Details

Time bar (total: 16.9s)

analyze398.0ms (2.3%)

Algorithm
1×search
Search
TrueOtherFalseIter
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

sample89.0ms (0.5%)

Algorithm
1×intervals
Results
23.0ms256×body80valid
18.0ms29×body1280nan
15.0ms85×body80overflowed
14.0ms32×body640nan
4.0ms15×body320nan
1.0ms23×body80nan
1.0ms7×body160nan
0.0ms4×body80invalid

simplify55.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
0498716
1498716

prune6.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.4b

Counts
2 → 1

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 (-.f64 1.0 k) 2.0))
0.2b
(*.f64 (/.f64 1.0 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 (-.f64 1.0 k) 2.0)))
0.3b
(/.f64 1.0 (sqrt.f64 k))
0.3b
(*.f64 (*.f64 2.0 PI.f64) n)

rewrite39.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
62×add-sqr-sqrt_binary64
55×times-frac_binary64
49×*-un-lft-identity_binary64
46×add-exp-log_binary64
43×add-cube-cbrt_binary64
23×associate-*l*_binary64 sqrt-prod_binary64
22×prod-exp_binary64
19×pow-unpow_binary64
16×add-cbrt-cube_binary64
15×pow1_binary64
9×pow-exp_binary64
8×associate-*r*_binary64
6×pow-prod-down_binary64 associate-/r*_binary64 unswap-sqr_binary64 div-exp_binary64
5×cbrt-unprod_binary64 sqr-pow_binary64
4×add-log-exp_binary64
3×pow-to-exp_binary64 pow-pow_binary64 div-sub_binary64 pow-sub_binary64 difference-of-squares_binary64 associate-/l*_binary64 distribute-lft-out--_binary64 div-inv_binary64
2×cbrt-undiv_binary64 unpow-prod-down_binary64 *-commutative_binary64
1×associate-*r/_binary64 clear-num_binary64 frac-2neg_binary64 frac-times_binary64 associate-*l/_binary64
Counts
4 → 149
Calls

4 calls:

12.0ms
(*.f64 (/.f64 1.0 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 (-.f64 1.0 k) 2.0)))
11.0ms
(pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 (-.f64 1.0 k) 2.0))
6.0ms
(*.f64 (*.f64 2.0 PI.f64) n)
4.0ms
(/.f64 1.0 (sqrt.f64 k))

series132.0ms (0.8%)

Counts
4 → 12
Calls

4 calls:

91.0ms
(*.f64 (/.f64 1.0 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 (-.f64 1.0 k) 2.0)))
21.0ms
(pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 (-.f64 1.0 k) 2.0))
14.0ms
(/.f64 1.0 (sqrt.f64 k))
5.0ms
(*.f64 (*.f64 2.0 PI.f64) n)

simplify62.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
049812442
149812442

prune312.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New15110161
Fresh000
Picked101
Done000
Total15210162

Merged error: 0.0b

Counts
162 → 10

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b
(pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 1.0 2.0))
0.2b
(/.f64 (*.f64 1.0 (pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 1.0 2.0))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 k 2.0))))
0.3b
(*.f64 (*.f64 2.0 PI.f64) n)
0.3b
(*.f64 (*.f64 2.0 PI.f64) n)

rewrite38.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
176×add-exp-log_binary64
105×prod-exp_binary64
39×pow-exp_binary64
36×div-exp_binary64
26×add-cbrt-cube_binary64
20×pow1_binary64
13×pow-to-exp_binary64 *-un-lft-identity_binary64 pow-unpow_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64
10×cbrt-unprod_binary64 times-frac_binary64
9×pow-prod-down_binary64
6×associate-*r*_binary64
4×add-log-exp_binary64 cbrt-undiv_binary64
3×pow-pow_binary64
2×associate-*l*_binary64 div-inv_binary64 *-commutative_binary64
1×associate-/r*_binary64 sqr-pow_binary64 clear-num_binary64 unpow-prod-down_binary64 frac-2neg_binary64 associate-/l*_binary64
Counts
4 → 118
Calls

4 calls:

11.0ms
(/.f64 (*.f64 1.0 (pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 1.0 2.0))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 k 2.0))))
7.0ms
(pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 1.0 2.0))
6.0ms
(*.f64 (*.f64 2.0 PI.f64) n)
6.0ms
(*.f64 (*.f64 2.0 PI.f64) n)

series233.0ms (1.4%)

Counts
4 → 12
Calls

4 calls:

196.0ms
(/.f64 (*.f64 1.0 (pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 1.0 2.0))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 k 2.0))))
27.0ms
(pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 1.0 2.0))
5.0ms
(*.f64 (*.f64 2.0 PI.f64) n)
5.0ms
(*.f64 (*.f64 2.0 PI.f64) n)

simplify59.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
049862219
149862219

prune255.0ms (1.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1273130
Fresh189
Picked101
Done000
Total12911140

Merged error: 0.0b

Counts
140 → 11

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b
(/.f64 1.0 (sqrt.f64 k))
0.3b
(*.f64 (*.f64 2.0 PI.f64) n)
0.3b
(*.f64 (*.f64 2.0 PI.f64) n)
0.3b
(*.f64 (/.f64 1.0 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 1.0 2.0)))

rewrite35.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
48×add-sqr-sqrt_binary64
45×add-exp-log_binary64
40×times-frac_binary64
35×*-un-lft-identity_binary64 add-cube-cbrt_binary64
24×associate-*l*_binary64
23×sqrt-prod_binary64
22×prod-exp_binary64
21×add-cbrt-cube_binary64
14×pow1_binary64
11×associate-*r*_binary64
8×cbrt-unprod_binary64
6×pow-prod-down_binary64 associate-/r*_binary64 unswap-sqr_binary64 div-exp_binary64 pow-exp_binary64
4×add-log-exp_binary64 sqr-pow_binary64
3×associate-/l*_binary64 *-commutative_binary64
2×pow-to-exp_binary64 cbrt-undiv_binary64 div-inv_binary64
1×clear-num_binary64 unpow-prod-down_binary64 frac-2neg_binary64 associate-*l/_binary64
Counts
4 → 129
Calls

4 calls:

12.0ms
(*.f64 (/.f64 1.0 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 1.0 2.0)))
7.0ms
(/.f64 1.0 (sqrt.f64 k))
6.0ms
(*.f64 (*.f64 2.0 PI.f64) n)
5.0ms
(*.f64 (*.f64 2.0 PI.f64) n)

series135.0ms (0.8%)

Counts
4 → 12
Calls

4 calls:

115.0ms
(*.f64 (/.f64 1.0 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 1.0 2.0)))
11.0ms
(/.f64 1.0 (sqrt.f64 k))
5.0ms
(*.f64 (*.f64 2.0 PI.f64) n)
5.0ms
(*.f64 (*.f64 2.0 PI.f64) n)

simplify62.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
049601620
149601620

prune269.0ms (1.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1410141
Fresh01010
Picked011
Done000
Total14111152

Merged error: 0.0b

Counts
152 → 11

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(/.f64 1.0 (/.f64 (sqrt.f64 k) (/.f64 (pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 1.0 2.0)) (pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 k 2.0)))))
0.2b
(/.f64 (sqrt.f64 k) (/.f64 (pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 1.0 2.0)) (pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 k 2.0))))
0.3b
(*.f64 (*.f64 2.0 PI.f64) n)
0.3b
(*.f64 (*.f64 2.0 PI.f64) n)

rewrite170.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
2182×times-frac_binary64
823×*-un-lft-identity_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64
438×sqrt-prod_binary64
310×sqr-pow_binary64 unpow-prod-down_binary64
236×add-exp-log_binary64
208×associate-/r*_binary64
129×div-exp_binary64
66×prod-exp_binary64
60×pow-exp_binary64
37×div-inv_binary64
28×add-cbrt-cube_binary64
20×pow-to-exp_binary64
14×pow1_binary64
9×cbrt-undiv_binary64 associate-/l*_binary64
6×pow-prod-down_binary64 cbrt-unprod_binary64 associate-*r*_binary64 associate-/r/_binary64
4×add-log-exp_binary64
2×associate-*l*_binary64 clear-num_binary64 frac-2neg_binary64 *-commutative_binary64
Counts
4 → 1044
Calls

4 calls:

42.0ms
(/.f64 1.0 (/.f64 (sqrt.f64 k) (/.f64 (pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 1.0 2.0)) (pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 k 2.0)))))
16.0ms
(/.f64 (sqrt.f64 k) (/.f64 (pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 1.0 2.0)) (pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 k 2.0))))
6.0ms
(*.f64 (*.f64 2.0 PI.f64) n)
6.0ms
(*.f64 (*.f64 2.0 PI.f64) n)

series365.0ms (2.2%)

Counts
4 → 12
Calls

4 calls:

186.0ms
(/.f64 1.0 (/.f64 (sqrt.f64 k) (/.f64 (pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 1.0 2.0)) (pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 k 2.0)))))
169.0ms
(/.f64 (sqrt.f64 k) (/.f64 (pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 1.0 2.0)) (pow.f64 (*.f64 (*.f64 2.0 PI.f64) n) (/.f64 k 2.0))))
5.0ms
(*.f64 (*.f64 2.0 PI.f64) n)
5.0ms
(*.f64 (*.f64 2.0 PI.f64) n)

simplify301.0ms (1.8%)

Algorithm
1×egg-herbie
Counts
1056 → 1056
Iterations

Useful iterations: 0 (77.0ms)

IterNodesCost
0499943593
1499943593

prune11.1s (65.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New105421056
Fresh279
Picked011
Done101
Total1057101067

Merged error: 0b

Counts
1067 → 10

regimes267.0ms (1.6%)

Accuracy

Total 0.4b remaining (79%)

Threshold costs 0.4b (79%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01724
11724

end0.0ms (0%)

sample2.5s (14.8%)

Algorithm
1×intervals
Results
705.0ms8000×body80valid
576.0ms934×body1280nan
378.0ms832×body640nan
330.0ms2322×body80overflowed
127.0ms417×body320nan
42.0ms742×body80nan
41.0ms226×body160nan
28.0ms224×body80invalid

Profiling

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