Details

Time bar (total: 10.1s)

analyze111.0ms (1.1%)

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
Compiler

Compiled 19 to 16 computations (15.8% saved)

sample2.6s (26.1%)

Results
1.3s8256×body256valid
747.0ms1380×body1024invalid
349.0ms2277×body256invalid
222.0ms693×body512invalid

preprocess64.0ms (0.6%)

Algorithm
2×egg-herbie
Rules
454×neg-mul-1_binary64
436×fma-def_binary64
428×unswap-sqr_binary64
424×div-sub_binary64
419×associate-/l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02150
15244
211944
325744
467044
5187940
6423040
7736440
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 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 -1/2 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 n -2))) (sqrt.f64 n))
(/.f64 (pow.f64 (*.f64 k (*.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 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 k (*.f64 2 (PI.f64))) (fma.f64 n -1/2 1/2)) (sqrt.f64 n))
Compiler

Compiled 20 to 17 computations (15% saved)

simplify43.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
667×associate-/l*_binary64
561×associate-/r*_binary64
453×div-sub_binary64
450×distribute-frac-neg_binary64
416×distribute-rgt-in_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01425
13222
26822
314122
436022
598320
6221320
7566320
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 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))

eval1.0ms (0%)

Compiler

Compiled 31 to 23 computations (25.8% saved)

prune2.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.3b
Counts
3 → 2
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.4b
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
▶0.4b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
Compiler

Compiled 33 to 27 computations (18.2% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiled 56 to 38 computations (32.1% saved)

series85.0ms (0.8%)

Counts
4 → 48
Calls

18 calls:

TimeVariablePointExpression
34.0ms
n
@0
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
26.0ms
n
@-inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
10.0ms
n
@inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
3.0ms
k
@0
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
2.0ms
k
@-inf
(/.f64 1 (sqrt.f64 k))

rewrite81.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
751×log-prod_binary64
382×pow2_binary64
265×pow1/3_binary64
260×expm1-udef_binary64
259×log1p-udef_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01453
130751
2392647
Stop Event
1×node limit
Counts
4 → 105
Calls
Call 1
Inputs
(/.f64 1 (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (*.f64 2 (PI.f64)) n)
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 k -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 k -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 k) -1/2) (pow.f64 (sqrt.f64 k) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 k)) (cbrt.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 k -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 k) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 k -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 k -1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (sqrt.f64 k))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 k -1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 -1/2 (log.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/2 (log.f64 k)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 (sqrt.f64 k) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4)) (pow.f64 k 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 1) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) -1) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 k 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 2 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n)) 2)) (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 2 (*.f64 (PI.f64) n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) 3) (pow.f64 n 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 n 3) (pow.f64 (*.f64 2 (PI.f64)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 4 (pow.f64 (*.f64 (PI.f64) n) 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 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 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 cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (*.f64 2 (PI.f64)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (pow.f64 n (-.f64 1/2 (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 (-.f64 1/2 (/.f64 k 2))) (pow.f64 (*.f64 (PI.f64) n) (-.f64 1/2 (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1/2 (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1/2 (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 k 2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) 1))))))

simplify60.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
534×associate-+r+_binary64
527×associate-+l+_binary64
424×associate-*r*_binary64
407×associate-*l*_binary64
325×distribute-lft-in_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0821206
12271124
2748969
34136958
Stop Event
1×node limit
Counts
153 → 126
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (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 2 (*.f64 n (PI.f64)))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 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))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
Outputs
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 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 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 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 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 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 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 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 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 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 1/2) (*.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 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 1/2) (*.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 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 1/2) (*.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 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 1/2) (*.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))
(+.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 2 (*.f64 (PI.f64) n)))) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (sqrt.f64 2)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (+.f64 (*.f64 (*.f64 k -1/2) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1) (sqrt.f64 2)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 (*.f64 k -1/2) (sqrt.f64 2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (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 2 (*.f64 (PI.f64) n)))) (sqrt.f64 (*.f64 (PI.f64) n)))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)) (sqrt.f64 (*.f64 (PI.f64) n)))))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 k (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)))))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 k -1/2) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (fma.f64 (*.f64 (*.f64 1/8 (*.f64 k k)) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)) (sqrt.f64 2) (sqrt.f64 2))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (+.f64 (+.f64 (*.f64 (*.f64 k -1/2) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1) (*.f64 (*.f64 1/8 (*.f64 k k)) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 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 (*.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 2 (*.f64 (PI.f64) n)))) (sqrt.f64 (*.f64 (PI.f64) n)))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 -1/48 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 3)) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3)))))))
(+.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (sqrt.f64 2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 (*.f64 -1/48 (*.f64 (sqrt.f64 2) (pow.f64 k 3))) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3)) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)))))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 k -1/2) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1) (sqrt.f64 2)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3))) (*.f64 (*.f64 1/8 (*.f64 k k)) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2))))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2) (+.f64 (*.f64 -1/48 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 3))) (*.f64 1/8 (*.f64 k k)))) (*.f64 (*.f64 k -1/2) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (sqrt.f64 2)))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))

localize23.0ms (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))
Compiler

Compiled 45 to 26 computations (42.2% saved)

series11.0ms (0.1%)

Counts
3 → 48
Calls

15 calls:

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

rewrite73.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
655×log-prod_binary64
377×pow-unpow_binary64
376×pow-prod-down_binary64
340×pow2_binary64
258×pow-pow_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01340
127440
2330540
Stop Event
1×node limit
Counts
3 → 87
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 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2)) (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 (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 (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 1 (/.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 (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)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k)) (cbrt.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 (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 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 2) 1) (/.f64 (cbrt.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 (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.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 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 2) (cbrt.f64 k)) (cbrt.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 (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.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)) (pow.f64 k 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/4) (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 2) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.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 pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 3) (fma.f64 k -1/2 1/2)) (pow.f64 k 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.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 log.f64 (+.f64 1 (expm1.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 cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 3) (fma.f64 k -1/2 1/2)) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.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 log1p.f64 (expm1.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 exp.f64 (log.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 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 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) n)) 2)) (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) 2) 1/2)))) (#(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 expm1.f64 (log1p.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.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 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))) 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 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -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 (cbrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.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 *.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 (*.f64 k -1/2) 1)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log1p.f64 (fma.f64 k -1/2 1/2)))) (*.f64 n (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))))))) (#(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))) 3) (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 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 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))))))

simplify80.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
683×exp-sum_binary64
401×associate-+r+_binary64
394×associate-+l+_binary64
391×associate-*r*_binary64
369×associate-*l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0731106
12041024
2643901
33622842
46905842
Stop Event
1×node limit
Counts
135 → 108
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)))
(*.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 (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 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 -2 (*.f64 (*.f64 -1 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 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 -2 (*.f64 (*.f64 -1 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 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 -2 (*.f64 (*.f64 -1 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 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 -2 (*.f64 (*.f64 -1 n) (PI.f64))) (fma.f64 -1/2 k 1/2)))
(*.f64 n (PI.f64))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(*.f64 (PI.f64) n)
(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 (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))
(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 (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))
(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 (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))
(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 (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))
(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 (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))
(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 (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))
(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 (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))
(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 (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))
(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 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 -2 (*.f64 (*.f64 -1 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 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 -2 (*.f64 (*.f64 -1 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 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 -2 (*.f64 (*.f64 -1 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 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 -2 (*.f64 (*.f64 -1 n) (PI.f64))) (fma.f64 -1/2 k 1/2))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))
(+.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 2 (*.f64 (PI.f64) n)))) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 -1/2 (sqrt.f64 2)) (*.f64 k (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 (*.f64 -1/2 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (sqrt.f64 2) (sqrt.f64 2)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 (*.f64 -1/2 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 2) (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 2 (*.f64 (PI.f64) n)))) (sqrt.f64 (*.f64 (PI.f64) n)))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 1/8 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k k)) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2))))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 (PI.f64) n))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)))))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (fma.f64 (*.f64 1/8 (*.f64 k (*.f64 k (sqrt.f64 2)))) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2) (sqrt.f64 2))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (+.f64 (+.f64 1 (*.f64 (*.f64 -1/2 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 (*.f64 1/8 (*.f64 k k)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.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 (*.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 2 (*.f64 (PI.f64) n)))) (sqrt.f64 (*.f64 (PI.f64) n)))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 1/8 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k k)) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2))) (*.f64 -1/48 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 3)) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3)))))))
(+.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 -1/2 (sqrt.f64 2)) (*.f64 k (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 -1/48 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3)))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)))))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (fma.f64 (*.f64 (*.f64 -1/2 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3))) (*.f64 1/8 (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 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 1/8 (*.f64 k k)) (*.f64 -1/48 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k 3))))) (*.f64 (*.f64 -1/2 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))
(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))
(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))

eval101.0ms (1%)

Compiler

Compiled 4815 to 3266 computations (32.2% saved)

prune85.0ms (0.8%)

Pruning

24 alts after pruning (22 fresh and 2 done)

PrunedKeptTotal
New21222234
Fresh000
Picked011
Done011
Total21224236
Error
0.0b
Counts
236 → 24
Alt Table
Click to see full alt table
StatusErrorProgram
0.5b
(*.f64 (pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 2) (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))
▶0.4b
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 k 2))))
1.8b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (expm1.f64 (log1p.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2)))
12.1b
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
▶14.1b
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))
0.4b
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓0.4b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
21.3b
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 (*.f64 k -1/2) (sqrt.f64 2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 2))))
▶0.3b
(/.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))
21.4b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (+.f64 (+.f64 1 (*.f64 (*.f64 -1/2 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 (*.f64 1/8 (*.f64 k k)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))) (sqrt.f64 k))
0.6b
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))
0.8b
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
21.3b
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
0.5b
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
21.3b
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 k))
▶12.0b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
0.5b
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))
0.3b
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶0.4b
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))
3.0b
(*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))
0.5b
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
3.3b
(*.f64 (exp.f64 (*.f64 -1/2 (log.f64 k))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
0.5b
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4))))
Compiler

Compiled 925 to 743 computations (19.7% saved)

localize53.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))
✓0.1b
(sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))
✓0.2b
(*.f64 n (*.f64 2 (PI.f64)))
✓0.2b
(/.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 70 to 46 computations (34.3% saved)

series39.0ms (0.4%)

Counts
4 → 24
Calls

18 calls:

TimeVariablePointExpression
6.0ms
k
@0
(/.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))
5.0ms
n
@0
(/.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))
4.0ms
k
@inf
(/.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))
3.0ms
k
@-inf
(/.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))
3.0ms
n
@-inf
(/.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))

rewrite108.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
808×log-prod_binary64
700×pow-unpow_binary64
378×pow2_binary64
260×pow1/3_binary64
256×expm1-udef_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01475
129857
2381053
Stop Event
1×node limit
Counts
4 → 121
Calls
Call 1
Inputs
(/.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))
(*.f64 n (*.f64 2 (PI.f64)))
(sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))
Outputs
((#(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)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (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 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (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 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (/.f64 1 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 n 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.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 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 2) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 2) k)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(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) (*.f64 (cbrt.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 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(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))) (*.f64 (sqrt.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 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (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 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) 1) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) 1) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) 2) 1) (/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) 2) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) 2) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k 1/4)))))) (#(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)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 2) k) 1/2)))) (#(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)) (sqrt.f64 k)) 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)) (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 2) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(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)) (sqrt.f64 k)))))))) (#(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)) (sqrt.f64 k)) 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 k 3/2)))))) (#(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)) (sqrt.f64 k))))))) (#(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)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))))))
((#(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 (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n)) 2)) (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 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 2) 1/2)))) (#(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 (*.f64 (pow.f64 n 3) (pow.f64 (*.f64 2 (PI.f64)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) 3) (pow.f64 n 3)) 1/3)))) (#(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 expm1.f64 (log1p.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.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 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 n 2)) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.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)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.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))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 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 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))) 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 pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) 3) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 3/2) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 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 cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) 3) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 3/2) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) 3)))))) (#(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 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 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))))))

simplify108.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
660×distribute-lft-out_binary64
544×+-commutative_binary64
377×sqr-pow_binary64
373×associate-*r*_binary64
354×associate-*l*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
041598
1123572
2410513
32675502
44213495
55818495
67276495
Stop Event
1×node limit
Counts
145 → 132
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 (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))))))))
(*.f64 (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))
Outputs
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.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 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.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 k (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) -1/2)) (sqrt.f64 2))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 2) (sqrt.f64 2)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 -1/2 k)) (sqrt.f64 2) (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 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (*.f64 k k) (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 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 k (*.f64 k (pow.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 2))))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) k))) (fma.f64 (*.f64 (sqrt.f64 2) 1/8) (*.f64 k (*.f64 k (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 k) (*.f64 k (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (+.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 1))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (+.f64 (*.f64 1/8 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) -1/2)))))
(+.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 (*.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 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.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 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))))))
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) -1/2)) (sqrt.f64 2)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 k (*.f64 k (pow.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 2))))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (fma.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (*.f64 1/8 k) (*.f64 k (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 (*.f64 -1/48 (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 (sqrt.f64 2) (+.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.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 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (*.f64 -1/48 (pow.f64 k 3)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)) (*.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (+.f64 (*.f64 1/8 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) -1/2))))))
(*.f64 (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 (exp.f64 -1/2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (exp.f64 -1/2) (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))))
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 -1/2 k))))
(*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 -1/2 k)))
(*.f64 (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 (exp.f64 -1/2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (exp.f64 -1/2) (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))))
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 -1/2 k))))
(*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 -1/2 k)))
(*.f64 (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 (exp.f64 -1/2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (exp.f64 -1/2) (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))))
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 -1/2 k))))
(*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 -1/2 k)))
(*.f64 (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 (exp.f64 -1/2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (exp.f64 -1/2) (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))))
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 -1/2 k))))
(*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 -1/2 k)))
(*.f64 (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 (exp.f64 -1/2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (exp.f64 -1/2) (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))))
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 -1/2 k))))
(*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 -1/2 k)))
(*.f64 (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 (exp.f64 -1/2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (exp.f64 -1/2) (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))))
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 -1/2 k))))
(*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 -1/2 k)))
(*.f64 (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 (exp.f64 -1/2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (exp.f64 -1/2) (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))))
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 -1/2 k))))
(*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 -1/2 k)))
(*.f64 (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 (exp.f64 -1/2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (exp.f64 -1/2) (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))))
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 -1/2 k))))
(*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 -1/2 k)))

localize36.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))
✓0.1b
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)
0.2b
(*.f64 (PI.f64) n)
✓11.1b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
Compiler

Compiled 50 to 28 computations (44% saved)

series35.0ms (0.3%)

Counts
3 → 60
Calls

18 calls:

TimeVariablePointExpression
9.0ms
n
@0
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)
3.0ms
k
@0
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
3.0ms
k
@-inf
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
3.0ms
n
@inf
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
2.0ms
k
@inf
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))

rewrite106.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
656×log-prod_binary64
453×pow-unpow_binary64
332×pow2_binary64
226×pow1/3_binary64
222×expm1-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01250
125950
2338550
Stop Event
1×node limit
Counts
3 → 116
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4) (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (sqrt.f64 (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 2))) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (sqrt.f64 (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 2)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 2 (-.f64 1 k)))) (*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4) (*.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4) (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (*.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 1/2 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 1 k)) (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 1 (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4) 3) (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 2 (-.f64 1 k)))) 1) (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 1) (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 2 (pow.f64 1/2 k)) 1) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (*.f64 k k))) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 2 (-.f64 1 k)))) (cbrt.f64 (*.f64 k k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 (*.f64 k k))) (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 2 (pow.f64 1/2 k)) (cbrt.f64 (*.f64 k k))) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 1 k)) (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 2 (-.f64 1 k)))) (sqrt.f64 k)) (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 2 (pow.f64 1/2 k)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 1 k)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 3) (pow.f64 k 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 3) (pow.f64 k 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (*.f64 (PI.f64) n)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 1 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (*.f64 (PI.f64) n)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (neg.f64 k) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 2 (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 2 (-.f64 1 k)))) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 1/2 k)) (pow.f64 (*.f64 (PI.f64) n) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 1 k)) (*.f64 2 (pow.f64 1/2 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 (-.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2) (-.f64 1 k)) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 k)) (*.f64 2 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 2 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) n) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (PI.f64) n)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) (*.f64 2 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (PI.f64)) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) n))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (*.f64 (PI.f64) n))) (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 2 (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1))))))

simplify81.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
582×associate-+l+_binary64
465×associate-*l*_binary64
439×fma-def_binary64
401×associate-*r*_binary64
351×distribute-lft-out_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0841569
12411477
27781289
342231184
Stop Event
1×node limit
Counts
176 → 151
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(+.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 -2 (*.f64 n (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))
(+.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) (+.f64 (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))) (*.f64 -2 (*.f64 n (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (PI.f64))))))
(+.f64 (*.f64 -1/3 (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) (+.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) (+.f64 (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))) (*.f64 -2 (*.f64 n (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))))
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(*.f64 2 (*.f64 n (PI.f64)))
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (*.f64 2 (*.f64 n (PI.f64))))
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))))))
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 -1/3 (*.f64 (pow.f64 k 3) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) (+.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64)))))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
Outputs
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 2 (*.f64 (/.f64 (PI.f64) k) n))
(*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))
(+.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 -2 (*.f64 n (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))
(fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (*.f64 -2 (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))
(fma.f64 2 (/.f64 (*.f64 n (PI.f64)) k) (*.f64 n (*.f64 (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) -2)))
(fma.f64 (*.f64 -2 (*.f64 n (PI.f64))) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n)))
(*.f64 (*.f64 n (PI.f64)) (+.f64 (/.f64 2 k) (*.f64 -2 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))
(+.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) (+.f64 (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))) (*.f64 -2 (*.f64 n (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (PI.f64))))))
(fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (fma.f64 k (*.f64 (*.f64 n (PI.f64)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (*.f64 -2 (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))
(fma.f64 2 (/.f64 (*.f64 n (PI.f64)) k) (fma.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 n (*.f64 (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) -2))))
(fma.f64 2 (*.f64 (/.f64 (PI.f64) k) n) (*.f64 (*.f64 n (PI.f64)) (+.f64 (*.f64 -2 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (*.f64 k (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))))
(fma.f64 2 (*.f64 (PI.f64) (/.f64 n k)) (*.f64 n (*.f64 (PI.f64) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (+.f64 -2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))
(+.f64 (*.f64 -1/3 (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) (+.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) (+.f64 (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))) (*.f64 -2 (*.f64 n (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))))
(fma.f64 -1/3 (*.f64 (*.f64 k k) (*.f64 (*.f64 n (PI.f64)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (fma.f64 k (*.f64 (*.f64 n (PI.f64)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (*.f64 -2 (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))))
(fma.f64 -1/3 (*.f64 k (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) (fma.f64 2 (/.f64 (*.f64 n (PI.f64)) k) (fma.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 n (*.f64 (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) -2)))))
(fma.f64 2 (*.f64 (/.f64 (PI.f64) k) n) (fma.f64 -1/3 (*.f64 k (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) (*.f64 (*.f64 n (PI.f64)) (+.f64 (*.f64 -2 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (*.f64 k (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))))
(fma.f64 2 (*.f64 (PI.f64) (/.f64 n k)) (*.f64 (*.f64 n (PI.f64)) (+.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (+.f64 -2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3) (*.f64 -1/3 (*.f64 k k))))))
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 n (*.f64 2 (PI.f64)))
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (*.f64 2 (*.f64 n (PI.f64))))
(fma.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (*.f64 2 (*.f64 n (PI.f64))))
(fma.f64 2 (*.f64 n (PI.f64)) (*.f64 -2 (*.f64 (*.f64 k (*.f64 n (PI.f64))) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(*.f64 (PI.f64) (+.f64 (*.f64 n 2) (*.f64 k (*.f64 n (*.f64 -2 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))
(*.f64 n (*.f64 (PI.f64) (+.f64 (*.f64 (*.f64 k -2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 2)))
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))))))
(fma.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (fma.f64 2 (*.f64 n (PI.f64)) (*.f64 (*.f64 (*.f64 n (PI.f64)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (*.f64 k k))))
(fma.f64 -2 (*.f64 (*.f64 k (*.f64 n (PI.f64))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (fma.f64 2 (*.f64 n (PI.f64)) (*.f64 (*.f64 (*.f64 k k) (*.f64 n (PI.f64))) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))
(fma.f64 n (*.f64 2 (PI.f64)) (*.f64 k (*.f64 (*.f64 n (PI.f64)) (+.f64 (*.f64 -2 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (*.f64 k (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))))
(*.f64 (PI.f64) (+.f64 (*.f64 n 2) (*.f64 k (*.f64 n (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (+.f64 -2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))))
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 -1/3 (*.f64 (pow.f64 k 3) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) (+.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64)))))))
(fma.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (fma.f64 -1/3 (*.f64 (*.f64 (*.f64 n (PI.f64)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)) (pow.f64 k 3)) (fma.f64 2 (*.f64 n (PI.f64)) (*.f64 (*.f64 (*.f64 n (PI.f64)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (*.f64 k k)))))
(fma.f64 -2 (*.f64 (*.f64 k (*.f64 n (PI.f64))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (fma.f64 -1/3 (*.f64 (*.f64 n (PI.f64)) (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3) (pow.f64 k 3))) (fma.f64 2 (*.f64 n (PI.f64)) (*.f64 (*.f64 (*.f64 k k) (*.f64 n (PI.f64))) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))))
(fma.f64 -1/3 (*.f64 n (*.f64 (PI.f64) (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3) (pow.f64 k 3)))) (fma.f64 n (*.f64 2 (PI.f64)) (*.f64 k (*.f64 (*.f64 n (PI.f64)) (+.f64 (*.f64 -2 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (*.f64 k (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))))))
(*.f64 n (+.f64 (*.f64 (PI.f64) (+.f64 2 (*.f64 (*.f64 -1/3 (pow.f64 k 3)) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3)))) (*.f64 k (*.f64 (PI.f64) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (+.f64 -2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiled 67 to 38 computations (43.3% saved)

series14.0ms (0.1%)

Counts
2 → 24
Calls

12 calls:

TimeVariablePointExpression
4.0ms
k
@-inf
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
3.0ms
k
@0
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
1.0ms
k
@inf
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
1.0ms
n
@-inf
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
1.0ms
n
@inf
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))

rewrite76.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
769×log-prod_binary64
379×pow2_binary64
261×pow1/3_binary64
257×expm1-udef_binary64
256×log1p-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01441
130738
2401638
Stop Event
1×node limit
Counts
2 → 85
Calls
Call 1
Inputs
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 k) (*.f64 (cbrt.f64 (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))) (cbrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k 1/4) (*.f64 (pow.f64 k 1/4) (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))) (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 k)) (/.f64 1 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 k) 1) (/.f64 (cbrt.f64 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 k 1/4) 1) (/.f64 (pow.f64 k 1/4) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (/.f64 (sqrt.f64 k) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 k) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 k 1/4) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (/.f64 (pow.f64 k 1/4) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 1/4)) (/.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 k) (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 1/4)) (/.f64 (cbrt.f64 (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 k 3/2) (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 k) (neg.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 k 3/2) (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 1 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 1) (/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 1/4) 1) (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 1/4) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 k)) (/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 1/4) (cbrt.f64 k)) (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 1/4) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 1/4) (pow.f64 k 1/4)) (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 1/4) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (neg.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 k -1/2) 1) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 k -1/2) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 1/4)) (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 3/2) (pow.f64 k 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 1/4) (pow.f64 k 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 3/2) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 1))))))

simplify52.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
541×exp-sum_binary64
413×unsub-neg_binary64
308×associate--l+_binary64
308×fma-neg_binary64
305×fma-def_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
041600
189600
2241600
3827456
43374456
Stop Event
1×node limit
Counts
109 → 93
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
Outputs
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 k (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(sqrt.f64 (/.f64 k (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(sqrt.f64 (/.f64 k (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))
(sqrt.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 n (-.f64 1 k)) (/.f64 k (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 n (-.f64 1 k)) (/.f64 k (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 n (-.f64 1 k)) (/.f64 k (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 n (-.f64 1 k)) (/.f64 k (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 n (-.f64 1 k)) (/.f64 k (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 n (-.f64 1 k)) (/.f64 k (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 n (-.f64 1 k)) (/.f64 k (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 n (-.f64 1 k)) (/.f64 k (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 n (-.f64 1 k)) (/.f64 k (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 n (-.f64 1 k)) (/.f64 k (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 n (-.f64 1 k)) (/.f64 k (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 n (-.f64 1 k)) (/.f64 k (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))

localize34.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)
0.2b
(*.f64 (PI.f64) n)
✓3.5b
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))
11.1b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
Compiler

Compiled 77 to 45 computations (41.6% saved)

series3.0ms (0%)

Counts
1 → 12
Calls

6 calls:

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

rewrite71.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
694×log-prod_binary64
467×pow-unpow_binary64
352×pow2_binary64
240×pow1/3_binary64
236×expm1-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01419
128319
2357119
Stop Event
1×node limit
Counts
1 → 50
Calls
Call 1
Inputs
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4) (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (E.f64) (*.f64 1/4 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) (pow.f64 (E.f64) (*.f64 1/4 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (E.f64) (log.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) (pow.f64 (E.f64) (log.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) (sqrt.f64 (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) 2))) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (E.f64)) (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (E.f64) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) (cbrt.f64 (pow.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (E.f64) (cbrt.f64 (pow.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) 2))) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (E.f64) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) 2))) 1) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) 2))) (cbrt.f64 (cbrt.f64 (pow.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) 2)))) (cbrt.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) 2))) (cbrt.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (cbrt.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) 2))) (pow.f64 (cbrt.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) 2)) (cbrt.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) 2))) (sqrt.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (sqrt.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) 1) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) (cbrt.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) (sqrt.f64 (cbrt.f64 (pow.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) 2)))) (sqrt.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) (sqrt.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (sqrt.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))

simplify47.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
541×exp-sum_binary64
412×unsub-neg_binary64
324×associate--r+_binary64
308×associate--l+_binary64
308×fma-neg_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
035300
183300
2233300
3818228
43341228
Stop Event
1×node limit
Counts
62 → 54
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
Outputs
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (pow.f64 n (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiled 76 to 42 computations (44.7% saved)

series15.0ms (0.1%)

Counts
2 → 0
Calls

9 calls:

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

rewrite73.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
857×log-prod_binary64
277×pow1/3_binary64
270×expm1-udef_binary64
270×log1p-udef_binary64
259×log-pow_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01541
132432
2427531
Stop Event
1×node limit
Counts
2 → 94
Calls
Call 1
Inputs
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 k 2))))
(sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))
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 (exp.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k 1/2 -1/2))))) (cbrt.f64 (exp.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k 1/2 -1/2))))))) (log.f64 (cbrt.f64 (exp.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 +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k 1/2 -1/2)))))) (log.f64 (sqrt.f64 (exp.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 -.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 /.f64 1 (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k 1/2 -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k 1/2 -1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.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 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (*.f64 k 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) 2)) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (/.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))) (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 2) (/.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))) (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (/.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k 1/2 -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k 1/2 -1/2)) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (neg.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (*.f64 (neg.f64 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (*.f64 (sqrt.f64 k) (neg.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k))) (neg.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1) (*.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (*.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) -1) (*.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) -1) (*.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (pow.f64 k 1/4)) (pow.f64 k 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) 1) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)) 1) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)) (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 k 4))) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 k 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)) (pow.f64 (pow.f64 2 k) 1/2)) (pow.f64 (*.f64 (PI.f64) n) (*.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (pow.f64 k -1/2)) (neg.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 k -1/2) (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (neg.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) -1) (neg.f64 (sqrt.f64 k)))))) (#(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 (sqrt.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 pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) 3) (pow.f64 k 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) 3) (pow.f64 (pow.f64 k -1/2) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 k) (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 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k 1/2 -1/2)) (sqrt.f64 k)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) 2) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.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 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 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) 3) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) 3) (pow.f64 (pow.f64 k -1/2) 3)))))) (#(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 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 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 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (PI.f64)) 1/2) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1))))))

simplify8.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
94 → 94
Calls
Call 1
Inputs
Outputs

eval381.0ms (3.8%)

Compiler

Compiled 17408 to 11346 computations (34.8% saved)

prune141.0ms (1.4%)

Pruning

20 alts after pruning (19 fresh and 1 done)

PrunedKeptTotal
New80515820
Fresh13417
Picked101
Done516
Total82420844
Error
0b
Counts
844 → 20
Alt Table
Click to see full alt table
StatusErrorProgram
▶32.8b
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))
0.6b
(pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 1/4) (pow.f64 k 1/4)) 2)
11.9b
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))
0.4b
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶13.9b
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k))
21.2b
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
0.4b
(*.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2)))
▶0.3b
(/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k 1/2 -1/2)))
▶11.9b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
21.3b
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
11.9b
(sqrt.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 1 (neg.f64 k))))
0.4b
(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))))
21.3b
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 k))
✓12.0b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
▶0.3b
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
0.4b
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
32.8b
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
0.5b
(/.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
11.6b
(pow.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) -1/2)
14.1b
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1/2))
Compiler

Compiled 620 to 505 computations (18.5% saved)

localize27.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

Compiled 47 to 29 computations (38.3% saved)

series16.0ms (0.2%)

Counts
2 → 36
Calls

12 calls:

TimeVariablePointExpression
4.0ms
k
@0
(/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k 1/2 -1/2)))
3.0ms
n
@inf
(/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k 1/2 -1/2)))
2.0ms
n
@0
(/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k 1/2 -1/2)))
1.0ms
n
@-inf
(/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k 1/2 -1/2)))
1.0ms
k
@0
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k 1/2 -1/2))

rewrite67.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
671×log-prod_binary64
377×pow-unpow_binary64
353×pow2_binary64
279×pow-pow_binary64
241×pow1/3_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01336
128036
2340536
Stop Event
1×node limit
Counts
2 → 69
Calls
Call 1
Inputs
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k 1/2 -1/2))
(/.f64 (pow.f64 k -1/2) (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 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (*.f64 2 n) (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 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2))) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 n) (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 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2))) 2) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 n) (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 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2))) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 n) (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 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 n) (PI.f64))) (*.f64 2 (fma.f64 k 1/2 -1/2))) (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 n) (PI.f64))) (fma.f64 k 1/2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 n) (PI.f64))) (fma.f64 k 1/2 -1/2)) (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 n) (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 (sqrt.f64 (*.f64 (*.f64 2 n) (PI.f64))) k) (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) -1/2) (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 n) (PI.f64))) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (*.f64 (*.f64 k 1/2) 1)) (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (exp.f64 (log1p.f64 (fma.f64 k 1/2 -1/2)))) (*.f64 (*.f64 2 n) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (*.f64 2 (fma.f64 k 1/2 -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 (*.f64 2 n) (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 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (*.f64 (fma.f64 k 1/2 -1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 (*.f64 2 n) (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 (*.f64 2 n) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 k 1/2 -1/2) (log.f64 (*.f64 (*.f64 2 n) (PI.f64)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (neg.f64 (fma.f64 k 1/2 -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 k -1)) (*.f64 (pow.f64 k -1/6) (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (neg.f64 (fma.f64 k 1/2 -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 k -1/6) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)))) (cbrt.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)) (sqrt.f64 k)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)) (sqrt.f64 k)) -2)) (/.f64 (pow.f64 k -1/6) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)) (sqrt.f64 k)) -1/2) (pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)) (sqrt.f64 k)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 k -1/2)) (/.f64 1 (neg.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (neg.f64 (fma.f64 k 1/2 -1/2))) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/4) (*.f64 (pow.f64 k -1/4) (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (neg.f64 (fma.f64 k 1/2 -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 k -1)) 1) (/.f64 (pow.f64 k -1/6) (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 k -1/4) 1) (/.f64 (pow.f64 k -1/4) (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2))) -2) (/.f64 (pow.f64 k -1/2) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 k -1)) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2))) 2)) (/.f64 (pow.f64 k -1/6) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 k -1/4) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2))) 2)) (/.f64 (pow.f64 k -1/4) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)) -1/2) (/.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 k -1)) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)))) (/.f64 (pow.f64 k -1/6) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 (neg.f64 (fma.f64 k 1/2 -1/2))) (/.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 *.f64 (/.f64 (cbrt.f64 (pow.f64 k -1)) (pow.f64 2 (fma.f64 k 1/2 -1/2))) (/.f64 (pow.f64 k -1/6) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k 1/2 -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 k -1/4) (pow.f64 2 (fma.f64 k 1/2 -1/2))) (/.f64 (pow.f64 k -1/4) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k 1/2 -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)) (sqrt.f64 k)) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)) (sqrt.f64 k)) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 k -1/6) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)) (sqrt.f64 k)) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)) (sqrt.f64 k)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (*.f64 (fma.f64 k 1/2 -1/2) 3))) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)) (sqrt.f64 k)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 k -1/2) (neg.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)) (sqrt.f64 k)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)) (sqrt.f64 k)) -3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (*.f64 (fma.f64 k 1/2 -1/2) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (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 (*.f64 2 n) (PI.f64)) (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 (*.f64 2 n) (PI.f64)) (fma.f64 k 1/2 -1/2)))) 1))))))

simplify72.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
749×fma-neg_binary64
390×associate-*r*_binary64
368×associate-*l*_binary64
316×exp-prod_binary64
305×associate-+r+_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0711100
1199982
2615832
33447796
46979796
Stop Event
1×node limit
Counts
105 → 88
Calls
Call 1
Inputs
(exp.f64 (*.f64 (-.f64 (*.f64 1/2 k) 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 (*.f64 1/2 k) 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 (*.f64 1/2 k) 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 (*.f64 1/2 k) 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/2 (*.f64 (*.f64 k (*.f64 (sqrt.f64 1/2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2)))
(+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 1/2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) (+.f64 (*.f64 1/2 (*.f64 (*.f64 k (*.f64 (sqrt.f64 1/2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2))))
(+.f64 (*.f64 1/48 (*.f64 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 1/2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 1/2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) (+.f64 (*.f64 1/2 (*.f64 (*.f64 k (*.f64 (sqrt.f64 1/2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 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))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k 1/2 -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (*.f64 (-.f64 (*.f64 1/2 k) 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (*.f64 (-.f64 (*.f64 1/2 k) 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (*.f64 (-.f64 (*.f64 1/2 k) 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (*.f64 (-.f64 (*.f64 1/2 k) 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))))
Outputs
(exp.f64 (*.f64 (-.f64 (*.f64 1/2 k) 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 1/2 k -1/2))
(exp.f64 (*.f64 (-.f64 (*.f64 1/2 k) 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 1/2 k -1/2))
(exp.f64 (*.f64 (-.f64 (*.f64 1/2 k) 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 1/2 k -1/2))
(exp.f64 (*.f64 (-.f64 (*.f64 1/2 k) 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 1/2 k -1/2))
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 1/2 k -1/2))
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 1/2 k -1/2))
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 1/2 k -1/2))
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 1/2 k -1/2))
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (fma.f64 1/2 k -1/2))
(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 (pow.f64 (/.f64 -1 n) -1) (*.f64 (PI.f64) -2)) (fma.f64 1/2 k -1/2))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 1/2 k -1/2))
(pow.f64 (*.f64 (PI.f64) (*.f64 (*.f64 -1 n) -2)) (fma.f64 1/2 k -1/2))
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (fma.f64 1/2 k -1/2))
(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 (pow.f64 (/.f64 -1 n) -1) (*.f64 (PI.f64) -2)) (fma.f64 1/2 k -1/2))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 1/2 k -1/2))
(pow.f64 (*.f64 (PI.f64) (*.f64 (*.f64 -1 n) -2)) (fma.f64 1/2 k -1/2))
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (fma.f64 1/2 k -1/2))
(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 (pow.f64 (/.f64 -1 n) -1) (*.f64 (PI.f64) -2)) (fma.f64 1/2 k -1/2))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 1/2 k -1/2))
(pow.f64 (*.f64 (PI.f64) (*.f64 (*.f64 -1 n) -2)) (fma.f64 1/2 k -1/2))
(exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (fma.f64 1/2 k -1/2))
(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 (pow.f64 (/.f64 -1 n) -1) (*.f64 (PI.f64) -2)) (fma.f64 1/2 k -1/2))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 1/2 k -1/2))
(pow.f64 (*.f64 (PI.f64) (*.f64 (*.f64 -1 n) -2)) (fma.f64 1/2 k -1/2))
(*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2))
(*.f64 (sqrt.f64 (/.f64 (pow.f64 n -1) (PI.f64))) (sqrt.f64 1/2))
(+.f64 (*.f64 1/2 (*.f64 (*.f64 k (*.f64 (sqrt.f64 1/2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2)))
(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (sqrt.f64 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (+.f64 (sqrt.f64 1/2) (*.f64 1/2 (*.f64 k (*.f64 (sqrt.f64 1/2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))
(*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (fma.f64 1/2 (*.f64 k (*.f64 (sqrt.f64 1/2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (sqrt.f64 1/2)))
(*.f64 (sqrt.f64 (/.f64 (pow.f64 n -1) (PI.f64))) (fma.f64 1/2 (*.f64 (sqrt.f64 1/2) (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (sqrt.f64 1/2)))
(+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 1/2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) (+.f64 (*.f64 1/2 (*.f64 (*.f64 k (*.f64 (sqrt.f64 1/2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2))))
(fma.f64 1/8 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (*.f64 k k) (sqrt.f64 1/2)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (sqrt.f64 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2))))
(fma.f64 1/8 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2) (*.f64 k k)))) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (+.f64 (sqrt.f64 1/2) (*.f64 1/2 (*.f64 k (*.f64 (sqrt.f64 1/2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))
(*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (+.f64 (fma.f64 (*.f64 (*.f64 1/8 (*.f64 k k)) (sqrt.f64 1/2)) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 1/2 (*.f64 k (sqrt.f64 1/2))))) (sqrt.f64 1/2)))
(*.f64 (sqrt.f64 (/.f64 (pow.f64 n -1) (PI.f64))) (+.f64 (sqrt.f64 1/2) (*.f64 (*.f64 (sqrt.f64 1/2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (+.f64 (*.f64 1/2 k) (*.f64 (*.f64 1/8 (*.f64 k k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))
(+.f64 (*.f64 1/48 (*.f64 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 1/2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 1/2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) (+.f64 (*.f64 1/2 (*.f64 (*.f64 k (*.f64 (sqrt.f64 1/2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2)))))
(fma.f64 1/48 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (pow.f64 k 3) (sqrt.f64 1/2)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (fma.f64 1/8 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (*.f64 k k) (sqrt.f64 1/2)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (sqrt.f64 1/2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2)))))
(+.f64 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (+.f64 (sqrt.f64 1/2) (*.f64 1/2 (*.f64 k (*.f64 (sqrt.f64 1/2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/48 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3) (pow.f64 k 3)))) (*.f64 1/8 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2) (*.f64 k k)))))))
(*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (+.f64 (fma.f64 1/2 (*.f64 k (*.f64 (sqrt.f64 1/2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (sqrt.f64 1/2)) (fma.f64 1/48 (*.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3))) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2) (*.f64 (*.f64 1/8 (*.f64 k k)) (sqrt.f64 1/2))))))
(*.f64 (sqrt.f64 (/.f64 (pow.f64 n -1) (PI.f64))) (+.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (+.f64 (*.f64 1/2 k) (*.f64 (*.f64 1/8 (*.f64 k k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) (*.f64 (+.f64 (*.f64 (*.f64 1/48 (pow.f64 k 3)) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3)) 1) (sqrt.f64 1/2))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k 1/2 -1/2))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (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 1/2 k -1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (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 1/2 k -1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (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 1/2 k -1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (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 1/2 k -1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (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 1/2 k -1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (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 1/2 k -1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (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 1/2 k -1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 1/2 k -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (*.f64 (-.f64 (*.f64 1/2 k) 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (neg.f64 (*.f64 (fma.f64 1/2 k -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(/.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))
(/.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 1/2 k -1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (*.f64 (-.f64 (*.f64 1/2 k) 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (neg.f64 (*.f64 (fma.f64 1/2 k -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(/.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))
(/.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 1/2 k -1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (*.f64 (-.f64 (*.f64 1/2 k) 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (neg.f64 (*.f64 (fma.f64 1/2 k -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(/.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))
(/.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 1/2 k -1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (*.f64 (-.f64 (*.f64 1/2 k) 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (neg.f64 (*.f64 (fma.f64 1/2 k -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(/.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))
(/.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 1/2 k -1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (neg.f64 (*.f64 (fma.f64 1/2 k -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(/.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))
(/.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 1/2 k -1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (neg.f64 (*.f64 (fma.f64 1/2 k -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(/.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))
(/.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 1/2 k -1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (neg.f64 (*.f64 (fma.f64 1/2 k -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(/.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))
(/.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 1/2 k -1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (neg.f64 (*.f64 (fma.f64 1/2 k -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(/.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 1/2 k -1/2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))
(/.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 1/2 k -1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (neg.f64 (*.f64 (fma.f64 1/2 k -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 (pow.f64 (/.f64 -1 n) -1) (*.f64 (PI.f64) -2)) (fma.f64 1/2 k -1/2)))
(/.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 1/2 k -1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (*.f64 (*.f64 -1 n) -2)) (fma.f64 k -1/2 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (neg.f64 (*.f64 (fma.f64 1/2 k -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 (pow.f64 (/.f64 -1 n) -1) (*.f64 (PI.f64) -2)) (fma.f64 1/2 k -1/2)))
(/.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 1/2 k -1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (*.f64 (*.f64 -1 n) -2)) (fma.f64 k -1/2 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (neg.f64 (*.f64 (fma.f64 1/2 k -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 (pow.f64 (/.f64 -1 n) -1) (*.f64 (PI.f64) -2)) (fma.f64 1/2 k -1/2)))
(/.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 1/2 k -1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (*.f64 (*.f64 -1 n) -2)) (fma.f64 k -1/2 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 1 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (-.f64 (*.f64 1/2 k) 1/2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (neg.f64 (*.f64 (fma.f64 1/2 k -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 (pow.f64 (/.f64 -1 n) -1) (*.f64 (PI.f64) -2)) (fma.f64 1/2 k -1/2)))
(/.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 1/2 k -1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (*.f64 (*.f64 -1 n) -2)) (fma.f64 k -1/2 1/2)))

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))
✓0.3b
(/.f64 (PI.f64) k)
✓11.2b
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))
Compiler

Compiled 27 to 14 computations (48.1% saved)

series11.0ms (0.1%)

Counts
3 → 24
Calls

15 calls:

TimeVariablePointExpression
1.0ms
k
@inf
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))
1.0ms
k
@-inf
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))
1.0ms
k
@0
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))
1.0ms
n
@-inf
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))
1.0ms
n
@inf
(*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))

rewrite63.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
956×pow1_binary64
885×add-log-exp_binary64
885×log1p-expm1-u_binary64
885×expm1-log1p-u_binary64
94×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0929
118929
2239829
Stop Event
1×node limit
Counts
3 → 83
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))
(/.f64 (PI.f64) k)
(*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) (cbrt.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))) (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 1/4) (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 n 2)) (sqrt.f64 (/.f64 (PI.f64) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) n) 1/2) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (PI.f64) k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (PI.f64) (pow.f64 k -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (PI.f64) k) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (PI.f64) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (*.f64 (cbrt.f64 (PI.f64)) (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (PI.f64) k)) (cbrt.f64 (pow.f64 (/.f64 (PI.f64) k) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 (PI.f64) k) 2)) (cbrt.f64 (/.f64 (PI.f64) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (/.f64 (PI.f64) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (PI.f64)) (/.f64 1 (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1) (PI.f64))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) 1) (/.f64 (cbrt.f64 (PI.f64)) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (PI.f64)) 1) (/.f64 (sqrt.f64 (PI.f64)) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 k) 2)) (/.f64 (PI.f64) (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (pow.f64 (cbrt.f64 k) 2)) (cbrt.f64 (/.f64 (PI.f64) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 k) 2)) (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (PI.f64) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (sqrt.f64 k)) (/.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (PI.f64) k) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (PI.f64) k) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (PI.f64) k)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 k (PI.f64)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (PI.f64) (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (PI.f64) k) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (PI.f64) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (PI.f64) k))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (PI.f64) k) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 k 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (PI.f64) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (PI.f64) k)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (PI.f64) k)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (PI.f64) (/.f64 k (*.f64 n 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n 2) (/.f64 k (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 k (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n 2))) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1) k)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n 2)) (pow.f64 (cbrt.f64 k) 2)) (cbrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n 2)) (sqrt.f64 k)) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (PI.f64)) (*.f64 n 2)) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 n 2) (neg.f64 (PI.f64))) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (/.f64 (PI.f64) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 (PI.f64) k) 3) (pow.f64 (*.f64 n 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 n 2) 3) (pow.f64 (/.f64 (PI.f64) k) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))))))))

simplify15.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
16×*-commutative_binary64
15×associate-/l*_binary64
11×associate-/r/_binary64
10×associate-*r*_binary64
8×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08264
114264
229264
356264
486264
597264
Stop Event
1×saturated
Counts
107 → 85
Calls
Call 1
Inputs
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
Outputs
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
✓0.1b
(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)
✓0.3b
(/.f64 (PI.f64) (/.f64 -1 n))
✓11.1b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
Compiler

Compiled 64 to 45 computations (29.7% saved)

series7.0ms (0.1%)

Counts
4 → 72
Calls

21 calls:

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

rewrite89.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
767×log-prod_binary64
265×pow1/3_binary64
260×expm1-udef_binary64
259×log1p-udef_binary64
246×pow3_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01467
130963
2418663
Stop Event
1×node limit
Counts
4 → 162
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(/.f64 (PI.f64) (/.f64 -1 n))
(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)))) (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k) 1/4) (pow.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))) (pow.f64 (/.f64 1 k) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))) (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)) 2) 1/2) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (neg.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)))) (sqrt.f64 (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (PI.f64) (neg.f64 n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (neg.f64 n))) (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (neg.f64 n))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (neg.f64 n)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (neg.f64 n)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (neg.f64 n)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (neg.f64 n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (PI.f64) (neg.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 (PI.f64) (/.f64 1 n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 n (*.f64 (PI.f64) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (PI.f64) (neg.f64 n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (PI.f64) (neg.f64 n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (*.f64 (cbrt.f64 (PI.f64)) (neg.f64 n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (PI.f64) (neg.f64 n))) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (neg.f64 n))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (neg.f64 n))) 2) (cbrt.f64 (*.f64 (PI.f64) (neg.f64 n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (neg.f64 n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (neg.f64 n))) (sqrt.f64 (*.f64 (PI.f64) (neg.f64 n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (PI.f64)) (/.f64 1 (/.f64 1 n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 n) (PI.f64))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (PI.f64) -1) n)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) -1) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 1 n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (PI.f64)) -1) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 1 n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) 1) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 -1 n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (PI.f64)) 1) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 -1 n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (/.f64 -1 (cbrt.f64 n)) 2)) (/.f64 (PI.f64) (/.f64 -1 (cbrt.f64 n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (pow.f64 (/.f64 -1 (cbrt.f64 n)) 2)) (cbrt.f64 (*.f64 (PI.f64) (neg.f64 n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (/.f64 -1 (cbrt.f64 n)) 2)) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 -1 (cbrt.f64 n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (/.f64 -1 n))) (/.f64 (PI.f64) (sqrt.f64 (/.f64 -1 n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (sqrt.f64 (/.f64 -1 n))) (/.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (/.f64 -1 n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (PI.f64) 1) (neg.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 (PI.f64) -1) 1) n)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 (PI.f64) -1) (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 (PI.f64) -1) (sqrt.f64 n)) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) (neg.f64 n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (neg.f64 n)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (PI.f64) (neg.f64 n))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) (neg.f64 n))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 -1 (*.f64 (PI.f64) n)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (/.f64 -1 n) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 -1 (*.f64 (PI.f64) n)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (PI.f64) (/.f64 1 n)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (PI.f64) (neg.f64 n)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (PI.f64)) (neg.f64 n)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (neg.f64 n)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) (neg.f64 n)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (/.f64 -1 n) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (PI.f64) (neg.f64 n))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (PI.f64) (neg.f64 n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (PI.f64) (neg.f64 n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (neg.f64 n))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k))) (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) (/.f64 1 k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)) (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (*.f64 2 (-.f64 1 k)))) (*.f64 (cbrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))) (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)) (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)) 2) (cbrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k) 1/4) (*.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k) 1/4) (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))) (*.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))) (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -2 (pow.f64 -2 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) (neg.f64 n)) (-.f64 1 k)) (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))) (/.f64 1 (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 k) (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k) 1/4) 3) (pow.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (*.f64 2 (-.f64 1 k)))) 1) (/.f64 (cbrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))) 1) (/.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 -2 (pow.f64 -2 k)) 1) (/.f64 (pow.f64 (*.f64 (PI.f64) (neg.f64 n)) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 k) 2)) (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (*.f64 2 (-.f64 1 k)))) (pow.f64 (cbrt.f64 k) 2)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))) (pow.f64 (cbrt.f64 k) 2)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))) (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 -2 (pow.f64 -2 k)) (pow.f64 (cbrt.f64 k) 2)) (/.f64 (pow.f64 (*.f64 (PI.f64) (neg.f64 n)) (-.f64 1 k)) (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (*.f64 2 (-.f64 1 k)))) (sqrt.f64 k)) (/.f64 (cbrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 -2 (pow.f64 -2 k)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (neg.f64 n)) (-.f64 1 k)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k))) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 k (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) 3) (pow.f64 k 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 k (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) 3) (pow.f64 k 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) k)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)))) (cbrt.f64 (exp.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (/.f64 1 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))) (cbrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (*.f64 2 (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (*.f64 2 (-.f64 1 k)))) (cbrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))) (sqrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -2 (pow.f64 -2 k)) (pow.f64 (*.f64 (PI.f64) (neg.f64 n)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (neg.f64 n)) (-.f64 1 k)) (/.f64 -2 (pow.f64 -2 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 (-.f64 1 k)) (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n)))) 2) (-.f64 1 k)) (pow.f64 (cbrt.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n)))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n)))) (-.f64 1 k)) (pow.f64 (sqrt.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n)))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -2 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) k) (*.f64 (PI.f64) (neg.f64 n))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) (neg.f64 n)) (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) k) -2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) k) (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n)))) 2) (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) k) (cbrt.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n)))) (/.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) k) (sqrt.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -2 (PI.f64)) (*.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) k) (/.f64 -1 n)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n)))) (neg.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (*.f64 2 (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 -2 (*.f64 (PI.f64) (neg.f64 n))))) 1))))))

simplify63.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
581×associate-+l+_binary64
474×associate-*l*_binary64
439×fma-def_binary64
404×associate-*r*_binary64
351×distribute-lft-out_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0851653
12471561
27941373
342581268
Stop Event
1×node limit
Counts
234 → 199
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(*.f64 -1 (*.f64 n (PI.f64)))
(*.f64 -1 (*.f64 n (PI.f64)))
(*.f64 -1 (*.f64 n (PI.f64)))
(*.f64 -1 (*.f64 n (PI.f64)))
(*.f64 -1 (*.f64 n (PI.f64)))
(*.f64 -1 (*.f64 n (PI.f64)))
(*.f64 -1 (*.f64 n (PI.f64)))
(*.f64 -1 (*.f64 n (PI.f64)))
(*.f64 -1 (*.f64 n (PI.f64)))
(*.f64 -1 (*.f64 n (PI.f64)))
(*.f64 -1 (*.f64 n (PI.f64)))
(*.f64 -1 (*.f64 n (PI.f64)))
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(+.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 -2 (*.f64 n (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))
(+.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) (+.f64 (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))) (*.f64 -2 (*.f64 n (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (PI.f64))))))
(+.f64 (*.f64 -1/3 (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) (+.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) (+.f64 (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))) (*.f64 -2 (*.f64 n (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))))
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(*.f64 2 (*.f64 n (PI.f64)))
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (*.f64 2 (*.f64 n (PI.f64))))
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))))))
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 -1/3 (*.f64 (pow.f64 k 3) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) (+.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64)))))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
Outputs
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(*.f64 -1 (*.f64 n (PI.f64)))
(neg.f64 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (neg.f64 n))
(*.f64 n (neg.f64 (PI.f64)))
(*.f64 -1 (*.f64 n (PI.f64)))
(neg.f64 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (neg.f64 n))
(*.f64 n (neg.f64 (PI.f64)))
(*.f64 -1 (*.f64 n (PI.f64)))
(neg.f64 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (neg.f64 n))
(*.f64 n (neg.f64 (PI.f64)))
(*.f64 -1 (*.f64 n (PI.f64)))
(neg.f64 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (neg.f64 n))
(*.f64 n (neg.f64 (PI.f64)))
(*.f64 -1 (*.f64 n (PI.f64)))
(neg.f64 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (neg.f64 n))
(*.f64 n (neg.f64 (PI.f64)))
(*.f64 -1 (*.f64 n (PI.f64)))
(neg.f64 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (neg.f64 n))
(*.f64 n (neg.f64 (PI.f64)))
(*.f64 -1 (*.f64 n (PI.f64)))
(neg.f64 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (neg.f64 n))
(*.f64 n (neg.f64 (PI.f64)))
(*.f64 -1 (*.f64 n (PI.f64)))
(neg.f64 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (neg.f64 n))
(*.f64 n (neg.f64 (PI.f64)))
(*.f64 -1 (*.f64 n (PI.f64)))
(neg.f64 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (neg.f64 n))
(*.f64 n (neg.f64 (PI.f64)))
(*.f64 -1 (*.f64 n (PI.f64)))
(neg.f64 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (neg.f64 n))
(*.f64 n (neg.f64 (PI.f64)))
(*.f64 -1 (*.f64 n (PI.f64)))
(neg.f64 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (neg.f64 n))
(*.f64 n (neg.f64 (PI.f64)))
(*.f64 -1 (*.f64 n (PI.f64)))
(neg.f64 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (neg.f64 n))
(*.f64 n (neg.f64 (PI.f64)))
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(+.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 -2 (*.f64 n (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))
(fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (*.f64 -2 (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))
(fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (*.f64 n (*.f64 (*.f64 (PI.f64) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) -2)))
(fma.f64 n (*.f64 (PI.f64) (*.f64 -2 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (*.f64 n (PI.f64)) (+.f64 (/.f64 2 k) (*.f64 -2 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))
(+.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) (+.f64 (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))) (*.f64 -2 (*.f64 n (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (PI.f64))))))
(fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (fma.f64 k (*.f64 (*.f64 n (PI.f64)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (*.f64 -2 (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))
(fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (fma.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2))) (*.f64 n (*.f64 (*.f64 (PI.f64) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) -2))))
(fma.f64 2 (*.f64 (PI.f64) (/.f64 n k)) (*.f64 (*.f64 n (PI.f64)) (+.f64 (*.f64 -2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (*.f64 k (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2)))))
(fma.f64 2 (*.f64 (PI.f64) (/.f64 n k)) (*.f64 n (*.f64 (PI.f64) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (+.f64 -2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))
(+.f64 (*.f64 -1/3 (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) (+.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) (+.f64 (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))) (*.f64 -2 (*.f64 n (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))))
(fma.f64 -1/3 (*.f64 (*.f64 k k) (*.f64 (*.f64 n (PI.f64)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (fma.f64 k (*.f64 (*.f64 n (PI.f64)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (*.f64 -2 (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))))
(fma.f64 -1/3 (*.f64 n (*.f64 (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3)) (*.f64 k k))) (fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (fma.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2))) (*.f64 n (*.f64 (*.f64 (PI.f64) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) -2)))))
(fma.f64 2 (*.f64 (PI.f64) (/.f64 n k)) (fma.f64 -1/3 (*.f64 k (*.f64 (*.f64 n (PI.f64)) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3) k))) (*.f64 (*.f64 n (PI.f64)) (+.f64 (*.f64 -2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (*.f64 k (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2))))))
(fma.f64 2 (*.f64 (PI.f64) (/.f64 n k)) (*.f64 (*.f64 n (PI.f64)) (+.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (+.f64 -2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3) (*.f64 k (*.f64 k -1/3))))))
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 n (*.f64 2 (PI.f64)))
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (*.f64 2 (*.f64 n (PI.f64))))
(fma.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (*.f64 2 (*.f64 n (PI.f64))))
(fma.f64 2 (*.f64 n (PI.f64)) (*.f64 -2 (*.f64 (*.f64 n (PI.f64)) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) k))))
(*.f64 (PI.f64) (+.f64 (*.f64 n 2) (*.f64 (*.f64 n (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (*.f64 k -2))))
(*.f64 (*.f64 n (PI.f64)) (+.f64 (*.f64 (*.f64 -2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k) 2))
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))))))
(fma.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (fma.f64 2 (*.f64 n (PI.f64)) (*.f64 (*.f64 (*.f64 n (PI.f64)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (*.f64 k k))))
(fma.f64 -2 (*.f64 (*.f64 n (PI.f64)) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) k)) (fma.f64 2 (*.f64 n (PI.f64)) (*.f64 (*.f64 (*.f64 k k) (*.f64 n (PI.f64))) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2))))
(fma.f64 n (*.f64 2 (PI.f64)) (*.f64 k (*.f64 (*.f64 n (PI.f64)) (+.f64 (*.f64 -2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (*.f64 k (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2))))))
(*.f64 (PI.f64) (+.f64 (*.f64 n 2) (*.f64 k (*.f64 n (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (+.f64 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) -2))))))
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 -1/3 (*.f64 (pow.f64 k 3) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) (+.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64)))))))
(fma.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (fma.f64 -1/3 (*.f64 (*.f64 (*.f64 n (PI.f64)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)) (pow.f64 k 3)) (fma.f64 2 (*.f64 n (PI.f64)) (*.f64 (*.f64 (*.f64 n (PI.f64)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (*.f64 k k)))))
(fma.f64 -2 (*.f64 (*.f64 n (PI.f64)) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) k)) (fma.f64 -1/3 (*.f64 n (*.f64 (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3)) (pow.f64 k 3))) (fma.f64 2 (*.f64 n (PI.f64)) (*.f64 (*.f64 (*.f64 k k) (*.f64 n (PI.f64))) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2)))))
(fma.f64 -1/3 (*.f64 n (*.f64 (PI.f64) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3) (pow.f64 k 3)))) (fma.f64 n (*.f64 2 (PI.f64)) (*.f64 k (*.f64 (*.f64 n (PI.f64)) (+.f64 (*.f64 -2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (*.f64 k (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2)))))))
(*.f64 n (+.f64 (*.f64 (PI.f64) (+.f64 2 (*.f64 (*.f64 -1/3 (pow.f64 k 3)) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3)))) (*.f64 k (*.f64 (PI.f64) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (+.f64 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) -2))))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiled 57 to 41 computations (28.1% saved)

series5.0ms (0%)

Counts
2 → 12
Calls

9 calls:

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

rewrite66.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
734×log-prod_binary64
518×pow-unpow_binary64
380×pow2_binary64
262×pow1/3_binary64
258×expm1-udef_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01431
130626
2386125
Stop Event
1×node limit
Counts
2 → 54
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(sqrt.f64 (/.f64 1 k))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 1 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (pow.f64 k -1/2) k) (pow.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3) (/.f64 (pow.f64 k -1/2) k)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (/.f64 1 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (/.f64 (pow.f64 k -1/2) k) (pow.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3) (/.f64 (pow.f64 k -1/2) k)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 k -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 k -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 k -1/2)) (/.f64 1 (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 k)) (cbrt.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 k -2))) (sqrt.f64 (/.f64 1 (cbrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 k) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 -1) (sqrt.f64 (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 k -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 k) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 k -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 k -1/2) k) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 k -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 k) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 k -1/2) k))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 -1/2 (log.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 k)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/2 (log.f64 k)) 1))))))

simplify53.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
811×exp-sum_binary64
717×unsub-neg_binary64
629×exp-prod_binary64
473×distribute-rgt-in_binary64
460×distribute-lft-in_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
038388
196384
2309372
31180360
45300288
Stop Event
1×node limit
Counts
66 → 59
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
Outputs
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(*.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 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(*.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 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(*.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 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(*.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 1/2 (*.f64 (-.f64 1 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 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(*.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 1/2 (*.f64 (-.f64 1 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 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(*.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 1/2 (*.f64 (-.f64 1 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 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(*.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 1/2 (*.f64 (-.f64 1 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 1/2) (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(*.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 1/2 (*.f64 (-.f64 1 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 1/2) (*.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(*.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 -2 (PI.f64)) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 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 1/2) (*.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(*.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 -2 (PI.f64)) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 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 1/2) (*.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(*.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 -2 (PI.f64)) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 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 1/2) (*.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (*.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(*.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 -2 (PI.f64)) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2)))

localize35.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k)
0.2b
(*.f64 (PI.f64) n)
✓3.6b
(exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
✓11.1b
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k))
Compiler

Compiled 72 to 43 computations (40.3% saved)

series7.0ms (0.1%)

Counts
3 → 60
Calls

18 calls:

TimeVariablePointExpression
1.0ms
k
@-inf
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k))
1.0ms
k
@-inf
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k)
1.0ms
k
@0
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k))
0.0ms
k
@inf
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k))
0.0ms
k
@0
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k)

rewrite86.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
689×log-prod_binary64
351×pow2_binary64
267×pow-unpow_binary64
248×pow1/3_binary64
242×expm1-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01462
128550
2353250
Stop Event
1×node limit
Counts
3 → 158
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k))
(exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k) 1/4) (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))) (sqrt.f64 (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 n (*.f64 2 (PI.f64))) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 n (*.f64 2 (PI.f64))) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 (neg.f64 k) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 n (*.f64 2 (PI.f64))) (pow.f64 (E.f64) (*.f64 (neg.f64 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 n (*.f64 2 (PI.f64))) (pow.f64 (E.f64) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (neg.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) 2) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 2)) (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 (PI.f64) n))) (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (neg.f64 k)) (*.f64 n (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (E.f64) (log.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))) (pow.f64 (E.f64) (log.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (E.f64) (*.f64 2 (log.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))))) (pow.f64 (E.f64) (log.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (E.f64) (*.f64 (log.f64 2) (-.f64 1 k))) (pow.f64 (E.f64) (*.f64 (log.f64 (*.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (E.f64) (*.f64 (-.f64 1 k) (log.f64 2))) (pow.f64 (E.f64) (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (PI.f64)))) (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (*.f64 2 (log.f64 (cbrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))) (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (cbrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (*.f64 (log.f64 2) 1)) (pow.f64 (exp.f64 (-.f64 1 k)) (*.f64 (log.f64 (*.f64 (PI.f64) n)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) 2)) (cbrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) (sqrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (pow.f64 (cbrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 2)) (cbrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (sqrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (sqrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (cbrt.f64 (-.f64 1 k))) (pow.f64 (cbrt.f64 (-.f64 1 k)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (pow.f64 (cbrt.f64 (-.f64 1 k)) 2)) (cbrt.f64 (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (sqrt.f64 (-.f64 1 k))) (sqrt.f64 (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 (pow.f64 k 3))) (/.f64 1 (+.f64 1 (fma.f64 k k k))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 (*.f64 k k))) (/.f64 1 (+.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (E.f64) (cbrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (E.f64) (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) 2)) (cbrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (E.f64) (pow.f64 (cbrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 2)) (*.f64 (cbrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (E.f64) (pow.f64 (cbrt.f64 (-.f64 1 k)) 2)) (*.f64 (cbrt.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (E.f64) (sqrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) (sqrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (E.f64) (sqrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (E.f64) (sqrt.f64 (-.f64 1 k))) (*.f64 (sqrt.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (E.f64) (*.f64 (-.f64 1 k) (pow.f64 (cbrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 2))) (cbrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (E.f64) (*.f64 (-.f64 1 k) (sqrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) (sqrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (E.f64) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (pow.f64 (cbrt.f64 (-.f64 1 k)) 2))) (cbrt.f64 (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (E.f64) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 (-.f64 1 k)))) (sqrt.f64 (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (cbrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (pow.f64 (cbrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) 2)) 1) (cbrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) 2)) (cbrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (cbrt.f64 (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) 2)) (cbrt.f64 (-.f64 1 k))) (cbrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) 2)) (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) 2)) (cbrt.f64 (cbrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) 2))) (cbrt.f64 (cbrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) 2)) (cbrt.f64 (sqrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))) (cbrt.f64 (sqrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))) (sqrt.f64 (cbrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (sqrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) 1) (sqrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (sqrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) (cbrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) (cbrt.f64 (sqrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (sqrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) (sqrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (sqrt.f64 (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (sqrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) (sqrt.f64 (-.f64 1 k))) (sqrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (sqrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) 2))) (sqrt.f64 (cbrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (sqrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))) (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (pow.f64 (cbrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 2)) 1) (cbrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (pow.f64 (cbrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 2)) (cbrt.f64 (sqrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) (cbrt.f64 (sqrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (pow.f64 (cbrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 2)) (pow.f64 (cbrt.f64 (cbrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) 2)) (cbrt.f64 (cbrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (pow.f64 (cbrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 2))) (cbrt.f64 (cbrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (pow.f64 (cbrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 2)) (sqrt.f64 (cbrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) (sqrt.f64 (cbrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (sqrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) 1) (sqrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (sqrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (cbrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (cbrt.f64 (sqrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (sqrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (sqrt.f64 (sqrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) (sqrt.f64 (sqrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (sqrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (sqrt.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 2))) (sqrt.f64 (cbrt.f64 (log.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))) (-.f64 1 k)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) 2) (*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 2) (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k) 1/4) (*.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k) 1/4) (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (/.f64 1 (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 k) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k) 1/4) 3) (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) 2) 1) (/.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) 1) (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 k) 2)) (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) 2) (pow.f64 (cbrt.f64 k) 2)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (pow.f64 (cbrt.f64 k) 2)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) 2) (sqrt.f64 k)) (/.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 k (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) 3) (pow.f64 k 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 k (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) 3) (pow.f64 k 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1))))))

simplify60.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
581×associate-+l+_binary64
476×associate-*l*_binary64
439×fma-def_binary64
401×associate-*r*_binary64
353×distribute-lft-out_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0841377
12421349
27791289
342311184
Stop Event
1×node limit
Counts
218 → 192
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(*.f64 2 (*.f64 n (PI.f64)))
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (*.f64 2 (*.f64 n (PI.f64))))
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))))))
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 -1/3 (*.f64 (pow.f64 k 3) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) (+.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64)))))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(+.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 -2 (*.f64 n (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))
(+.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) (+.f64 (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))) (*.f64 -2 (*.f64 n (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (PI.f64))))))
(+.f64 (*.f64 -1/3 (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) (+.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) (+.f64 (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))) (*.f64 -2 (*.f64 n (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))))
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
Outputs
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k)) k))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 n (*.f64 2 (PI.f64)))
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (*.f64 2 (*.f64 n (PI.f64))))
(fma.f64 -2 (*.f64 k (*.f64 (*.f64 n (PI.f64)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 2 (*.f64 n (PI.f64))))
(fma.f64 2 (*.f64 n (PI.f64)) (*.f64 k (*.f64 (*.f64 (*.f64 n -2) (PI.f64)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))
(*.f64 (PI.f64) (+.f64 (*.f64 n 2) (*.f64 k (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 n -2)))))
(*.f64 n (*.f64 (PI.f64) (+.f64 2 (*.f64 (*.f64 k -2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))))))
(fma.f64 -2 (*.f64 k (*.f64 (*.f64 n (PI.f64)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (fma.f64 2 (*.f64 n (PI.f64)) (*.f64 (*.f64 k k) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))))
(fma.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) (fma.f64 2 (*.f64 n (PI.f64)) (*.f64 k (*.f64 (*.f64 k (*.f64 n (PI.f64))) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2)))))
(fma.f64 n (*.f64 2 (PI.f64)) (*.f64 k (*.f64 (*.f64 n (PI.f64)) (+.f64 (*.f64 -2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (*.f64 k (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2))))))
(*.f64 (PI.f64) (+.f64 (*.f64 k (*.f64 n (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (+.f64 -2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (*.f64 n 2)))
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 -1/3 (*.f64 (pow.f64 k 3) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) (+.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64)))))))
(fma.f64 -2 (*.f64 k (*.f64 (*.f64 n (PI.f64)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (fma.f64 -1/3 (*.f64 (pow.f64 k 3) (*.f64 (*.f64 n (PI.f64)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (fma.f64 2 (*.f64 n (PI.f64)) (*.f64 (*.f64 k k) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))))))
(fma.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) (fma.f64 -1/3 (*.f64 (*.f64 n (PI.f64)) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3) (pow.f64 k 3))) (fma.f64 2 (*.f64 n (PI.f64)) (*.f64 k (*.f64 (*.f64 k (*.f64 n (PI.f64))) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2))))))
(fma.f64 -1/3 (*.f64 n (*.f64 (PI.f64) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3)))) (fma.f64 n (*.f64 2 (PI.f64)) (*.f64 k (*.f64 (*.f64 n (PI.f64)) (+.f64 (*.f64 -2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (*.f64 k (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2)))))))
(*.f64 n (+.f64 (*.f64 (PI.f64) (+.f64 2 (*.f64 (*.f64 -1/3 (pow.f64 k 3)) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3)))) (*.f64 k (*.f64 (PI.f64) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (+.f64 -2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 2 (*.f64 (/.f64 (PI.f64) k) n))
(+.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 -2 (*.f64 n (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))
(fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (*.f64 -2 (*.f64 (*.f64 n (PI.f64)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(fma.f64 2 (/.f64 (*.f64 n (PI.f64)) k) (*.f64 (*.f64 (*.f64 n -2) (PI.f64)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))
(fma.f64 2 (/.f64 (*.f64 n (PI.f64)) k) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 -2 (*.f64 n (PI.f64)))))
(*.f64 (*.f64 n (PI.f64)) (+.f64 (/.f64 2 k) (*.f64 -2 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))
(+.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) (+.f64 (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))) (*.f64 -2 (*.f64 n (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (PI.f64))))))
(fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (fma.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 -2 (*.f64 (*.f64 n (PI.f64)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))
(fma.f64 2 (/.f64 (*.f64 n (PI.f64)) k) (fma.f64 (*.f64 k n) (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2)) (*.f64 (*.f64 (*.f64 n -2) (PI.f64)) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))
(fma.f64 2 (/.f64 (*.f64 n (PI.f64)) k) (*.f64 (*.f64 n (PI.f64)) (+.f64 (*.f64 -2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (*.f64 k (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2)))))
(fma.f64 2 (*.f64 (/.f64 (PI.f64) k) n) (*.f64 n (*.f64 (PI.f64) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (+.f64 -2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))
(+.f64 (*.f64 -1/3 (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) (+.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) (+.f64 (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))) (*.f64 -2 (*.f64 n (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))))
(fma.f64 -1/3 (*.f64 (*.f64 k k) (*.f64 (*.f64 n (PI.f64)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (fma.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 -2 (*.f64 (*.f64 n (PI.f64)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))
(fma.f64 -1/3 (*.f64 (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3)) (*.f64 k (*.f64 k n))) (fma.f64 2 (/.f64 (*.f64 n (PI.f64)) k) (fma.f64 (*.f64 k n) (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2)) (*.f64 (*.f64 (*.f64 n -2) (PI.f64)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))
(fma.f64 2 (/.f64 (*.f64 n (PI.f64)) k) (fma.f64 (*.f64 k k) (*.f64 n (*.f64 -1/3 (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3)))) (*.f64 (*.f64 n (PI.f64)) (+.f64 (*.f64 -2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (*.f64 k (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2))))))
(fma.f64 2 (*.f64 (/.f64 (PI.f64) k) n) (*.f64 (*.f64 n (PI.f64)) (+.f64 (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3) (*.f64 k (*.f64 k -1/3))) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (+.f64 -2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (-.f64 1 k)) k)

eval283.0ms (2.8%)

Compiler

Compiled 14393 to 9757 computations (32.2% saved)

prune121.0ms (1.2%)

Pruning

24 alts after pruning (19 fresh and 5 done)

PrunedKeptTotal
New70714721
Fresh9514
Picked011
Done145
Total71724741
Error
0b
Counts
741 → 24
Alt Table
Click to see full alt table
StatusErrorProgram
21.3b
(/.f64 (pow.f64 k -1/2) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2)))
▶0.4b
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
▶32.8b
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
32.8b
(sqrt.f64 (*.f64 (pow.f64 (/.f64 k (PI.f64)) -1) (*.f64 n 2)))
41.9b
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2) 1/3)
▶32.8b
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 (PI.f64) (*.f64 n 2)))))
21.2b
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (sqrt.f64 k))
11.9b
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))
32.8b
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
✓13.9b
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k))
21.2b
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
32.9b
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
0.4b
(*.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2)))
▶40.5b
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2))
0.4b
(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))))
✓12.0b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
✓0.3b
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓32.8b
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))
32.8b
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n 2)) k))
32.8b
(sqrt.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))))
14.1b
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))
✓11.9b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
21.2b
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n 2)))
▶11.9b
(sqrt.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))
Compiler

Compiled 582 to 474 computations (18.6% saved)

localize24.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiled 51 to 35 computations (31.4% saved)

series9.0ms (0.1%)

Counts
3 → 48
Calls

15 calls:

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

rewrite75.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
779×log-prod_binary64
392×pow2_binary64
266×pow1/3_binary64
264×expm1-udef_binary64
264×log1p-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01447
130743
2398443
Stop Event
1×node limit
Counts
3 → 92
Calls
Call 1
Inputs
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(*.f64 (PI.f64) (*.f64 n 2))
(pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (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 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (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 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 2 (fma.f64 k -1/2 1/2))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 2 (fma.f64 k -1/2 1/2))) k)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 2 (fma.f64 k -1/2 1/2)))) (*.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2)) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (+.f64 n 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 (PI.f64) (+.f64 n n)) (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 (PI.f64) (+.f64 n 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 n)) (fma.f64 k -1/2 1/2))) (*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 2 (fma.f64 k -1/2 1/2)))) 1) (/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (+.f64 n n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 (+.f64 n n) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2)) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 2 (fma.f64 k -1/2 1/2)))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 (+.f64 n n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 2 (fma.f64 k -1/2 1/2))) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (PI.f64) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64))) 2)) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64)))) (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (+.f64 n n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (+.f64 n n) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (+.f64 n n) 3) (pow.f64 (PI.f64) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) 2) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (+.f64 n n) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (+.f64 n n) 3) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n 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) (+.f64 n n)) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n 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) (+.f64 n n)) (fma.f64 k -1/2 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 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 n)) (*.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (pow.f64 (+.f64 n n) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 n 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 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n 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) (+.f64 n 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) (+.f64 n n))) 2) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n 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 sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n 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) (+.f64 n 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) (+.f64 n n)) (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 n)) (fma.f64 k -1/2 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n 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) (+.f64 n n)))))))) (#(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 n)))) 1))))))

simplify83.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
411×associate-*r*_binary64
402×associate-+r+_binary64
395×associate-+l+_binary64
386×associate-*l*_binary64
344×fma-neg_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0751206
12101060
2662937
33761878
47606878
Stop Event
1×node limit
Counts
140 → 114
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 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)))
(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))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
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 (+.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 -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 (+.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 -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 (+.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 -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 (+.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 -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 (+.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 -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 (+.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 -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 (+.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 -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 (+.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 -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 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (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 -2 (PI.f64)) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 -1 n) (*.f64 -2 (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 (+.f64 1/2 (*.f64 -1/2 k))) (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 -2 (PI.f64)) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 -1 n) (*.f64 -2 (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 (+.f64 1/2 (*.f64 -1/2 k))) (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 -2 (PI.f64)) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 -1 n) (*.f64 -2 (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 (+.f64 1/2 (*.f64 -1/2 k))) (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 -2 (PI.f64)) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 -1 n) (*.f64 -2 (PI.f64))) (fma.f64 -1/2 k 1/2)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (+.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))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (+.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))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (+.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))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (+.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))
(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 (+.f64 1/2 (*.f64 -1/2 k))) (+.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))
(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 (+.f64 1/2 (*.f64 -1/2 k))) (+.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))
(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 (+.f64 1/2 (*.f64 -1/2 k))) (+.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))
(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 (+.f64 1/2 (*.f64 -1/2 k))) (+.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))
(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 (+.f64 1/2 (*.f64 -1/2 k))) (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 -2 (PI.f64)) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 (*.f64 -1 n) (*.f64 -2 (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 (+.f64 1/2 (*.f64 -1/2 k))) (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 -2 (PI.f64)) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 (*.f64 -1 n) (*.f64 -2 (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 (+.f64 1/2 (*.f64 -1/2 k))) (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 -2 (PI.f64)) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 (*.f64 -1 n) (*.f64 -2 (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 (+.f64 1/2 (*.f64 -1/2 k))) (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 -2 (PI.f64)) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 (*.f64 -1 n) (*.f64 -2 (PI.f64))) (fma.f64 -1/2 k 1/2))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))
(+.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 (*.f64 (PI.f64) n)) (*.f64 (*.f64 (sqrt.f64 2) k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 2))))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (+.f64 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) 1) (sqrt.f64 2)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 (*.f64 -1/2 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 (*.f64 (PI.f64) n)) (*.f64 (*.f64 (sqrt.f64 2) k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k k)) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2))) (sqrt.f64 (*.f64 (PI.f64) n)))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 2)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 k k))) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 (+.f64 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) 1) (sqrt.f64 2)) (*.f64 (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)) (*.f64 (sqrt.f64 2) 1/8))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 1/8 (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 2 (*.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))))))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 (sqrt.f64 2) k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 1/8 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k k)) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2))) (*.f64 -1/48 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3)) (sqrt.f64 (*.f64 (PI.f64) n))))))))
(+.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 2)))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 k k))) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)) (*.f64 (*.f64 -1/48 (sqrt.f64 2)) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3))))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 (+.f64 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) 1) (sqrt.f64 2)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (*.f64 -1/48 (pow.f64 k 3)) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3)) (*.f64 1/8 (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 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 1/8 (*.f64 k k)) (*.f64 -1/48 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k 3))))) (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (+.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))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (+.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))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (+.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))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (+.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))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (+.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))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (+.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))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (+.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))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (+.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))

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.3b
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
✓11.2b
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
Compiler

Compiled 27 to 14 computations (48.1% saved)

series4.0ms (0%)

Counts
2 → 24
Calls

12 calls:

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

rewrite55.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
954×pow1_binary64
883×add-log-exp_binary64
883×log1p-expm1-u_binary64
883×expm1-log1p-u_binary64
94×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0924
118924
2239224
Stop Event
1×node limit
Counts
2 → 51
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))) (cbrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))) (cbrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/4) (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 n k) 2) 1/2) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 n (/.f64 k (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (PI.f64)) (/.f64 k n))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 k (*.f64 n (*.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (*.f64 2 (PI.f64))) k)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 n (*.f64 2 (PI.f64)))) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) 1) k)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (pow.f64 (cbrt.f64 k) 2)) (cbrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (sqrt.f64 k)) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 n) (*.f64 2 (PI.f64))) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (PI.f64)) (neg.f64 n)) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 n k) 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 (/.f64 n k) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))))))))

simplify15.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
16×*-commutative_binary64
15×associate-/l*_binary64
11×associate-/r/_binary64
10×associate-*r*_binary64
8×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08264
114264
229264
356264
486264
597264
Stop Event
1×saturated
Counts
75 → 52
Calls
Call 1
Inputs
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
Outputs
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
(/.f64 (PI.f64) (/.f64 k (*.f64 2 n)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 k (*.f64 (PI.f64) (*.f64 n 2)))
✓0.2b
(/.f64 1 (/.f64 k (*.f64 (PI.f64) (*.f64 n 2))))
0.2b
(*.f64 (PI.f64) (*.f64 n 2))
✓11.2b
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 (PI.f64) (*.f64 n 2)))))
Compiler

Compiled 41 to 27 computations (34.1% saved)

series9.0ms (0.1%)

Counts
3 → 48
Calls

18 calls:

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

rewrite87.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
589×log-prod_binary64
449×exp-prod_binary64
347×pow-prod-down_binary64
276×pow2_binary64
232×pow-unpow_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01141
123035
2296435
Stop Event
1×node limit
Counts
3 → 193
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 (PI.f64) (*.f64 n 2)))))
(/.f64 1 (/.f64 k (*.f64 (PI.f64) (*.f64 n 2))))
(/.f64 k (*.f64 (PI.f64) (*.f64 n 2)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/6) (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/4) (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 -1) (sqrt.f64 (neg.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 3) -1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/2) (log.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))))))) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/4)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))))) 1) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 1 k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) (pow.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 2) (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/4) (pow.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 k) (*.f64 (PI.f64) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) (/.f64 (*.f64 (PI.f64) (+.f64 n n)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (PI.f64) 1) (/.f64 (+.f64 n n) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 n n) 1) (/.f64 (PI.f64) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) 1) (/.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (PI.f64) n) 1) (/.f64 2 k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 k) -2) (/.f64 (*.f64 (PI.f64) (+.f64 n n)) (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (PI.f64) (pow.f64 (cbrt.f64 k) 2)) (/.f64 (+.f64 n n) (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 n n) (pow.f64 (cbrt.f64 k) 2)) (/.f64 (PI.f64) (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (pow.f64 (cbrt.f64 k) 2)) (/.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (pow.f64 (cbrt.f64 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (PI.f64) n) (pow.f64 (cbrt.f64 k) 2)) (/.f64 2 (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (PI.f64) (sqrt.f64 k)) (/.f64 (+.f64 n n) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 n n) (sqrt.f64 k)) (/.f64 (PI.f64) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 k)) (/.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (PI.f64) n) (sqrt.f64 k)) (/.f64 2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (neg.f64 k)) (*.f64 (*.f64 (PI.f64) n) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 k (PI.f64))) (+.f64 n n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -2) (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))) 3/4) (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))) 5/6) (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 k) 1) (*.f64 (PI.f64) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 k) (PI.f64)) (+.f64 n n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 k) (+.f64 n n)) (PI.f64))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 k) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2)) (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 k) (*.f64 (PI.f64) n)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3/2) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/6) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 -1) (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3) (pow.f64 k 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))))) 2)) (cbrt.f64 (log.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))))) (sqrt.f64 (log.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3) (pow.f64 k 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -2 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))))) 1) 2))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (/.f64 k (*.f64 (PI.f64) n))))) 2)) (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (/.f64 k (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (sqrt.f64 (exp.f64 (/.f64 k (*.f64 (PI.f64) n)))))) (log.f64 (sqrt.f64 (sqrt.f64 (exp.f64 (/.f64 k (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 k (/.f64 (/.f64 1 (PI.f64)) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) (pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) 2) (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 k) 2) (*.f64 (cbrt.f64 k) (/.f64 (/.f64 1 (PI.f64)) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 k) (/.f64 (/.f64 1 (PI.f64)) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 k) (/.f64 1 (*.f64 (*.f64 (PI.f64) n) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (PI.f64)) (+.f64 n n)) k)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 k (PI.f64)) (/.f64 1 (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 k) 2) 1) (/.f64 (cbrt.f64 k) (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 k) 1) (/.f64 (sqrt.f64 k) (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (PI.f64)) (/.f64 k (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 k) 2) (PI.f64)) (/.f64 (cbrt.f64 k) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 k) (PI.f64)) (/.f64 (sqrt.f64 k) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 k) (+.f64 n n)) (/.f64 (sqrt.f64 k) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 n n)) (/.f64 k (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 k) 2) (+.f64 n n)) (/.f64 (cbrt.f64 k) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))) -2) (/.f64 k (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 k) 2) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2)) (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 k) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2)) (/.f64 (sqrt.f64 k) (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) -1/2) (/.f64 k (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 k) 2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (/.f64 (cbrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 (PI.f64) n)) (/.f64 k 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 k) 2) (*.f64 (PI.f64) n)) (/.f64 (cbrt.f64 k) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 k) (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 k 3) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)))) 2)) (cbrt.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))) (sqrt.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 k (*.f64 (*.f64 (PI.f64) n) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (sqrt.f64 (exp.f64 (/.f64 k (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 k 3) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 1) -1))))))

simplify26.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
26×associate-/l*_binary64
21×*-commutative_binary64
17×associate-/r/_binary64
12×associate-*r/_binary64
10×associate-*r*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
011528
122528
251528
3100528
4144528
5158528
Stop Event
1×saturated
Counts
241 → 197
Calls
Call 1
Inputs
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
Outputs
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(/.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)
(*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))
(*.f64 (PI.f64) (/.f64 (*.f64 2 n) k))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))
✓0.2b
(pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2)
0.3b
(/.f64 (PI.f64) k)
✓22.2b
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2))
Compiler

Compiled 39 to 22 computations (43.6% saved)

series186.0ms (1.9%)

Counts
2 → 24
Calls

12 calls:

TimeVariablePointExpression
60.0ms
k
@0
(pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2)
27.0ms
n
@-inf
(pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2)
27.0ms
k
@-inf
(pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2)
26.0ms
n
@0
(pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2)
20.0ms
n
@inf
(pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2)

rewrite89.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
574×log-prod_binary64
427×exp-prod_binary64
340×pow-prod-down_binary64
291×pow2_binary64
229×pow-unpow_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01130
123527
2293227
Stop Event
1×node limit
Counts
2 → 78
Calls
Call 1
Inputs
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2))
(pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/6) (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/4) (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (/.f64 (PI.f64) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) n) 2) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 9/2) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 2) 3/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/4) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/3) (log.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))))) (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))))) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/4)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2)) 1) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2)) 1/3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))) 1) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (PI.f64) k) 3/2) (pow.f64 (+.f64 n n) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 n n) 3/2) (pow.f64 (/.f64 (PI.f64) k) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/4) (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) n) 3/2) (pow.f64 2 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 4) (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 5/2) (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 9/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 9/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3/4 (log.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2)) 1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)))) 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 3/4) 2))))))

simplify77.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
656×fma-def_binary64
540×exp-sum_binary64
315×distribute-rgt-in_binary64
291×associate-+l-_binary64
286×associate--r+_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
050504
1135480
2343408
3909336
42765336
Stop Event
1×node limit
Counts
102 → 85
Calls
Call 1
Inputs
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
Outputs
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (log.f64 k)))
(*.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))
(pow.f64 (*.f64 2 (/.f64 (*.f64 (PI.f64) n) k)) 3/2)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (log.f64 k)))
(*.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))
(pow.f64 (*.f64 2 (/.f64 (*.f64 (PI.f64) n) k)) 3/2)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (log.f64 k)))
(*.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))
(pow.f64 (*.f64 2 (/.f64 (*.f64 (PI.f64) n) k)) 3/2)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (log.f64 k)))
(*.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))
(pow.f64 (*.f64 2 (/.f64 (*.f64 (PI.f64) n) k)) 3/2)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (log.f64 k)))
(*.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))
(pow.f64 (*.f64 2 (/.f64 (*.f64 (PI.f64) n) k)) 3/2)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (log.f64 k)))
(*.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))
(pow.f64 (*.f64 2 (/.f64 (*.f64 (PI.f64) n) k)) 3/2)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (log.f64 k)))
(*.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))
(pow.f64 (*.f64 2 (/.f64 (*.f64 (PI.f64) n) k)) 3/2)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (log.f64 k)))
(*.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))
(pow.f64 (*.f64 2 (/.f64 (*.f64 (PI.f64) n) k)) 3/2)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (log.f64 k)))
(*.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))
(pow.f64 (*.f64 2 (/.f64 (*.f64 (PI.f64) n) k)) 3/2)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (log.f64 k)))
(*.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))
(pow.f64 (*.f64 2 (/.f64 (*.f64 (PI.f64) n) k)) 3/2)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (log.f64 k)))
(*.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))
(pow.f64 (*.f64 2 (/.f64 (*.f64 (PI.f64) n) k)) 3/2)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (log.f64 k)))
(*.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))
(pow.f64 (*.f64 2 (/.f64 (*.f64 (PI.f64) n) k)) 3/2)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (log.f64 k)))
(*.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))
(pow.f64 (*.f64 2 (/.f64 (*.f64 (PI.f64) n) k)) 3/2)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (log.f64 k)))
(*.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))
(pow.f64 (*.f64 2 (/.f64 (*.f64 (PI.f64) n) k)) 3/2)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (log.f64 k)))
(*.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))
(pow.f64 (*.f64 2 (/.f64 (*.f64 (PI.f64) n) k)) 3/2)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (log.f64 k)))
(*.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))
(pow.f64 (*.f64 2 (/.f64 (*.f64 (PI.f64) n) k)) 3/2)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (log.f64 k)))
(*.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))
(pow.f64 (*.f64 2 (/.f64 (*.f64 (PI.f64) n) k)) 3/2)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (log.f64 k)))
(*.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))
(pow.f64 (*.f64 2 (/.f64 (*.f64 (PI.f64) n) k)) 3/2)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (log.f64 k)))
(*.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))
(pow.f64 (*.f64 2 (/.f64 (*.f64 (PI.f64) n) k)) 3/2)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (log.f64 k)))
(*.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))
(pow.f64 (*.f64 2 (/.f64 (*.f64 (PI.f64) n) k)) 3/2)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (log.f64 k)))
(*.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))
(pow.f64 (*.f64 2 (/.f64 (*.f64 (PI.f64) n) k)) 3/2)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (log.f64 k)))
(*.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))
(pow.f64 (*.f64 2 (/.f64 (*.f64 (PI.f64) n) k)) 3/2)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (log.f64 k)))
(*.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))
(pow.f64 (*.f64 2 (/.f64 (*.f64 (PI.f64) n) k)) 3/2)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (log.f64 k)))
(*.f64 (pow.f64 k -3/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))
(pow.f64 (*.f64 2 (/.f64 (*.f64 (PI.f64) n) k)) 3/2)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)

localize43.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
✓0.2b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k))
0.2b
(*.f64 n (*.f64 2 (PI.f64)))
✓11.1b
(sqrt.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))
Compiler

Compiled 57 to 39 computations (31.6% saved)

series11.0ms (0.1%)

Counts
3 → 60
Calls

18 calls:

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

rewrite94.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
700×log-prod_binary64
519×pow-unpow_binary64
349×pow2_binary64
239×pow1/3_binary64
235×expm1-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01350
128250
2361250
Stop Event
1×node limit
Counts
3 → 107
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4) (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 2))) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k) k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (-.f64 1 k)))) (/.f64 k (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) (/.f64 k (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 n (pow.f64 n k)) (/.f64 k (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (PI.f64) (*.f64 n 2)) -1) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k) (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 (neg.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) (sqrt.f64 k)) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1) k)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) (pow.f64 (cbrt.f64 k) 2)) (cbrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (PI.f64) (*.f64 n 2)) (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) -1) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 k) (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 3) (pow.f64 k 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 3) (/.f64 (pow.f64 k -2) k)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (pow.f64 k -2) k) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 3) (pow.f64 k 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 3) (/.f64 (pow.f64 k -2) k)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (/.f64 (pow.f64 k -2) k) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (PI.f64) (*.f64 n 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (PI.f64) (*.f64 n 2)) (/.f64 1 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (PI.f64) (*.f64 n 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 (neg.f64 k) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (-.f64 1 k)))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (-.f64 1 k)))) (*.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) (*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 n (pow.f64 n k)) (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 n (pow.f64 n k)) (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1 k)) (/.f64 n (pow.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 (-.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 2)) (-.f64 1 k)) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (-.f64 1 k)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 n 2) (-.f64 1 k)) (pow.f64 (PI.f64) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (neg.f64 k)) (*.f64 (PI.f64) (*.f64 n 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 n (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k) (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (PI.f64)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k) n))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) (*.f64 n 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k) (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 2)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k) (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n 2) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n 2))) (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) 1))))))

simplify97.0ms (1%)

Algorithm
1×egg-herbie
Rules
582×associate-+l+_binary64
465×associate-*l*_binary64
439×fma-def_binary64
401×associate-*r*_binary64
351×distribute-lft-out_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0841569
12411477
27781289
342231184
Stop Event
1×node limit
Counts
167 → 142
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(+.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 -2 (*.f64 n (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))
(+.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) (+.f64 (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))) (*.f64 -2 (*.f64 n (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (PI.f64))))))
(+.f64 (*.f64 -1/3 (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) (+.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) (+.f64 (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))) (*.f64 -2 (*.f64 n (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))))
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(*.f64 2 (*.f64 n (PI.f64)))
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (*.f64 2 (*.f64 n (PI.f64))))
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))))))
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 -1/3 (*.f64 (pow.f64 k 3) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) (+.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64)))))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
Outputs
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 2 (*.f64 (/.f64 (PI.f64) k) n))
(*.f64 (/.f64 (PI.f64) k) (*.f64 n 2))
(+.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) (*.f64 -2 (*.f64 n (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))
(fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (*.f64 -2 (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))
(fma.f64 2 (/.f64 (*.f64 n (PI.f64)) k) (*.f64 n (*.f64 (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) -2)))
(fma.f64 (*.f64 -2 (*.f64 n (PI.f64))) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 2 (*.f64 (/.f64 (PI.f64) k) n)))
(*.f64 (*.f64 n (PI.f64)) (+.f64 (/.f64 2 k) (*.f64 -2 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))
(+.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) (+.f64 (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))) (*.f64 -2 (*.f64 n (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (PI.f64))))))
(fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (fma.f64 k (*.f64 (*.f64 n (PI.f64)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (*.f64 -2 (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))
(fma.f64 2 (/.f64 (*.f64 n (PI.f64)) k) (fma.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 n (*.f64 (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) -2))))
(fma.f64 2 (*.f64 (/.f64 (PI.f64) k) n) (*.f64 (*.f64 n (PI.f64)) (+.f64 (*.f64 -2 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (*.f64 k (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))))
(fma.f64 2 (*.f64 (PI.f64) (/.f64 n k)) (*.f64 n (*.f64 (PI.f64) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (+.f64 -2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))
(+.f64 (*.f64 -1/3 (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) (+.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) (+.f64 (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))) (*.f64 -2 (*.f64 n (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))))
(fma.f64 -1/3 (*.f64 (*.f64 k k) (*.f64 (*.f64 n (PI.f64)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (fma.f64 k (*.f64 (*.f64 n (PI.f64)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (*.f64 -2 (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))))
(fma.f64 -1/3 (*.f64 k (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) (fma.f64 2 (/.f64 (*.f64 n (PI.f64)) k) (fma.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 n (*.f64 (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) -2)))))
(fma.f64 2 (*.f64 (/.f64 (PI.f64) k) n) (fma.f64 -1/3 (*.f64 k (*.f64 k (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) (*.f64 (*.f64 n (PI.f64)) (+.f64 (*.f64 -2 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (*.f64 k (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))))
(fma.f64 2 (*.f64 (PI.f64) (/.f64 n k)) (*.f64 (*.f64 n (PI.f64)) (+.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (+.f64 -2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3) (*.f64 -1/3 (*.f64 k k))))))
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
(exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 n (*.f64 2 (PI.f64)))
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (*.f64 2 (*.f64 n (PI.f64))))
(fma.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (*.f64 2 (*.f64 n (PI.f64))))
(fma.f64 2 (*.f64 n (PI.f64)) (*.f64 -2 (*.f64 (*.f64 k (*.f64 n (PI.f64))) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(*.f64 (PI.f64) (+.f64 (*.f64 n 2) (*.f64 k (*.f64 n (*.f64 -2 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))
(*.f64 n (*.f64 (PI.f64) (+.f64 (*.f64 (*.f64 k -2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 2)))
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))))))
(fma.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (fma.f64 2 (*.f64 n (PI.f64)) (*.f64 (*.f64 (*.f64 n (PI.f64)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (*.f64 k k))))
(fma.f64 -2 (*.f64 (*.f64 k (*.f64 n (PI.f64))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (fma.f64 2 (*.f64 n (PI.f64)) (*.f64 (*.f64 (*.f64 k k) (*.f64 n (PI.f64))) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))
(fma.f64 n (*.f64 2 (PI.f64)) (*.f64 k (*.f64 (*.f64 n (PI.f64)) (+.f64 (*.f64 -2 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (*.f64 k (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))))
(*.f64 (PI.f64) (+.f64 (*.f64 n 2) (*.f64 k (*.f64 n (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (+.f64 -2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))))
(+.f64 (*.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 -1/3 (*.f64 (pow.f64 k 3) (*.f64 n (*.f64 (PI.f64) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))) (+.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64)))))))
(fma.f64 -2 (*.f64 k (*.f64 n (*.f64 (PI.f64) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (fma.f64 -1/3 (*.f64 (*.f64 (*.f64 n (PI.f64)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)) (pow.f64 k 3)) (fma.f64 2 (*.f64 n (PI.f64)) (*.f64 (*.f64 (*.f64 n (PI.f64)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (*.f64 k k)))))
(fma.f64 -2 (*.f64 (*.f64 k (*.f64 n (PI.f64))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (fma.f64 -1/3 (*.f64 (*.f64 n (PI.f64)) (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3) (pow.f64 k 3))) (fma.f64 2 (*.f64 n (PI.f64)) (*.f64 (*.f64 (*.f64 k k) (*.f64 n (PI.f64))) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))))
(fma.f64 -1/3 (*.f64 n (*.f64 (PI.f64) (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3) (pow.f64 k 3)))) (fma.f64 n (*.f64 2 (PI.f64)) (*.f64 k (*.f64 (*.f64 n (PI.f64)) (+.f64 (*.f64 -2 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (*.f64 k (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))))))
(*.f64 n (+.f64 (*.f64 (PI.f64) (+.f64 2 (*.f64 (*.f64 -1/3 (pow.f64 k 3)) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3)))) (*.f64 k (*.f64 (PI.f64) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (+.f64 -2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))

eval221.0ms (2.2%)

Compiler

Compiled 11169 to 6026 computations (46% saved)

prune126.0ms (1.3%)

Pruning

42 alts after pruning (32 fresh and 10 done)

PrunedKeptTotal
New67025695
Fresh7714
Picked011
Done099
Total67742719
Error
0b
Counts
719 → 42
Alt Table
Click to see full alt table
StatusErrorProgram
21.3b
(/.f64 (pow.f64 k -1/2) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2)))
✓0.4b
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
21.2b
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
32.9b
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
✓32.8b
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
32.9b
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
33.0b
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
32.5b
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))
✓32.8b
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))
32.8b
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n 2)) k))
21.2b
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
21.2b
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n)))
✓32.8b
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 (PI.f64) (*.f64 n 2)))))
34.6b
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -1/2))
33.0b
(pow.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 3/2)
14.1b
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 1/2))
11.9b
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))
32.8b
(sqrt.f64 (*.f64 (*.f64 (/.f64 1 k) (+.f64 n n)) (PI.f64)))
32.8b
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
32.7b
(pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -3/2)
35.3b
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/4) 2/3)
✓13.9b
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k))
32.8b
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) 1) (/.f64 2 k)))
21.2b
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
33.0b
(pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 3/2)
0.4b
(*.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2)))
48.0b
(pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 3) -1/6)
35.3b
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/6) 3)
✓11.9b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
40.4b
(cbrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3/2))
50.9b
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 9/2) 1/9)
32.8b
(sqrt.f64 (*.f64 (/.f64 1 (/.f64 k (PI.f64))) (+.f64 n n)))
✓40.5b
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2))
0.4b
(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))))
✓11.9b
(sqrt.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))
32.8b
(sqrt.f64 (/.f64 1 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
✓12.0b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
✓0.3b
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
32.4b
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/2)
41.9b
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2) 1/3)
40.5b
(cbrt.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))) 3/2))
32.8b
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
Compiler

Compiled 546 to 432 computations (20.9% saved)

regimes262.0ms (2.6%)

Counts
78 → 1
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n 2)) k))
(sqrt.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))
(sqrt.f64 (*.f64 (*.f64 (/.f64 1 k) (+.f64 n n)) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) 1) (/.f64 2 k)))
(sqrt.f64 (*.f64 (/.f64 1 (/.f64 k (PI.f64))) (+.f64 n n)))
(sqrt.f64 (/.f64 1 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 (PI.f64) (*.f64 n 2)))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n 2)))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(pow.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -3/2)
(pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 3/2)
(cbrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3/2))
(cbrt.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))) 3/2))
(sqrt.f64 (*.f64 (pow.f64 (/.f64 k (PI.f64)) -1) (*.f64 n 2)))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -1/2))
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/4) 2/3)
(pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 3) -1/6)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/6) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 9/2) 1/9)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2) 1/3)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2) 1/3)
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) -1/2)
(sqrt.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(sqrt.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 1 (neg.f64 k))))
(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
(/.f64 (pow.f64 k -1/2) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2)))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k))
(/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k 1/2 -1/2)))
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 1/2))
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1/2))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))
(*.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2)))
(*.f64 (exp.f64 (*.f64 -1/2 (log.f64 k))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))
(/.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
(pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 1/4) (pow.f64 k 1/4)) 2)
(*.f64 (pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (expm1.f64 (log1p.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2)))
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(/.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))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 k 2))))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4))))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 (*.f64 k -1/2) (sqrt.f64 2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 2))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (+.f64 (+.f64 1 (*.f64 (*.f64 -1/2 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 (*.f64 1/8 (*.f64 k k)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))) (sqrt.f64 k))
Outputs
(/.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))
Calls

5 calls:

58.0ms
n
49.0ms
(*.f64 (*.f64 2 (PI.f64)) n)
47.0ms
k
47.0ms
(*.f64 (*.f64 2 (PI.f64)) n)
29.0ms
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
Results
ErrorSegmentsBranch
0.3b1k
0.3b1n
0.3b1(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
0.3b1(*.f64 (*.f64 2 (PI.f64)) n)
0.3b1(*.f64 (*.f64 2 (PI.f64)) n)
Compiler

Compiled 1078 to 656 computations (39.1% saved)

regimes227.0ms (2.3%)

Counts
71 → 1
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n 2)) k))
(sqrt.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))
(sqrt.f64 (*.f64 (*.f64 (/.f64 1 k) (+.f64 n n)) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) 1) (/.f64 2 k)))
(sqrt.f64 (*.f64 (/.f64 1 (/.f64 k (PI.f64))) (+.f64 n n)))
(sqrt.f64 (/.f64 1 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 (PI.f64) (*.f64 n 2)))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n 2)))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(pow.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -3/2)
(pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 3/2)
(cbrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3/2))
(cbrt.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))) 3/2))
(sqrt.f64 (*.f64 (pow.f64 (/.f64 k (PI.f64)) -1) (*.f64 n 2)))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -1/2))
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/4) 2/3)
(pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 3) -1/6)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/6) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 9/2) 1/9)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2) 1/3)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2) 1/3)
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) -1/2)
(sqrt.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(sqrt.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 1 (neg.f64 k))))
(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
(/.f64 (pow.f64 k -1/2) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2)))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k))
(/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k 1/2 -1/2)))
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 1/2))
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1/2))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))
(*.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) -1/2)))
(*.f64 (exp.f64 (*.f64 -1/2 (log.f64 k))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))
(/.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
(pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 1/4) (pow.f64 k 1/4)) 2)
(*.f64 (pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (expm1.f64 (log1p.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2)))
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
Outputs
(/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k 1/2 -1/2)))
Calls

5 calls:

45.0ms
k
44.0ms
(*.f64 (*.f64 2 (PI.f64)) n)
44.0ms
n
43.0ms
(*.f64 (*.f64 2 (PI.f64)) n)
23.0ms
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
Results
ErrorSegmentsBranch
0.3b1k
0.3b1n
0.3b1(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
0.3b1(*.f64 (*.f64 2 (PI.f64)) n)
0.3b1(*.f64 (*.f64 2 (PI.f64)) n)
Compiler

Compiled 916 to 556 computations (39.3% saved)

regimes281.0ms (2.8%)

Counts
53 → 1
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n 2)) k))
(sqrt.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))
(sqrt.f64 (*.f64 (*.f64 (/.f64 1 k) (+.f64 n n)) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) 1) (/.f64 2 k)))
(sqrt.f64 (*.f64 (/.f64 1 (/.f64 k (PI.f64))) (+.f64 n n)))
(sqrt.f64 (/.f64 1 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 (PI.f64) (*.f64 n 2)))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n 2)))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(pow.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -3/2)
(pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 3/2)
(cbrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3/2))
(cbrt.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))) 3/2))
(sqrt.f64 (*.f64 (pow.f64 (/.f64 k (PI.f64)) -1) (*.f64 n 2)))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -1/2))
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/4) 2/3)
(pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 3) -1/6)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/6) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 9/2) 1/9)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2) 1/3)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2) 1/3)
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) -1/2)
(sqrt.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(sqrt.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 1 (neg.f64 k))))
(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
(/.f64 (pow.f64 k -1/2) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2)))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k))
Outputs
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
Calls

4 calls:

74.0ms
(*.f64 (*.f64 2 (PI.f64)) n)
72.0ms
k
70.0ms
n
39.0ms
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
Results
ErrorSegmentsBranch
0.3b1k
0.3b1n
0.3b1(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
0.3b1(*.f64 (*.f64 2 (PI.f64)) n)
Compiler

Compiled 606 to 344 computations (43.2% saved)

regimes219.0ms (2.2%)

Counts
46 → 1
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n 2)) k))
(sqrt.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))
(sqrt.f64 (*.f64 (*.f64 (/.f64 1 k) (+.f64 n n)) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) 1) (/.f64 2 k)))
(sqrt.f64 (*.f64 (/.f64 1 (/.f64 k (PI.f64))) (+.f64 n n)))
(sqrt.f64 (/.f64 1 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 (PI.f64) (*.f64 n 2)))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n 2)))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(pow.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -3/2)
(pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 3/2)
(cbrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3/2))
(cbrt.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))) 3/2))
(sqrt.f64 (*.f64 (pow.f64 (/.f64 k (PI.f64)) -1) (*.f64 n 2)))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -1/2))
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/4) 2/3)
(pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 3) -1/6)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/6) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 9/2) 1/9)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2) 1/3)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2) 1/3)
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) -1/2)
(sqrt.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(sqrt.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 1 (neg.f64 k))))
(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))))
Outputs
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
Calls

3 calls:

63.0ms
(*.f64 (*.f64 2 (PI.f64)) n)
62.0ms
n
62.0ms
k
Results
ErrorSegmentsBranch
0.4b1k
0.4b1n
0.4b1(*.f64 (*.f64 2 (PI.f64)) n)
Compiler

Compiled 494 to 269 computations (45.5% saved)

regimes93.0ms (0.9%)

Counts
43 → 1
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n 2)) k))
(sqrt.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))
(sqrt.f64 (*.f64 (*.f64 (/.f64 1 k) (+.f64 n n)) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) 1) (/.f64 2 k)))
(sqrt.f64 (*.f64 (/.f64 1 (/.f64 k (PI.f64))) (+.f64 n n)))
(sqrt.f64 (/.f64 1 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 (PI.f64) (*.f64 n 2)))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n 2)))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(pow.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -3/2)
(pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 3/2)
(cbrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3/2))
(cbrt.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))) 3/2))
(sqrt.f64 (*.f64 (pow.f64 (/.f64 k (PI.f64)) -1) (*.f64 n 2)))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -1/2))
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/4) 2/3)
(pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 3) -1/6)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/6) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 9/2) 1/9)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2) 1/3)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2) 1/3)
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) -1/2)
(sqrt.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
Outputs
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
Calls

2 calls:

45.0ms
n
25.0ms
k
Results
ErrorSegmentsBranch
0.4b1k
0.4b1n
Compiler

Compiled 440 to 231 computations (47.5% saved)

regimes160.0ms (1.6%)

Counts
42 → 2
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n 2)) k))
(sqrt.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))
(sqrt.f64 (*.f64 (*.f64 (/.f64 1 k) (+.f64 n n)) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) 1) (/.f64 2 k)))
(sqrt.f64 (*.f64 (/.f64 1 (/.f64 k (PI.f64))) (+.f64 n n)))
(sqrt.f64 (/.f64 1 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 (PI.f64) (*.f64 n 2)))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n 2)))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(pow.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -3/2)
(pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 3/2)
(cbrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3/2))
(cbrt.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))) 3/2))
(sqrt.f64 (*.f64 (pow.f64 (/.f64 k (PI.f64)) -1) (*.f64 n 2)))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -1/2))
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/4) 2/3)
(pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 3) -1/6)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/6) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 9/2) 1/9)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2) 1/3)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2) 1/3)
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) -1/2)
(sqrt.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
Outputs
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k))
Calls

2 calls:

103.0ms
n
43.0ms
k
Results
ErrorSegmentsBranch
0.3b2k
9.5b5n
Compiler

Compiled 426 to 222 computations (47.9% saved)

bsearch32.0ms (0.3%)

Algorithm
1×binary-search
Steps
TimeLeftRight
32.0ms
4.3348438571376286e-55
6.517613717385855e-55
Compiler

Compiled 23 to 19 computations (17.4% saved)

regimes157.0ms (1.6%)

Counts
41 → 2
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n 2)) k))
(sqrt.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))
(sqrt.f64 (*.f64 (*.f64 (/.f64 1 k) (+.f64 n n)) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) 1) (/.f64 2 k)))
(sqrt.f64 (*.f64 (/.f64 1 (/.f64 k (PI.f64))) (+.f64 n n)))
(sqrt.f64 (/.f64 1 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 (PI.f64) (*.f64 n 2)))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n 2)))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(pow.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -3/2)
(pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 3/2)
(cbrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3/2))
(cbrt.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))) 3/2))
(sqrt.f64 (*.f64 (pow.f64 (/.f64 k (PI.f64)) -1) (*.f64 n 2)))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -1/2))
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/4) 2/3)
(pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 3) -1/6)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/6) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 9/2) 1/9)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2) 1/3)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2) 1/3)
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) -1/2)
(sqrt.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (/.f64 1 k)))
Outputs
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(pow.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) -1/2)
Calls

2 calls:

101.0ms
n
44.0ms
k
Results
ErrorSegmentsBranch
0.3b2k
9.5b5n
Compiler

Compiled 412 to 212 computations (48.5% saved)

bsearch32.0ms (0.3%)

Algorithm
1×binary-search
Steps
TimeLeftRight
32.0ms
6.517613717385855e-55
2.953640797973544e-54
Compiler

Compiled 23 to 19 computations (17.4% saved)

regimes156.0ms (1.5%)

Counts
39 → 2
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n 2)) k))
(sqrt.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))
(sqrt.f64 (*.f64 (*.f64 (/.f64 1 k) (+.f64 n n)) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) 1) (/.f64 2 k)))
(sqrt.f64 (*.f64 (/.f64 1 (/.f64 k (PI.f64))) (+.f64 n n)))
(sqrt.f64 (/.f64 1 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 (PI.f64) (*.f64 n 2)))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n 2)))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(pow.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -3/2)
(pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 3/2)
(cbrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3/2))
(cbrt.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))) 3/2))
(sqrt.f64 (*.f64 (pow.f64 (/.f64 k (PI.f64)) -1) (*.f64 n 2)))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -1/2))
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/4) 2/3)
(pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 3) -1/6)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/6) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 9/2) 1/9)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2) 1/3)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2) 1/3)
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
Outputs
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
Calls

2 calls:

102.0ms
n
41.0ms
k
Results
ErrorSegmentsBranch
0.3b2k
9.7b5n
Compiler

Compiled 385 to 194 computations (49.6% saved)

bsearch32.0ms (0.3%)

Algorithm
1×binary-search
Steps
TimeLeftRight
32.0ms
4.3348438571376286e-55
6.517613717385855e-55
Compiler

Compiled 23 to 19 computations (17.4% saved)

regimes70.0ms (0.7%)

Counts
38 → 2
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n 2)) k))
(sqrt.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))
(sqrt.f64 (*.f64 (*.f64 (/.f64 1 k) (+.f64 n n)) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) 1) (/.f64 2 k)))
(sqrt.f64 (*.f64 (/.f64 1 (/.f64 k (PI.f64))) (+.f64 n n)))
(sqrt.f64 (/.f64 1 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 (PI.f64) (*.f64 n 2)))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n 2)))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(pow.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -3/2)
(pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 3/2)
(cbrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3/2))
(cbrt.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))) 3/2))
(sqrt.f64 (*.f64 (pow.f64 (/.f64 k (PI.f64)) -1) (*.f64 n 2)))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -1/2))
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/4) 2/3)
(pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 3) -1/6)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/6) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 9/2) 1/9)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/2) 1/3)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2) 1/3)
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
Outputs
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 9/2) 1/9)
Calls

2 calls:

37.0ms
k
23.0ms
n
Results
ErrorSegmentsBranch
15.7b2k
21.2b1n
Compiler

Compiled 373 to 187 computations (49.9% saved)

bsearch82.0ms (0.8%)

Algorithm
1×binary-search
Steps
TimeLeftRight
81.0ms
3.774528745462614e+119
3.012887082174734e+122
Compiler

Compiled 239 to 187 computations (21.8% saved)

regimes62.0ms (0.6%)

Counts
34 → 2
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n 2)) k))
(sqrt.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))
(sqrt.f64 (*.f64 (*.f64 (/.f64 1 k) (+.f64 n n)) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) 1) (/.f64 2 k)))
(sqrt.f64 (*.f64 (/.f64 1 (/.f64 k (PI.f64))) (+.f64 n n)))
(sqrt.f64 (/.f64 1 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 (PI.f64) (*.f64 n 2)))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n 2)))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(pow.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -3/2)
(pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 3/2)
(cbrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3/2))
(cbrt.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))) 3/2))
(sqrt.f64 (*.f64 (pow.f64 (/.f64 k (PI.f64)) -1) (*.f64 n 2)))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -1/2))
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/4) 2/3)
(pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 3) -1/6)
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 1/6) 3)
Outputs
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 3) -1/6)
Calls

2 calls:

34.0ms
k
18.0ms
n
Results
ErrorSegmentsBranch
16.9b2k
21.2b1n
Compiler

Compiled 329 to 165 computations (49.8% saved)

bsearch83.0ms (0.8%)

Algorithm
1×binary-search
Steps
TimeLeftRight
83.0ms
1.4013181559535002e+128
5.334597919029146e+132
Compiler

Compiled 239 to 187 computations (21.8% saved)

regimes59.0ms (0.6%)

Counts
32 → 2
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n 2)) k))
(sqrt.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))
(sqrt.f64 (*.f64 (*.f64 (/.f64 1 k) (+.f64 n n)) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) 1) (/.f64 2 k)))
(sqrt.f64 (*.f64 (/.f64 1 (/.f64 k (PI.f64))) (+.f64 n n)))
(sqrt.f64 (/.f64 1 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 (PI.f64) (*.f64 n 2)))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n 2)))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(pow.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -3/2)
(pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 3/2)
(cbrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3/2))
(cbrt.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))) 3/2))
(sqrt.f64 (*.f64 (pow.f64 (/.f64 k (PI.f64)) -1) (*.f64 n 2)))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)) 3/2))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -1/2))
(pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 3/4) 2/3)
Outputs
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(cbrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3/2))
Calls

2 calls:

32.0ms
k
18.0ms
n
Results
ErrorSegmentsBranch
20.0b2k
21.2b1n
Compiler

Compiled 307 to 157 computations (48.9% saved)

bsearch72.0ms (0.7%)

Algorithm
1×binary-search
Steps
TimeLeftRight
72.0ms
3.898334757606448e+170
1.1362093997082586e+172
Compiler

Compiled 205 to 159 computations (22.4% saved)

regimes39.0ms (0.4%)

Counts
26 → 1
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n 2)) k))
(sqrt.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))
(sqrt.f64 (*.f64 (*.f64 (/.f64 1 k) (+.f64 n n)) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) 1) (/.f64 2 k)))
(sqrt.f64 (*.f64 (/.f64 1 (/.f64 k (PI.f64))) (+.f64 n n)))
(sqrt.f64 (/.f64 1 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 (PI.f64) (*.f64 n 2)))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n 2)))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(pow.f64 (cbrt.f64 (/.f64 (PI.f64) (/.f64 k (+.f64 n n)))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))) -3/2)
(pow.f64 (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n))) 3/2)
Outputs
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
Calls

2 calls:

16.0ms
k
15.0ms
n
Results
ErrorSegmentsBranch
21.2b1k
21.2b1n
Compiler

Compiled 245 to 127 computations (48.2% saved)

regimes30.0ms (0.3%)

Counts
22 → 1
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n 2)) k))
(sqrt.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))
(sqrt.f64 (*.f64 (*.f64 (/.f64 1 k) (+.f64 n n)) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) 1) (/.f64 2 k)))
(sqrt.f64 (*.f64 (/.f64 1 (/.f64 k (PI.f64))) (+.f64 n n)))
(sqrt.f64 (/.f64 1 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 (PI.f64) (*.f64 n 2)))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (+.f64 n n)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n 2)))
Outputs
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
Calls

2 calls:

12.0ms
n
12.0ms
k
Results
ErrorSegmentsBranch
21.2b1k
21.2b1n
Compiler

Compiled 205 to 112 computations (45.4% saved)

regimes23.0ms (0.2%)

Counts
14 → 1
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n 2)) k))
(sqrt.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/2)
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n))))
(sqrt.f64 (*.f64 (*.f64 (/.f64 1 k) (+.f64 n n)) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 (*.f64 (PI.f64) n) 1) (/.f64 2 k)))
(sqrt.f64 (*.f64 (/.f64 1 (/.f64 k (PI.f64))) (+.f64 n n)))
(sqrt.f64 (/.f64 1 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 (PI.f64) (*.f64 n 2)))))
Outputs
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/2)
Calls

2 calls:

9.0ms
k
8.0ms
n
Results
ErrorSegmentsBranch
32.4b1k
32.4b1n
Compiler

Compiled 133 to 78 computations (41.4% saved)

regimes13.0ms (0.1%)

Accuracy

Total -0.1b remaining (-0.4%)

Threshold costs -0.1b (-0.4%)

Counts
7 → 1
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) (*.f64 n 2)) k))
(sqrt.f64 (/.f64 (PI.f64) (/.f64 k (*.f64 n 2))))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (*.f64 n 2)))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
Outputs
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
Calls

2 calls:

6.0ms
n
5.0ms
k
Results
ErrorSegmentsBranch
32.8b1k
32.8b1n
Compiler

Compiled 64 to 42 computations (34.4% saved)

simplify22.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
16×*-commutative_binary64
3×+-commutative_binary64
2×sub-neg_binary64
1×neg-sub0_binary64
1×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0924294967692
11124294967692
21154294967692
31174294967692
41184294967692
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(/.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))
(/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k 1/2 -1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(if (<=.f64 k 5983598550981429/13803492693581127574869511724554050904902217944340773110325048447598592) (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)))
(if (<=.f64 k 4498291666375989/6901746346790563787434755862277025452451108972170386555162524223799296) (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (pow.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) -1/2))
(if (<=.f64 k 5983598550981429/13803492693581127574869511724554050904902217944340773110325048447598592) (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(if (<=.f64 k 299999999999999985973795348253010063862768424311798262668617031460247791306667679785206764169300903681367886668883208175616) (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 9/2) 1/9))
(if (<=.f64 k 5200000000000000015356960406509804870816830180138703630444862410636594257378387555038578091125553144184757724330180935460549988188160) (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 3) -1/6))
(if (<=.f64 k 11200000000000000170968481385217917869599542302017249677047835410128996928237739026487709290074669030841695286866056523448207421791633361339993966472888516873425244418736128) (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (cbrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3/2)))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/2)
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
Outputs
(/.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))
(/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k 1/2 -1/2)))
(/.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k 1/2 -1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (-.f64 1 k) 2)))
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (-.f64 1 k) 2)))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 (*.f64 k -1/2) 1/2)) (sqrt.f64 k))
(if (<=.f64 k 5983598550981429/13803492693581127574869511724554050904902217944340773110325048447598592) (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (-.f64 1 k)) k)))
(if (<=.f64 k 4498291666375989/6901746346790563787434755862277025452451108972170386555162524223799296) (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (pow.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) -1/2))
(if (<=.f64 k 4498291666375989/6901746346790563787434755862277025452451108972170386555162524223799296) (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (pow.f64 (/.f64 k (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) -1/2))
(if (<=.f64 k 5983598550981429/13803492693581127574869511724554050904902217944340773110325048447598592) (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(if (<=.f64 k 5983598550981429/13803492693581127574869511724554050904902217944340773110325048447598592) (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)))
(if (<=.f64 k 299999999999999985973795348253010063862768424311798262668617031460247791306667679785206764169300903681367886668883208175616) (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (pow.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) k) (+.f64 n n)) 9/2) 1/9))
(if (<=.f64 k 299999999999999985973795348253010063862768424311798262668617031460247791306667679785206764169300903681367886668883208175616) (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (pow.f64 (pow.f64 (*.f64 (+.f64 n n) (/.f64 (PI.f64) k)) 9/2) 1/9))
(if (<=.f64 k 5200000000000000015356960406509804870816830180138703630444862410636594257378387555038578091125553144184757724330180935460549988188160) (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) 3) -1/6))
(if (<=.f64 k 11200000000000000170968481385217917869599542302017249677047835410128996928237739026487709290074669030841695286866056523448207421791633361339993966472888516873425244418736128) (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (cbrt.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -3/2)))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (+.f64 n n)) -1/2)
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
Compiler

Compiled 309 to 228 computations (26.2% saved)

soundness105.0ms (1%)

Algorithm
1×egg-herbie
Rules
667×associate-/l*_binary64
561×associate-/r*_binary64
453×div-sub_binary64
450×distribute-frac-neg_binary64
416×distribute-rgt-in_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01425
13222
26822
314122
436022
598320
6221320
7566320
Stop Event
1×node limit
Compiler

Compiled 350 to 293 computations (16.3% saved)

end147.0ms (1.5%)

Compiler

Compiled 279 to 153 computations (45.2% saved)

Profiling

Loading profile data...