Details

analyze718.0ms (3.8%)

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)

sample148.0ms (0.8%)

Algorithm

1×

intervals

Results

51.0ms	57×	body	1024	nan
38.0ms	256×	body	128	valid
18.0ms	67×	body	128	overflowed
13.0ms	22×	body	512	nan
3.0ms	29×	body	128	nan
3.0ms	8×	body	256	nan
1.0ms	6×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify244.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4933	22
1	4933	22

prune8.0ms (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: 0.3b

Counts

2 → 2

Compiler

Compiled 44 to 41 computations (6.8% saved)

localize20.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite57.0ms (0.3%)

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:

18.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
12.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
9.0ms	(.f64 (.f64 2 PI.f64) n)

series499.0ms (2.6%)

Counts

3 → 9

Calls

3 calls:

317.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
151.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
32.0ms	(.f64 (.f64 2 PI.f64) n)

simplify152.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4989	3537
1	4989	3537

prune344.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	115	9	124
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	117	9	126

Merged error: 0.0b

Counts

126 → 9

Compiler

Compiled 3185 to 2169 computations (31.9% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
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))))
0.3b	(.f64 (.f64 2 PI.f64) n)
0.3b	(.f64 (.f64 2 PI.f64) n)

rewrite69.0ms (0.4%)

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:

17.0ms	(/.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))))
12.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
10.0ms	(.f64 (.f64 2 PI.f64) n)
8.0ms	(.f64 (.f64 2 PI.f64) n)

series703.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

440.0ms	(/.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))))
195.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
37.0ms	(.f64 (.f64 2 PI.f64) n)
30.0ms	(.f64 (.f64 2 PI.f64) n)

simplify106.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5259	2652

prune301.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	131	8	139

Merged error: 0b

Counts

139 → 8

Compiler

Compiled 3335 to 2302 computations (31% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite472.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

1787×	`times-frac_binary64_1107`
712×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
518×	`sqrt-prod_binary64_1117`
173×	`associate-/r*_binary64_1045`
124×	`unpow-prod-down_binary64_1180` `sqr-pow_binary64_1073`
100×	`add-exp-log_binary64_1139`
58×	`div-exp_binary64_1152`
37×	`div-inv_binary64_1098`
28×	`add-cbrt-cube_binary64_1137`
18×	`prod-exp_binary64_1150`
15×	`pow1_binary64_1162`
12×	`pow-exp_binary64_1169`
9×	`associate-/l*_binary64_1046` `cbrt-undiv_binary64_1135`
7×	`1-exp_binary64_1145` `rec-exp_binary64_1151`
6×	`cbrt-unprod_binary64_1134` `associate-/r/_binary64_1047` `associate-r_binary64_1041` `pow-prod-down_binary64_1172`
4×	`add-log-exp_binary64_1140` `pow-to-exp_binary64_1170`
2×	`-commutative_binary64_1032` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-l*_binary64_1042`
1×	`inv-pow_binary64_1186` `pow-flip_binary64_1175`

Counts

4 → 865

Calls

4 calls:

81.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2)))))
31.0ms	(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))))
11.0ms	(.f64 (.f64 2 PI.f64) n)
11.0ms	(.f64 (.f64 2 PI.f64) n)

series1.0s (5.3%)

Counts

4 → 12

Calls

4 calls:

484.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2)))))
462.0ms	(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))))
35.0ms	(.f64 (.f64 2 PI.f64) n)
35.0ms	(.f64 (.f64 2 PI.f64) n)

simplify807.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

877 → 877

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5097	50243

prune5.1s (26.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	877	0	877
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	877	8	885

Merged error: 0b

Counts

885 → 8

Compiler

Compiled 35900 to 23905 computations (33.4% saved)

localize27.0ms (0.1%)

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

rewrite113.0ms (0.6%)

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:

30.0ms	(pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2))
19.0ms	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
16.0ms	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
13.0ms	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))

series596.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

322.0ms	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
194.0ms	(pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2))
40.0ms	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
38.0ms	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))

simplify145.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5062	4348

prune376.0ms (2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	157	8	165

Merged error: 0b

Counts

165 → 8

Compiler

Compiled 3944 to 2530 computations (35.9% saved)

regimes692.0ms (3.6%)

Compiler: Compiled 4718 to 3922 computations (16.9% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	31
1	15	31

end0.0ms (0%)

sample6.3s (33.1%)

Algorithm

1×

intervals

Results

1.2s	1337×	body	1024	nan
1.2s	8000×	body	128	valid
614.0ms	2285×	body	128	overflowed
432.0ms	707×	body	512	nan
113.0ms	311×	body	256	nan
106.0ms	987×	body	128	nan
46.0ms	263×	body	128	invalid

Compiler

Compiled 1204 to 1002 computations (16.8% saved)

Details

analyze718.0ms (3.8%)

sample148.0ms (0.8%)

simplify244.0ms (1.3%)

prune8.0ms (0%)

localize20.0ms (0.1%)

rewrite57.0ms (0.3%)

series499.0ms (2.6%)

simplify152.0ms (0.8%)

prune344.0ms (1.8%)

localize29.0ms (0.2%)

rewrite69.0ms (0.4%)

series703.0ms (3.7%)

simplify106.0ms (0.6%)

prune301.0ms (1.6%)

localize26.0ms (0.1%)

rewrite472.0ms (2.5%)

series1.0s (5.3%)

simplify807.0ms (4.2%)

prune5.1s (26.6%)

localize27.0ms (0.1%)

rewrite113.0ms (0.6%)

series596.0ms (3.1%)

simplify145.0ms (0.8%)

prune376.0ms (2%)

regimes692.0ms (3.6%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.3s (33.1%)

Profiling