Details

Time bar (total: 8.6s)

analyze396.0ms (4.6%)

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)

sample81.0ms (0.9%)

Algorithm
1×intervals
Results
24.0ms256×body128valid
17.0ms37×body1024nan
16.0ms77×body128overflowed
7.0ms22×body512nan
2.0ms27×body128nan
1.0ms7×body256nan
1.0ms6×body128invalid
Compiler

Compiled 33 to 33 computations (0% saved)

simplify54.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
0490822
1490822

prune5.0ms (0.1%)

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))

rewrite35.0ms (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
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 → 115
Calls

3 calls:

11.0ms
(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)

series482.0ms (5.6%)

Counts
3 → 9
Calls

3 calls:

294.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
148.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
39.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify61.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
052413540

prune197.0ms (2.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New11311124
Fresh101
Picked101
Done000
Total11511126

Merged error: 0.0b

Counts
126 → 11
Compiler

Compiled 3225 to 2202 computations (31.7% saved)

localize19.0ms (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))

rewrite46.0ms (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
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 → 129
Calls

4 calls:

10.0ms
(/.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))))
8.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2))
8.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))
6.0ms
(*.f64 (*.f64 2 PI.f64) n)

series772.0ms (9%)

Counts
4 → 12
Calls

4 calls:

417.0ms
(/.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))))
210.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2))
111.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))
35.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify64.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
051103041

prune199.0ms (2.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1383141
Fresh3710
Picked101
Done000
Total14210152

Merged error: 0.0b

Counts
152 → 10
Compiler

Compiled 3749 to 2601 computations (30.6% saved)

localize12.0ms (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))

rewrite74.0ms (0.9%)

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
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 → 252
Calls

4 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))
7.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))
5.0ms
(*.f64 (*.f64 2 PI.f64) n)
4.0ms
(sqrt.f64 (*.f64 (*.f64 2 PI.f64) n))

series638.0ms (7.4%)

Counts
4 → 12
Calls

4 calls:

445.0ms
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
107.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))
46.0ms
(sqrt.f64 (*.f64 (*.f64 2 PI.f64) n))
40.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify178.0ms (2.1%)

Algorithm
1×egg-herbie
Counts
264 → 264
Iterations

Useful iterations: 0 (74.0ms)

IterNodesCost
0495912124
1495912124

prune564.0ms (6.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2631264
Fresh189
Picked011
Done000
Total26410274

Merged error: 0.0b

Counts
274 → 10
Compiler

Compiled 9258 to 6008 computations (35.1% saved)

localize14.0ms (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))

rewrite108.0ms (1.2%)

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
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 → 356
Calls

4 calls:

25.0ms
(/.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))
6.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) k)
5.0ms
(*.f64 (*.f64 2 PI.f64) n)
4.0ms
(sqrt.f64 (*.f64 (*.f64 2 PI.f64) n))

series773.0ms (9%)

Counts
4 → 12
Calls

4 calls:

586.0ms
(/.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))
107.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) k)
42.0ms
(sqrt.f64 (*.f64 (*.f64 2 PI.f64) n))
37.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify226.0ms (2.6%)

Algorithm
1×egg-herbie
Counts
368 → 368
Iterations

Useful iterations: 0 (73.0ms)

IterNodesCost
0496118236
1496118236

prune819.0ms (9.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New3671368
Fresh178
Picked011
Done011
Total36810378

Merged error: 0.0b

Counts
378 → 10
Compiler

Compiled 13003 to 8236 computations (36.7% saved)

regimes82.0ms (0.9%)

Compiler

Compiled 791 to 644 computations (18.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01831
11831

end0.0ms (0%)

sample2.7s (31.4%)

Algorithm
1×intervals
Results
783.0ms8000×body128valid
622.0ms1284×body1024nan
335.0ms2256×body128overflowed
209.0ms634×body512nan
70.0ms355×body256nan
64.0ms945×body128nan
25.0ms245×body128invalid
Compiler

Compiled 295 to 242 computations (18% saved)

Profiling

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