Details

Time bar (total: 5.3s)

analyze395.0ms (7.4%)

Algorithm
1×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
12.5%34.3%53.2%6
15.6%26.5%57.9%7
15.6%22.6%61.8%8
17.2%17.6%65.3%9
17.2%15%67.8%10
18%12.2%69.9%11
18%10.8%71.3%12
18.3%9.3%72.4%13
18.3%8.5%73.1%14
Compiler

Compiled 19 to 16 computations (15.8% saved)

sample3.2s (61.1%)

Results
1.4s8256×body128valid
1.2s1365×body1024invalid
409.0ms739×body512invalid
190.0ms1166×body128invalid
111.0ms324×body256invalid
Compiler

Compiled 38 to 32 computations (15.8% saved)

preprocess35.0ms (0.7%)

Algorithm
2×egg-herbie
Rules
421×div-sub_binary64
418×associate-/l*_binary64
293×associate-*l*_binary64
268×associate-/r*_binary64
224×associate-/l/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02150
15244
211944
325644
466844
5183640
6416340
022
Stop Event
1×saturated
1×node limit
Calls
Call 1
Inputs
0
1
Outputs
0
1
Call 2
Inputs
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2)))
Outputs
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2)))
(*.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) k)) (-.f64 1/2 (/.f64 n 2))))
(/.f64 (pow.f64 (*.f64 k (*.f64 2 (PI.f64))) (/.f64 (-.f64 1 n) 2)) (sqrt.f64 n))
(/.f64 (pow.f64 (*.f64 k (*.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 n))) (sqrt.f64 n))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 k 2)) (fma.f64 -1/2 n 1/2)) (sqrt.f64 n))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 k 2)) (fma.f64 n -1/2 1/2)) (sqrt.f64 n))
Compiler

Compiled 18 to 15 computations (16.7% saved)

simplify20.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
664×associate-/l*_binary64
544×associate-/r*_binary64
257×associate-*l/_binary64
214×unswap-sqr_binary64
214×div-sub_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01425
13222
26822
314022
435422
595820
6218720
Stop Event
1×node limit
Counts
1 → 2
Calls
Call 1
Inputs
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
Outputs
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

prune4.0ms (0.1%)

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 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
Compiler

Compiled 97 to 77 computations (20.6% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series72.0ms (1.3%)

Counts
3 → 48
Calls

15 calls:

TimeVariablePointExpression
29.0ms
n
@0
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
26.0ms
n
@-inf
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
8.0ms
n
@inf
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
3.0ms
k
@0
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
2.0ms
k
@-inf
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

rewrite57.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
655×log-prod_binary64
233×expm1-udef_binary64
233×log1p-udef_binary64
212×log-pow_binary64
135×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01340
127440
2330640
Stop Event
1×node limit
Counts
3 → 82
Calls
Call 1
Inputs
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(*.f64 (PI.f64) n)
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 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(PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 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-1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) n)) (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) n)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) n) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) n) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (PI.f64)) n))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))) (cbrt.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 2) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 2 (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 1))))))

simplify43.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
393×associate-*r*_binary64
367×associate-*l*_binary64
239×fma-def_binary64
225×distribute-rgt-in_binary64
224×distribute-lft-in_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0731106
12031024
2637901
33619845
Stop Event
1×node limit
Counts
130 → 103
Calls
Call 1
Inputs
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
Outputs
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) (sqrt.f64 (/.f64 1 k)))
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) (sqrt.f64 (/.f64 1 k)))
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) (sqrt.f64 (/.f64 1 k)))
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) (sqrt.f64 (/.f64 1 k)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) (sqrt.f64 (/.f64 1 k)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) (sqrt.f64 (/.f64 1 k)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (sqrt.f64 (/.f64 1 k)))
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(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))

prune133.0ms (2.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New949103
Fresh101
Picked101
Done000
Total969105
Error
0.0b
Counts
105 → 9
Alt Table
StatusErrorProgram
10.3b
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2) k))
▶0.4b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
0.5b
(/.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
1.0b
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 2) (*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
21.7b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (+.f64 (*.f64 -1/48 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k 3))) (*.f64 1/8 (*.f64 k k))))) (fma.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 2)))) (sqrt.f64 k))
0.9b
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
0.5b
(*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
0.5b
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
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 k))
Compiler

Compiled 2631 to 1807 computations (31.3% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series7.0ms (0.1%)

Counts
3 → 48
Calls

15 calls:

TimeVariablePointExpression
1.0ms
k
@0
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
1.0ms
k
@-inf
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
1.0ms
k
@inf
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
0.0ms
k
@0
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
0.0ms
n
@0
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))

rewrite49.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
641×log-prod_binary64
232×expm1-udef_binary64
232×log1p-udef_binary64
211×log-pow_binary64
135×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01344
127444
2318144
Stop Event
1×node limit
Counts
3 → 60
Calls
Call 1
Inputs
(*.f64 n (*.f64 2 (PI.f64)))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (PI.f64) (*.f64 n 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n)) (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n)))) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n))) (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (*.f64 2 (PI.f64)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) 3) (pow.f64 n 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 (pow.f64 k -1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 -1/2 (log.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 -1/2 (log.f64 k))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))) (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) 2) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) 2) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 n 2) (fma.f64 k -1/2 1/2)) (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 1))))))

simplify43.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
389×associate-*r*_binary64
367×associate-*l*_binary64
239×fma-def_binary64
225×distribute-rgt-in_binary64
224×distribute-lft-in_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0731142
12031060
2639937
33616878
Stop Event
1×node limit
Counts
108 → 80
Calls
Call 1
Inputs
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
Outputs
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (*.f64 2 n) (PI.f64))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (*.f64 2 n) (PI.f64))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (*.f64 2 n) (PI.f64))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (*.f64 2 n) (PI.f64))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (*.f64 2 n) (PI.f64))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (*.f64 2 n) (PI.f64))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (*.f64 2 n) (PI.f64))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (*.f64 2 n) (PI.f64))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (*.f64 2 n) (PI.f64))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (*.f64 2 n) (PI.f64))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (*.f64 2 n) (PI.f64))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (*.f64 2 n) (PI.f64))
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)))
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)))
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)))
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(*.f64 (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2)))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 k (log.f64 (*.f64 (*.f64 2 n) (PI.f64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 -1/2 (*.f64 k (sqrt.f64 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 -1/2 (*.f64 k (sqrt.f64 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2)))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 k (log.f64 (*.f64 (*.f64 2 n) (PI.f64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 2 n) (PI.f64))) 2) (*.f64 k k)) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (*.f64 (sqrt.f64 2) (*.f64 k k)))) (sqrt.f64 2))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 -1/2 k))) (fma.f64 (*.f64 1/8 (*.f64 k (*.f64 k (sqrt.f64 2)))) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (sqrt.f64 2))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (+.f64 (+.f64 (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (*.f64 k k))) 1) (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 -1/2 k)))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 k (log.f64 (*.f64 (*.f64 2 n) (PI.f64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 2 n) (PI.f64))) 2) (*.f64 k k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 (*.f64 2 n) (PI.f64))) 3)) (sqrt.f64 (*.f64 n (PI.f64)))))))))
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (*.f64 (sqrt.f64 2) (*.f64 k k)))) (*.f64 -1/48 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 -1/2 (*.f64 k (sqrt.f64 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (*.f64 k k))) (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) (fma.f64 (*.f64 -1/2 (*.f64 k (sqrt.f64 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (+.f64 (*.f64 -1/48 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k 3))) (*.f64 1/8 (*.f64 k k)))) (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 -1/2 k))))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))

prune108.0ms (2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New77380
Fresh448
Picked101
Done000
Total82789
Error
0.0b
Counts
89 → 7
Alt Table
StatusErrorProgram
0.5b
(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) (pow.f64 k -1/2))
10.2b
(sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 k -1)))
0.9b
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
21.6b
(*.f64 (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) (pow.f64 k -1/2))
▶0.5b
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
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 k))
1.0b
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 2) (*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
Compiler

Compiled 2068 to 1539 computations (25.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series87.0ms (1.6%)

Counts
3 → 48
Calls

18 calls:

TimeVariablePointExpression
43.0ms
n
@0
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
22.0ms
n
@-inf
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
7.0ms
n
@inf
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
5.0ms
k
@0
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
2.0ms
k
@-inf
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))

rewrite64.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
695×log-prod_binary64
250×expm1-udef_binary64
250×log1p-udef_binary64
238×log-pow_binary64
146×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01458
129751
2347451
Stop Event
1×node limit
Counts
3 → 59
Calls
Call 1
Inputs
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
(*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2))) (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 3) (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3) (pow.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2))) (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 3) (pow.f64 (pow.f64 k -1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))) (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) 2) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 2) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 2 (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 (PI.f64) n))) 1))))))

simplify45.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
317×associate-*r*_binary64
306×associate-*l*_binary64
271×unswap-sqr_binary64
236×fma-def_binary64
168×distribute-rgt-in_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0681308
11901132
25911116
330841029
Stop Event
1×node limit
Counts
107 → 83
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n)))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))
(exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))
(sqrt.f64 (*.f64 n (PI.f64)))
(+.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (*.f64 k (log.f64 (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 n (PI.f64))))))
(+.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 k (log.f64 (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 1/8 (*.f64 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 n (PI.f64))) 2)) (sqrt.f64 (*.f64 n (PI.f64)))))))
(+.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/48 (*.f64 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 n (PI.f64))) 3)) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 k (log.f64 (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 1/8 (*.f64 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 n (PI.f64))) 2)) (sqrt.f64 (*.f64 n (PI.f64))))))))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
Outputs
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (neg.f64 (PI.f64))) (neg.f64 (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (/.f64 (neg.f64 (PI.f64)) (/.f64 -1 n)) (fma.f64 k -1/2 1/2))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (neg.f64 (PI.f64))) (neg.f64 (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (/.f64 (neg.f64 (PI.f64)) (/.f64 -1 n)) (fma.f64 k -1/2 1/2))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (neg.f64 (PI.f64))) (neg.f64 (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (/.f64 (neg.f64 (PI.f64)) (/.f64 -1 n)) (fma.f64 k -1/2 1/2))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (neg.f64 (PI.f64))) (neg.f64 (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (/.f64 (neg.f64 (PI.f64)) (/.f64 -1 n)) (fma.f64 k -1/2 1/2))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (neg.f64 (PI.f64))) (neg.f64 (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (neg.f64 (PI.f64)) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (neg.f64 (PI.f64))) (neg.f64 (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (neg.f64 (PI.f64)) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (neg.f64 (PI.f64))) (neg.f64 (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (neg.f64 (PI.f64)) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (neg.f64 (PI.f64))) (neg.f64 (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (neg.f64 (PI.f64)) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))
(exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))
(exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))
(exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))
(exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (neg.f64 (PI.f64))) (neg.f64 (log.f64 (/.f64 -1 n)))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n))))
(exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n)))))
(pow.f64 (/.f64 (neg.f64 (PI.f64)) (/.f64 -1 n)) (fma.f64 k -1/2 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (neg.f64 (PI.f64))) (neg.f64 (log.f64 (/.f64 -1 n)))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n))))
(exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n)))))
(pow.f64 (/.f64 (neg.f64 (PI.f64)) (/.f64 -1 n)) (fma.f64 k -1/2 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (neg.f64 (PI.f64))) (neg.f64 (log.f64 (/.f64 -1 n)))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n))))
(exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n)))))
(pow.f64 (/.f64 (neg.f64 (PI.f64)) (/.f64 -1 n)) (fma.f64 k -1/2 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (neg.f64 (PI.f64))) (neg.f64 (log.f64 (/.f64 -1 n)))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n))))
(exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n)))))
(pow.f64 (/.f64 (neg.f64 (PI.f64)) (/.f64 -1 n)) (fma.f64 k -1/2 1/2))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt.f64 (*.f64 (PI.f64) n))
(+.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (*.f64 k (log.f64 (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 n (PI.f64))))))
(+.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) n)))) (sqrt.f64 (*.f64 (PI.f64) n))))
(*.f64 (+.f64 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) n)))) 1) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) n))) 1))
(+.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 k (log.f64 (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 1/8 (*.f64 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 n (PI.f64))) 2)) (sqrt.f64 (*.f64 n (PI.f64)))))))
(+.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 -1/2 (*.f64 k (*.f64 (log.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 1/8 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) 2))))))
(+.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) 2))) (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) n)))))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) 2))) (fma.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) n))) 1)))
(*.f64 (+.f64 (*.f64 (*.f64 k (log.f64 (*.f64 (PI.f64) n))) (+.f64 (*.f64 1/8 (*.f64 k (log.f64 (*.f64 (PI.f64) n)))) -1/2)) 1) (sqrt.f64 (*.f64 (PI.f64) n)))
(+.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/48 (*.f64 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 n (PI.f64))) 3)) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 k (log.f64 (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 1/8 (*.f64 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 n (PI.f64))) 2)) (sqrt.f64 (*.f64 n (PI.f64))))))))
(+.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 -1/48 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) 3))) (fma.f64 -1/2 (*.f64 k (*.f64 (log.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 1/8 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) 2)))))))
(+.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) 2))) (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) n)))))) (*.f64 (+.f64 (*.f64 (*.f64 -1/48 (pow.f64 k 3)) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) 3)) 1) (sqrt.f64 (*.f64 (PI.f64) n))))
(fma.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) n))) (*.f64 1/8 (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) 2)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) 3)) 1)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 (*.f64 k (log.f64 (*.f64 (PI.f64) n))) (+.f64 (*.f64 1/8 (*.f64 k (log.f64 (*.f64 (PI.f64) n)))) -1/2)) (fma.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) 3)) 1)))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))

prune129.0ms (2.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1003103
Fresh246
Picked101
Done000
Total1037110
Error
0.0b
Counts
110 → 7
Alt Table
StatusErrorProgram
1.0b
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))) 3)
0.5b
(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) (pow.f64 k -1/2))
0.5b
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))
10.2b
(sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 k -1)))
0.9b
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
▶0.4b
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) n))) (pow.f64 k -1/2)))
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 k))
Compiler

Compiled 2840 to 1998 computations (29.6% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series27.0ms (0.5%)

Counts
3 → 0
Calls

15 calls:

TimeVariablePointExpression
5.0ms
n
@inf
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) n))) (pow.f64 k -1/2)))
3.0ms
k
@0
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) n))) (pow.f64 k -1/2)))
3.0ms
n
@0
(sqrt.f64 (*.f64 (PI.f64) n))
2.0ms
n
@-inf
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) n))) (pow.f64 k -1/2)))
2.0ms
k
@inf
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) n))) (pow.f64 k -1/2)))

rewrite59.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
302×expm1-udef_binary64
302×log1p-udef_binary64
176×add-sqr-sqrt_binary64
172×pow1_binary64
169×*-un-lft-identity_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01769
136153
2431753
Stop Event
1×node limit
Counts
3 → 55
Calls
Call 1
Inputs
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) n))) (pow.f64 k -1/2)))
(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) n))) (pow.f64 k -1/2))
(sqrt.f64 (*.f64 (PI.f64) n))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 (pow.f64 k -1) (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 2)) (pow.f64 4 (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 2 (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 3) (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3) (pow.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 k -1) (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 3) (pow.f64 (pow.f64 k -1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (cbrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (PI.f64) n)) (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) 1/4) (pow.f64 (*.f64 (PI.f64) n) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) 2))) (sqrt.f64 (cbrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) 2)) 1/2) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) n) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) n) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) n))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) n) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) n))) 1))))))

simplify6.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
55 → 55
Calls
Call 1
Inputs
Outputs

prune122.0ms (2.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New93295
Fresh156
Picked011
Done000
Total948102
Error
0.0b
Counts
102 → 8
Alt Table
StatusErrorProgram
0.5b
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))
10.4b
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (sqrt.f64 (*.f64 (pow.f64 k -1) (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 2))))
0.5b
(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) (pow.f64 k -1/2))
0.9b
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 k -1/2)) (pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) n))) 3)) (pow.f64 k -1/2)))
10.2b
(sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 k -1)))
0.9b
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
✓0.4b
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) n))) (pow.f64 k -1/2)))
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 k))
Compiler

Compiled 2587 to 1668 computations (35.5% saved)

regimes341.0ms (6.4%)

Accuracy

Total 0.4b remaining (89.8%)

Threshold costs 0.4b (89.8%)

Counts
146 → 1
Compiler

Compiled 2885 to 1986 computations (31.2% saved)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Rules
2×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01525
11725
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 (sqrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2)) (sqrt.f64 k))
Outputs
(/.f64 (sqrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2)) (sqrt.f64 k))

end170.0ms (3.2%)

Stop Event
1×fuel
Compiler

Compiled 221 to 175 computations (20.8% saved)

Profiling

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