Details

Time bar (total: 12.2s)

analyze354.0ms (2.9%)

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)

sample3.8s (31.5%)

Results
1.6s8256×body128valid
1.3s1330×body1024invalid
441.0ms665×body512invalid
251.0ms1228×body128invalid
155.0ms382×body256invalid
Compiler

Compiled 56 to 47 computations (16.1% saved)

simplify58.0ms (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

prune8.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.4b
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)

localize20.0ms (0.2%)

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

series934.0ms (7.7%)

Counts
3 → 48
Calls

3 calls:

483.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
444.0ms
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
7.0ms
(*.f64 (*.f64 2 (PI.f64)) n)

rewrite37.0ms (0.3%)

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

3 calls:

9.0ms
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
8.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
7.0ms
(*.f64 (*.f64 2 (PI.f64)) n)

simplify210.0ms (1.7%)

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

prune408.0ms (3.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1608168
Fresh101
Picked101
Done000
Total1628170
Error
0.0b
Counts
170 → 8
Alt Table
StatusErrorProgram
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))))
23.7b
(/.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 (*.f64 1/2 (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 1/48 (*.f64 (*.f64 (pow.f64 k 3) (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) (sqrt.f64 k))
1.1b
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
0.7b
(*.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))))
0.4b
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
0.5b
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2))) (sqrt.f64 k))
0.6b
(*.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)))
0.8b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k)))
Compiler

Compiled 4399 to 2866 computations (34.8% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series533.0ms (4.4%)

Counts
2 → 12
Calls

2 calls:

508.0ms
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
25.0ms
(/.f64 1 (sqrt.f64 k))

rewrite47.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
59×add-exp-log_binary64
50×add-sqr-sqrt_binary64
44×times-frac_binary64
35×*-un-lft-identity_binary64
32×prod-exp_binary64
Counts
2 → 119
Calls

2 calls:

22.0ms
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
6.0ms
(/.f64 1 (sqrt.f64 k))

simplify216.0ms (1.8%)

Algorithm
egg-herbie
Rules
761×fma-def_binary64
657×times-frac_binary64
385×associate-*l*_binary64
297×distribute-rgt-in_binary64
283×associate-*r*_binary64
Counts
131 → 147
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01352775
12482509
26212509
319562470
446212470
549912470

prune552.0ms (4.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2171218
Fresh167
Picked011
Done000
Total2188226
Error
0.0b
Counts
226 → 8
Alt Table
StatusErrorProgram
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))))
23.7b
(/.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 (*.f64 1/2 (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 1/48 (*.f64 (*.f64 (pow.f64 k 3) (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) (sqrt.f64 k))
1.1b
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
0.4b
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
0.5b
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2))) (sqrt.f64 k))
0.6b
(*.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)))
0.8b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k)))
0.5b
(*.f64 (pow.f64 (*.f64 (*.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
Compiler

Compiled 5407 to 3675 computations (32% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series366.0ms (3%)

Counts
3 → 28
Calls

3 calls:

333.0ms
(pow.f64 (*.f64 (*.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2))
18.0ms
(*.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n))
16.0ms
(*.f64 (*.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n))

rewrite51.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
27×add-exp-log_binary64
27×pow1_binary64
17×add-cbrt-cube_binary64
15×prod-exp_binary64
15×pow-prod-down_binary64
Counts
3 → 73
Calls

3 calls:

18.0ms
(*.f64 (*.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n))
14.0ms
(pow.f64 (*.f64 (*.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2))
9.0ms
(*.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n))

simplify139.0ms (1.1%)

Algorithm
egg-herbie
Rules
881×fma-def_binary64
515×*-commutative_binary64
297×distribute-rgt-in_binary64
291×distribute-lft-in_binary64
262×associate-*l*_binary64
Counts
101 → 99
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01431755
13571553
212181461
331381453
447601453
549511453

prune494.0ms (4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1531154
Fresh156
Picked011
Done011
Total1548162
Error
0.0b
Counts
162 → 8
Alt Table
StatusErrorProgram
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))))
23.7b
(/.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 (*.f64 1/2 (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 1/48 (*.f64 (*.f64 (pow.f64 k 3) (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) (sqrt.f64 k))
0.6b
(*.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)))
0.5b
(*.f64 (pow.f64 (*.f64 (*.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
1.1b
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
0.4b
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
0.8b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k)))
0.5b
(*.f64 (pow.f64 (*.f64 (*.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
Compiler

Compiled 4310 to 2647 computations (38.6% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series395.0ms (3.2%)

Counts
1 → 8
Calls

1 calls:

395.0ms
(*.f64 (pow.f64 (*.f64 (*.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))

rewrite24.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
46×add-exp-log_binary64
36×prod-exp_binary64
18×pow-exp_binary64
11×add-sqr-sqrt_binary64
pow-to-exp_binary64
Counts
1 → 48
Calls

1 calls:

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

simplify163.0ms (1.3%)

Algorithm
egg-herbie
Rules
873×fma-def_binary64
670×associate-*l*_binary64
579×associate-*r*_binary64
246×distribute-rgt-in_binary64
243×distribute-lft-in_binary64
Counts
56 → 62
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01111917
12011457
26111417
322311399
444111399
549391399

prune410.0ms (3.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1601161
Fresh145
Picked011
Done112
Total1627169
Error
0.0b
Counts
169 → 7
Alt Table
StatusErrorProgram
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))))
23.7b
(/.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 (*.f64 1/2 (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 1/48 (*.f64 (*.f64 (pow.f64 k 3) (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) (sqrt.f64 k))
0.6b
(*.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)))
0.5b
(*.f64 (pow.f64 (*.f64 (*.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
0.7b
(*.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (pow.f64 k -1/2))
0.8b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k)))
0.4b
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
Compiler

Compiled 4362 to 2805 computations (35.7% saved)

regimes2.6s (21%)

Accuracy

Total 0.5b remaining (92.4%)

Threshold costs 0.5b (92.4%)

Counts
277 → 1
Compiler

Compiled 29430 to 22442 computations (23.7% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01421
11721
21621

end310.0ms (2.5%)

Compiler

Compiled 240 to 177 computations (26.3% saved)

Profiling

Loading profile data...