Details

analyze378.0ms (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)

sample81.0ms (1.2%)

Algorithm

1×

intervals

Results

22.0ms	50×	body	1024	nan
19.0ms	256×	body	128	valid
15.0ms	78×	body	128	overflowed
10.0ms	30×	body	512	nan
2.0ms	10×	body	256	nan
2.0ms	29×	body	128	nan
1.0ms	7×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify140.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

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: 0.4b

Counts

2 → 2

Compiler

Compiled 44 to 41 computations (6.8% saved)

localize15.0ms (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_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))
6.0ms	(/.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)

series265.0ms (3.9%)

Counts

3 → 9

Calls

3 calls:

169.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
77.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
18.0ms	(.f64 (.f64 2 PI.f64) n)

simplify82.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4989	3537
1	4989	3537

prune201.0ms (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 3322 to 2278 computations (31.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
0.2b	(/.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	(.f64 (.f64 2 PI.f64) n)
0.2b	(.f64 (.f64 2 PI.f64) n)

rewrite38.0ms (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:

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))))
6.0ms	(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)

series381.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

239.0ms	(/.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))))
103.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
20.0ms	(.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

prune182.0ms (2.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	125	5	130
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	132	10	142

Merged error: 0.0b

Counts

142 → 10

Compiler

Compiled 3359 to 2330 computations (30.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
0.2b	(.f64 (.f64 2 PI.f64) n)
0.2b	(.f64 (.f64 2 PI.f64) n)
0.4b	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (sqrt.f64 k))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64_1107`
23×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `sqrt-prod_binary64_1117` `add-cube-cbrt_binary64_1136`
20×	`pow1_binary64_1162`
16×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
9×	`pow-prod-down_binary64_1172`
6×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `associate-r_binary64_1041` `associate-/r*_binary64_1045`
4×	`add-log-exp_binary64_1140` `associate-/l*_binary64_1046`
3×	`sqrt-pow1_binary64_1119`
2×	`-commutative_binary64_1032` `associate-l*_binary64_1042`
1×	`sqrt-undiv_binary64_1122` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `pow1/2_binary64_1181`

Counts

4 → 95

Calls

4 calls:

8.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (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))

series142.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

82.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (sqrt.f64 k))
24.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
18.0ms	(.f64 (.f64 2 PI.f64) n)
18.0ms	(.f64 (.f64 2 PI.f64) n)

simplify56.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5110	1956

prune142.0ms (2.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	108	9	117

Merged error: 0b

Counts

117 → 9

Compiler

Compiled 2908 to 1893 computations (34.9% saved)

localize16.0ms (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 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))))
0.2b	(.f64 (.f64 2 PI.f64) n)
0.3b	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))
0.3b	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))

rewrite49.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

167×	`add-exp-log_binary64_1139`
96×	`prod-exp_binary64_1150`
42×	`pow-exp_binary64_1169`
36×	`div-exp_binary64_1152`
28×	`add-cbrt-cube_binary64_1137`
23×	`pow1_binary64_1162`
15×	`associate-r_binary64_1041`
13×	`cbrt-unprod_binary64_1134`
12×	`pow-prod-down_binary64_1172` `pow-to-exp_binary64_1170`
11×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
6×	`sqrt-prod_binary64_1117`
5×	`associate-/l*_binary64_1046` `times-frac_binary64_1107`
4×	`add-log-exp_binary64_1140`
3×	`-commutative_binary64_1032` `associate-l*_binary64_1042`
2×	`unpow-prod-down_binary64_1180` `cbrt-undiv_binary64_1135` `sqr-pow_binary64_1073`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/r*_binary64_1045`

Counts

4 → 122

Calls

4 calls:

13.0ms	(/.f64 (pow.f64 (.f64 (.f64 (.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))))
10.0ms	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
6.0ms	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))
5.0ms	(.f64 (.f64 2 PI.f64) n)

series297.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

236.0ms	(/.f64 (pow.f64 (.f64 (.f64 (.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))))
22.0ms	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
20.0ms	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))
18.0ms	(.f64 (.f64 2 PI.f64) n)

simplify64.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4967	2872
1	4967	2872

prune174.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	134	9	143

Merged error: 0b

Counts

143 → 9

Compiler

Compiled 3505 to 2258 computations (35.6% saved)

regimes457.0ms (6.7%)

Compiler: Compiled 6062 to 5026 computations (17.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	31
1	15	31

end0.0ms (0%)

sample3.5s (51.3%)

Algorithm

1×

intervals

Results

593.0ms	1327×	body	1024	nan
590.0ms	8000×	body	128	valid
310.0ms	2308×	body	128	overflowed
223.0ms	718×	body	512	nan
67.0ms	957×	body	128	nan
54.0ms	318×	body	256	nan
23.0ms	219×	body	128	invalid

Compiler

Compiled 1540 to 1278 computations (17% saved)

Details

analyze378.0ms (5.5%)

sample81.0ms (1.2%)

simplify140.0ms (2%)

prune5.0ms (0.1%)

localize15.0ms (0.2%)

rewrite33.0ms (0.5%)

series265.0ms (3.9%)

simplify82.0ms (1.2%)

prune201.0ms (2.9%)

localize13.0ms (0.2%)

rewrite38.0ms (0.6%)

series381.0ms (5.6%)

simplify57.0ms (0.8%)

prune182.0ms (2.7%)

localize11.0ms (0.2%)

rewrite31.0ms (0.5%)

series142.0ms (2.1%)

simplify56.0ms (0.8%)

prune142.0ms (2.1%)

localize16.0ms (0.2%)

rewrite49.0ms (0.7%)

series297.0ms (4.4%)

simplify64.0ms (0.9%)

prune174.0ms (2.6%)

regimes457.0ms (6.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.5s (51.3%)

Profiling