Details

Time bar (total: 9.4s)

analyze352.0ms (3.8%)

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%25%57.9%7
18%20.3%61.8%8
18.3%16.4%65.3%9
18.5%13.7%67.8%10
18.6%11.5%69.9%11
18.7%10%71.3%12
18.7%8.9%72.4%13
18.7%8.2%73.1%14
Compiler

Compiled 19 to 16 computations (15.8% saved)

sample3.3s (35.4%)

Results
1.3s8256×body128valid
1.1s1439×body1024invalid
442.0ms795×body512invalid
196.0ms1168×body128invalid
136.0ms398×body256invalid
Compiler

Compiled 56 to 47 computations (16.1% saved)

simplify45.0ms (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 → 2
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01425
13222
26522
312922
428022
563420
6133220
7312120
8491420
9455020

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.3b
Counts
3 → 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 97 to 77 computations (20.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series492.0ms (5.2%)

Counts
3 → 48
Calls

3 calls:

263.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
225.0ms
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
3.0ms
(*.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 (*.f64 2 (PI.f64)) n)
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))

simplify118.0ms (1.3%)

Algorithm
egg-herbie
Rules
405×distribute-rgt-in_binary64
399×distribute-lft-in_binary64
243×fma-neg_binary64
211×associate-/l*_binary64
162×associate-*l*_binary64
Counts
156 → 168
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02134057
14283712
213903636
345063636
449603636

prune217.0ms (2.3%)

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
0.4b
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
0.6b
(*.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
0.3b
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
0.5b
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)))))
0.2b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))
22.8b
(/.f64 (-.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)) (*.f64 1/8 (*.f64 (*.f64 (pow.f64 k 2) (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 1/2 (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64)))))) (sqrt.f64 k))
0.5b
(*.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)))
0.6b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
0.5b
(*.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))))
Compiler

Compiled 4404 to 2784 computations (36.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series112.0ms (1.2%)

Counts
3 → 0
Calls

3 calls:

76.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))
34.0ms
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))
2.0ms
(*.f64 n (PI.f64))

rewrite58.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
308×times-frac_binary64
143×add-sqr-sqrt_binary64
141×*-un-lft-identity_binary64
141×add-cube-cbrt_binary64
130×sqrt-prod_binary64
Counts
3 → 267
Calls

3 calls:

14.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))
5.0ms
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))
3.0ms
(*.f64 n (PI.f64))

simplify349.0ms (3.7%)

Algorithm
egg-herbie
Rules
743×associate-/r*_binary64
350×fma-neg_binary64
297×associate-/r/_binary64
237×associate-/l/_binary64
208×*-commutative_binary64
Counts
267 → 346
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
036212589
171912274
2246612046
3324712046
4475712046
5502012046

prune576.0ms (6.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New3722374
Fresh358
Picked011
Done000
Total3758383
Error
0b
Counts
383 → 8
Alt Table
StatusErrorProgram
0.3b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (*.f64 (sqrt.f64 k) (/.f64 1 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
0.5b
(*.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))))
0.3b
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
10.0b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (sqrt.f64 (/.f64 k (*.f64 2 (*.f64 n (PI.f64))))))
0.2b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))
22.8b
(/.f64 (-.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)) (*.f64 1/8 (*.f64 (*.f64 (pow.f64 k 2) (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 1/2 (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64)))))) (sqrt.f64 k))
0.5b
(*.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)))
0.6b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
Compiler

Compiled 13357 to 7742 computations (42% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series47.0ms (0.5%)

Counts
2 → 0
Calls

2 calls:

33.0ms
(*.f64 (sqrt.f64 k) (/.f64 1 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))
14.0ms
(/.f64 1 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))

rewrite20.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt_binary64
28×times-frac_binary64
23×*-un-lft-identity_binary64
21×add-cube-cbrt_binary64
16×associate-*r*_binary64
Counts
2 → 88
Calls

2 calls:

10.0ms
(*.f64 (sqrt.f64 k) (/.f64 1 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))
5.0ms
(/.f64 1 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))

simplify123.0ms (1.3%)

Algorithm
egg-herbie
Rules
909×times-frac_binary64
580×fma-def_binary64
547×fma-neg_binary64
460×unswap-sqr_binary64
419×associate-/l*_binary64
Counts
88 → 109
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0831697
11511517
23361517
37501517
427491517
527171517
630131517
737291517
847761517
949611517

prune233.0ms (2.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1590159
Fresh066
Picked011
Done011
Total1598167
Error
0b
Counts
167 → 8
Alt Table
StatusErrorProgram
0.3b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (*.f64 (sqrt.f64 k) (/.f64 1 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
0.5b
(*.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))))
0.3b
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
10.0b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (sqrt.f64 (/.f64 k (*.f64 2 (*.f64 n (PI.f64))))))
0.2b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))
22.8b
(/.f64 (-.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)) (*.f64 1/8 (*.f64 (*.f64 (pow.f64 k 2) (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 1/2 (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64)))))) (sqrt.f64 k))
0.5b
(*.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)))
0.6b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
Compiler

Compiled 4771 to 3044 computations (36.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series493.0ms (5.3%)

Counts
3 → 28
Calls

3 calls:

255.0ms
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
233.0ms
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
5.0ms
(sqrt.f64 (/.f64 1 k))

rewrite22.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt_binary64
32×sqrt-prod_binary64
24×times-frac_binary64
23×*-un-lft-identity_binary64
21×add-exp-log_binary64
Counts
3 → 99
Calls

3 calls:

8.0ms
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
4.0ms
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
2.0ms
(sqrt.f64 (/.f64 1 k))

simplify157.0ms (1.7%)

Algorithm
egg-herbie
Rules
389×distribute-rgt-in_binary64
383×distribute-lft-in_binary64
355×*-commutative_binary64
258×fma-neg_binary64
225×exp-sum_binary64
Counts
127 → 147
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01593052
13282830
210072678
329672678
446832678
549652678
649992678
749272678

prune248.0ms (2.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1690169
Fresh055
Picked011
Done022
Total1698177
Error
0b
Counts
177 → 8
Alt Table
StatusErrorProgram
0.3b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (*.f64 (sqrt.f64 k) (/.f64 1 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
0.5b
(*.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))))
0.3b
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
10.0b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (sqrt.f64 (/.f64 k (*.f64 2 (*.f64 n (PI.f64))))))
0.2b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))
22.8b
(/.f64 (-.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)) (*.f64 1/8 (*.f64 (*.f64 (pow.f64 k 2) (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 1/2 (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64)))))) (sqrt.f64 k))
0.5b
(*.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)))
0.6b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
Compiler

Compiled 4193 to 2939 computations (29.9% saved)

regimes2.2s (23.3%)

Accuracy

Total 0.3b remaining (80.8%)

Threshold costs 0.3b (80.8%)

Counts
395 → 1
Compiler

Compiled 49254 to 36161 computations (26.6% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01634
12334
22234

end145.0ms (1.5%)

Compiler

Compiled 261 to 191 computations (26.8% saved)

Profiling

Loading profile data...