Details

Time bar (total: 9.5s)

analyze608.0ms (6.4%)

Algorithm
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 19 to 16 computations (15.8% saved)

sample142.0ms (1.5%)

Algorithm
intervals
Results
30.0ms256×body128valid
26.0ms43×body1024nan
14.0ms78×body128overflowed
9.0ms22×body512nan
3.0ms40×body128nan
3.0ms12×body256nan
1.0ms10×body128invalid
Compiler

Compiled 39 to 33 computations (15.4% saved)

simplify52.0ms (0.5%)

Algorithm
egg-herbie
Rules
672×associate-/l*_binary64
625×associate-/r*_binary64
461×div-sub_binary64
445×distribute-frac-neg_binary64
288×distribute-rgt-neg-out_binary64
Counts
1 → 1
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01425
13222
26522
312922
428022
563420
6133220
7312120
8491420
9455020

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.3b
Counts
2 → 2
Alt Table
StatusErrorProgram
0.4b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
0.4b
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
Compiler

Compiled 81 to 66 computations (18.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite21.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
36×times-frac_binary64
26×*-un-lft-identity_binary64
26×add-sqr-sqrt_binary64
26×add-cube-cbrt_binary64
26×add-exp-log_binary64
Counts
3 → 108
Calls

3 calls:

5.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
4.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (fma.f64 k -1/2 1/2))
4.0ms
(*.f64 (*.f64 2 PI.f64) n)

series740.0ms (7.8%)

Counts
3 → 60
Calls

3 calls:

414.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
315.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (fma.f64 k -1/2 1/2))
11.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify272.0ms (2.9%)

Algorithm
egg-herbie
Rules
477×times-frac_binary64
348×associate-*l*_binary64
306×associate-*r*_binary64
302×cancel-sign-sub-inv_binary64
300×fma-neg_binary64
Counts
168 → 168
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02835067
16794661
226424470
346034470
449374470
549954470
649504470

prune112.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1599168
Fresh101
Picked101
Done000
Total1619170
Error
0.0b
Counts
170 → 9
Alt Table
StatusErrorProgram
0.9b
(*.f64 (/.f64 (pow.f64 (*.f64 2 PI.f64) (fma.f64 k -1/2 1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (cbrt.f64 k))))
0.8b
(/.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n PI.f64)))) (sqrt.f64 k))
21.0b
(/.f64 (-.f64 (*.f64 (sqrt.f64 (*.f64 n PI.f64)) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n PI.f64))) 2)))))) (*.f64 (sqrt.f64 (*.f64 n PI.f64)) (+.f64 (*.f64 1/2 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 n PI.f64))) (sqrt.f64 2)))) (*.f64 1/48 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n PI.f64))) 3))))))) (sqrt.f64 k))
1.0b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))) (sqrt.f64 (sqrt.f64 k))))
0.8b
(*.f64 (pow.f64 (*.f64 2 PI.f64) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
0.9b
(*.f64 (/.f64 (pow.f64 (*.f64 2 PI.f64) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))))
0.5b
(*.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
0.6b
(*.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
0.4b
(*.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
Compiler

Compiled 2198 to 1371 computations (37.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (/.f64 1 k))
0.2b
(pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2))
0.2b
(*.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
0.3b
(*.f64 n PI.f64)

rewrite33.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt_binary64
32×sqrt-prod_binary64
26×*-un-lft-identity_binary64
24×times-frac_binary64
24×add-exp-log_binary64
Counts
4 → 119
Calls

4 calls:

14.0ms
(*.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
4.0ms
(pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2))
3.0ms
(*.f64 n PI.f64)
2.0ms
(sqrt.f64 (/.f64 1 k))

series684.0ms (7.2%)

Counts
4 → 52
Calls

4 calls:

349.0ms
(*.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
325.0ms
(pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2))
6.0ms
(*.f64 n PI.f64)
4.0ms
(sqrt.f64 (/.f64 1 k))

simplify247.0ms (2.6%)

Algorithm
egg-herbie
Rules
489×fma-neg_binary64
386×times-frac_binary64
360×cancel-sign-sub-inv_binary64
346×associate-*l*_binary64
314×associate-*r*_binary64
Counts
171 → 171
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02774633
17014336
226163975
343743975
449613975
549863975
650003975
749343975

prune165.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1701171
Fresh268
Picked011
Done000
Total1728180
Error
0b
Counts
180 → 8
Alt Table
StatusErrorProgram
0.9b
(*.f64 (/.f64 (pow.f64 (*.f64 2 PI.f64) (fma.f64 k -1/2 1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (cbrt.f64 k))))
0.8b
(/.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n PI.f64)))) (sqrt.f64 k))
0.5b
(*.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
20.9b
(*.f64 (*.f64 (sqrt.f64 (*.f64 n PI.f64)) (+.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) (sqrt.f64 2)))))) (sqrt.f64 (/.f64 1 k)))
1.0b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))) (sqrt.f64 (sqrt.f64 k))))
0.9b
(*.f64 (/.f64 (pow.f64 (*.f64 2 PI.f64) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))))
0.6b
(*.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
0.4b
(*.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
Compiler

Compiled 2223 to 1582 computations (28.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2))
0.3b
(*.f64 n PI.f64)
0.3b
(*.f64 n PI.f64)
0.4b
(*.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))

rewrite73.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
382×sqrt-prod_binary64
305×add-sqr-sqrt_binary64
272×times-frac_binary64
85×*-un-lft-identity_binary64
85×add-cube-cbrt_binary64
Counts
1 → 243
Calls

1 calls:

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

series346.0ms (3.6%)

Counts
1 → 24
Calls

1 calls:

346.0ms
(*.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))

simplify309.0ms (3.3%)

Algorithm
egg-herbie
Rules
780×fma-def_binary64
653×unswap-sqr_binary64
447×times-frac_binary64
398×associate-*l*_binary64
386×associate-*r*_binary64
Counts
267 → 267
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
038410446
17529837
229609587
341879561
451269561

prune222.0ms (2.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New3641365
Fresh156
Picked011
Done011
Total3658373
Error
0b
Counts
373 → 8
Alt Table
StatusErrorProgram
0.9b
(*.f64 (/.f64 (pow.f64 (*.f64 2 PI.f64) (fma.f64 k -1/2 1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (cbrt.f64 k))))
0.8b
(/.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n PI.f64)))) (sqrt.f64 k))
0.5b
(*.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
20.9b
(*.f64 (*.f64 (sqrt.f64 (*.f64 n PI.f64)) (+.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) (sqrt.f64 2)))))) (sqrt.f64 (/.f64 1 k)))
1.0b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))) (sqrt.f64 (sqrt.f64 k))))
0.9b
(*.f64 (/.f64 (pow.f64 (*.f64 2 PI.f64) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))))
0.7b
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 (*.f64 n PI.f64) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
0.4b
(*.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
Compiler

Compiled 5795 to 3618 computations (37.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite35.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
84×times-frac_binary64
77×add-sqr-sqrt_binary64
51×add-exp-log_binary64
46×*-un-lft-identity_binary64
46×add-cube-cbrt_binary64
Counts
3 → 176
Calls

3 calls:

15.0ms
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 (*.f64 n PI.f64) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
4.0ms
(/.f64 (pow.f64 (*.f64 n PI.f64) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
3.0ms
(pow.f64 (*.f64 n PI.f64) (fma.f64 k -1/2 1/2))

series1.2s (12.3%)

Counts
3 → 64
Calls

3 calls:

568.0ms
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 (*.f64 n PI.f64) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
311.0ms
(/.f64 (pow.f64 (*.f64 n PI.f64) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
284.0ms
(pow.f64 (*.f64 n PI.f64) (fma.f64 k -1/2 1/2))

simplify165.0ms (1.7%)

Algorithm
egg-herbie
Rules
826×associate-*r*_binary64
796×associate-*l*_binary64
296×fma-def_binary64
199×*-commutative_binary64
171×associate-/l*_binary64
Counts
240 → 240
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04609273
112918667
253058667

prune181.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New3182320
Fresh235
Picked011
Done112
Total3217328
Error
0b
Counts
328 → 7
Alt Table
StatusErrorProgram
0.9b
(*.f64 (/.f64 (pow.f64 (*.f64 2 PI.f64) (fma.f64 k -1/2 1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (cbrt.f64 k))))
0.8b
(/.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n PI.f64)))) (sqrt.f64 k))
1.0b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))) (sqrt.f64 (sqrt.f64 k))))
1.3b
(*.f64 (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 (*.f64 n PI.f64) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k)))) (/.f64 (pow.f64 (*.f64 n PI.f64) 1/2) (sqrt.f64 (sqrt.f64 k))))
0.7b
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 (*.f64 n PI.f64) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
0.7b
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 (*.f64 (*.f64 n (sqrt.f64 PI.f64)) (sqrt.f64 PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
0.4b
(*.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
Compiler

Compiled 4079 to 2475 computations (39.3% saved)

regimes674.0ms (7.1%)

Accuracy

Total 0.4b remaining (93.7%)

Threshold costs 0.4b (93.7%)

Compiler

Compiled 13086 to 10047 computations (23.2% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
*-lft-identity_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01620
12120
21920

end1.0ms (0%)

Compiler

Compiled 15 to 12 computations (20% saved)

sample3.2s (33.7%)

Algorithm
intervals
Results
867.0ms1359×body1024nan
780.0ms8000×body128valid
501.0ms2286×body128overflowed
264.0ms655×body512nan
85.0ms316×body256nan
76.0ms1021×body128nan
28.0ms224×body128invalid
Compiler

Compiled 199 to 149 computations (25.1% saved)

Profiling

Loading profile data...