Details

Time bar (total: 8.9s)

analyze396.0ms (4.4%)

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
Compiler

Compiled 17 to 16 computations (5.9% saved)

sample86.0ms (1%)

Algorithm
1×intervals
Results
28.0ms256×body80valid
18.0ms30×body1280nan
12.0ms27×body640nan
11.0ms81×body80overflowed
2.0ms12×body160nan
2.0ms5×body320nan
1.0ms15×body80nan
1.0ms6×body80invalid
Compiler

Compiled 33 to 33 computations (0% saved)

simplify95.0ms (1.1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (80.0ms)

IterNodesCost
0490922
1490922

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.9b

Counts
2 → 2
Compiler

Compiled 44 to 41 computations (6.8% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b
(*.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))
0.8b
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))

rewrite36.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
48×times-frac_binary64
42×*-un-lft-identity_binary64 add-sqr-sqrt_binary64
33×add-cube-cbrt_binary64
26×add-exp-log_binary64
22×pow-unpow_binary64
18×sqrt-prod_binary64
14×pow1_binary64
10×add-cbrt-cube_binary64
9×prod-exp_binary64
8×sqr-pow_binary64 unpow-prod-down_binary64
6×pow-prod-down_binary64 associate-/r*_binary64 difference-of-squares_binary64 pow-exp_binary64
5×associate-/l*_binary64 div-exp_binary64
3×add-log-exp_binary64 cbrt-unprod_binary64 associate-*r*_binary64 pow-pow_binary64 distribute-lft-out--_binary64 insert-posit16
2×pow-to-exp_binary64 div-sub_binary64 pow-sub_binary64 div-inv_binary64
1×associate-/l/_binary64 cbrt-undiv_binary64 associate-*l*_binary64 clear-num_binary64 frac-2neg_binary64 *-commutative_binary64
Counts
3 → 118
Calls

3 calls:

12.0ms
(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))
6.0ms
(*.f64 (*.f64 2 PI.f64) n)

series466.0ms (5.2%)

Counts
3 → 9
Calls

3 calls:

283.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
144.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
38.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify89.0ms (1%)

Algorithm
1×egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
052463593

prune199.0ms (2.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New11611127
Fresh101
Picked101
Done000
Total11811129

Merged error: 0.0b

Counts
129 → 11
Compiler

Compiled 3273 to 2235 computations (31.7% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (*.f64 2 PI.f64) n)
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))))
0.5b
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))
0.6b
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2))

rewrite44.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
128×add-exp-log_binary64
67×prod-exp_binary64
39×pow-exp_binary64
30×div-exp_binary64
26×pow-unpow_binary64
23×times-frac_binary64
21×*-un-lft-identity_binary64 pow1_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64
14×add-cbrt-cube_binary64
13×pow-to-exp_binary64
9×pow-prod-down_binary64
6×pow-pow_binary64
5×associate-/l*_binary64
4×add-log-exp_binary64 cbrt-unprod_binary64 sqr-pow_binary64 unpow-prod-down_binary64 insert-posit16
3×associate-*r*_binary64 div-inv_binary64
2×cbrt-undiv_binary64
1×associate-/r*_binary64 associate-*l*_binary64 clear-num_binary64 frac-2neg_binary64 *-commutative_binary64
Counts
4 → 133
Calls

4 calls:

13.0ms
(/.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))))
9.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))
9.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2))
6.0ms
(*.f64 (*.f64 2 PI.f64) n)

series749.0ms (8.4%)

Counts
4 → 12
Calls

4 calls:

392.0ms
(/.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))))
201.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2))
114.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))
42.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify91.0ms (1%)

Algorithm
1×egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
051163112

prune213.0ms (2.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1423145
Fresh3710
Picked101
Done000
Total14610156

Merged error: 0.0b

Counts
156 → 10
Compiler

Compiled 3839 to 2663 computations (30.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.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))
0.5b
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))
0.6b
(sqrt.f64 (*.f64 (*.f64 2 PI.f64) n))

rewrite55.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
293×times-frac_binary64
132×*-un-lft-identity_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64
111×sqrt-prod_binary64
34×add-exp-log_binary64
29×sqr-pow_binary64 unpow-prod-down_binary64
24×associate-/l*_binary64
21×pow1_binary64
14×add-cbrt-cube_binary64
13×pow-unpow_binary64
11×div-exp_binary64
9×pow-prod-down_binary64 prod-exp_binary64 div-inv_binary64
6×associate-/r*_binary64 pow-exp_binary64
4×add-log-exp_binary64 insert-posit16
3×cbrt-unprod_binary64 associate-*r*_binary64 cbrt-undiv_binary64 pow-pow_binary64 sqrt-pow1_binary64
2×pow-to-exp_binary64
1×associate-/l/_binary64 pow1/2_binary64 associate-*l*_binary64 clear-num_binary64 frac-2neg_binary64 *-commutative_binary64
Counts
4 → 256
Calls

4 calls:

18.0ms
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
9.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))
6.0ms
(*.f64 (*.f64 2 PI.f64) n)
5.0ms
(sqrt.f64 (*.f64 (*.f64 2 PI.f64) n))

series648.0ms (7.3%)

Counts
4 → 12
Calls

4 calls:

434.0ms
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
116.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))
56.0ms
(sqrt.f64 (*.f64 (*.f64 2 PI.f64) n))
42.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify247.0ms (2.8%)

Algorithm
1×egg-herbie
Counts
268 → 268
Iterations

Useful iterations: 0 (139.0ms)

IterNodesCost
0495212195
1495212195

prune583.0ms (6.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2671268
Fresh189
Picked011
Done000
Total26810278

Merged error: 0.0b

Counts
278 → 10
Compiler

Compiled 9342 to 6064 computations (35.1% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (*.f64 2 PI.f64) n)
0.3b
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (pow.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) k) (/.f64 1 2))) (sqrt.f64 k))
0.5b
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) k)
0.6b
(sqrt.f64 (*.f64 (*.f64 2 PI.f64) n))

rewrite71.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
492×times-frac_binary64
214×*-un-lft-identity_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64
187×sqrt-prod_binary64
169×unpow-prod-down_binary64
57×sqr-pow_binary64
40×associate-/l*_binary64
39×add-exp-log_binary64
21×pow1_binary64
15×div-exp_binary64
14×add-cbrt-cube_binary64
11×pow-exp_binary64
9×pow-prod-down_binary64 prod-exp_binary64
8×div-inv_binary64
6×associate-/r*_binary64
4×add-log-exp_binary64 insert-posit16
3×pow-to-exp_binary64 pow-unpow_binary64 cbrt-unprod_binary64 associate-*r*_binary64 cbrt-undiv_binary64 pow-pow_binary64 sqrt-pow1_binary64
1×associate-/l/_binary64 pow1/2_binary64 associate-*l*_binary64 clear-num_binary64 frac-2neg_binary64 *-commutative_binary64
Counts
4 → 360
Calls

4 calls:

24.0ms
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (pow.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) k) (/.f64 1 2))) (sqrt.f64 k))
7.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) k)
6.0ms
(*.f64 (*.f64 2 PI.f64) n)
5.0ms
(sqrt.f64 (*.f64 (*.f64 2 PI.f64) n))

series742.0ms (8.3%)

Counts
4 → 12
Calls

4 calls:

549.0ms
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (pow.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) k) (/.f64 1 2))) (sqrt.f64 k))
103.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) k)
50.0ms
(sqrt.f64 (*.f64 (*.f64 2 PI.f64) n))
39.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify296.0ms (3.3%)

Algorithm
1×egg-herbie
Counts
372 → 372
Iterations

Useful iterations: 0 (140.0ms)

IterNodesCost
0494918303
1494918303

prune834.0ms (9.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New3711372
Fresh178
Picked011
Done011
Total37210382

Merged error: 0.0b

Counts
382 → 10
Compiler

Compiled 13092 to 8297 computations (36.6% saved)

regimes75.0ms (0.8%)

Compiler

Compiled 791 to 644 computations (18.6% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01931
11931

end0.0ms (0%)

sample2.8s (31.8%)

Algorithm
1×intervals
Results
744.0ms8000×body80valid
605.0ms984×body1280nan
360.0ms785×body640nan
329.0ms2389×body80overflowed
128.0ms418×body320nan
41.0ms704×body80nan
36.0ms194×body160nan
23.0ms245×body80invalid
Compiler

Compiled 295 to 242 computations (18% saved)

Profiling

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