Details

Time bar (total: 9.8s)

analyze567.0ms (5.8%)

Algorithm
1×search
2×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0494244
1494244
022
122
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)

sample88.0ms (0.9%)

Algorithm
1×intervals
Results
26.0ms54×body1024nan
21.0ms256×body128valid
13.0ms90×body128overflowed
8.0ms23×body512nan
3.0ms14×body256nan
2.0ms35×body128nan
1.0ms10×body128invalid
Compiler

Compiled 33 to 33 computations (0% saved)

simplify53.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
0493322
1493322

prune5.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.3b
Counts
2 → 2
Compiler

Compiled 44 to 41 computations (6.8% saved)

localize17.0ms (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
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
0.2b
(*.f64 (*.f64 2 PI.f64) n)

rewrite32.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
48×times-frac_binary64_425
42×*-un-lft-identity_binary64_419 add-sqr-sqrt_binary64_441
33×add-cube-cbrt_binary64_454
26×add-exp-log_binary64_457
22×pow-unpow_binary64_496
18×sqrt-prod_binary64_435
14×pow1_binary64_480
10×add-cbrt-cube_binary64_455
9×prod-exp_binary64_468
8×unpow-prod-down_binary64_498 sqr-pow_binary64_391
6×pow-prod-down_binary64_490 difference-of-squares_binary64_388 pow-exp_binary64_487 associate-/r*_binary64_363
5×div-exp_binary64_470 associate-/l*_binary64_364
3×add-log-exp_binary64_458 associate-*r*_binary64_359 cbrt-unprod_binary64_452 distribute-lft-out--_binary64_371 pow-pow_binary64_491
2×pow-sub_binary64_495 div-inv_binary64_416 pow-to-exp_binary64_488 div-sub_binary64_424
1×clear-num_binary64_418 *-commutative_binary64_350 associate-*l*_binary64_360 frac-2neg_binary64_430 cbrt-undiv_binary64_453 associate-/l/_binary64_366
Counts
3 → 115
Calls

3 calls:

10.0ms
(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)

series268.0ms (2.7%)

Counts
3 → 9
Calls

3 calls:

171.0ms
(/.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))
19.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify89.0ms (0.9%)

Algorithm
1×egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
049893537
149893537

prune207.0ms (2.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New11212124
Fresh101
Picked101
Done000
Total11412126
Error
0.0b
Counts
126 → 12
Compiler

Compiled 3252 to 2225 computations (31.6% saved)

localize16.0ms (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)

rewrite39.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
127×add-exp-log_binary64_457
67×prod-exp_binary64_468
36×pow-exp_binary64_487
30×div-exp_binary64_470
20×pow1_binary64_480
19×add-cbrt-cube_binary64_455
15×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454 add-sqr-sqrt_binary64_441
14×times-frac_binary64_425
13×pow-unpow_binary64_496
12×pow-to-exp_binary64_488
9×pow-prod-down_binary64_490
7×cbrt-unprod_binary64_452
6×associate-*r*_binary64_359
5×associate-/l*_binary64_364
4×add-log-exp_binary64_458
3×unpow-prod-down_binary64_498 sqr-pow_binary64_391 pow-pow_binary64_491
2×div-inv_binary64_416 *-commutative_binary64_350 associate-*l*_binary64_360 cbrt-undiv_binary64_453
1×clear-num_binary64_418 frac-2neg_binary64_430 associate-/r*_binary64_363
Counts
4 → 118
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))))
7.0ms
(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)

series372.0ms (3.8%)

Counts
4 → 12
Calls

4 calls:

233.0ms
(/.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))))
99.0ms
(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)

simplify60.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
052592652

prune187.0ms (1.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1291130
Fresh11011
Picked011
Done000
Total13012142
Error
0b
Counts
142 → 12
Compiler

Compiled 3389 to 2351 computations (30.6% saved)

localize14.0ms (0.1%)

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

rewrite65.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
284×times-frac_binary64_425
126×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454 add-sqr-sqrt_binary64_441
111×sqrt-prod_binary64_435
33×add-exp-log_binary64_457
28×unpow-prod-down_binary64_498 sqr-pow_binary64_391
24×associate-/r*_binary64_363
20×pow1_binary64_480
19×add-cbrt-cube_binary64_455
11×div-exp_binary64_470
9×pow-prod-down_binary64_490 prod-exp_binary64_468
8×div-inv_binary64_416
6×associate-*r*_binary64_359 cbrt-unprod_binary64_452 associate-/l*_binary64_364
4×add-log-exp_binary64_458
3×pow-exp_binary64_487 sqrt-pow1_binary64_437 cbrt-undiv_binary64_453
2×*-commutative_binary64_350 associate-*l*_binary64_360
1×clear-num_binary64_418 pow1/2_binary64_499 associate-/r/_binary64_365 pow-to-exp_binary64_488 frac-2neg_binary64_430
Counts
4 → 241
Calls

4 calls:

16.0ms
(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
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))

series301.0ms (3.1%)

Counts
4 → 12
Calls

4 calls:

240.0ms
(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
24.0ms
(sqrt.f64 (*.f64 (*.f64 2 PI.f64) n))
19.0ms
(*.f64 (*.f64 2 PI.f64) n)
18.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify156.0ms (1.6%)

Algorithm
1×egg-herbie
Counts
253 → 253
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
0497611847
1497611847

prune588.0ms (6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New2521253
Fresh3710
Picked011
Done011
Total25510265
Error
0b
Counts
265 → 10
Compiler

Compiled 9372 to 6221 computations (33.6% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
0.3b
(*.f64 (/.f64 1 (sqrt.f64 (*.f64 2 PI.f64))) (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))))
1.0b
(sqrt.f64 (*.f64 2 PI.f64))
1.0b
(/.f64 1 (sqrt.f64 (*.f64 2 PI.f64)))

rewrite231.0ms (2.3%)

Algorithm
1×rewrite-expression-head
Rules
898×times-frac_binary64_425
500×add-sqr-sqrt_binary64_441
437×sqrt-prod_binary64_435
392×*-un-lft-identity_binary64_419
381×add-cube-cbrt_binary64_454
209×associate-*r*_binary64_359
142×add-exp-log_binary64_457
90×sqr-pow_binary64_391
78×unpow-prod-down_binary64_498
71×div-exp_binary64_470
43×prod-exp_binary64_468
38×associate-/r*_binary64_363
33×unswap-sqr_binary64_387
32×add-cbrt-cube_binary64_455
17×div-inv_binary64_416
16×associate-*l*_binary64_360
15×pow-exp_binary64_487
13×pow1_binary64_480 cbrt-undiv_binary64_453
9×associate-/l*_binary64_364
8×1-exp_binary64_463 rec-exp_binary64_469
6×cbrt-unprod_binary64_452
5×pow-to-exp_binary64_488
4×add-log-exp_binary64_458 pow-flip_binary64_493 sqrt-pow1_binary64_437
3×pow-prod-down_binary64_490
2×clear-num_binary64_418 pow1/2_binary64_499 associate-/r/_binary64_365 frac-2neg_binary64_430
1×associate-*l/_binary64_362 inv-pow_binary64_504 frac-times_binary64_429 associate-*r/_binary64_361 *-commutative_binary64_350
Counts
4 → 616
Calls

4 calls:

101.0ms
(*.f64 (/.f64 1 (sqrt.f64 (*.f64 2 PI.f64))) (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))))
16.0ms
(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
5.0ms
(/.f64 1 (sqrt.f64 (*.f64 2 PI.f64)))
2.0ms
(sqrt.f64 (*.f64 2 PI.f64))

series419.0ms (4.3%)

Counts
4 → 8
Calls

4 calls:

260.0ms
(*.f64 (/.f64 1 (sqrt.f64 (*.f64 2 PI.f64))) (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))))
159.0ms
(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
0.0ms
(/.f64 1 (sqrt.f64 (*.f64 2 PI.f64)))
0.0ms
(sqrt.f64 (*.f64 2 PI.f64))

simplify242.0ms (2.5%)

Algorithm
1×egg-herbie
Counts
624 → 624
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
0500825887

prune1.8s (17.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New6240624
Fresh077
Picked011
Done022
Total62410634
Error
0b
Counts
634 → 10
Compiler

Compiled 24277 to 14691 computations (39.5% saved)

regimes386.0ms (3.9%)

Accuracy

Total 0.3b remaining (97.9%)

Threshold costs 0.3b (97.9%)

Compiler

Compiled 4490 to 3730 computations (16.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01531
11531

end0.0ms (0%)

sample3.7s (37.2%)

Algorithm
1×intervals
Results
686.0ms8000×body128valid
656.0ms1313×body1024nan
337.0ms2285×body128overflowed
232.0ms687×body512nan
68.0ms350×body256nan
61.0ms991×body128nan
25.0ms250×body128invalid
Compiler

Compiled 1147 to 954 computations (16.8% saved)

Profiling

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