log-exp_binary64_1140` `exp-prod_binary64_1153`
3×	`cbrt-unprod_binary64_1134` `pow-pow_binary64_1173` `distribute-lft-out--_binary64_1053` `div-inv_binary64_1098` `associate-r_binary64_1041`
2×	`log-pow_binary64_1190` `log-div_binary64_1188` `pow-to-exp_binary64_1170`
1×	`-commutative_binary64_1032` `rem-exp-log_binary64_1141` `exp-diff_binary64_1149` `pow-sub_binary64_1177` `associate-l*_binary64_1042` `div-sub_binary64_1106`

Counts

4 → 153

Calls

8 calls:

11.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
10.0ms	(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))))
6.0ms	(log.f64 (/.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	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))

series979.0ms (0.3%)

Counts

4 → 24

Calls

4 calls:

405.0ms	(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))))
360.0ms	(log.f64 (/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)))
183.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
31.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 1055 to 938 computations (11.1% saved)

simplify105.0ms (0%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4960	5210
1	4960	5210

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 (.f64 2 PI.f64) n)
0.2b	(/.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 k))
0.1b	(sqrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
0.1b	(sqrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
0.3b	(.f64 (.f64 2 PI.f64) n)
0.3b	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
0.3b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
0.3b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))

rewrite84.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

121×	`add-sqr-sqrt_binary64_1123`
102×	`times-frac_binary64_1107`
94×	`sqrt-prod_binary64_1117`
74×	`*-un-lft-identity_binary64_1101`
56×	`add-cube-cbrt_binary64_1136`
53×	`associate-l_binary64_1042`
44×	`pow-unpow_binary64_1178`
26×	`add-exp-log_binary64_1139`
23×	`pow1_binary64_1162`
22×	`sqr-pow_binary64_1073`
21×	`unswap-sqr_binary64_1069`
14×	`add-cbrt-cube_binary64_1137`
12×	`difference-of-squares_binary64_1070`
11×	`prod-exp_binary64_1150` `associate-r_binary64_1041`
10×	`pow-prod-down_binary64_1172`
9×	`unpow-prod-down_binary64_1180`
6×	`pow-exp_binary64_1169` `pow-pow_binary64_1173` `distribute-lft-out--_binary64_1053`
5×	`cbrt-unprod_binary64_1134`
4×	`add-log-exp_binary64_1140` `pow-sub_binary64_1177` `div-sub_binary64_1106`
3×	`div-inv_binary64_1098`
2×	`*-commutative_binary64_1032` `sqrt-div_binary64_1118` `pow-to-exp_binary64_1170`
1×	`sqrt-undiv_binary64_1122` `frac-times_binary64_1111` `associate-r/_binary64_1043` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `associate-l/_binary64_1044` `sqrt-unprod_binary64_1121`

Counts

4 → 194

Calls

8 calls:

27.0ms	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
12.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
11.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
5.0ms	(.f64 (.f64 2 PI.f64) n)
0.0ms	(sqrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))

series638.0ms (0.2%)

Counts

4 → 27

Calls

4 calls:

221.0ms	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
197.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
190.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
31.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 1519 to 1262 computations (16.9% saved)

simplify134.0ms (0%)

Algorithm

1×	egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4967	6683
1	4967	6683

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite42.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`cbrt-prod_binary64_1132`
27×	`add-sqr-sqrt_binary64_1123`
15×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
13×	`sqr-pow_binary64_1073`
11×	`pow1_binary64_1162`
9×	`pow1/3_binary64_1183` `unswap-sqr_binary64_1069`
8×	`swap-sqr_binary64_1068` `associate-r_binary64_1041` `associate-l_binary64_1042`
7×	`unpow-prod-down_binary64_1180` `pow-sub_binary64_1177` `cbrt-div_binary64_1133` `div-sub_binary64_1106`
6×	`add-exp-log_binary64_1139`
4×	`add-log-exp_binary64_1140` `add-cbrt-cube_binary64_1137`
2×	`pow-prod-up_binary64_1171` `pow-sqr_binary64_1074` `pow-prod-down_binary64_1172`
1×	`pow-plus_binary64_1164` `-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `frac-times_binary64_1111` `prod-exp_binary64_1150` `associate-r/_binary64_1043` `associate-*l/_binary64_1044` `pow2_binary64_1182`

Counts

4 → 96

Calls

8 calls:

16.0ms	(.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
4.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
4.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
3.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
0.0ms	(.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))) (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))

series2.9s (1%)

Counts

4 → 36

Calls

4 calls:

902.0ms	(.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
659.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
659.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
652.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))

Compiler

Compiled 4198 to 3474 computations (17.2% saved)

simplify109.0ms (0%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5061	5569

prune22.5s (7.4%)

Pruning

537 alts after pruning (530 fresh and 7 done)

	Pruned	Kept	Total
New	506	398	904
Fresh	9	132	141
Picked	0	0	0
Done	0	7	7
Total	515	537	1052

Error

Counts

1052 → 537

Compiler

Compiled 40571 to 30762 computations (24.2% saved)

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 (.f64 2 PI.f64) n)
0.3b	(.f64 (pow.f64 k -1/2) (/.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))
0.0b	(/.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 (pow.f64 k -1/2) (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (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)

rewrite50.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`add-exp-log_binary64_1139`
36×	`add-sqr-sqrt_binary64_1123`
33×	`prod-exp_binary64_1150`
30×	`associate-r_binary64_1041`
26×	`times-frac_binary64_1107`
20×	`pow1_binary64_1162`
19×	`add-cbrt-cube_binary64_1137`
18×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
15×	`pow-exp_binary64_1169` `div-exp_binary64_1152`
11×	`sqr-pow_binary64_1073`
10×	`unpow-prod-down_binary64_1180`
9×	`pow-prod-down_binary64_1172` `associate-l_binary64_1042` `unswap-sqr_binary64_1069` `pow-to-exp_binary64_1170`
8×	`cbrt-unprod_binary64_1134`
6×	`sqrt-prod_binary64_1117`
4×	`add-log-exp_binary64_1140`
3×	`*-commutative_binary64_1032` `sqrt-pow1_binary64_1119`
1×	`associate-*r/_binary64_1043` `div-inv_binary64_1098` `cbrt-undiv_binary64_1135` `pow1/2_binary64_1181`

Counts

4 → 117

Calls

8 calls:

19.0ms	(.f64 (pow.f64 k -1/2) (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
5.0ms	(.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)))

series241.0ms (0.1%)

Counts

4 → 15

Calls

4 calls:

158.0ms	(.f64 (pow.f64 k -1/2) (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
30.0ms	(.f64 (.f64 2 PI.f64) n)
27.0ms	(.f64 (.f64 2 PI.f64) n)
26.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

Compiler

Compiled 833 to 702 computations (15.7% saved)

simplify84.0ms (0%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4971	3360
1	4971	3360

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

7.2b	(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (-.f64 1 k)) k))
0.3b	(.f64 (.f64 2 PI.f64) n)
0.3b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (-.f64 1 k))
0.1b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (-.f64 1 k)) k)
0.1b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (-.f64 1 k)) k)
0.3b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (-.f64 1 k))
0.3b	(.f64 (.f64 2 PI.f64) n)
7.2b	(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (-.f64 1 k)) k))

rewrite42.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`times-frac_binary64_1107`
48×	`add-sqr-sqrt_binary64_1123`
44×	`*-un-lft-identity_binary64_1101`
41×	`add-cube-cbrt_binary64_1136`
32×	`unpow-prod-up_binary64_1179`
31×	`sqrt-prod_binary64_1117`
27×	`add-exp-log_binary64_1139`
24×	`cancel-sign-sub-inv_binary64_1067`
16×	`pow1_binary64_1162`
11×	`add-cbrt-cube_binary64_1137`
9×	`prod-exp_binary64_1150` `associate-/l*_binary64_1046` `sqr-pow_binary64_1073`
8×	`unpow-prod-down_binary64_1180` `sub-neg_binary64_1094`
6×	`pow-exp_binary64_1169` `pow-unpow_binary64_1178` `pow-prod-down_binary64_1172`
5×	`div-exp_binary64_1152`
4×	`add-log-exp_binary64_1140`
3×	`rem-sqrt-square_binary64_1114` `cbrt-unprod_binary64_1134` `pow-pow_binary64_1173` `associate-r_binary64_1041` `associate-/r*_binary64_1045`
2×	`difference-of-squares_binary64_1070` `div-inv_binary64_1098` `pow-sub_binary64_1177` `pow-to-exp_binary64_1170`
1×	`-commutative_binary64_1032` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `distribute-lft-out--_binary64_1053` `associate-/l/_binary64_1048` `sqrt-div_binary64_1118` `cbrt-undiv_binary64_1135` `associate-l*_binary64_1042` `pow1/2_binary64_1181`

Counts

4 → 145

Calls

8 calls:

9.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (-.f64 1 k))
7.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (-.f64 1 k)) k)
6.0ms	(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (-.f64 1 k)) k))
6.0ms	(.f64 (.f64 2 PI.f64) n)
0.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (-.f64 1 k)) k)

series597.0ms (0.2%)

Counts

4 → 27

Calls

4 calls:

222.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (-.f64 1 k)) k)
200.0ms	(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (-.f64 1 k)) k))
151.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (-.f64 1 k))
24.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 919 to 779 computations (15.2% saved)

simplify103.0ms (0%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4980	4083
1	4980	4083

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 (.f64 2 PI.f64) n)
0.3b	(.f64 (.f64 2 PI.f64) n)
0.0b	(/.f64 (sqrt.f64 (.f64 2 PI.f64)) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 4)))
0.0b	(/.f64 (sqrt.f64 n) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 4)))
0.3b	(.f64 (.f64 2 PI.f64) n)
0.3b	(/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 4))) (sqrt.f64 k))
0.3b	(.f64 (/.f64 (sqrt.f64 (.f64 2 PI.f64)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 4))) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 4))) (sqrt.f64 k)))
1.0b	(sqrt.f64 (*.f64 2 PI.f64))

rewrite267.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

894×	`times-frac_binary64_1107`
494×	`add-sqr-sqrt_binary64_1123`
435×	`sqrt-prod_binary64_1117`
375×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
239×	`add-exp-log_binary64_1139`
211×	`associate-r_binary64_1041`
112×	`div-exp_binary64_1152`
105×	`sqr-pow_binary64_1073`
87×	`prod-exp_binary64_1150`
82×	`unpow-prod-down_binary64_1180`
42×	`pow-exp_binary64_1169`
35×	`add-cbrt-cube_binary64_1137`
34×	`associate-/l*_binary64_1046`
33×	`unswap-sqr_binary64_1069`
25×	`associate-l_binary64_1042`
16×	`div-inv_binary64_1098`
14×	`pow1_binary64_1162` `pow-to-exp_binary64_1170`
12×	`cbrt-undiv_binary64_1135`
9×	`cbrt-unprod_binary64_1134`
6×	`associate-/r*_binary64_1045`
5×	`pow-prod-down_binary64_1172`
4×	`add-log-exp_binary64_1140`
2×	`*-commutative_binary64_1032` `sqrt-pow1_binary64_1119`
1×	`frac-times_binary64_1111` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l/_binary64_1048` `associate-r/_binary64_1043` `associate-l/_binary64_1044` `pow1/2_binary64_1181`

Counts

4 → 617

Calls

8 calls:

115.0ms	(.f64 (/.f64 (sqrt.f64 (.f64 2 PI.f64)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 4))) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 4))) (sqrt.f64 k)))
17.0ms	(/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 4))) (sqrt.f64 k))
6.0ms	(.f64 (.f64 2 PI.f64) n)
2.0ms	(sqrt.f64 (*.f64 2 PI.f64))
0.0ms	(/.f64 (sqrt.f64 n) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 4)))

series422.0ms (0.1%)

Counts

4 → 15

Calls

4 calls:

260.0ms	(.f64 (/.f64 (sqrt.f64 (.f64 2 PI.f64)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 4))) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 4))) (sqrt.f64 k)))
129.0ms	(/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 4))) (sqrt.f64 k))
33.0ms	(.f64 (.f64 2 PI.f64) n)
0.0ms	(sqrt.f64 (*.f64 2 PI.f64))

Compiler

Compiled 1151 to 939 computations (18.4% saved)

simplify278.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

632 → 632

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5106	30684

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 (.f64 2 PI.f64) n)
0.3b	(.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (+.f64 1 (sqrt.f64 k)) (sqrt.f64 2))) (/.f64 (-.f64 (sqrt.f64 1) (sqrt.f64 k)) (sqrt.f64 2))))
0.0b	(-.f64 (sqrt.f64 1) (sqrt.f64 k))
0.0b	(+.f64 1 (sqrt.f64 k))
0.7b	(/.f64 (-.f64 (sqrt.f64 1) (sqrt.f64 k)) (sqrt.f64 2))
0.7b	(/.f64 (+.f64 1 (sqrt.f64 k)) (sqrt.f64 2))
3.8b	(pow.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (+.f64 1 (sqrt.f64 k)) (sqrt.f64 2))) (/.f64 (-.f64 (sqrt.f64 1) (sqrt.f64 k)) (sqrt.f64 2)))
4.1b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (+.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))

rewrite96.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

244×	`add-sqr-sqrt_binary64_1123`
232×	`sqrt-prod_binary64_1117`
218×	`*-un-lft-identity_binary64_1101`
192×	`times-frac_binary64_1107`
104×	`pow-unpow_binary64_1178`
101×	`add-cube-cbrt_binary64_1136`
78×	`difference-of-squares_binary64_1070`
26×	`distribute-lft-out_binary64_1052` `distribute-lft-out--_binary64_1053`
21×	`add-exp-log_binary64_1139`
16×	`associate-/l*_binary64_1046`
12×	`associate-/r*_binary64_1045`
11×	`pow-exp_binary64_1169`
10×	`pow1_binary64_1162`
8×	`add-cbrt-cube_binary64_1137`
7×	`unpow-prod-down_binary64_1180`
6×	`prod-exp_binary64_1150`
4×	`add-log-exp_binary64_1140` `pow-pow_binary64_1173` `associate-/l/_binary64_1048` `div-inv_binary64_1098`
3×	`pow-prod-down_binary64_1172` `sqr-pow_binary64_1073` `pow-to-exp_binary64_1170`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `div-sub_binary64_1106`
1×	`flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `pow-sub_binary64_1177` `flip-+_binary64_1075`

Counts

4 → 294

Calls

8 calls:

17.0ms	(/.f64 (-.f64 (sqrt.f64 1) (sqrt.f64 k)) (sqrt.f64 2))
16.0ms	(pow.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (+.f64 1 (sqrt.f64 k)) (sqrt.f64 2))) (/.f64 (-.f64 (sqrt.f64 1) (sqrt.f64 k)) (sqrt.f64 2)))
13.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (+.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))
8.0ms	(/.f64 (+.f64 1 (sqrt.f64 k)) (sqrt.f64 2))
0.0ms	(+.f64 1 (sqrt.f64 k))

series790.0ms (0.3%)

Counts

4 → 18

Calls

4 calls:

519.0ms	(pow.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (+.f64 1 (sqrt.f64 k)) (sqrt.f64 2))) (/.f64 (-.f64 (sqrt.f64 1) (sqrt.f64 k)) (sqrt.f64 2)))
214.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (+.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))
29.0ms	(/.f64 (-.f64 (sqrt.f64 1) (sqrt.f64 k)) (sqrt.f64 2))
28.0ms	(/.f64 (+.f64 1 (sqrt.f64 k)) (sqrt.f64 2))

Compiler

Compiled 1438 to 1268 computations (11.8% saved)

simplify128.0ms (0%)

Algorithm

1×	egg-herbie

Counts

312 → 312

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5170	8048

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))) (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))) (sqrt.f64 k))
0.2b	(.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))) (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
0.1b	(sqrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
0.1b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))) (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))))
0.3b	(.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
0.4b	(cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
0.4b	(cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
0.4b	(cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))

rewrite44.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`cbrt-prod_binary64_1132`
27×	`add-sqr-sqrt_binary64_1123`
15×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
13×	`sqr-pow_binary64_1073`
11×	`pow1_binary64_1162`
9×	`pow1/3_binary64_1183` `unswap-sqr_binary64_1069`
8×	`swap-sqr_binary64_1068` `associate-r_binary64_1041` `associate-l_binary64_1042`
7×	`unpow-prod-down_binary64_1180` `pow-sub_binary64_1177` `cbrt-div_binary64_1133` `div-sub_binary64_1106`
6×	`add-exp-log_binary64_1139`
4×	`add-log-exp_binary64_1140` `add-cbrt-cube_binary64_1137`
2×	`pow-prod-up_binary64_1171` `pow-sqr_binary64_1074` `pow-prod-down_binary64_1172`
1×	`pow-plus_binary64_1164` `-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `frac-times_binary64_1111` `prod-exp_binary64_1150` `associate-r/_binary64_1043` `associate-*l/_binary64_1044` `pow2_binary64_1182`

Counts

4 → 96

Calls

8 calls:

12.0ms	(.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
3.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
3.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
3.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
0.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))) (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))))

series2.9s (0.9%)

Counts

4 → 36

Calls

4 calls:

883.0ms	(.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
666.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
659.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
655.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))

Compiler

Compiled 4870 to 3978 computations (18.3% saved)

simplify108.0ms (0%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5061	5569

prune1.0min (20.1%)

Pruning

1047 alts after pruning (1036 fresh and 11 done)

	Pruned	Kept	Total
New	848	532	1380
Fresh	21	504	525
Picked	0	0	0
Done	1	11	12
Total	870	1047	1917

Error

Counts

1917 → 1047

Compiler

Compiled 72622 to 53969 computations (25.7% saved)

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
0.1b	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
0.1b	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
0.0b	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (sqrt.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)
0.3b	(.f64 (.f64 2 PI.f64) n)
0.5b	(.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (sqrt.f64 (.f64 (*.f64 2 PI.f64) n)))

rewrite43.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

146×	`pow1_binary64_1162`
80×	`pow-prod-down_binary64_1172`
60×	`sqrt-pow1_binary64_1119`
21×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
17×	`pow-prod-up_binary64_1171`
13×	`add-sqr-sqrt_binary64_1123` `associate-r_binary64_1041`
12×	`pow1/2_binary64_1181`
11×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136` `pow-sqr_binary64_1074`
10×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150`
7×	`associate-l_binary64_1042`
4×	`*-commutative_binary64_1032` `add-log-exp_binary64_1140` `sqrt-prod_binary64_1117` `swap-sqr_binary64_1068`
1×	`pow-plus_binary64_1164` `rem-square-sqrt_binary64_1113` `unswap-sqr_binary64_1069` `sqrt-unprod_binary64_1121` `pow2_binary64_1182`

Counts

4 → 120

Calls

8 calls:

13.0ms	(.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (sqrt.f64 (.f64 (*.f64 2 PI.f64) n)))
5.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(.f64 (.f64 2 PI.f64) n)
0.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (sqrt.f64 (.f64 (*.f64 2 PI.f64) n))) (/.f64 k 2)))

series144.0ms (0%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (sqrt.f64 (.f64 (*.f64 2 PI.f64) n)))
33.0ms	(.f64 (.f64 2 PI.f64) n)
31.0ms	(.f64 (.f64 2 PI.f64) n)
27.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 652 to 543 computations (16.7% saved)

simplify85.0ms (0%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5026	1076

localize7.0ms (0%)

Local error

Found 6 expressions with local error:

7.2b	(sqrt.f64 (/.f64 (.f64 (.f64 2 PI.f64) n) k))
0.3b	(.f64 (.f64 2 PI.f64) n)
0.2b	(/.f64 (.f64 (.f64 2 PI.f64) n) k)
0.2b	(/.f64 (.f64 (.f64 2 PI.f64) n) k)
0.3b	(.f64 (.f64 2 PI.f64) n)
7.2b	(sqrt.f64 (/.f64 (.f64 (.f64 2 PI.f64) n) k))

rewrite20.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
9×	`add-sqr-sqrt_binary64_1123` `pow1_binary64_1162`
8×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
7×	`sqrt-prod_binary64_1117`
6×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `times-frac_binary64_1107`
3×	`add-log-exp_binary64_1140` `associate-r_binary64_1041` `pow-prod-down_binary64_1172` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `associate-/r*_binary64_1045`
2×	`div-inv_binary64_1098`
1×	`-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `associate-/l_binary64_1046` `sqrt-div_binary64_1118` `associate-l_binary64_1042` `pow1/2_binary64_1181`

Counts

3 → 59

Calls

6 calls:

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

series165.0ms (0.1%)

Counts

3 → 15

Calls

3 calls:

76.0ms	(/.f64 (.f64 (.f64 2 PI.f64) n) k)
62.0ms	(sqrt.f64 (/.f64 (.f64 (.f64 2 PI.f64) n) k))
27.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 344 to 326 computations (5.2% saved)

simplify69.0ms (0%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5097	939

localize17.0ms (0%)

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 (.f64 2 PI.f64) (.f64 (cbrt.f64 n) (cbrt.f64 n))) (cbrt.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 (.f64 2 PI.f64) (.f64 (cbrt.f64 n) (cbrt.f64 n))) (cbrt.f64 n)) (/.f64 k 2)))
0.5b	(*.f64 (cbrt.f64 n) (cbrt.f64 n))
0.6b	(cbrt.f64 n)
0.6b	(cbrt.f64 n)
0.6b	(cbrt.f64 n)

rewrite18.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_1132`
23×	`add-sqr-sqrt_binary64_1123`
15×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
11×	`pow1_binary64_1162`
9×	`pow1/3_binary64_1183`
6×	`add-exp-log_binary64_1139` `swap-sqr_binary64_1068` `associate-r_binary64_1041` `associate-l_binary64_1042`
4×	`add-log-exp_binary64_1140` `add-cbrt-cube_binary64_1137` `unswap-sqr_binary64_1069`
2×	`pow-prod-up_binary64_1171` `pow-sqr_binary64_1074` `pow-prod-down_binary64_1172`
1×	`pow-plus_binary64_1164` `*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow2_binary64_1182`

Counts

4 → 73

Calls

8 calls:

7.0ms	(*.f64 (cbrt.f64 n) (cbrt.f64 n))
1.0ms	(cbrt.f64 n)
1.0ms	(cbrt.f64 n)
1.0ms	(cbrt.f64 n)
0.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 (.f64 2 PI.f64) (.f64 (cbrt.f64 n) (cbrt.f64 n))) (cbrt.f64 n)) (/.f64 k 2)))

series324.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

84.0ms	(cbrt.f64 n)
84.0ms	(*.f64 (cbrt.f64 n) (cbrt.f64 n))
81.0ms	(cbrt.f64 n)
75.0ms	(cbrt.f64 n)

Compiler

Compiled 682 to 550 computations (19.4% saved)

simplify76.0ms (0%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4873	548
1	4873	548

localize25.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
0.0b	(/.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n))) (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)))) (pow.f64 (.f64 2 PI.f64) (/.f64 k 2)))
0.0b	(/.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n))) (pow.f64 n (/.f64 k 2)))
0.0b	(pow.f64 (*.f64 2 PI.f64) (/.f64 k 2))
0.5b	(.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n))) (cbrt.f64 (sqrt.f64 (.f64 (*.f64 2 PI.f64) n))))
0.5b	(cbrt.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)))
0.5b	(cbrt.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)))
0.5b	(cbrt.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)))

rewrite34.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`cbrt-prod_binary64_1132`
23×	`add-sqr-sqrt_binary64_1123`
15×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
11×	`pow1_binary64_1162`
9×	`pow1/3_binary64_1183`
7×	`sqrt-prod_binary64_1117` `swap-sqr_binary64_1068` `associate-r_binary64_1041` `associate-l_binary64_1042`
6×	`add-exp-log_binary64_1139`
4×	`add-log-exp_binary64_1140` `add-cbrt-cube_binary64_1137` `unswap-sqr_binary64_1069`
2×	`pow-prod-up_binary64_1171` `pow-sqr_binary64_1074` `pow-prod-down_binary64_1172`
1×	`pow-plus_binary64_1164` `*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow2_binary64_1182`

Counts

4 → 79

Calls

8 calls:

10.0ms	(.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n))) (cbrt.f64 (sqrt.f64 (.f64 (*.f64 2 PI.f64) n))))
4.0ms	(cbrt.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)))
4.0ms	(cbrt.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)))
4.0ms	(cbrt.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)))
0.0ms	(pow.f64 (*.f64 2 PI.f64) (/.f64 k 2))

series537.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

141.0ms	(cbrt.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)))
136.0ms	(cbrt.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)))
131.0ms	(cbrt.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)))
127.0ms	(.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n))) (cbrt.f64 (sqrt.f64 (.f64 (*.f64 2 PI.f64) n))))

Compiler

Compiled 1104 to 920 computations (16.7% saved)

simplify130.0ms (0%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4838	1439
1	4838	1439

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite746.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

2184×	`times-frac_binary64_1107`
1244×	`cbrt-prod_binary64_1132`
1163×	`add-sqr-sqrt_binary64_1123`
830×	`sqrt-prod_binary64_1117`
811×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
216×	`sqr-pow_binary64_1073`
199×	`swap-sqr_binary64_1068`
184×	`unpow-prod-down_binary64_1180`
151×	`associate-r_binary64_1041` `associate-l_binary64_1042`
64×	`unswap-sqr_binary64_1069`
53×	`div-inv_binary64_1098`
11×	`pow1_binary64_1162`
9×	`pow1/3_binary64_1183`
7×	`cbrt-div_binary64_1133`
6×	`add-exp-log_binary64_1139`
4×	`add-log-exp_binary64_1140` `add-cbrt-cube_binary64_1137`
2×	`pow-prod-up_binary64_1171` `pow-sqr_binary64_1074` `pow-prod-down_binary64_1172`
1×	`pow-plus_binary64_1164` `-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `frac-times_binary64_1111` `prod-exp_binary64_1150` `associate-r/_binary64_1043` `associate-*l/_binary64_1044` `pow2_binary64_1182`

Counts

4 → 1000

Calls

8 calls:

335.0ms	(.f64 (cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))) (cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))))
23.0ms	(cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k)))
18.0ms	(cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k)))
17.0ms	(cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k)))
0.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2)))

series3.2s (1%)

Counts

4 → 36

Calls

4 calls:

1.2s	(.f64 (cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))) (cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))))
669.0ms	(cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k)))
662.0ms	(cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k)))
649.0ms	(cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k)))

Compiler

Compiled 4410 to 3350 computations (24% saved)

simplify718.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1036 → 1036

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5117	88451

prune2.5min (48.8%)

Pruning

1604 alts after pruning (1589 fresh and 15 done)

	Pruned	Kept	Total
New	831	587	1418
Fresh	29	1002	1031
Picked	0	0	0
Done	1	15	16
Total	861	1604	2465

Error

Counts

2465 → 1604

Compiler

Compiled 62506 to 41217 computations (34.1% saved)

simplify3.0s (1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	6868	192480

regimes33.6s (11.1%)

Compiler: Compiled 449097 to 342994 computations (23.6% saved)

bsearch0.0ms (0%)

regimes2.9s (1%)

Compiler: Compiled 28290 to 25194 computations (10.9% saved)

bsearch0.0ms (0%)

regimes971.0ms (0.3%)

Compiler: Compiled 8476 to 7891 computations (6.9% saved)

bsearch0.0ms (0%)

regimes757.0ms (0.3%)

Compiler: Compiled 6497 to 6098 computations (6.1% saved)

bsearch0.0ms (0%)

regimes862.0ms (0.3%)

Compiler: Compiled 4507 to 4269 computations (5.3% saved)

bsearch0.0ms (0%)

regimes175.0ms (0.1%)

Compiler: Compiled 1190 to 1169 computations (1.8% saved)

bsearch0.0ms (0%)

regimes275.0ms (0.1%)

Compiler: Compiled 1112 to 1115 computations (-0.3% saved)

bsearch25.0ms (0%)

Steps

Iters	Range		Point
8	8.552243923073485e-78	2.7408112816788916e-74	2.7008463207183678e-74

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes266.0ms (0.1%)

Compiler: Compiled 1014 to 1024 computations (-1% saved)

bsearch24.0ms (0%)

Steps

Iters	Range		Point
8	8.552243923073485e-78	2.7408112816788916e-74	6.003961771686958e-75

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes274.0ms (0.1%)

Compiler: Compiled 581 to 605 computations (-4.1% saved)

bsearch25.0ms (0%)

Steps

Iters	Range		Point
8	1.8630834833025842	49650.39618479389	3.042568944369596

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes253.0ms (0.1%)

Compiler: Compiled 518 to 542 computations (-4.6% saved)

bsearch25.0ms (0%)

Steps

Iters	Range		Point
8	1.8630834833025842	49650.39618479389	3.157038681566503

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes187.0ms (0.1%)

Compiler: Compiled 490 to 522 computations (-6.5% saved)

bsearch26.0ms (0%)

Steps

Iters	Range		Point
8	1.8630834833025842	49650.39618479389	3.157038681566503

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes39.0ms (0%)

Compiler: Compiled 26 to 42 computations (-61.5% saved)

bsearch28.0ms (0%)

Steps

Iters	Range		Point
8	1.8630834833025842	49650.39618479389	2.9280992071726892

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes26.0ms (0%)

Compiler: Compiled 10 to 26 computations (-160% saved)

bsearch38.0ms (0%)

Steps

Iters	Range		Point
8	1.8630834833025842	49650.39618479389	3.157038681566503

Compiler

Compiled 223 to 201 computations (9.9% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	88	347
1	88	347

end0.0ms (0%)

sample5.1s (1.7%)

Algorithm

1×

intervals

Results

634.0ms	8000×	body	128	valid
627.0ms	1352×	body	1024	nan
321.0ms	2280×	body	128	overflowed
228.0ms	690×	body	512	nan
69.0ms	1049×	body	128	nan
65.0ms	349×	body	256	nan
23.0ms	247×	body	128	invalid

Compiler

Compiled 112702 to 86130 computations (23.6% saved)