Details

Time bar (total: 9.9s)

analyze536.0ms (5.4%)

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)

sample151.0ms (1.5%)

Algorithm
intervals
Results
31.0ms54×body1024nan
24.0ms256×body128valid
12.0ms64×body128overflowed
8.0ms20×body512nan
3.0ms13×body256nan
2.0ms31×body128nan
1.0msbody128invalid
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 → 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
0.5b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.6b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
0.7b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
Compiler

Compiled 97 to 77 computations (20.6% saved)

localize10.0ms (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))
0.3b
(*.f64 (*.f64 2 (PI.f64)) n)
0.4b
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))

series537.0ms (5.4%)

Counts
3 → 48
Calls

3 calls:

281.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
253.0ms
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
3.0ms
(*.f64 (*.f64 2 (PI.f64)) n)

rewrite20.0ms (0.2%)

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:

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)

simplify132.0ms (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

prune198.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1608168
Fresh101
Picked101
Done000
Total1628170
Error
0b
Counts
170 → 8
Alt Table
StatusErrorProgram
0.7b
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
0.8b
(*.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))))
0.8b
(/.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)))) (sqrt.f64 k))
23.7b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 (sqrt.f64 2) k)) -1/2))) (sqrt.f64 k))
0.7b
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.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)))
0.6b
(*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
0.7b
(*.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))))
Compiler

Compiled 4291 to 2802 computations (34.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(pow.f64 n (fma.f64 k -1/2 1/2))
0.2b
(/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
0.3b
(*.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)))
0.6b
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))

series440.0ms (4.4%)

Counts
4 → 44
Calls

4 calls:

343.0ms
(*.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)))
59.0ms
(/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
32.0ms
(pow.f64 n (fma.f64 k -1/2 1/2))
5.0ms
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))

rewrite48.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
108×times-frac_binary64
98×add-sqr-sqrt_binary64
69×*-un-lft-identity_binary64
69×add-cube-cbrt_binary64
57×sqrt-prod_binary64
Counts
4 → 219
Calls

4 calls:

16.0ms
(*.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)))
5.0ms
(/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
4.0ms
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
2.0ms
(pow.f64 n (fma.f64 k -1/2 1/2))

simplify206.0ms (2.1%)

Algorithm
egg-herbie
Rules
836×fma-def_binary64
474×times-frac_binary64
289×unswap-sqr_binary64
267×associate-*l*_binary64
260×associate-*r*_binary64
Counts
263 → 289
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03007120
16646701
224706684
343886684
449636684

prune374.0ms (3.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2881289
Fresh167
Picked011
Done000
Total2898297
Error
0b
Counts
297 → 8
Alt Table
StatusErrorProgram
0.7b
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
0.8b
(*.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))))
0.6b
(*.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)))
0.4b
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (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 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)))) (sqrt.f64 k))
23.7b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 (sqrt.f64 2) k)) -1/2))) (sqrt.f64 k))
0.7b
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
0.6b
(*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
Compiler

Compiled 8820 to 5782 computations (34.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
0.3b
(*.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
0.3b
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
0.6b
(pow.f64 (PI.f64) (fma.f64 k -1/2 1/2))

series727.0ms (7.3%)

Counts
3 → 28
Calls

3 calls:

418.0ms
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
302.0ms
(*.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
6.0ms
(pow.f64 (PI.f64) (fma.f64 k -1/2 1/2))

rewrite59.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
137×add-exp-log_binary64
87×prod-exp_binary64
85×add-sqr-sqrt_binary64
66×times-frac_binary64
53×associate-*r*_binary64
Counts
3 → 188
Calls

3 calls:

18.0ms
(*.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
15.0ms
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
2.0ms
(pow.f64 (PI.f64) (fma.f64 k -1/2 1/2))

simplify194.0ms (2%)

Algorithm
egg-herbie
Rules
684×fma-def_binary64
437×times-frac_binary64
411×unswap-sqr_binary64
335×associate-*r*_binary64
327×associate-*l*_binary64
Counts
216 → 205
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02877362
16736627
225976497
344046496
450766496

prune418.0ms (4.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2940294
Fresh066
Picked011
Done011
Total2948302
Error
0b
Counts
302 → 8
Alt Table
StatusErrorProgram
0.7b
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
0.8b
(*.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))))
0.6b
(*.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)))
0.4b
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (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 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)))) (sqrt.f64 k))
23.7b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 (sqrt.f64 2) k)) -1/2))) (sqrt.f64 k))
0.7b
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
0.6b
(*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
Compiler

Compiled 10302 to 6913 computations (32.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (/.f64 1 k))
0.3b
(*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
0.3b
(/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n))
0.4b
(pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2))

series535.0ms (5.4%)

Counts
4 → 48
Calls

4 calls:

282.0ms
(*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
245.0ms
(pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2))
5.0ms
(sqrt.f64 (/.f64 1 k))
3.0ms
(/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n))

rewrite49.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
101×times-frac_binary64
78×add-sqr-sqrt_binary64
55×*-un-lft-identity_binary64
51×add-cube-cbrt_binary64
50×add-exp-log_binary64
Counts
4 → 187
Calls

4 calls:

16.0ms
(*.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
6.0ms
(pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2))
6.0ms
(/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n))
2.0ms
(sqrt.f64 (/.f64 1 k))

simplify157.0ms (1.6%)

Algorithm
egg-herbie
Rules
522×times-frac_binary64
329×distribute-rgt-in_binary64
320×distribute-lft-in_binary64
186×sqr-pow_binary64
176×associate-*l*_binary64
Counts
235 → 297
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03105290
16854762
221074734
349734734
449444734

prune371.0ms (3.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2961297
Fresh145
Picked101
Done022
Total2987305
Error
0b
Counts
305 → 7
Alt Table
StatusErrorProgram
0.7b
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
0.5b
(*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 (/.f64 1 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)))
0.4b
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (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 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)))) (sqrt.f64 k))
23.7b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 (sqrt.f64 2) k)) -1/2))) (sqrt.f64 k))
0.8b
(*.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))))
Compiler

Compiled 7792 to 5877 computations (24.6% saved)

regimes1.5s (15.4%)

Accuracy

Total 0.4b remaining (95%)

Threshold costs 0.4b (95%)

Counts
231 → 1
Compiler

Compiled 20864 to 16768 computations (19.6% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01838
12138
22138

end1.0ms (0%)

Compiler

Compiled 27 to 21 computations (22.2% saved)

sample3.1s (31.6%)

Algorithm
intervals
Results
845.0ms1361×body1024nan
834.0ms8000×body128valid
439.0ms2432×body128overflowed
273.0ms654×body512nan
77.0ms341×body256nan
72.0ms940×body128nan
27.0ms244×body128invalid
Compiler

Compiled 222 to 173 computations (22.1% saved)

Profiling

Loading profile data...