Details

Time bar (total: 8.6s)

analyze115.0ms (1.3%)

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)

sample2.9s (33.3%)

Results
1.4s8256×body256valid
862.0ms1436×body1024invalid
350.0ms2286×body256invalid
220.0ms653×body512invalid

preprocess68.0ms (0.8%)

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 (0.5%)

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 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶0.4b
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
Compiler

Compiled 33 to 27 computations (18.2% saved)

localize29.0ms (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)
✓0.2b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓0.2b
(/.f64 1 (sqrt.f64 k))
Compiler

Compiled 56 to 38 computations (32.1% saved)

series77.0ms (0.9%)

Counts
4 → 48
Calls

18 calls:

TimeVariablePointExpression
29.0ms
n
@0
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
25.0ms
n
@-inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
8.0ms
n
@inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
5.0ms
k
@-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)))

rewrite79.0ms (0.9%)

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))))))

simplify61.0ms (0.7%)

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))))))
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(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 (0.3%)

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)
✓0.3b
(/.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)

series10.0ms (0.1%)

Counts
3 → 48
Calls

15 calls:

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

rewrite72.0ms (0.8%)

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
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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))))))

simplify79.0ms (0.9%)

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)))
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(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(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))

eval106.0ms (1.2%)

Compiler

Compiled 4815 to 3266 computations (32.2% saved)

prune62.0ms (0.7%)

Pruning

21 alts after pruning (20 fresh and 1 done)

PrunedKeptTotal
New21420234
Fresh000
Picked101
Done011
Total21521236
Error
0.0b
Counts
236 → 21
Alt Table
Click to see full alt table
StatusErrorProgram
3.0b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 (log.f64 (*.f64 2 (*.f64 (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)))))
0.5b
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (pow.f64 2 (-.f64 1/2 (/.f64 k 2))) (pow.f64 (*.f64 (PI.f64) n) (-.f64 1/2 (/.f64 k 2)))))
✓0.4b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
14.3b
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))
20.9b
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3) 1/3)
0.4b
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 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))
22.1b
(/.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)))))
0.4b
(*.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)))
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))))
▶12.2b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
▶0.6b
(/.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)))))
0.4b
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
3.1b
(*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))
▶12.7b
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
3.3b
(*.f64 (exp.f64 (*.f64 -1/2 (log.f64 k))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶22.0b
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
3.3b
(*.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
22.0b
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 k))
Compiler

Compiled 818 to 663 computations (18.9% saved)

localize34.0ms (0.4%)

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)))
✓0.3b
(/.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))
Compiler

Compiled 70 to 46 computations (34.3% saved)

series28.0ms (0.3%)

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

rewrite95.0ms (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 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simplify90.0ms (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)))

localize22.0ms (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)
✓0.1b
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))
0.2b
(*.f64 (PI.f64) n)
✓11.4b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
Compiler

Compiled 50 to 28 computations (44% saved)

series20.0ms (0.2%)

Counts
3 → 60
Calls

18 calls:

TimeVariablePointExpression
6.0ms
n
@-inf
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
2.0ms
k
@0
(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))
1.0ms
k
@inf
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
1.0ms
n
@0
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))

rewrite82.0ms (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))
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))
(/.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 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 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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))))))

simplify66.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
581×associate-+l+_binary64
473×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
27801289
342321184
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))
(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)))
(/.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)
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))
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(*.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 (*.f64 n (PI.f64)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(fma.f64 2 (/.f64 (*.f64 n (PI.f64)) k) (*.f64 (*.f64 -2 (*.f64 n (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 n (*.f64 (PI.f64) -2))))
(*.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 (*.f64 n (PI.f64)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))
(fma.f64 2 (/.f64 (*.f64 n (PI.f64)) k) (fma.f64 k (*.f64 (*.f64 n (PI.f64)) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2)) (*.f64 (*.f64 -2 (*.f64 n (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 (PI.f64) (/.f64 n k)) (*.f64 (*.f64 (PI.f64) (*.f64 n (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 (*.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 n (*.f64 2 (PI.f64)))) 3) (*.f64 k k))) (fma.f64 2 (/.f64 (*.f64 n (PI.f64)) k) (fma.f64 k (*.f64 (*.f64 n (PI.f64)) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2)) (*.f64 (*.f64 -2 (*.f64 n (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 (PI.f64) (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3) -1/3))) (*.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 (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 (*.f64 k 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)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (PI.f64) n)
0.2b
(/.f64 1 (sqrt.f64 k))
✓0.3b
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
✓0.5b
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))
Compiler

Compiled 41 to 21 computations (48.8% saved)

series8.0ms (0.1%)

Counts
2 → 0
Calls

9 calls:

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

rewrite67.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
606×log-prod_binary64
426×pow-prod-down_binary64
296×pow2_binary64
261×pow-unpow_binary64
211×pow1/3_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01325
126123
2301223
Stop Event
1×node limit
Counts
2 → 58
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
Outputs
((#(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 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) 2)) (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 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 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/6) 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 pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x 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 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4)) 2))))) (#(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 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/4)) (pow.f64 k 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 1) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (cbrt.f64 k)) (pow.f64 k 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) -1) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2) (pow.f64 k 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))) 1) 1))))))

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
58 → 58
Calls
Call 1
Inputs
Outputs

localize35.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

Compiled 66 to 46 computations (30.3% saved)

series99.0ms (1.2%)

Counts
4 → 60
Calls

21 calls:

TimeVariablePointExpression
53.0ms
n
@0
(/.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)))))
15.0ms
n
@-inf
(/.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)))))
10.0ms
n
@inf
(/.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)))))
4.0ms
k
@0
(/.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)))))
4.0ms
k
@0
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))

rewrite94.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
869×log-prod_binary64
287×expm1-udef_binary64
287×log1p-udef_binary64
271×log-pow_binary64
231×log-div_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01470
132770
2458860
Stop Event
1×node limit
Counts
4 → 140
Calls
Call 1
Inputs
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))
(/.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 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (/.f64 k 2))))
(pow.f64 n (-.f64 1/2 (/.f64 k 2)))
Outputs
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simplify65.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
700×associate-*r*_binary64
665×associate-*l*_binary64
502×unswap-sqr_binary64
394×fma-def_binary64
276×*-commutative_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0951248
12851056
29601020
354371020
Stop Event
1×node limit
Counts
200 → 171
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64)))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 (PI.f64)))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2))) (sqrt.f64 (PI.f64))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 (PI.f64)))) (+.f64 (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 3))) (sqrt.f64 (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2))) (sqrt.f64 (PI.f64)))))))
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k)))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k)))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k)))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k)))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k))))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k))))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k))))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k))))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k)))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k)))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k)))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k)))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))))
(exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k)))))
(exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k)))))
(exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k)))))
(exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k)))))
(exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))
(exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))
(exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))
(exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))
(sqrt.f64 n)
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 k (log.f64 n)) (sqrt.f64 n))) (sqrt.f64 n))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 k (log.f64 n)) (sqrt.f64 n))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 n) 2)) (sqrt.f64 n))) (sqrt.f64 n)))
(+.f64 (*.f64 -1/48 (*.f64 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 n) 3)) (sqrt.f64 n))) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 k (log.f64 n)) (sqrt.f64 n))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 n) 2)) (sqrt.f64 n))) (sqrt.f64 n))))
(pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
Outputs
(*.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64)))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 (PI.f64)))))
(fma.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64)) (*.f64 -1/2 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 (sqrt.f64 2) k) (log.f64 (*.f64 2 (PI.f64)))))))
(*.f64 (sqrt.f64 (PI.f64)) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 -1/2 (sqrt.f64 2)) (*.f64 k (log.f64 (*.f64 2 (PI.f64)))))))
(*.f64 (sqrt.f64 (PI.f64)) (fma.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 (sqrt.f64 2) k)) (sqrt.f64 2)))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2))) (sqrt.f64 (PI.f64))))))
(fma.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64)) (fma.f64 -1/2 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 (sqrt.f64 2) k) (log.f64 (*.f64 2 (PI.f64))))) (*.f64 1/8 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k k)) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2))))))
(fma.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (+.f64 (*.f64 (*.f64 -1/2 (sqrt.f64 2)) (*.f64 k (log.f64 (*.f64 2 (PI.f64))))) (*.f64 (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 k k))) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2)))))
(*.f64 (sqrt.f64 (PI.f64)) (+.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 1/8 (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2))) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (PI.f64))))))) (sqrt.f64 2)))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 (PI.f64)))) (+.f64 (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 3))) (sqrt.f64 (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2))) (sqrt.f64 (PI.f64)))))))
(fma.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64)) (fma.f64 -1/2 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 (sqrt.f64 2) k) (log.f64 (*.f64 2 (PI.f64))))) (fma.f64 -1/48 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 3)) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 3))) (*.f64 1/8 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k k)) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2)))))))
(+.f64 (*.f64 (sqrt.f64 (PI.f64)) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 -1/2 (sqrt.f64 2)) (*.f64 k (log.f64 (*.f64 2 (PI.f64))))))) (*.f64 (sqrt.f64 (PI.f64)) (+.f64 (*.f64 (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 k k))) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2)) (*.f64 (*.f64 -1/48 (sqrt.f64 2)) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 3))))))
(*.f64 (sqrt.f64 (PI.f64)) (+.f64 (fma.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 (sqrt.f64 2) k)) (sqrt.f64 2)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 1/8 (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2))) (*.f64 (*.f64 -1/48 (pow.f64 k 3)) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 3))))))
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k)))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.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)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k)))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.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)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k)))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.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)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k)))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.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)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k))))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.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)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k))))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.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)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k))))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.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)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k))))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.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)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.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)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.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)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.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)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) (exp.f64 (*.f64 (log.f64 (*.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 -1/2 k))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.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)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 -1/2)))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 -1/2)))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 -1/2)))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 -1/2)))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k)))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 -1/2)))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k)))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 -1/2)))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k)))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 -1/2)))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k)))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 -1/2)))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 -1/2)))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 -1/2)))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 -1/2)))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 -1/2)))
(exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k))))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k))))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k))))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k))))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k)))))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k)))))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k)))))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 -1 (*.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k)))))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(sqrt.f64 n)
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 k (log.f64 n)) (sqrt.f64 n))) (sqrt.f64 n))
(fma.f64 -1/2 (*.f64 k (*.f64 (log.f64 n) (sqrt.f64 n))) (sqrt.f64 n))
(*.f64 (sqrt.f64 n) (fma.f64 -1/2 (*.f64 k (log.f64 n)) 1))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 k (log.f64 n)) (sqrt.f64 n))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 n) 2)) (sqrt.f64 n))) (sqrt.f64 n)))
(fma.f64 -1/2 (*.f64 k (*.f64 (log.f64 n) (sqrt.f64 n))) (fma.f64 1/8 (*.f64 (*.f64 k k) (*.f64 (pow.f64 (log.f64 n) 2) (sqrt.f64 n))) (sqrt.f64 n)))
(+.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 n) (+.f64 (*.f64 -1/2 (*.f64 k (log.f64 n))) (*.f64 1/8 (*.f64 (*.f64 k k) (pow.f64 (log.f64 n) 2))))))
(fma.f64 (sqrt.f64 n) (fma.f64 -1/2 (*.f64 k (log.f64 n)) (*.f64 (*.f64 k k) (*.f64 1/8 (pow.f64 (log.f64 n) 2)))) (sqrt.f64 n))
(+.f64 (*.f64 -1/48 (*.f64 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 n) 3)) (sqrt.f64 n))) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 k (log.f64 n)) (sqrt.f64 n))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 n) 2)) (sqrt.f64 n))) (sqrt.f64 n))))
(fma.f64 -1/48 (*.f64 (pow.f64 k 3) (*.f64 (pow.f64 (log.f64 n) 3) (sqrt.f64 n))) (fma.f64 -1/2 (*.f64 k (*.f64 (log.f64 n) (sqrt.f64 n))) (fma.f64 1/8 (*.f64 (*.f64 k k) (*.f64 (pow.f64 (log.f64 n) 2) (sqrt.f64 n))) (sqrt.f64 n))))
(fma.f64 -1/48 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 n) (pow.f64 (log.f64 n) 3))) (+.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 n) (+.f64 (*.f64 -1/2 (*.f64 k (log.f64 n))) (*.f64 1/8 (*.f64 (*.f64 k k) (pow.f64 (log.f64 n) 2)))))))
(fma.f64 (sqrt.f64 n) (fma.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 n) 3)) (*.f64 -1/2 (*.f64 k (log.f64 n)))) (*.f64 (sqrt.f64 n) (fma.f64 1/8 (*.f64 k (*.f64 k (pow.f64 (log.f64 n) 2))) 1)))
(pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (fma.f64 -1/2 k 1/2))

localize32.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (PI.f64) n)
✓0.3b
(cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))
✓0.5b
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
11.4b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
Compiler

Compiled 79 to 47 computations (40.5% saved)

series181.0ms (2.1%)

Counts
2 → 48
Calls

12 calls:

TimeVariablePointExpression
87.0ms
k
@inf
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
23.0ms
k
@-inf
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
22.0ms
n
@-inf
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
20.0ms
n
@inf
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
20.0ms
n
@0
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)

rewrite72.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
721×log-prod_binary64
492×pow-unpow_binary64
369×pow2_binary64
250×pow1/3_binary64
248×expm1-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01540
132539
2385439
Stop Event
1×node limit
Counts
2 → 58
Calls
Call 1
Inputs
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
(cbrt.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 (*.f64 2 n) (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 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (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 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 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simplify87.0ms (1%)

Algorithm
1×egg-herbie
Rules
491×*-commutative_binary64
471×associate-+l+_binary64
469×unswap-sqr_binary64
444×associate-+r+_binary64
227×exp-sum_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01732996
15882407
222941972
358081806
Stop Event
1×node limit
Counts
106 → 92
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) 1/6) (pow.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) 1/3)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) 1/6) (pow.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) 1/3)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) 1/6) (pow.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) 1/3)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) 1/6) (pow.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) 1/3)))
(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))
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3)
(+.f64 (*.f64 k (+.f64 (*.f64 -1/3 (*.f64 (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 -1/6 (*.f64 (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3))
(+.f64 (*.f64 k (+.f64 (*.f64 -1/3 (*.f64 (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 -1/6 (*.f64 (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 (pow.f64 k 2) (+.f64 (*.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (+.f64 (*.f64 1/36 (*.f64 (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 2 (*.f64 (+.f64 (*.f64 1/12 (+.f64 (*.f64 -1 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 1/72 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2))))) (+.f64 (*.f64 1/18 (*.f64 (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 (+.f64 (*.f64 1/12 (+.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (*.f64 -1 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))) (*.f64 1/72 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3))))) (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3)))
(+.f64 (*.f64 k (+.f64 (*.f64 -1/3 (*.f64 (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 -1/6 (*.f64 (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 (pow.f64 k 2) (+.f64 (*.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (+.f64 (*.f64 1/36 (*.f64 (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 2 (*.f64 (+.f64 (*.f64 1/12 (+.f64 (*.f64 -1 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 1/72 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2))))) (+.f64 (*.f64 1/18 (*.f64 (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 (+.f64 (*.f64 1/12 (+.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (*.f64 -1 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))) (*.f64 1/72 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3))))) (+.f64 (*.f64 (pow.f64 k 3) (+.f64 (*.f64 -1/6 (*.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (*.f64 (+.f64 (*.f64 1/36 (*.f64 (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 2 (*.f64 (+.f64 (*.f64 1/12 (+.f64 (*.f64 -1 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 1/72 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2)))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (+.f64 (*.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (+.f64 (*.f64 -1/3 (*.f64 (+.f64 (*.f64 1/12 (+.f64 (*.f64 -1 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 1/72 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (*.f64 2 (*.f64 (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2) (+.f64 (*.f64 -1/1296 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)) (+.f64 (*.f64 -1/72 (*.f64 (+.f64 (*.f64 -1 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 1/36 (+.f64 (*.f64 -2 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)) (+.f64 (*.f64 3 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)) (*.f64 -1 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))))))))) (+.f64 (*.f64 -1/3 (*.f64 (+.f64 (*.f64 1/12 (+.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (*.f64 -1 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))) (*.f64 1/72 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (*.f64 (+.f64 (*.f64 -1/1296 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)) (+.f64 (*.f64 -1/72 (*.f64 (+.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (*.f64 -1 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 1/36 (+.f64 (*.f64 3 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)) (+.f64 (*.f64 -2 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)) (*.f64 -1 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))))) (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3)))))) (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3))))
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k))))) 3)
(*.f64 (*.f64 (sqrt.f64 -1) (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))) (log.f64 (/.f64 -1 k))))) 3)) (pow.f64 1 1/3))
(*.f64 (*.f64 (sqrt.f64 -1) (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))) (log.f64 (/.f64 -1 k))))) 3)) (pow.f64 1 1/3))
(*.f64 (*.f64 (sqrt.f64 -1) (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))) (log.f64 (/.f64 -1 k))))) 3)) (pow.f64 1 1/3))
(*.f64 (*.f64 (sqrt.f64 -1) (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))) (log.f64 (/.f64 -1 k))))) 3)) (pow.f64 1 1/3))
(pow.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k) 1/6)
(pow.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k) 1/6)
(pow.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k) 1/6)
(pow.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) k) 1/6)
(pow.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k) 1/6)
(pow.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k) 1/6)
(pow.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k) 1/6)
(pow.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k) 1/6)
(pow.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k) 1/6)
(pow.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k) 1/6)
(pow.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k) 1/6)
(pow.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k) 1/6)
(exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(+.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (*.f64 -1/6 (*.f64 k (*.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))
(+.f64 (*.f64 (pow.f64 k 2) (*.f64 (+.f64 (*.f64 1/12 (+.f64 (*.f64 -1 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 1/72 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (+.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (*.f64 -1/6 (*.f64 k (*.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))
(+.f64 (*.f64 (pow.f64 k 2) (*.f64 (+.f64 (*.f64 1/12 (+.f64 (*.f64 -1 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 1/72 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (+.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (+.f64 (*.f64 -1/6 (*.f64 k (*.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (*.f64 (pow.f64 k 3) (*.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (+.f64 (*.f64 -1/1296 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)) (+.f64 (*.f64 -1/72 (*.f64 (+.f64 (*.f64 -1 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 1/36 (+.f64 (*.f64 -2 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)) (+.f64 (*.f64 3 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)) (*.f64 -1 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))))))))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))))
(*.f64 (pow.f64 (*.f64 (sqrt.f64 -1) 1) 1/3) (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))) (log.f64 (/.f64 -1 k))))))
(*.f64 (pow.f64 (*.f64 (sqrt.f64 -1) 1) 1/3) (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))) (log.f64 (/.f64 -1 k))))))
(*.f64 (pow.f64 (*.f64 (sqrt.f64 -1) 1) 1/3) (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))) (log.f64 (/.f64 -1 k))))))
(*.f64 (pow.f64 (*.f64 (sqrt.f64 -1) 1) 1/3) (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))) (log.f64 (/.f64 -1 k))))))
Outputs
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) 1/6) (pow.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) 1/3)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 1/6) (cbrt.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 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1/6) 3))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 1/6) 3))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) 1/6) 3))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) 1/6) (pow.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) 1/3)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 1/6) (cbrt.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 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1/6) 3))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 1/6) 3))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) 1/6) 3))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) 1/6) (pow.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) 1/3)))
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(*.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) (/.f64 -1 k)) 1/6) (cbrt.f64 (sqrt.f64 -1)))
(*.f64 (pow.f64 (*.f64 (sqrt.f64 -1) 1) 1/3) (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))) (log.f64 (/.f64 -1 k))))))
(*.f64 (pow.f64 (exp.f64 1/6) (+.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (log.f64 (/.f64 -1 k)))) (cbrt.f64 (sqrt.f64 -1)))
(*.f64 (pow.f64 (exp.f64 1/6) (fma.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (log.f64 (/.f64 -1 k)))) (cbrt.f64 (sqrt.f64 -1)))
(*.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 1/6) (pow.f64 (/.f64 -1 k) 1/6)) (cbrt.f64 (sqrt.f64 -1)))
(*.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) (/.f64 -1 k)) 1/6) (cbrt.f64 (sqrt.f64 -1)))

eval352.0ms (4.1%)

Compiler

Compiled 17287 to 11771 computations (31.9% saved)

prune122.0ms (1.4%)

Pruning

24 alts after pruning (23 fresh and 1 done)

PrunedKeptTotal
New73020750
Fresh12315
Picked101
Done415
Total74724771
Error
0b
Counts
771 → 24
Alt Table
Click to see full alt table
StatusErrorProgram
10.6b
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)))))
22.1b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) 2))
0.4b
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
12.1b
(sqrt.f64 (/.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) n)) k))
▶0.4b
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
34.2b
(sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (+.f64 (/.f64 2 k) (*.f64 -2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))
22.1b
(/.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
33.8b
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.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)))))
▶33.8b
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
19.4b
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 3/2))
12.1b
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))
12.4b
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4) 2)
22.0b
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
20.9b
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2) 1/3)
21.9b
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k))
14.1b
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k))
22.0b
(*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
✓12.2b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
0.4b
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶22.0b
(*.f64 (pow.f64 k -1/2) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
▶1.6b
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (sqrt.f64 n)))
22.0b
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
▶36.1b
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6) 3)
Compiler

Compiled 726 to 589 computations (18.9% saved)

localize30.0ms (0.3%)

Local error

Found 3 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)
✓0.2b
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
Compiler

Compiled 53 to 38 computations (28.3% saved)

series4.0ms (0.1%)

Counts
1 → 12
Calls

6 calls:

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

rewrite58.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
723×log-prod_binary64
505×pow-unpow_binary64
387×pow2_binary64
265×pow1/3_binary64
261×expm1-udef_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01423
130723
2379422
Stop Event
1×node limit
Counts
1 → 21
Calls
Call 1
Inputs
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))))) (#(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)) (pow.f64 k -1))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))))) (#(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)) (pow.f64 k -1)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))))) (#(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)) (pow.f64 k -1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)) 1/2)))) (#(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)) (pow.f64 k -1))) 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)) (pow.f64 k -1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (pow.f64 k -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (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) (pow.f64 (pow.f64 k -1/2) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))) (#(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)) (pow.f64 k -1)))))))) (#(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)) (pow.f64 k -1))))))))) (#(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)) (pow.f64 k -1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (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) (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)) (pow.f64 k -1)))))))) (#(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)) (pow.f64 k -1)))))))) (#(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)) (pow.f64 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)) (pow.f64 k -1)))) 1))))))

simplify51.0ms (0.6%)

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
33 → 26
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)))

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.3b
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
✓11.4b
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
Compiler

Compiled 27 to 14 computations (48.1% saved)

series9.0ms (0.1%)

Counts
2 → 24
Calls

12 calls:

TimeVariablePointExpression
2.0ms
n
@inf
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
1.0ms
k
@-inf
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
1.0ms
n
@-inf
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
1.0ms
n
@0
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
1.0ms
n
@0
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))

rewrite55.0ms (0.6%)

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 n (PI.f64))
✓0.2b
(/.f64 (*.f64 n (PI.f64)) k)
✓0.7b
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6) 3)
✓14.6b
(pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6)
Compiler

Compiled 43 to 20 computations (53.5% saved)

series90.0ms (1%)

Counts
4 → 48
Calls

21 calls:

TimeVariablePointExpression
17.0ms
n
@0
(pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6)
16.0ms
k
@0
(pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6)
16.0ms
n
@-inf
(pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6)
16.0ms
k
@-inf
(pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6)
8.0ms
n
@inf
(pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6)

rewrite81.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
613×log-prod_binary64
346×pow-prod-down_binary64
312×pow2_binary64
271×pow-unpow_binary64
220×pow-to-exp_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01241
126840
2325140
Stop Event
1×node limit
Counts
4 → 130
Calls
Call 1
Inputs
(pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6)
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6) 3)
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 n (PI.f64))
Outputs
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(/.f64 n k) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 2) (*.f64 (cbrt.f64 (*.f64 n (PI.f64))) (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (cbrt.f64 (pow.f64 (/.f64 k (*.f64 n (PI.f64))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 k (*.f64 n (PI.f64))) -2)) (cbrt.f64 (*.f64 (/.f64 n k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 n (neg.f64 (PI.f64))) (/.f64 1 (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 k) (*.f64 n (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 n 1) (/.f64 (PI.f64) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (PI.f64) 1) (/.f64 n k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 n k) (PI.f64))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 2) 1) (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 n (pow.f64 (cbrt.f64 k) 2)) (/.f64 (PI.f64) (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (PI.f64) (pow.f64 (cbrt.f64 k) 2)) (/.f64 n (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 k) -2) (/.f64 (*.f64 n (PI.f64)) (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 2) (pow.f64 (cbrt.f64 k) 2)) (cbrt.f64 (*.f64 (/.f64 n k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (cbrt.f64 k) 2)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 n (sqrt.f64 k)) (/.f64 (PI.f64) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (PI.f64) (sqrt.f64 k)) (/.f64 n (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) (/.f64 (*.f64 n (PI.f64)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 2) (sqrt.f64 k)) (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 k (*.f64 n (PI.f64))) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 k (*.f64 n (PI.f64))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 n (PI.f64)) 3) (pow.f64 k 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 k (*.f64 n (PI.f64))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (*.f64 n (PI.f64)) (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 k (*.f64 n (PI.f64))) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 (/.f64 n k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 n k) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 n (PI.f64)) 3) (pow.f64 k 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (/.f64 n k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (/.f64 n k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (/.f64 n k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 n k) (PI.f64))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 (/.f64 n k) (PI.f64)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (/.f64 n k) (PI.f64)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 k (*.f64 n (PI.f64)))) -1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 n (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 n (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 n (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (PI.f64)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (PI.f64)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 n (PI.f64))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 n (PI.f64)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 n) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 n (PI.f64)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 n (PI.f64)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (PI.f64)))) 2))))))

simplify65.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
711×exp-sum_binary64
331×fma-def_binary64
329×associate-+l+_binary64
323×associate-+r+_binary64
322×div-sub_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0571032
11761032
2413888
31302744
45292672
Stop Event
1×node limit
Counts
178 → 144
Calls
Call 1
Inputs
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) 3)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) 3)
Outputs
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) k) 1/6) (pow.f64 n 1/6))
(pow.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n) 1/6)
(pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/6)
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) k) 1/6) (pow.f64 n 1/6))
(pow.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n) 1/6)
(pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/6)
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) k) 1/6) (pow.f64 n 1/6))
(pow.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n) 1/6)
(pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/6)
(exp.f64 (*.f64 1/6 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) k) 1/6) (pow.f64 n 1/6))
(pow.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n) 1/6)
(pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/6)
(exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) k) 1/6) (pow.f64 n 1/6))
(pow.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n) 1/6)
(pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/6)
(exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) k) 1/6) (pow.f64 n 1/6))
(pow.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n) 1/6)
(pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/6)
(exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) k) 1/6) (pow.f64 n 1/6))
(pow.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n) 1/6)
(pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/6)
(exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) k) 1/6) (pow.f64 n 1/6))
(pow.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n) 1/6)
(pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/6)
(exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 1/6) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
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(pow.f64 (pow.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n) 1/6) 3)
(pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/2)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) 3)
(pow.f64 (pow.f64 (exp.f64 1/6) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 3)
(pow.f64 (*.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) k) 1/6) (pow.f64 n 1/6)) 3)
(pow.f64 (pow.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n) 1/6) 3)
(pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/2)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) 3)
(pow.f64 (pow.f64 (exp.f64 1/6) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 3)
(pow.f64 (*.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) k) 1/6) (pow.f64 n 1/6)) 3)
(pow.f64 (pow.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n) 1/6) 3)
(pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/2)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) 3)
(pow.f64 (pow.f64 (exp.f64 1/6) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 3)
(pow.f64 (*.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) k) 1/6) (pow.f64 n 1/6)) 3)
(pow.f64 (pow.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n) 1/6) 3)
(pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/2)
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) 3)
(pow.f64 (pow.f64 (exp.f64 1/6) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 3)
(pow.f64 (*.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) k) 1/6) (pow.f64 n 1/6)) 3)
(pow.f64 (pow.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n) 1/6) 3)
(pow.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 1/2)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(sqrt.f64 (*.f64 (PI.f64) n))
0.2b
(*.f64 (PI.f64) n)
✓0.3b
(*.f64 (pow.f64 k -1/2) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
0.5b
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))
Compiler

Compiled 37 to 20 computations (45.9% saved)

series5.0ms (0.1%)

Counts
2 → 0
Calls

9 calls:

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

rewrite59.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
570×log-prod_binary64
422×exp-prod_binary64
403×pow-prod-down_binary64
294×pow2_binary64
246×pow-unpow_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01223
124823
2279623
Stop Event
1×node limit
Counts
2 → 62
Calls
Call 1
Inputs
(*.f64 (pow.f64 k -1/2) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
(sqrt.f64 (*.f64 (PI.f64) n))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 1 k)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2) (pow.f64 k -3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/6) (pow.f64 k -1/6)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) 2)) (cbrt.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) (sqrt.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2) (pow.f64 k -3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2) (pow.f64 k -3/2))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/6) (pow.f64 k -1/6))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k -1/4))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) 1) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) n)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) n))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (*.f64 (PI.f64) n) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) 1/6) (cbrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) 1/4) (pow.f64 (*.f64 (PI.f64) n) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) n) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) n) 2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) n) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) n) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) n) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) n) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/2) (log.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) n)))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) n))))) (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) n) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) n) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/4 (log.f64 (*.f64 (PI.f64) n))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) n))) 1) 1))))))

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
62 → 62
Calls
Call 1
Inputs
Outputs

localize24.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.3b
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (sqrt.f64 n)))
✓0.4b
(/.f64 (sqrt.f64 k) (sqrt.f64 n))
0.6b
(pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2)))
Compiler

Compiled 51 to 31 computations (39.2% saved)

series18.0ms (0.2%)

Counts
2 → 0
Calls

12 calls:

TimeVariablePointExpression
6.0ms
k
@-inf
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (sqrt.f64 n)))
2.0ms
k
@0
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (sqrt.f64 n)))
1.0ms
n
@0
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (sqrt.f64 n)))
1.0ms
n
@-inf
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (sqrt.f64 n)))
1.0ms
k
@inf
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (sqrt.f64 n)))

rewrite71.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
842×log-prod_binary64
279×expm1-udef_binary64
279×log1p-udef_binary64
256×log-pow_binary64
222×log-div_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01428
132228
2445026
Stop Event
1×node limit
Counts
2 → 88
Calls
Call 1
Inputs
(/.f64 (sqrt.f64 k) (sqrt.f64 n))
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (sqrt.f64 n)))
Outputs
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k)))) 1))))))

simplify8.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
88 → 88
Calls
Call 1
Inputs
Outputs

eval192.0ms (2.2%)

Compiler

Compiled 8766 to 5682 computations (35.2% saved)

prune120.0ms (1.4%)

Pruning

33 alts after pruning (27 fresh and 6 done)

PrunedKeptTotal
New49416510
Fresh71118
Picked011
Done055
Total50133534
Error
0b
Counts
534 → 33
Alt Table
Click to see full alt table
StatusErrorProgram
▶34.0b
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
33.9b
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 2))
▶0.4b
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
12.1b
(sqrt.f64 (/.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) n)) k))
36.1b
(pow.f64 (pow.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))) 1/6) 3)
40.6b
(cbrt.f64 (pow.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))) 3/2))
42.0b
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2) 1/3)
▶22.2b
(pow.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k -1/4)) 2)
✓0.4b
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
34.2b
(sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (+.f64 (/.f64 2 k) (*.f64 -2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))
33.8b
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 n (*.f64 2 (PI.f64))))))
21.9b
(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k))
✓33.8b
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
19.4b
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 3/2))
▶33.8b
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
12.1b
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))
12.4b
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4) 2)
33.8b
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
33.8b
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
✓1.6b
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (sqrt.f64 n)))
▶22.0b
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
20.9b
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2) 1/3)
21.9b
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
40.5b
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))
✓12.2b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
0.4b
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓22.0b
(*.f64 (pow.f64 k -1/2) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
33.9b
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
33.9b
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/4) 2)
14.1b
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k))
22.0b
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
✓36.1b
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6) 3)
35.8b
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))) 1/2))
Compiler

Compiled 822 to 669 computations (18.6% saved)

localize26.0ms (0.3%)

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))
✓0.3b
(/.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
k
@0
(/.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))

rewrite76.0ms (0.9%)

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
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(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))))))

simplify106.0ms (1.2%)

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

localize17.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
✓11.4b
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
Compiler

Compiled 27 to 14 computations (48.1% saved)

series5.0ms (0.1%)

Counts
2 → 24
Calls

12 calls:

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

rewrite67.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
563×log-prod_binary64
432×exp-prod_binary64
302×pow-prod-down_binary64
251×pow2_binary64
195×pow-unpow_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0924
119524
2275624
Stop Event
1×node limit
Counts
2 → 125
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
Outputs
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1/4) (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (PI.f64) -2) (/.f64 1 (neg.f64 (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 n k) (*.f64 2 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (/.f64 (PI.f64) k)) n)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 n k)) (/.f64 (*.f64 2 (PI.f64)) (sqrt.f64 (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 k) (/.f64 (PI.f64) (/.f64 1 n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (PI.f64) k) (/.f64 2 (/.f64 1 n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 k) (/.f64 (*.f64 2 (PI.f64)) (/.f64 1 n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) 2)) k) (/.f64 (cbrt.f64 (*.f64 2 (PI.f64))) (/.f64 1 n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) k) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (/.f64 1 n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (PI.f64) 1) (/.f64 2 (/.f64 k n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (/.f64 k n)) (PI.f64))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) 2)) 1) (/.f64 (cbrt.f64 (*.f64 2 (PI.f64))) (/.f64 k n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) 1) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (/.f64 k n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (cbrt.f64 (pow.f64 (/.f64 k n) 2))) (/.f64 (PI.f64) (cbrt.f64 (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (PI.f64) (cbrt.f64 (pow.f64 (/.f64 k n) 2))) (/.f64 2 (cbrt.f64 (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 k n)) -2) (/.f64 (*.f64 2 (PI.f64)) (cbrt.f64 (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) 2)) (cbrt.f64 (pow.f64 (/.f64 k n) 2))) (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (cbrt.f64 (pow.f64 (/.f64 k n) 2))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (cbrt.f64 (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (sqrt.f64 (/.f64 k n))) (/.f64 (PI.f64) (sqrt.f64 (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (PI.f64) (sqrt.f64 (/.f64 k n))) (/.f64 2 (sqrt.f64 (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) 2)) (sqrt.f64 (/.f64 k n))) (/.f64 (cbrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 2 (PI.f64)) 1) (/.f64 n k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 2 (PI.f64)) (neg.f64 k)) (neg.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 3/4) (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 5/6) (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) 1) n)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 4 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 3/2) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 1/6) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) 3) (pow.f64 (/.f64 k n) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 2)) (cbrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))) (sqrt.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (*.f64 2 (PI.f64)) (neg.f64 (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 4 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 2) (/.f64 (PI.f64) (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) 3) (pow.f64 (/.f64 k n) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 4 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) 2))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))))) 1) 2))))))

simplify35.0ms (0.4%)

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
149 → 127
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)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.5b
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
✓1.0b
(sqrt.f64 (*.f64 2 (PI.f64)))
✓11.4b
(sqrt.f64 (/.f64 n k))
Compiler

Compiled 29 to 15 computations (48.3% saved)

series7.0ms (0.1%)

Counts
3 → 0
Calls

12 calls:

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

rewrite64.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
986×pow1_binary64
911×add-log-exp_binary64
911×log1p-expm1-u_binary64
911×expm1-log1p-u_binary64
101×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01026
120726
2252526
Stop Event
1×node limit
Counts
3 → 69
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 n k))
(sqrt.f64 (*.f64 2 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 n k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 n k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (/.f64 n k))) (cbrt.f64 (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 n k)) (cbrt.f64 (sqrt.f64 (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 n k) 1/4) (pow.f64 (/.f64 n k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 n) (pow.f64 (/.f64 1 k) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 n) (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 n k)) 2)) (sqrt.f64 (cbrt.f64 (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 n k)) 2) 1/2) (pow.f64 (cbrt.f64 (/.f64 n k)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 (/.f64 k n)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 n)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 n) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (neg.f64 n)) (sqrt.f64 (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 n)) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 n k) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 n k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 n k) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 n k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 n k) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 n k) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 n k))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (PI.f64))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2 (PI.f64))) (cbrt.f64 (sqrt.f64 (*.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (PI.f64)))) (cbrt.f64 (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (PI.f64)) 1/4) (pow.f64 (*.f64 2 (PI.f64)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 (PI.f64) 2)))) (sqrt.f64 (cbrt.f64 (*.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 4 (pow.f64 (PI.f64) 2))) 1/2) (pow.f64 (cbrt.f64 (*.f64 2 (PI.f64))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (PI.f64)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 2 (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (PI.f64)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (PI.f64)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (PI.f64)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (PI.f64)))))))))
((#(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 (*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 2 (PI.f64)))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 n)) (sqrt.f64 k))))) (#(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 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))) 3) 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 (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x 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 (sqrt.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) 3/2) (pow.f64 (*.f64 2 (PI.f64)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) 3/2) (pow.f64 (/.f64 n k) 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))))))))))

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
69 → 69
Calls
Call 1
Inputs
Outputs

localize17.0ms (0.2%)

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 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
✓0.4b
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
Compiler

Compiled 43 to 22 computations (48.8% saved)

series11.0ms (0.1%)

Counts
3 → 0
Calls

15 calls:

TimeVariablePointExpression
2.0ms
k
@0
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
1.0ms
k
@0
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
1.0ms
n
@0
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
1.0ms
n
@-inf
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
1.0ms
k
@-inf
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))

rewrite77.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
619×log-prod_binary64
364×pow-prod-down_binary64
289×pow2_binary64
248×pow-unpow_binary64
205×pow-to-exp_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01239
124936
2309536
Stop Event
1×node limit
Counts
3 → 152
Calls
Call 1
Inputs
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 k) (*.f64 (pow.f64 k 1/6) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) 1/6) (cbrt.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k 1/4) (*.f64 (pow.f64 k 1/4) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) 1/4) (pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 k)) (/.f64 1 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) -1/2) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 k) (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 k) 1) (/.f64 (pow.f64 k 1/6) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 k 1/4) 1) (/.f64 (pow.f64 k 1/4) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 k 1/4) (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (pow.f64 k 1/4) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) -1/4) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 k) 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(pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) -1/6) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) -1/4) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 k 3/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 k) (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 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((#(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 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) 2)) (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 (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 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/6) (cbrt.f64 (*.f64 2 (*.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 (*.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 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) -1/2))))) (#(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 (*.f64 (pow.f64 (*.f64 (PI.f64) n) 2) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3) 1/6)))) (#(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 (*.f64 2 (*.f64 (PI.f64) n))) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/6) 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 pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) -1/2) -1)))) (#(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))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/2 (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3/2 (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/4 (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1) 1))))))

simplify9.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
152 → 152
Calls
Call 1
Inputs
Outputs

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4)
0.2b
(*.f64 (PI.f64) n)
✓0.3b
(*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k -1/4))
✓0.5b
(pow.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k -1/4)) 2)
Compiler

Compiled 50 to 31 computations (38% saved)

series66.0ms (0.8%)

Counts
3 → 60
Calls

15 calls:

TimeVariablePointExpression
11.0ms
k
@-inf
(pow.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k -1/4)) 2)
11.0ms
k
@0
(pow.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k -1/4)) 2)
11.0ms
n
@-inf
(pow.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k -1/4)) 2)
11.0ms
n
@0
(pow.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k -1/4)) 2)
9.0ms
n
@inf
(pow.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k -1/4)) 2)

rewrite72.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
620×log-prod_binary64
373×pow-prod-down_binary64
325×pow2_binary64
280×pow-unpow_binary64
236×pow-to-exp_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01348
128144
2316144
Stop Event
1×node limit
Counts
3 → 84
Calls
Call 1
Inputs
(pow.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k -1/4)) 2)
(*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k -1/4))
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) (pow.f64 k -1/2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) (pow.f64 k -1/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4) (*.f64 (pow.f64 k -1/4) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4) (pow.f64 k -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/4) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4) (pow.f64 k -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4) (pow.f64 k -1/4)) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4) (pow.f64 k -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))) (cbrt.f64 (*.f64 (*.f64 (PI.f64) (*.f64 n 2)) (pow.f64 k -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (*.f64 (PI.f64) (*.f64 n 2)) (pow.f64 k -1))) (cbrt.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 k -1/8) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/8)) (sqrt.f64 (*.f64 (pow.f64 k -3/4) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 3/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (pow.f64 k -3/4) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 3/4))) (*.f64 (pow.f64 k -1/8) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4) (pow.f64 k -1/4)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4)) (pow.f64 k -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4) (pow.f64 k -1/4)) (pow.f64 k -1/4)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 5/6) (*.f64 (pow.f64 k -1/12) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 (PI.f64) (*.f64 n 2)) (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 1/4 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 -1/4 (log.f64 k))) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))) 1) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4) (pow.f64 k -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/4)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/4)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/4)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/4)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4) (pow.f64 k -1/4)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4) (pow.f64 k -1/4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k -3/4) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 3/4)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k -1/12) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/12)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k -1/8) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/8)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4) (pow.f64 k -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 k -1/4)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4) (pow.f64 k -1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 k -3/4) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 3/4)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4) (pow.f64 k -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4) (pow.f64 k -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 1/4 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 -1/4 (log.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 1/4 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 -1/4 (log.f64 k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 k -3/4) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 3/4))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 k -1/12) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/12))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 k -1/8) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/8))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 1/4 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 -1/4 (log.f64 k))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))) 1) 1/2))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/12) (cbrt.f64 (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)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 4 1/8) (pow.f64 (*.f64 (PI.f64) n) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) 1/4) (pow.f64 4 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/8) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (PI.f64)) 1/4) (pow.f64 n 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/4 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/4 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 3/4)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 2)) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 1/12)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/8 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 1/4 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) 1/8) 2))))))

simplify74.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
773×exp-sum_binary64
388×fma-def_binary64
365×div-sub_binary64
352×exp-diff_binary64
323×associate-+l+_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0691236
11971212
2495972
31472780
45558780
Stop Event
1×node limit
Counts
144 → 102
Calls
Call 1
Inputs
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) 2)
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
Outputs
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 2)
(pow.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log.f64 k))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 2)
(pow.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log.f64 k))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 2)
(pow.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log.f64 k))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 2)
(pow.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log.f64 k))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 2)
(pow.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log.f64 k))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 2)
(pow.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log.f64 k))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 2)
(pow.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log.f64 k))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 2)
(pow.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log.f64 k))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 2)
(pow.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log.f64 k))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 2)
(pow.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log.f64 k))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 2)
(pow.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log.f64 k))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 2)
(pow.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log.f64 k))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 2)
(pow.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log.f64 k))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 2)
(pow.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log.f64 k))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 2)
(pow.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log.f64 k))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 2)
(pow.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log.f64 k))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 2)
(pow.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log.f64 k))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 2)
(pow.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log.f64 k))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 2)
(pow.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log.f64 k))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 2)
(pow.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log.f64 k))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 2)
(pow.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log.f64 k))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 2)
(pow.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log.f64 k))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 2)
(pow.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log.f64 k))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))) 2)
(pow.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (exp.f64 (log.f64 k))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))))
(sqrt.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))))
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 k -1/4))
(pow.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 k -1/4))
(pow.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 k -1/4))
(pow.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 k -1/4))
(pow.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 k -1/4))
(pow.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 k -1/4))
(pow.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 k -1/4))
(pow.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 k -1/4))
(pow.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 k -1/4))
(pow.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 k -1/4))
(pow.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 k -1/4))
(pow.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 k -1/4))
(pow.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 k -1/4))
(pow.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 k -1/4))
(pow.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 k -1/4))
(pow.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 k -1/4))
(pow.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 k -1/4))
(pow.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 k -1/4))
(pow.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 k -1/4))
(pow.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 k -1/4))
(pow.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 k -1/4))
(pow.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 k -1/4))
(pow.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 k -1/4))
(pow.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 k -1/4))
(pow.f64 (/.f64 (*.f64 2 n) (/.f64 k (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 1/4) (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 1/4) (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 1/4) (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 1/4) (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 1/4) (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 1/4) (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 1/4) (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 1/4) (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 1/4) (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 1/4) (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 1/4) (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (exp.f64 1/4) (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4)
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)

eval193.0ms (2.2%)

Compiler

Compiled 9371 to 5829 computations (37.8% saved)

prune118.0ms (1.4%)

Pruning

38 alts after pruning (30 fresh and 8 done)

PrunedKeptTotal
New58616602
Fresh81422
Picked101
Done2810
Total59738635
Error
0b
Counts
635 → 38
Alt Table
Click to see full alt table
StatusErrorProgram
33.9b
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
34.5b
(pow.f64 (pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) -1/6) 3)
21.9b
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))
✓34.0b
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
41.7b
(pow.f64 (pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) 3/2) -1/3)
✓0.4b
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
40.5b
(cbrt.f64 (pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) -3/2))
34.1b
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 3/2)
12.1b
(sqrt.f64 (/.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) n)) k))
32.1b
(/.f64 1 (sqrt.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n)))))
42.0b
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2) 1/3)
33.8b
(sqrt.f64 (*.f64 (/.f64 2 k) (/.f64 (PI.f64) (/.f64 1 n))))
47.6b
(pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 3) 1/6)
✓0.4b
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
34.2b
(sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (+.f64 (/.f64 2 k) (*.f64 -2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))
21.9b
(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k))
✓33.8b
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
19.4b
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 3/2))
✓33.8b
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
12.1b
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))
12.4b
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4) 2)
33.8b
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
20.9b
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2) 1/3)
22.0b
(/.f64 1 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) -1/2) (sqrt.f64 k)))
✓22.0b
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
22.1b
(/.f64 1 (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 n))))
32.1b
(/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 (/.f64 k n)))
14.1b
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k))
22.0b
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
32.1b
(pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) -1/2)
32.1b
(/.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
34.5b
(pow.f64 (pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) 1/6) -3)
21.9b
(*.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n))
35.8b
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))) 1/2))
33.8b
(sqrt.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n))
33.8b
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
✓36.1b
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6) 3)
✓12.2b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
Compiler

Compiled 499 to 407 computations (18.4% saved)

regimes336.0ms (3.9%)

Counts
74 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) -1/2)
(/.f64 1 (sqrt.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n)))))
(sqrt.f64 (*.f64 (/.f64 2 k) (/.f64 (PI.f64) (/.f64 1 n))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 n (*.f64 2 (PI.f64))))))
(/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 (/.f64 k n)))
(/.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 2))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))
(cbrt.f64 (pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) -3/2))
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 3/2)
(cbrt.f64 (pow.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))) 3/2))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))
(pow.f64 (pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) -1/6) 3)
(pow.f64 (pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) 3/2) -1/3)
(pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 3) 1/6)
(pow.f64 (pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) 1/6) -3)
(pow.f64 (pow.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))) 1/6) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/4) 2)
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))) 1/2))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6) 3)
(/.f64 1 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) -1/2) (sqrt.f64 k)))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 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)))
(*.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 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 k))
(*.f64 (pow.f64 k -1/2) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
(/.f64 1 (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 n))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
(pow.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k -1/4)) 2)
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) 2))
(/.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 3/2))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4) 2)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2) 1/3)
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (sqrt.f64 n)))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))
(sqrt.f64 (/.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) n)) k))
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))
(sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (+.f64 (/.f64 2 k) (*.f64 -2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))
(*.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 (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 2 (-.f64 1/2 (/.f64 k 2))) (pow.f64 (*.f64 (PI.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 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3) 1/3)
(*.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2)))
(*.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)))
(/.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 (*.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))))
(/.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:

99.0ms
(*.f64 (*.f64 2 (PI.f64)) n)
56.0ms
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
56.0ms
k
50.0ms
n
45.0ms
(*.f64 (*.f64 2 (PI.f64)) n)
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 1005 to 640 computations (36.3% saved)

regimes191.0ms (2.2%)

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

4 calls:

50.0ms
n
46.0ms
(*.f64 (*.f64 2 (PI.f64)) n)
42.0ms
k
25.0ms
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
Results
ErrorSegmentsBranch
0.4b1k
0.4b1n
0.4b1(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
0.4b1(*.f64 (*.f64 2 (PI.f64)) n)
Compiler

Compiled 915 to 582 computations (36.4% saved)

regimes57.0ms (0.7%)

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

23.0ms
k
22.0ms
n
Results
ErrorSegmentsBranch
0.4b1k
0.4b1n
Compiler

Compiled 400 to 242 computations (39.5% saved)

regimes72.0ms (0.8%)

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

2 calls:

39.0ms
k
21.0ms
n
Results
ErrorSegmentsBranch
0.3b2k
10.6b1n
Compiler

Compiled 386 to 233 computations (39.6% saved)

bsearch33.0ms (0.4%)

Algorithm
1×binary-search
Steps
TimeLeftRight
32.0ms
8.29862116415168e-24
2.060966870275588e-23
Compiler

Compiled 23 to 19 computations (17.4% saved)

regimes69.0ms (0.8%)

Counts
36 → 2
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) -1/2)
(/.f64 1 (sqrt.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n)))))
(sqrt.f64 (*.f64 (/.f64 2 k) (/.f64 (PI.f64) (/.f64 1 n))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 n (*.f64 2 (PI.f64))))))
(/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 (/.f64 k n)))
(/.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 2))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))
(cbrt.f64 (pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) -3/2))
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 3/2)
(cbrt.f64 (pow.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))) 3/2))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))
(pow.f64 (pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) -1/6) 3)
(pow.f64 (pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) 3/2) -1/3)
(pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 3) 1/6)
(pow.f64 (pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) 1/6) -3)
(pow.f64 (pow.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))) 1/6) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/4) 2)
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64)))) 1/2))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6) 3)
(/.f64 1 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) -1/2) (sqrt.f64 k)))
Outputs
(*.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n))
(pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 3) 1/6)
Calls

2 calls:

39.0ms
k
19.0ms
n
Results
ErrorSegmentsBranch
16.7b2k
21.9b1n
Compiler

Compiled 360 to 216 computations (40% saved)

bsearch103.0ms (1.2%)

Algorithm
1×binary-search
Steps
TimeLeftRight
103.0ms
6.542894225085113e+128
1.0110273074019053e+141
Compiler

Compiled 283 to 239 computations (15.5% saved)

regimes37.0ms (0.4%)

Counts
26 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) -1/2)
(/.f64 1 (sqrt.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n)))))
(sqrt.f64 (*.f64 (/.f64 2 k) (/.f64 (PI.f64) (/.f64 1 n))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 n (*.f64 2 (PI.f64))))))
(/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 (/.f64 k n)))
(/.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 2))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))
(cbrt.f64 (pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) -3/2))
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))) 3/2)
(cbrt.f64 (pow.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))) 3/2))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))
(pow.f64 (pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) -1/6) 3)
(pow.f64 (pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) 3/2) -1/3)
Outputs
(*.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n))
Calls

2 calls:

15.0ms
n
15.0ms
k
Results
ErrorSegmentsBranch
21.9b1k
21.9b1n
Compiler

Compiled 249 to 149 computations (40.2% saved)

regimes19.0ms (0.2%)

Counts
12 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) -1/2)
(/.f64 1 (sqrt.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n)))))
(sqrt.f64 (*.f64 (/.f64 2 k) (/.f64 (PI.f64) (/.f64 1 n))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 n (*.f64 2 (PI.f64))))))
(/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 (/.f64 k n)))
(/.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
Outputs
(pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) -1/2)
Calls

2 calls:

8.0ms
k
7.0ms
n
Results
ErrorSegmentsBranch
32.1b1k
32.1b1n
Compiler

Compiled 113 to 71 computations (37.2% saved)

regimes12.0ms (0.1%)

Accuracy

Total -0.1b remaining (-0.3%)

Threshold costs -0.1b (-0.3%)

Counts
6 → 1
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (*.f64 n 2) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
Outputs
(sqrt.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n))
Calls

2 calls:

5.0ms
k
5.0ms
n
Results
ErrorSegmentsBranch
33.8b1k
33.8b1n
Compiler

Compiled 56 to 37 computations (33.9% saved)

simplify11.0ms (0.1%)

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
056196
176196
280196
382196
483196
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 (*.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 5647748903835455/680564733841876926926749214863536422912) (*.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n)) (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(if (<=.f64 k 1000000000000000016976219238238959704141045173573106739630601035115997744067216908958262325956255112879408454231155599236459402033650892537856) (*.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n)) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 3) 1/6))
(*.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n))
(pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) -1/2)
(sqrt.f64 (*.f64 (*.f64 2 (/.f64 (PI.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 (*.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 5647748903835455/680564733841876926926749214863536422912) (*.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n)) (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(if (<=.f64 k 5647748903835455/680564733841876926926749214863536422912) (*.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n)) (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)))
(if (<=.f64 k 1000000000000000016976219238238959704141045173573106739630601035115997744067216908958262325956255112879408454231155599236459402033650892537856) (*.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n)) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 (/.f64 n k))) 3) 1/6))
(*.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))) (sqrt.f64 n))
(pow.f64 (*.f64 1/2 (/.f64 k (*.f64 (PI.f64) n))) -1/2)
(pow.f64 (*.f64 1/2 (/.f64 k (*.f64 n (PI.f64)))) -1/2)
(sqrt.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n))
(sqrt.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))))
Compiler

Compiled 139 to 109 computations (21.6% saved)

soundness97.0ms (1.1%)

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)

end85.0ms (1%)

Compiler

Compiled 125 to 81 computations (35.2% saved)

Profiling

Loading profile data...