Details

Time bar (total: 8.8s)

analyze334.0ms (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)

sample3.1s (35.7%)

Results
1.4s8256×body128valid
1.0s1353×body1024invalid
360.0ms668×body512invalid
179.0ms1195×body128invalid
124.0ms374×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
0.6b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.7b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
0.6b
(/.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
(/.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))

series514.0ms (5.8%)

Counts
3 → 48
Calls

3 calls:

273.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
238.0ms
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
3.0ms
(*.f64 (*.f64 2 (PI.f64)) n)

rewrite22.0ms (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)

simplify126.0ms (1.4%)

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

prune220.0ms (2.5%)

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
0.9b
(*.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 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))
0.5b
(*.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)))
0.7b
(*.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))))
0.5b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
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)))
25.3b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (-.f64 (*.f64 1/8 (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2))) (*.f64 1/2 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) k)))))) (sqrt.f64 k))
0.9b
(/.f64 (pow.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
Compiler

Compiled 4327 to 2832 computations (34.6% 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))

series465.0ms (5.3%)

Counts
4 → 44
Calls

4 calls:

355.0ms
(*.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)))
62.0ms
(/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
30.0ms
(pow.f64 n (fma.f64 k -1/2 1/2))
18.0ms
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))

rewrite46.0ms (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:

15.0ms
(*.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)))
4.0ms
(/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
4.0ms
(pow.f64 n (fma.f64 k -1/2 1/2))
2.0ms
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))

simplify205.0ms (2.3%)

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

prune455.0ms (5.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2863289
Fresh347
Picked011
Done000
Total2898297
Error
0.0b
Counts
297 → 8
Alt Table
StatusErrorProgram
0.6b
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (fabs.f64 (cbrt.f64 k))) (sqrt.f64 (cbrt.f64 k))))
0.9b
(*.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))))
0.5b
(*.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))))
0.5b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
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)))
0.8b
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
0.9b
(/.f64 (pow.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
Compiler

Compiled 8812 to 5776 computations (34.5% saved)

localize14.0ms (0.2%)

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))
0.2b
(*.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))

series713.0ms (8.1%)

Counts
3 → 28
Calls

3 calls:

412.0ms
(*.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))))
297.0ms
(*.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)))
4.0ms
(pow.f64 (PI.f64) (fma.f64 k -1/2 1/2))

rewrite52.0ms (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:

16.0ms
(*.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)))
11.0ms
(*.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))))
1.0ms
(pow.f64 (PI.f64) (fma.f64 k -1/2 1/2))

simplify194.0ms (2.2%)

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

prune459.0ms (5.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2922294
Fresh156
Picked101
Done101
Total2957302
Error
0b
Counts
302 → 7
Alt Table
StatusErrorProgram
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 (*.f64 k -1/2)) (/.f64 (sqrt.f64 n) (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)))
0.6b
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (fabs.f64 (cbrt.f64 k))) (sqrt.f64 (cbrt.f64 k))))
0.9b
(*.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))))
0.5b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
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 (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 n)))))
0.9b
(/.f64 (pow.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
Compiler

Compiled 10323 to 6927 computations (32.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series310.0ms (3.5%)

Counts
3 → 0
Calls

3 calls:

180.0ms
(*.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 (*.f64 k -1/2)) (/.f64 (sqrt.f64 n) (sqrt.f64 k)))))
90.0ms
(*.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 n (*.f64 k -1/2)) (/.f64 (sqrt.f64 n) (sqrt.f64 k))))
40.0ms
(/.f64 (sqrt.f64 n) (sqrt.f64 k))

rewrite54.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
276×add-exp-log_binary64
222×prod-exp_binary64
74×pow-exp_binary64
74×pow-to-exp_binary64
42×sqrt-prod_binary64
Counts
3 → 198
Calls

3 calls:

13.0ms
(*.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 (*.f64 k -1/2)) (/.f64 (sqrt.f64 n) (sqrt.f64 k)))))
9.0ms
(*.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 n (*.f64 k -1/2)) (/.f64 (sqrt.f64 n) (sqrt.f64 k))))
4.0ms
(/.f64 (sqrt.f64 n) (sqrt.f64 k))

simplify193.0ms (2.2%)

Algorithm
egg-herbie
Rules
642×associate-*r/_binary64
635×*-commutative_binary64
438×associate-*l/_binary64
430×fma-def_binary64
235×associate-*r*_binary64
Counts
198 → 171
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02076387
13865700
213895566
343045566
449645566

prune293.0ms (3.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2000200
Fresh066
Picked011
Done000
Total2007207
Error
0b
Counts
207 → 7
Alt Table
StatusErrorProgram
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 (*.f64 k -1/2)) (/.f64 (sqrt.f64 n) (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)))
0.6b
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (fabs.f64 (cbrt.f64 k))) (sqrt.f64 (cbrt.f64 k))))
0.9b
(*.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))))
0.5b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
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 (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 n)))))
0.9b
(/.f64 (pow.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
Compiler

Compiled 7067 to 4241 computations (40% saved)

regimes743.0ms (8.5%)

Accuracy

Total 0.4b remaining (91.6%)

Threshold costs 0.4b (91.6%)

Counts
148 → 1
Compiler

Compiled 15264 to 11907 computations (22% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01838
12238
22238

end148.0ms (1.7%)

Compiler

Compiled 229 to 177 computations (22.7% saved)

Profiling

Loading profile data...