Details

Time bar (total: 11.6s)

analyze118.0ms (1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%50%50%2
0%50%50%3
0%50%50%4
12.5%37.5%50%5
12.5%34.3%53.2%6
15.6%26.5%57.9%7
15.6%22.6%61.8%8
17.2%17.6%65.3%9
17.2%15%67.8%10
18%12.2%69.9%11
18%10.8%71.3%12
Compiler

Compiled 19 to 16 computations (15.8% saved)

sample4.4s (37.8%)

Results
2.4s8256×body256valid
1.2s1438×body1024invalid
463.0ms2296×body256invalid
353.0ms637×body512invalid

preprocess65.0ms (0.6%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02150
15244
211944
325744
467044
5187940
6423040
7736440
022
Stop Event
1×saturated
1×node limit
Calls
Call 1
Inputs
0
1
Outputs
0
1
Call 2
Inputs
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2)))
Outputs
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2)))
(*.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) k)) (-.f64 1/2 (/.f64 n 2))))
(/.f64 (pow.f64 (*.f64 k (*.f64 2 (PI.f64))) (/.f64 (-.f64 1 n) 2)) (sqrt.f64 n))
(/.f64 (pow.f64 (*.f64 k (*.f64 2 (PI.f64))) (+.f64 1/2 (/.f64 n -2))) (sqrt.f64 n))
(/.f64 (pow.f64 (*.f64 k (*.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 n))) (sqrt.f64 n))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 k 2)) (fma.f64 -1/2 n 1/2)) (sqrt.f64 n))
(/.f64 (pow.f64 (*.f64 k (*.f64 2 (PI.f64))) (fma.f64 n -1/2 1/2)) (sqrt.f64 n))
Compiler

Compiled 20 to 17 computations (15% saved)

simplify45.0ms (0.4%)

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

Useful iterations: 5 (0.0ms)

IterNodesCost
01425
13222
26822
314122
436022
598320
6221320
7566320
Stop Event
1×node limit
Counts
1 → 2
Calls
Call 1
Inputs
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
Outputs
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

eval1.0ms (0%)

Compiler

Compiled 31 to 23 computations (25.8% saved)

prune2.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.3b
Counts
3 → 2
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.4b
(*.f64 (/.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)

localize28.0ms (0.2%)

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)))
✓0.3b
(/.f64 1 (sqrt.f64 k))
Compiler

Compiled 56 to 38 computations (32.1% saved)

series81.0ms (0.7%)

Counts
4 → 48
Calls

18 calls:

TimeVariablePointExpression
32.0ms
n
@0
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
28.0ms
n
@-inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
9.0ms
n
@inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
3.0ms
k
@0
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
2.0ms
k
@inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

rewrite82.0ms (0.7%)

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))))))

simplify66.0ms (0.6%)

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

Useful iterations: 3 (0.0ms)

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

localize22.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series11.0ms (0.1%)

Counts
3 → 48
Calls

15 calls:

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

rewrite75.0ms (0.6%)

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))))))

simplify80.0ms (0.7%)

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))

eval105.0ms (0.9%)

Compiler

Compiled 4815 to 3266 computations (32.2% saved)

prune59.0ms (0.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New21915234
Fresh000
Picked101
Done011
Total22016236
Error
0.0b
Counts
236 → 16
Alt Table
Click to see full alt table
StatusErrorProgram
▶20.4b
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 k))
0.6b
(/.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))
0.8b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3) (/.f64 (-.f64 1 k) 2)))
0.5b
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4))))
▶11.2b
(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)))))
0.3b
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶3.3b
(*.f64 (exp.f64 (*.f64 -1/2 (log.f64 k))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
20.4b
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
✓0.4b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
0.3b
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 k 2))))
0.4b
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))
3.4b
(*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))
▶11.7b
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 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))
Compiler

Compiled 584 to 473 computations (19% saved)

localize30.0ms (0.3%)

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)

series26.0ms (0.2%)

Counts
4 → 24
Calls

18 calls:

TimeVariablePointExpression
4.0ms
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
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))
3.0ms
n
@-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))

rewrite91.0ms (0.8%)

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 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simplify95.0ms (0.8%)

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)))

localize20.0ms (0.2%)

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)
✓10.4b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
Compiler

Compiled 50 to 28 computations (44% saved)

series16.0ms (0.1%)

Counts
3 → 60
Calls

18 calls:

TimeVariablePointExpression
2.0ms
k
@-inf
(/.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 (0.7%)

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))))))

simplify68.0ms (0.6%)

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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(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)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(sqrt.f64 (*.f64 (PI.f64) n))
0.2b
(*.f64 (PI.f64) n)
✓0.4b
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 k))
✓0.5b
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))
Compiler

Compiled 34 to 16 computations (52.9% saved)

series13.0ms (0.1%)

Counts
3 → 0
Calls

12 calls:

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

rewrite77.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
573×log-prod_binary64
424×exp-prod_binary64
378×pow-prod-down_binary64
274×pow2_binary64
219×pow-unpow_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01132
122730
2281330
Stop Event
1×node limit
Counts
3 → 120
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 k))
(sqrt.f64 (*.f64 (PI.f64) n))
Outputs
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((#(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 1 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (pow.f64 k 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1) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 k 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (cbrt.f64 k)) (/.f64 (sqrt.f64 2) (pow.f64 k 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 k 1/4)))))) (#(struct:change 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#<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 k (*.f64 2 (*.f64 (PI.f64) n)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))))))) (#(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 (/.f64 k (*.f64 2 (*.f64 (PI.f64) n)))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))))) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k))))))) (#(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 (log.f64 (sqrt.f64 (/.f64 k (*.f64 2 (*.f64 (PI.f64) n))))) -1))))) (#(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))))))
((#(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) (log.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(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 (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 (*.f64 3/2 (log.f64 (*.f64 (PI.f64) n))) 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))))))

simplify8.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
120 → 120
Calls
Call 1
Inputs
Outputs

localize33.0ms (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 (exp.f64 (*.f64 -1/2 (log.f64 k))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓4.7b
(exp.f64 (*.f64 -1/2 (log.f64 k)))
Compiler

Compiled 63 to 43 computations (31.7% saved)

series66.0ms (0.6%)

Counts
2 → 24
Calls

9 calls:

TimeVariablePointExpression
39.0ms
k
@0
(exp.f64 (*.f64 -1/2 (log.f64 k)))
14.0ms
k
@-inf
(exp.f64 (*.f64 -1/2 (log.f64 k)))
8.0ms
k
@inf
(exp.f64 (*.f64 -1/2 (log.f64 k)))
1.0ms
k
@-inf
(*.f64 (exp.f64 (*.f64 -1/2 (log.f64 k))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
1.0ms
n
@0
(*.f64 (exp.f64 (*.f64 -1/2 (log.f64 k))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

rewrite71.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
807×log-prod_binary64
422×pow2_binary64
292×pow1/3_binary64
288×expm1-udef_binary64
287×log1p-udef_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01635
133627
2411526
Stop Event
1×node limit
Counts
2 → 46
Calls
Call 1
Inputs
(exp.f64 (*.f64 -1/2 (log.f64 k)))
(*.f64 (exp.f64 (*.f64 -1/2 (log.f64 k))) (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 (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 (cbrt.f64 (pow.f64 k -1/2)) (pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 2) (cbrt.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 k -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 k -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (*.f64 -1/2 (log.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 -1/2) (log.f64 k))))) (#(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 (sqrt.f64 (pow.f64 k -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (cbrt.f64 (*.f64 1/4 (pow.f64 (log.f64 k) 2)))) (cbrt.f64 (*.f64 -1/2 (log.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (*.f64 -1/2 (log.f64 k)))) (sqrt.f64 (*.f64 -1/2 (log.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 -1/2) (pow.f64 (cbrt.f64 (log.f64 k)) 2)) (cbrt.f64 (log.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 -1/2) (sqrt.f64 (log.f64 k))) (sqrt.f64 (log.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 k -1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (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 +.f64 0 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (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 (cbrt.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))) 2)))) (#(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 sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 (pow.f64 k -1/2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (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 (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 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))) 1))))))

simplify61.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
846×exp-sum_binary64
661×exp-prod_binary64
486×distribute-rgt-in_binary64
472×distribute-lft-in_binary64
458×fma-def_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
046508
1117496
2367472
31320440
45691352
Stop Event
1×node limit
Counts
70 → 53
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k))))))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k))))))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k))))))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.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)) (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
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k))))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 k)))))
(pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 k))))
(*.f64 (pow.f64 -1 -1/2) (pow.f64 (/.f64 -1 k) 1/2))
(pow.f64 (exp.f64 -1/2) (log.f64 k))
(pow.f64 k -1/2)
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k))))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 k)))))
(pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 k))))
(*.f64 (pow.f64 -1 -1/2) (pow.f64 (/.f64 -1 k) 1/2))
(pow.f64 (exp.f64 -1/2) (log.f64 k))
(pow.f64 k -1/2)
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k))))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 k)))))
(pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 k))))
(*.f64 (pow.f64 -1 -1/2) (pow.f64 (/.f64 -1 k) 1/2))
(pow.f64 (exp.f64 -1/2) (log.f64 k))
(pow.f64 k -1/2)
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k))))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 k)))))
(pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 k))))
(*.f64 (pow.f64 -1 -1/2) (pow.f64 (/.f64 -1 k) 1/2))
(pow.f64 (exp.f64 -1/2) (log.f64 k))
(pow.f64 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 (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 n (*.f64 (*.f64 -2 (PI.f64)) -1)) (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 n (*.f64 (*.f64 -2 (PI.f64)) -1)) (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 n (*.f64 (*.f64 -2 (PI.f64)) -1)) (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 n (*.f64 (*.f64 -2 (PI.f64)) -1)) (fma.f64 -1/2 k 1/2)))

localize30.0ms (0.3%)

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)
10.4b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
Compiler

Compiled 79 to 47 computations (40.5% saved)

series180.0ms (1.5%)

Counts
2 → 48
Calls

12 calls:

TimeVariablePointExpression
79.0ms
k
@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)
19.0ms
k
@-inf
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
18.0ms
n
@-inf
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
18.0ms
n
@inf
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)

rewrite72.0ms (0.6%)

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 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)) (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k))) (*.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/4) (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)) 1/6) (*.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)) 1/6) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k))) (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)) 2)) (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)) 1) (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)) (cbrt.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)))) (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)) (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)) 1/6)) (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)))) (sqrt.f64 (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.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 log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6)) (cbrt.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k))) (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)) 1/6) (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)))) (cbrt.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/6 (log.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/6 (log.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k))) 1))))))

simplify96.0ms (0.8%)

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)))
(*.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))
(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 (neg.f64 (log.f64 n)) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) k))
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(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (neg.f64 (log.f64 n)) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) k))
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(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (neg.f64 (log.f64 n)) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 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 (neg.f64 (log.f64 n)) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (/.f64 (*.f64 -2 (PI.f64)) (/.f64 -1 n)) (-.f64 1 k)) k))
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(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (/.f64 (*.f64 -2 (PI.f64)) (/.f64 -1 n)) (-.f64 1 k)) k))
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(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (/.f64 (*.f64 -2 (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 (*.f64 -2 (PI.f64)) (/.f64 -1 n)) (-.f64 1 k)) k))
(pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 3)
(pow.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) 3)
(pow.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (log.f64 k))) 3)
(pow.f64 (*.f64 (pow.f64 k -1/6) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/6)) 3)
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6) 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))
(fma.f64 k (*.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) 3)) -1/2) (pow.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) 3))
(fma.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (log.f64 k))) 3) -1/2)) (pow.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (log.f64 k))) 3))
(fma.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (*.f64 (pow.f64 k -1/6) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/6)) 3) -1/2)) (pow.f64 (*.f64 (pow.f64 k -1/6) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/6)) 3))
(fma.f64 k (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) (*.f64 (pow.f64 (pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6) 3) -1/2)) (pow.f64 (pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6) 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)))
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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)))

eval336.0ms (2.9%)

Compiler

Compiled 15694 to 10506 computations (33.1% saved)

prune119.0ms (1%)

Pruning

19 alts after pruning (17 fresh and 2 done)

PrunedKeptTotal
New71017727
Fresh10010
Picked101
Done325
Total72419743
Error
0b
Counts
743 → 19
Alt Table
Click to see full alt table
StatusErrorProgram
▶33.9b
(/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2)) (sqrt.f64 k))
11.1b
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))
30.7b
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
11.2b
(sqrt.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 1 (neg.f64 k))))
▶30.7b
(pow.f64 (sqrt.f64 (/.f64 k (*.f64 2 (*.f64 (PI.f64) n)))) -1)
20.4b
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))
20.4b
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k))
13.4b
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k))
0.3b
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓11.2b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
33.8b
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6) 3)
▶0.4b
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
31.2b
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
▶31.2b
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
✓20.4b
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 k))
13.8b
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6) 3)
20.4b
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
20.4b
(*.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
▶0.3b
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))
Compiler

Compiled 516 to 419 computations (18.8% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiled 66 to 42 computations (36.4% saved)

series17.0ms (0.1%)

Counts
4 → 24
Calls

18 calls:

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

rewrite88.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
796×log-prod_binary64
700×pow-unpow_binary64
379×pow2_binary64
261×pow1/3_binary64
256×expm1-udef_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01468
129859
2377057
Stop Event
1×node limit
Counts
4 → 125
Calls
Call 1
Inputs
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))
(*.f64 (PI.f64) (*.f64 n 2))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (sqrt.f64 k))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))
Outputs
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pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2)) (sqrt.f64 k)) 3) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3/2) (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2)) (sqrt.f64 k)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) 2) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (*.f64 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((#(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 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) 2) 4) 1/2)))) (#(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 (*.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 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2)) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2)) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/4) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.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)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.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))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) 1))))))

simplify68.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
842×fma-def_binary64
570×div-sub_binary64
549×exp-sum_binary64
385×fma-neg_binary64
351×exp-prod_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
039432
199432
2268432
3761396
42164360
55651360
Stop Event
1×node limit
Counts
149 → 131
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 (/.f64 1 k)) (exp.f64 (*.f64 -1/2 (*.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 -1/2 (*.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 -1/2 (*.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 -1/2 (*.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 -1/2 (*.f64 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 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 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 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 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 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 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 k (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
Outputs
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 n (*.f64 2 (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 n (*.f64 2 (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 n (*.f64 2 (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 n (*.f64 2 (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 n (*.f64 2 (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 n (*.f64 2 (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 n (*.f64 2 (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 n (*.f64 2 (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 n (*.f64 2 (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 n (*.f64 2 (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 n (*.f64 2 (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 n (*.f64 2 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 -1/2 (*.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 -1/2) (*.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) k) (pow.f64 n k)) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 -1/2 (*.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 -1/2) (*.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) k) (pow.f64 n k)) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 -1/2 (*.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 -1/2) (*.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) k) (pow.f64 n k)) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 -1/2 (*.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 -1/2) (*.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) k) (pow.f64 n k)) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 -1/2 (*.f64 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 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) k) (pow.f64 n k)) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 -1/2 (*.f64 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 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) k) (pow.f64 n k)) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 -1/2 (*.f64 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 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) k) (pow.f64 n k)) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 -1/2 (*.f64 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 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) k) (pow.f64 n k)) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 -1/2 (*.f64 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 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) k) (pow.f64 n k)) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 -1/2 (*.f64 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 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) k) (pow.f64 n k)) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 -1/2 (*.f64 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 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) k) (pow.f64 n k)) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 -1/2 (*.f64 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 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) k) (pow.f64 n k)) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2))

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.3b
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
✓10.5b
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
Compiler

Compiled 27 to 14 computations (48.1% saved)

series8.0ms (0.1%)

Counts
2 → 24
Calls

12 calls:

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

rewrite80.0ms (0.7%)

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)))))))))

simplify16.0ms (0.1%)

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)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (PI.f64) n)
✓0.2b
(/.f64 k (*.f64 2 (*.f64 (PI.f64) n)))
✓0.3b
(pow.f64 (sqrt.f64 (/.f64 k (*.f64 2 (*.f64 (PI.f64) n)))) -1)
✓10.0b
(sqrt.f64 (/.f64 k (*.f64 2 (*.f64 (PI.f64) n))))
Compiler

Compiled 40 to 21 computations (47.5% saved)

series19.0ms (0.2%)

Counts
3 → 24
Calls

18 calls:

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

rewrite80.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
573×log-prod_binary64
433×exp-prod_binary64
339×pow-prod-down_binary64
280×pow2_binary64
213×pow-unpow_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01138
123137
2288537
Stop Event
1×node limit
Counts
3 → 150
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 k (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (sqrt.f64 (/.f64 k (*.f64 2 (*.f64 (PI.f64) n)))) -1)
(/.f64 k (*.f64 2 (*.f64 (PI.f64) n)))
Outputs
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n)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n)) -3/2) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n)) 2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n)) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n)) -1/6) -3)))) 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simplify18.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
08264
114264
232264
358264
482264
584264
Stop Event
1×saturated
Counts
174 → 152
Calls
Call 1
Inputs
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
Outputs
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(/.f64 k (/.f64 n (/.f64 1/2 (PI.f64))))
(/.f64 k (*.f64 n (/.f64 (PI.f64) 1/2)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(/.f64 k (/.f64 n (/.f64 1/2 (PI.f64))))
(/.f64 k (*.f64 n (/.f64 (PI.f64) 1/2)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(/.f64 k (/.f64 n (/.f64 1/2 (PI.f64))))
(/.f64 k (*.f64 n (/.f64 (PI.f64) 1/2)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(/.f64 k (/.f64 n (/.f64 1/2 (PI.f64))))
(/.f64 k (*.f64 n (/.f64 (PI.f64) 1/2)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(/.f64 k (/.f64 n (/.f64 1/2 (PI.f64))))
(/.f64 k (*.f64 n (/.f64 (PI.f64) 1/2)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(/.f64 k (/.f64 n (/.f64 1/2 (PI.f64))))
(/.f64 k (*.f64 n (/.f64 (PI.f64) 1/2)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(/.f64 k (/.f64 n (/.f64 1/2 (PI.f64))))
(/.f64 k (*.f64 n (/.f64 (PI.f64) 1/2)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(/.f64 k (/.f64 n (/.f64 1/2 (PI.f64))))
(/.f64 k (*.f64 n (/.f64 (PI.f64) 1/2)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(/.f64 k (/.f64 n (/.f64 1/2 (PI.f64))))
(/.f64 k (*.f64 n (/.f64 (PI.f64) 1/2)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(/.f64 k (/.f64 n (/.f64 1/2 (PI.f64))))
(/.f64 k (*.f64 n (/.f64 (PI.f64) 1/2)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(/.f64 k (/.f64 n (/.f64 1/2 (PI.f64))))
(/.f64 k (*.f64 n (/.f64 (PI.f64) 1/2)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(/.f64 k (/.f64 n (/.f64 1/2 (PI.f64))))
(/.f64 k (*.f64 n (/.f64 (PI.f64) 1/2)))
(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
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(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
(/.f64 k (/.f64 n (/.f64 1/2 (PI.f64))))
(/.f64 k (*.f64 n (/.f64 (PI.f64) 1/2)))
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(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
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(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
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(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
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(/.f64 k (/.f64 n (/.f64 1/2 (PI.f64))))
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(*.f64 1/2 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (/.f64 1/2 n) (/.f64 k (PI.f64)))
(*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))
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localize27.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.2b
(pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2)))
0.2b
(*.f64 (PI.f64) (*.f64 n 2))
✓0.3b
(/.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
2 → 36
Calls

12 calls:

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

rewrite81.0ms (0.7%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
01439
130735
2398435
Stop Event
1×node limit
Counts
2 → 71
Calls
Call 1
Inputs
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(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 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))))))

simplify91.0ms (0.8%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
0751110
1210964
2662841
33762782
47625782
Stop Event
1×node limit
Counts
107 → 91
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)))))))
(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 (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 -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 -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 -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 (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 -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 (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 -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 (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 -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 (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 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) (sqrt.f64 (/.f64 1 k)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (*.f64 -2 (PI.f64)) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (*.f64 -2 (PI.f64)) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (*.f64 -2 (PI.f64)) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (*.f64 -2 (PI.f64)) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2)))
(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 (*.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (/.f64 (*.f64 -2 (PI.f64)) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (/.f64 (*.f64 -2 (PI.f64)) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (/.f64 (*.f64 -2 (PI.f64)) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (/.f64 (*.f64 -2 (PI.f64)) (/.f64 -1 n)) (fma.f64 -1/2 k 1/2))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 (sqrt.f64 2) k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 (*.f64 -1/2 (*.f64 k (sqrt.f64 2))) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 2)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 (*.f64 -1/2 (*.f64 k (sqrt.f64 2))) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2)))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 (sqrt.f64 2) k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k k)) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2))) (sqrt.f64 (*.f64 (PI.f64) n)))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 (*.f64 (PI.f64) n))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)))))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (fma.f64 (*.f64 -1/2 (*.f64 k (sqrt.f64 2))) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 2)) (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2) (*.f64 1/8 (*.f64 k (*.f64 k (sqrt.f64 2)))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 1/8 (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 (sqrt.f64 2) k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 1/8 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k k)) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2))) (*.f64 -1/48 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3)) (sqrt.f64 (*.f64 (PI.f64) n))))))))
(+.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)))) (*.f64 (*.f64 -1/48 (sqrt.f64 2)) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3))))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (fma.f64 (*.f64 -1/2 (*.f64 k (sqrt.f64 2))) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 2)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3))) (*.f64 1/8 (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (+.f64 (*.f64 1/8 (*.f64 k k)) (*.f64 -1/48 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k 3))))) (*.f64 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)))
(exp.f64 (*.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)))
(exp.f64 (*.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)))
(exp.f64 (*.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)))
(exp.f64 (*.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)))
(exp.f64 (*.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)))
(exp.f64 (*.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)))
(exp.f64 (*.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)))
(exp.f64 (*.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))

localize53.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (PI.f64) n)
✓0.2b
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2)
✓0.4b
(/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2)) (sqrt.f64 k))
✓20.5b
(cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2))
Compiler

Compiled 43 to 24 computations (44.2% saved)

series12.0ms (0.1%)

Counts
3 → 12
Calls

12 calls:

TimeVariablePointExpression
1.0ms
n
@-inf
(cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2))
1.0ms
n
@inf
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2)
1.0ms
n
@0
(cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2))
1.0ms
n
@-inf
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2)
1.0ms
n
@0
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2)

rewrite84.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
590×log-prod_binary64
341×pow-prod-down_binary64
304×pow2_binary64
242×pow-unpow_binary64
220×pow-to-exp_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01242
125334
2305434
Stop Event
1×node limit
Counts
3 → 117
Calls
Call 1
Inputs
(cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2))
(/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2)) (sqrt.f64 k))
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2)
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 *.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 (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 (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 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/2)))) (#(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 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 8 (pow.f64 (*.f64 (PI.f64) n) 3)) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 9/2) 1/9)))) (#(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)) 1/6) 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 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2) 3/4)))) (#(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)) 3/4) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (#(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 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 (*.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 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 3/2))))) (#(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 (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 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 3/2 (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 3/2 (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1/3) 1))))) (#(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 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)))))) (#(struct:change #<rule 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(#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/6) (pow.f64 k 1/4)))))) (#(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 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) -1)))) (#(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 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (neg.f64 (sqrt.f64 k))))))) (#(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 (neg.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 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))) 1) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 2 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 3/2) (pow.f64 (*.f64 (PI.f64) n) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) 3/2) (pow.f64 2 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/4) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (PI.f64)) 3/2) (pow.f64 n 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 4) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 5/2) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 8 (pow.f64 (*.f64 (PI.f64) n) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 9/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 3/2 (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3/2 (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 9/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3/4 (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) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 3/2 (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 3/2 (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3/4) 2))))))

simplify49.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
621×times-frac_binary64
514×fma-def_binary64
414×unswap-sqr_binary64
314×exp-sum_binary64
289×div-sub_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
028204
174204
2173168
3440132
41080132
52874132
Stop Event
1×node limit
Counts
129 → 121
Calls
Call 1
Inputs
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
Outputs
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (PI.f64)) 3/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2)
(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (PI.f64)) 3/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2)
(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (PI.f64)) 3/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2)
(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (PI.f64)) 3/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2)
(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (PI.f64)) 3/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2)
(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (PI.f64)) 3/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2)
(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (PI.f64)) 3/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2)
(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (PI.f64)) 3/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2)
(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (PI.f64)) 3/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2)
(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (PI.f64)) 3/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2)
(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (PI.f64)) 3/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2)
(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (PI.f64)) 3/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2)
(pow.f64 (/.f64 (PI.f64) (/.f64 1/2 n)) 3/2)

eval211.0ms (1.8%)

Compiler

Compiled 10975 to 6304 computations (42.6% saved)

prune127.0ms (1.1%)

Pruning

29 alts after pruning (23 fresh and 6 done)

PrunedKeptTotal
New61815633
Fresh4812
Picked011
Done156
Total62329652
Error
0b
Counts
652 → 29
Alt Table
Click to see full alt table
StatusErrorProgram
▶31.4b
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
✓31.2b
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
40.3b
(cbrt.f64 (pow.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n)) -3/2))
✓33.9b
(/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2)) (sqrt.f64 k))
31.5b
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
11.1b
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))
30.7b
(pow.f64 (sqrt.f64 (*.f64 (/.f64 1/2 (*.f64 (PI.f64) n)) k)) -1)
40.3b
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))
✓20.4b
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 k))
11.2b
(sqrt.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 1 (neg.f64 k))))
31.2b
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k 1/2)))
20.4b
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))
13.4b
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k))
▶0.3b
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶20.4b
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
✓11.2b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
31.4b
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/4) 2)
13.8b
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6) 3)
20.4b
(*.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
▶41.8b
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2) 1/3)
31.2b
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 n (*.f64 2 (PI.f64))))))
20.4b
(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k))
33.8b
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6) 3)
31.2b
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
32.7b
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n))) -1/2))
✓0.4b
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
30.7b
(/.f64 1 (sqrt.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n))))
✓0.3b
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))
▶31.2b
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
Compiler

Compiled 688 to 563 computations (18.2% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiled 57 to 41 computations (28.1% saved)

series7.0ms (0.1%)

Counts
2 → 12
Calls

9 calls:

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

rewrite72.0ms (0.6%)

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

Useful iterations: 2 (0.0ms)

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

simplify57.0ms (0.5%)

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

Useful iterations: 4 (0.0ms)

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

localize34.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 n (/.f64 k (*.f64 2 (PI.f64))))
✓0.2b
(/.f64 k (*.f64 2 (PI.f64)))
✓10.5b
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
Compiler

Compiled 29 to 18 computations (37.9% saved)

series14.0ms (0.1%)

Counts
3 → 36
Calls

15 calls:

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

rewrite111.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
543×log-prod_binary64
414×exp-prod_binary64
305×pow-prod-down_binary64
250×pow2_binary64
206×pow-unpow_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0932
119532
2269932
Stop Event
1×node limit
Counts
3 → 176
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
(/.f64 k (*.f64 2 (PI.f64)))
(/.f64 n (/.f64 k (*.f64 2 (PI.f64))))
Outputs
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(/.f64 1/2 (PI.f64))))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k)))) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))))) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 n) 1) (log.f64 (*.f64 k (/.f64 1/2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 n) (*.f64 (log.f64 (*.f64 k (/.f64 1/2 (PI.f64)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 n) 1) (*.f64 (log.f64 (*.f64 k (/.f64 1/2 (PI.f64)))) 1)))))))

simplify22.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
011360
119360
238360
367360
498360
5109360
Stop Event
1×saturated
Counts
212 → 179
Calls
Call 1
Inputs
(*.f64 1/2 (/.f64 k (PI.f64)))
(*.f64 1/2 (/.f64 k (PI.f64)))
(*.f64 1/2 (/.f64 k (PI.f64)))
(*.f64 1/2 (/.f64 k (PI.f64)))
(*.f64 1/2 (/.f64 k (PI.f64)))
(*.f64 1/2 (/.f64 k (PI.f64)))
(*.f64 1/2 (/.f64 k (PI.f64)))
(*.f64 1/2 (/.f64 k (PI.f64)))
(*.f64 1/2 (/.f64 k (PI.f64)))
(*.f64 1/2 (/.f64 k (PI.f64)))
(*.f64 1/2 (/.f64 k (PI.f64)))
(*.f64 1/2 (/.f64 k (PI.f64)))
(*.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 1/2 (/.f64 k (PI.f64)))
(/.f64 (*.f64 1/2 k) (PI.f64))
(*.f64 1/2 (/.f64 k (PI.f64)))
(/.f64 (*.f64 1/2 k) (PI.f64))
(*.f64 1/2 (/.f64 k (PI.f64)))
(/.f64 (*.f64 1/2 k) (PI.f64))
(*.f64 1/2 (/.f64 k (PI.f64)))
(/.f64 (*.f64 1/2 k) (PI.f64))
(*.f64 1/2 (/.f64 k (PI.f64)))
(/.f64 (*.f64 1/2 k) (PI.f64))
(*.f64 1/2 (/.f64 k (PI.f64)))
(/.f64 (*.f64 1/2 k) (PI.f64))
(*.f64 1/2 (/.f64 k (PI.f64)))
(/.f64 (*.f64 1/2 k) (PI.f64))
(*.f64 1/2 (/.f64 k (PI.f64)))
(/.f64 (*.f64 1/2 k) (PI.f64))
(*.f64 1/2 (/.f64 k (PI.f64)))
(/.f64 (*.f64 1/2 k) (PI.f64))
(*.f64 1/2 (/.f64 k (PI.f64)))
(/.f64 (*.f64 1/2 k) (PI.f64))
(*.f64 1/2 (/.f64 k (PI.f64)))
(/.f64 (*.f64 1/2 k) (PI.f64))
(*.f64 1/2 (/.f64 k (PI.f64)))
(/.f64 (*.f64 1/2 k) (PI.f64))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))
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(*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))
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(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
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(*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))
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(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
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(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
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(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))
(*.f64 2 (/.f64 (*.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (*.f64 2 (/.f64 n k)))

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.3b
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
✓1.0b
(sqrt.f64 (PI.f64))
✓10.5b
(sqrt.f64 (*.f64 (/.f64 n k) 2))
Compiler

Compiled 31 to 15 computations (51.6% saved)

series10.0ms (0.1%)

Counts
3 → 0
Calls

12 calls:

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

rewrite77.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
517×log-prod_binary64
436×prod-exp_binary64
376×exp-prod_binary64
348×pow-prod-down_binary64
254×pow2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01026
120826
2255526
Stop Event
1×node limit
Counts
3 → 116
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (/.f64 n k) 2))
(sqrt.f64 (PI.f64))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (/.f64 n k) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 (/.f64 n k) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (/.f64 n k) 2)) (pow.f64 (*.f64 (/.f64 n k) 2) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 n k) 2) 1/6) (cbrt.f64 (*.f64 (/.f64 n k) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 n k) 2) 1/4) (pow.f64 (*.f64 (/.f64 n k) 2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 n 2)) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 n k) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 4 (pow.f64 (/.f64 n k) 2)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 n k) 2) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 n k) 2) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (/.f64 n k) 2)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 n k) 2) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 n k) 2) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/2) (log.f64 (*.f64 (/.f64 n k) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2))))) (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) 2) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 n k) 2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 n k) 2) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 n k) 2) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 n k) 2) 1/4)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 n k) 2)) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 n k) 2)) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2))) 1) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (PI.f64)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (PI.f64))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) 1/6) (cbrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) 1/4) (pow.f64 (PI.f64) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (PI.f64) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (PI.f64) 2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (PI.f64) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (PI.f64) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (PI.f64)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (PI.f64) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (PI.f64) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/2) (log.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (PI.f64)))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (PI.f64))))) (sqrt.f64 (log.f64 (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (PI.f64) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (PI.f64))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3/2 (log.f64 (PI.f64))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (PI.f64) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/4 (log.f64 (PI.f64))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (PI.f64)) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (PI.f64)) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (PI.f64))) 1) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.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 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 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/6) 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 pow.f64 (exp.f64 1) (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))))) (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))))))))) (#(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 (*.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 exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/4)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 (/.f64 n k) 2)) 1/2) (log.f64 (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2))) 1) (log.f64 (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2))) (*.f64 (log.f64 (PI.f64)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 (/.f64 n k) 2)) 1/2) (*.f64 (log.f64 (PI.f64)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2))) 1) (*.f64 (log.f64 (PI.f64)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2))) (*.f64 (log.f64 (sqrt.f64 (PI.f64))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 (/.f64 n k) 2)) 1/2) (*.f64 (log.f64 (sqrt.f64 (PI.f64))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2))) 1) (*.f64 (log.f64 (sqrt.f64 (PI.f64))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (PI.f64)) 1/2) (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (PI.f64))) 1) (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log.f64 (sqrt.f64 (PI.f64))) (*.f64 (log.f64 (*.f64 (/.f64 n k) 2)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (PI.f64)) 1/2) (*.f64 (log.f64 (*.f64 (/.f64 n k) 2)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (PI.f64))) 1) (*.f64 (log.f64 (*.f64 (/.f64 n k) 2)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log.f64 (sqrt.f64 (PI.f64))) (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (PI.f64)) 1/2) (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (PI.f64))) 1) (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2))) 1)))))))

simplify8.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
116 → 116
Calls
Call 1
Inputs
Outputs

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(pow.f64 k -1/2)
✓0.1b
(sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))
0.2b
(*.f64 (PI.f64) n)
✓0.4b
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
Compiler

Compiled 34 to 19 computations (44.1% saved)

series6.0ms (0%)

Counts
3 → 12
Calls

12 calls:

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

rewrite72.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
531×log-prod_binary64
404×prod-exp_binary64
394×exp-prod_binary64
332×pow-prod-down_binary64
274×pow2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01130
122730
2257530
Stop Event
1×node limit
Counts
3 → 101
Calls
Call 1
Inputs
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))
(pow.f64 k -1/2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 1 k))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 1 k)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 1 k))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 1 k))) 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 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 1 k))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 1 k)))))) (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 1 k))))))))) (#(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 (exp.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 1 k))))))))) (#(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)) (/.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 1 k)))) 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 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 1 k)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (*.f64 -1/2 (log.f64 k)) 1) (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 -1/2 (log.f64 k)) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (*.f64 -1/2 (log.f64 k)) 1) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 -1/2 (log.f64 k)) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (*.f64 -1/2 (log.f64 k)) 1) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 1/2) (*.f64 -1/2 (log.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1) (*.f64 -1/2 (log.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (*.f64 (*.f64 -1/2 (log.f64 k)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 1/2) (*.f64 (*.f64 -1/2 (log.f64 k)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1) (*.f64 (*.f64 -1/2 (log.f64 k)) 1)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (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 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 2) 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 (exp.f64 1) (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/2) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))) (#(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 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 (log.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4)) 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))))))
((#(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 (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 -1/6) (cbrt.f64 (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 k)) (pow.f64 k -1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/4) (pow.f64 k -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 k) -1) (pow.f64 k -1/6))))) (#(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 k -3/2))))) (#(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 (*.f64 -1/2 (log.f64 k)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 k)) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 k -3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 k -1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/4 (log.f64 k)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 k) 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 -1/2 (log.f64 k)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 k) -1/4) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 k) -1/4) (*.f64 -1/4 (log.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 -1/4 (log.f64 k)) (*.f64 (log.f64 k) -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 k) -1/4) (*.f64 (log.f64 k) -1/4)))))))

simplify52.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
676×fma-def_binary64
499×div-sub_binary64
494×fma-neg_binary64
396×associate-*r*_binary64
273×associate-*l*_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01472
13072
26572
314772
441772
5117048
6549248
Stop Event
1×node limit
Counts
113 → 103
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(sqrt.f64 (/.f64 1 k))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k))))))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k))))))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k))))))
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k))))))
Outputs
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k))))))
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k))))))
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k))))))
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)
(exp.f64 (*.f64 -1/2 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 k))))))
(sqrt.f64 (/.f64 1 k))
(pow.f64 k -1/2)

localize24.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.2b
(pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2)
0.3b
(*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))
✓25.4b
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2) 1/3)
Compiler

Compiled 41 to 24 computations (41.5% saved)

series106.0ms (0.9%)

Counts
2 → 48
Calls

12 calls:

TimeVariablePointExpression
24.0ms
k
@0
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2) 1/3)
20.0ms
k
@-inf
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2) 1/3)
18.0ms
n
@inf
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2) 1/3)
16.0ms
n
@-inf
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2) 1/3)
16.0ms
n
@0
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2) 1/3)

rewrite67.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
604×log-prod_binary64
349×pow-prod-down_binary64
314×pow2_binary64
244×pow-unpow_binary64
229×pow-to-exp_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01228
126727
2319227
Stop Event
1×node limit
Counts
2 → 64
Calls
Call 1
Inputs
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2) 1/3)
(pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.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 (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)))) (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/6) (cbrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))))))) (#(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 (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 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) 2)) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))))) (#(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 exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (cbrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))))) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/4 (log.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 3/2 (log.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))) 1) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 3/2 (log.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))) 1/6) 2))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) (sqrt.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))) 3/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))) (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 n k) 3/2) (pow.f64 (*.f64 2 (PI.f64)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (PI.f64)) 3/2) (pow.f64 (/.f64 n k) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/4) (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 n k) 2) 3/2) (pow.f64 (PI.f64) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))) 4) (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 5/4) (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 9/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 3/2 (log.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3/2 (log.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 9/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3/4 (log.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))) 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 3/2 (log.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))) 1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))) 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64)))) 3/4) 2))))))

simplify64.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
660×fma-def_binary64
538×exp-sum_binary64
315×distribute-rgt-in_binary64
293×associate--r+_binary64
265×exp-diff_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0571008
11621008
2383864
3986720
42902720
Stop Event
1×node limit
Counts
112 → 78
Calls
Call 1
Inputs
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 1/3)
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 1/3)
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 1/3)
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 1/3)
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) 1/3)
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) 1/3)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
Outputs
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(cbrt.f64 (*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (/.f64 (PI.f64) k)) 3/2)))
(cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2))
(cbrt.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2))
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(cbrt.f64 (*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (/.f64 (PI.f64) k)) 3/2)))
(cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2))
(cbrt.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2))
(pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(cbrt.f64 (*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (/.f64 (PI.f64) k)) 3/2)))
(cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2))
(cbrt.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2))
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(pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (/.f64 (PI.f64) k)) 3/2))
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (/.f64 (PI.f64) k)) 3/2))
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (/.f64 (PI.f64) k)) 3/2))
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (/.f64 (PI.f64) k)) 3/2))
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (/.f64 (PI.f64) k)) 3/2))
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (/.f64 (PI.f64) k)) 3/2))
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (/.f64 (PI.f64) k)) 3/2))
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (/.f64 (PI.f64) k)) 3/2))
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (/.f64 (PI.f64) k)) 3/2))
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (/.f64 (PI.f64) k)) 3/2))
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (*.f64 -2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(*.f64 (pow.f64 n 3/2) (pow.f64 (*.f64 2 (/.f64 (PI.f64) k)) 3/2))
(pow.f64 (*.f64 2 (*.f64 n (/.f64 (PI.f64) k))) 3/2)
(pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2)

eval229.0ms (2%)

Compiler

Compiled 9599 to 6394 computations (33.4% saved)

prune129.0ms (1.1%)

Pruning

40 alts after pruning (30 fresh and 10 done)

PrunedKeptTotal
New62119640
Fresh71118
Picked011
Done1910
Total62940669
Error
0b
Counts
669 → 40
Alt Table
Click to see full alt table
StatusErrorProgram
✓31.4b
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
✓31.2b
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
40.3b
(cbrt.f64 (pow.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n)) -3/2))
20.4b
(/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))))
11.1b
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))
30.7b
(pow.f64 (sqrt.f64 (*.f64 (/.f64 1/2 (*.f64 (PI.f64) n)) k)) -1)
20.4b
(/.f64 1 (/.f64 (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))) (sqrt.f64 n)))
✓20.4b
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 k))
20.4b
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) 2)) (sqrt.f64 k))
31.2b
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k 1/2)))
31.2b
(sqrt.f64 (/.f64 n (*.f64 (/.f64 1/2 (PI.f64)) k)))
20.4b
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))
13.4b
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k))
✓20.4b
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
31.3b
(sqrt.f64 (*.f64 (/.f64 1 k) (/.f64 n (/.f64 1/2 (PI.f64)))))
✓0.3b
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓11.2b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
30.7b
(pow.f64 (/.f64 k (/.f64 n (/.f64 1/2 (PI.f64)))) -1/2)
20.4b
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))))
31.5b
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
13.8b
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6) 3)
33.8b
(pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 1/6) 3)
✓41.8b
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2) 1/3)
11.2b
(sqrt.f64 (*.f64 (/.f64 1 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
31.2b
(sqrt.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n))
20.4b
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
31.5b
(pow.f64 (cbrt.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k)))) 3/2)
31.3b
(sqrt.f64 (*.f64 (neg.f64 n) (/.f64 1 (*.f64 (neg.f64 k) (/.f64 1/2 (PI.f64))))))
41.8b
(pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 3/2) 1/3)
41.8b
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2) 1/3)
✓0.3b
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))
47.7b
(pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 3) 1/6)
33.8b
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/6) 3)
33.8b
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6) 3)
31.2b
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
32.7b
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n))) -1/2))
✓0.4b
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
30.7b
(/.f64 1 (sqrt.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n))))
✓31.2b
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
40.3b
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))
Compiler

Compiled 514 to 421 computations (18.1% saved)

regimes205.0ms (1.8%)

Counts
68 → 1
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 n (*.f64 (/.f64 1/2 (PI.f64)) k)))
(sqrt.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k 1/2)))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(pow.f64 (/.f64 k (/.f64 n (/.f64 1/2 (PI.f64)))) -1/2)
(sqrt.f64 (*.f64 (/.f64 1 k) (/.f64 n (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 n (*.f64 2 (PI.f64))))))
(/.f64 1 (sqrt.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n))))
(sqrt.f64 (*.f64 (neg.f64 n) (/.f64 1 (*.f64 (neg.f64 k) (/.f64 1/2 (PI.f64))))))
(/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) 2)) (sqrt.f64 k))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n)) -3/2))
(pow.f64 (sqrt.f64 (*.f64 (/.f64 1/2 (*.f64 (PI.f64) n)) k)) -1)
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (sqrt.f64 (/.f64 k (*.f64 2 (*.f64 (PI.f64) n)))) -1)
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(/.f64 1 (/.f64 (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))) (sqrt.f64 n)))
(pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 1/6) 3)
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 3/2) 1/3)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2) 1/3)
(pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 3) 1/6)
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/6) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/4) 2)
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2) 1/3)
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n))) -1/2))
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6) 3)
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(sqrt.f64 (*.f64 (/.f64 1 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.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)))
(sqrt.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 1 (neg.f64 k))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2)) (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6) 3)
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))
(*.f64 (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)))))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3) (/.f64 (-.f64 1 k) 2)))
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 k 2))))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4))))
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:

42.0ms
(*.f64 (*.f64 2 (PI.f64)) n)
40.0ms
n
39.0ms
k
37.0ms
(*.f64 (*.f64 2 (PI.f64)) n)
21.0ms
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
Results
ErrorSegmentsBranch
0.3b1k
0.3b1n
0.3b1(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
0.3b1(*.f64 (*.f64 2 (PI.f64)) n)
0.3b1(*.f64 (*.f64 2 (PI.f64)) n)
Compiler

Compiled 871 to 555 computations (36.3% saved)

regimes199.0ms (1.7%)

Counts
65 → 1
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 n (*.f64 (/.f64 1/2 (PI.f64)) k)))
(sqrt.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k 1/2)))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(pow.f64 (/.f64 k (/.f64 n (/.f64 1/2 (PI.f64)))) -1/2)
(sqrt.f64 (*.f64 (/.f64 1 k) (/.f64 n (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 n (*.f64 2 (PI.f64))))))
(/.f64 1 (sqrt.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n))))
(sqrt.f64 (*.f64 (neg.f64 n) (/.f64 1 (*.f64 (neg.f64 k) (/.f64 1/2 (PI.f64))))))
(/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) 2)) (sqrt.f64 k))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n)) -3/2))
(pow.f64 (sqrt.f64 (*.f64 (/.f64 1/2 (*.f64 (PI.f64) n)) k)) -1)
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (sqrt.f64 (/.f64 k (*.f64 2 (*.f64 (PI.f64) n)))) -1)
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(/.f64 1 (/.f64 (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))) (sqrt.f64 n)))
(pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 1/6) 3)
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 3/2) 1/3)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2) 1/3)
(pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 3) 1/6)
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/6) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/4) 2)
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2) 1/3)
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n))) -1/2))
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6) 3)
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(sqrt.f64 (*.f64 (/.f64 1 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.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)))
(sqrt.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 1 (neg.f64 k))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2)) (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6) 3)
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))
(*.f64 (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)))))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3) (/.f64 (-.f64 1 k) 2)))
Outputs
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))
Calls

5 calls:

42.0ms
(*.f64 (*.f64 2 (PI.f64)) n)
40.0ms
k
39.0ms
(*.f64 (*.f64 2 (PI.f64)) n)
34.0ms
n
18.0ms
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
Results
ErrorSegmentsBranch
0.3b1k
0.3b1n
0.3b1(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
0.3b1(*.f64 (*.f64 2 (PI.f64)) n)
0.3b1(*.f64 (*.f64 2 (PI.f64)) n)
Compiler

Compiled 805 to 515 computations (36% saved)

regimes233.0ms (2%)

Counts
63 → 1
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 n (*.f64 (/.f64 1/2 (PI.f64)) k)))
(sqrt.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k 1/2)))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(pow.f64 (/.f64 k (/.f64 n (/.f64 1/2 (PI.f64)))) -1/2)
(sqrt.f64 (*.f64 (/.f64 1 k) (/.f64 n (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 n (*.f64 2 (PI.f64))))))
(/.f64 1 (sqrt.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n))))
(sqrt.f64 (*.f64 (neg.f64 n) (/.f64 1 (*.f64 (neg.f64 k) (/.f64 1/2 (PI.f64))))))
(/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) 2)) (sqrt.f64 k))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n)) -3/2))
(pow.f64 (sqrt.f64 (*.f64 (/.f64 1/2 (*.f64 (PI.f64) n)) k)) -1)
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (sqrt.f64 (/.f64 k (*.f64 2 (*.f64 (PI.f64) n)))) -1)
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(/.f64 1 (/.f64 (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))) (sqrt.f64 n)))
(pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 1/6) 3)
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 3/2) 1/3)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2) 1/3)
(pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 3) 1/6)
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/6) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/4) 2)
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2) 1/3)
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n))) -1/2))
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6) 3)
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(sqrt.f64 (*.f64 (/.f64 1 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.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)))
(sqrt.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 1 (neg.f64 k))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) n)))
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2)) (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n))))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(sqrt.f64 (/.f64 (exp.f64 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) k))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) k) 1/6) 3)
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))
(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) k) 2)) k))
(*.f64 (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)))))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
Outputs
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
Calls

4 calls:

52.0ms
(*.f64 (*.f64 2 (PI.f64)) n)
48.0ms
n
39.0ms
k
20.0ms
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
Results
ErrorSegmentsBranch
0.3b1k
0.3b1n
0.3b1(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
0.3b1(*.f64 (*.f64 2 (PI.f64)) n)
Compiler

Compiled 760 to 484 computations (36.3% saved)

regimes94.0ms (0.8%)

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

3 calls:

28.0ms
(*.f64 (*.f64 2 (PI.f64)) n)
26.0ms
n
24.0ms
k
Results
ErrorSegmentsBranch
0.4b1k
0.4b1n
0.4b1(*.f64 (*.f64 2 (PI.f64)) n)
Compiler

Compiled 490 to 308 computations (37.1% saved)

regimes83.0ms (0.7%)

Counts
44 → 1
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 n (*.f64 (/.f64 1/2 (PI.f64)) k)))
(sqrt.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k 1/2)))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(pow.f64 (/.f64 k (/.f64 n (/.f64 1/2 (PI.f64)))) -1/2)
(sqrt.f64 (*.f64 (/.f64 1 k) (/.f64 n (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 n (*.f64 2 (PI.f64))))))
(/.f64 1 (sqrt.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n))))
(sqrt.f64 (*.f64 (neg.f64 n) (/.f64 1 (*.f64 (neg.f64 k) (/.f64 1/2 (PI.f64))))))
(/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) 2)) (sqrt.f64 k))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n)) -3/2))
(pow.f64 (sqrt.f64 (*.f64 (/.f64 1/2 (*.f64 (PI.f64) n)) k)) -1)
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (sqrt.f64 (/.f64 k (*.f64 2 (*.f64 (PI.f64) n)))) -1)
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(/.f64 1 (/.f64 (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))) (sqrt.f64 n)))
(pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 1/6) 3)
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 3/2) 1/3)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2) 1/3)
(pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 3) 1/6)
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/6) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/4) 2)
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2) 1/3)
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n))) -1/2))
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6) 3)
(sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))
(*.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(sqrt.f64 (*.f64 (/.f64 1 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.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:

42.0ms
k
27.0ms
n
Results
ErrorSegmentsBranch
0.4b1k
0.4b1n
Compiler

Compiled 452 to 281 computations (37.8% saved)

regimes228.0ms (2%)

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

2 calls:

138.0ms
n
72.0ms
k
Results
ErrorSegmentsBranch
0.4b2k
7.9b6n
Compiler

Compiled 438 to 272 computations (37.9% saved)

bsearch65.0ms (0.6%)

Algorithm
1×binary-search
Steps
TimeLeftRight
64.0ms
9.013442644313379e-29
1.3416901664628e-25
Compiler

Compiled 23 to 19 computations (17.4% saved)

regimes278.0ms (2.4%)

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

2 calls:

179.0ms
n
74.0ms
k
Results
ErrorSegmentsBranch
0.4b2k
7.9b6n
Compiler

Compiled 424 to 263 computations (38% saved)

bsearch37.0ms (0.3%)

Algorithm
1×binary-search
Steps
TimeLeftRight
37.0ms
9.013442644313379e-29
1.3416901664628e-25
Compiler

Compiled 23 to 19 computations (17.4% saved)

regimes188.0ms (1.6%)

Counts
40 → 2
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 n (*.f64 (/.f64 1/2 (PI.f64)) k)))
(sqrt.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k 1/2)))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(pow.f64 (/.f64 k (/.f64 n (/.f64 1/2 (PI.f64)))) -1/2)
(sqrt.f64 (*.f64 (/.f64 1 k) (/.f64 n (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 n (*.f64 2 (PI.f64))))))
(/.f64 1 (sqrt.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n))))
(sqrt.f64 (*.f64 (neg.f64 n) (/.f64 1 (*.f64 (neg.f64 k) (/.f64 1/2 (PI.f64))))))
(/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) 2)) (sqrt.f64 k))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n)) -3/2))
(pow.f64 (sqrt.f64 (*.f64 (/.f64 1/2 (*.f64 (PI.f64) n)) k)) -1)
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (sqrt.f64 (/.f64 k (*.f64 2 (*.f64 (PI.f64) n)))) -1)
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(/.f64 1 (/.f64 (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))) (sqrt.f64 n)))
(pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 1/6) 3)
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 3/2) 1/3)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2) 1/3)
(pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 3) 1/6)
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/6) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 1/4) 2)
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2) 1/3)
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n))) -1/2))
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (*.f64 n (PI.f64)) k)) 1/6) 3)
Outputs
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 3) 1/6)
Calls

2 calls:

82.0ms
n
44.0ms
k
Results
ErrorSegmentsBranch
16.5b2k
20.4b1n
Compiler

Compiled 399 to 248 computations (37.8% saved)

bsearch93.0ms (0.8%)

Algorithm
1×binary-search
Steps
TimeLeftRight
92.0ms
3.78328323067937e+140
5.107323585678284e+151
Compiler

Compiled 303 to 259 computations (14.5% saved)

regimes69.0ms (0.6%)

Counts
33 → 1
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 n (*.f64 (/.f64 1/2 (PI.f64)) k)))
(sqrt.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k 1/2)))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(pow.f64 (/.f64 k (/.f64 n (/.f64 1/2 (PI.f64)))) -1/2)
(sqrt.f64 (*.f64 (/.f64 1 k) (/.f64 n (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 n (*.f64 2 (PI.f64))))))
(/.f64 1 (sqrt.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n))))
(sqrt.f64 (*.f64 (neg.f64 n) (/.f64 1 (*.f64 (neg.f64 k) (/.f64 1/2 (PI.f64))))))
(/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) 2)) (sqrt.f64 k))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n)) -3/2))
(pow.f64 (sqrt.f64 (*.f64 (/.f64 1/2 (*.f64 (PI.f64) n)) k)) -1)
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (sqrt.f64 (/.f64 k (*.f64 2 (*.f64 (PI.f64) n)))) -1)
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(/.f64 1 (/.f64 (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))) (sqrt.f64 n)))
(pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 1/6) 3)
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 3/2) 1/3)
(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 3/2) 1/3)
Outputs
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
Calls

2 calls:

36.0ms
k
20.0ms
n
Results
ErrorSegmentsBranch
20.4b1k
20.4b1n
Compiler

Compiled 322 to 199 computations (38.2% saved)

regimes87.0ms (0.7%)

Counts
30 → 1
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 n (*.f64 (/.f64 1/2 (PI.f64)) k)))
(sqrt.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k 1/2)))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(pow.f64 (/.f64 k (/.f64 n (/.f64 1/2 (PI.f64)))) -1/2)
(sqrt.f64 (*.f64 (/.f64 1 k) (/.f64 n (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 n (*.f64 2 (PI.f64))))))
(/.f64 1 (sqrt.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n))))
(sqrt.f64 (*.f64 (neg.f64 n) (/.f64 1 (*.f64 (neg.f64 k) (/.f64 1/2 (PI.f64))))))
(/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) 2)) (sqrt.f64 k))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n)) -3/2))
(pow.f64 (sqrt.f64 (*.f64 (/.f64 1/2 (*.f64 (PI.f64) n)) k)) -1)
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(pow.f64 (sqrt.f64 (/.f64 k (*.f64 2 (*.f64 (PI.f64) n)))) -1)
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(/.f64 1 (/.f64 (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))) (sqrt.f64 n)))
(pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 1/6) 3)
Outputs
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
Calls

2 calls:

61.0ms
n
16.0ms
k
Results
ErrorSegmentsBranch
20.4b1k
20.4b1n
Compiler

Compiled 289 to 178 computations (38.4% saved)

regimes36.0ms (0.3%)

Counts
25 → 1
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 n (*.f64 (/.f64 1/2 (PI.f64)) k)))
(sqrt.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k 1/2)))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))
(sqrt.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))))
(pow.f64 (/.f64 k (/.f64 n (/.f64 1/2 (PI.f64)))) -1/2)
(sqrt.f64 (*.f64 (/.f64 1 k) (/.f64 n (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (/.f64 1 (/.f64 k (*.f64 n (*.f64 2 (PI.f64))))))
(/.f64 1 (sqrt.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n))))
(sqrt.f64 (*.f64 (neg.f64 n) (/.f64 1 (*.f64 (neg.f64 k) (/.f64 1/2 (PI.f64))))))
(/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) 2)) (sqrt.f64 k))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 (/.f64 n k) 2)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (*.f64 2 (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 k 1/2) (*.f64 (PI.f64) n)) -3/2))
(pow.f64 (sqrt.f64 (*.f64 (/.f64 1/2 (*.f64 (PI.f64) n)) k)) -1)
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (*.f64 2 (PI.f64))) 3/2))
Outputs
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))))
Calls

2 calls:

14.0ms
n
14.0ms
k
Results
ErrorSegmentsBranch
20.4b1k
20.4b1n
Compiler

Compiled 237 to 146 computations (38.4% saved)

regimes22.0ms (0.2%)

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

2 calls:

9.0ms
n
8.0ms
k
Results
ErrorSegmentsBranch
20.4b1k
20.4b1n
Compiler

Compiled 133 to 89 computations (33.1% saved)

regimes20.0ms (0.2%)

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

2 calls:

9.0ms
k
7.0ms
n
Results
ErrorSegmentsBranch
30.7b1k
30.7b1n
Compiler

Compiled 115 to 77 computations (33% saved)

regimes15.0ms (0.1%)

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

2 calls:

7.0ms
n
5.0ms
k
Results
ErrorSegmentsBranch
31.2b1k
31.2b1n
Compiler

Compiled 64 to 42 computations (34.4% saved)

regimes11.0ms (0.1%)

Counts
4 → 1
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 n (*.f64 (/.f64 1/2 (PI.f64)) k)))
(sqrt.f64 (*.f64 (*.f64 2 (/.f64 (PI.f64) k)) n))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k 1/2)))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
Outputs
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k 1/2)))
Calls

2 calls:

5.0ms
n
4.0ms
k
Results
ErrorSegmentsBranch
31.2b1k
31.2b1n
Compiler

Compiled 40 to 27 computations (32.5% saved)

regimes8.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0.2%)

Threshold costs -0.0b (-0.2%)

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

2 calls:

3.0ms
n
3.0ms
k
Results
ErrorSegmentsBranch
31.2b1k
31.2b1n
Compiler

Compiled 24 to 17 computations (29.2% saved)

simplify46.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
20×*-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
078379
1102379
2106379
3108379
4109379
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 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))
(if (<=.f64 k 4020129755448055/44601490397061246283071436545296723011960832) (*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (sqrt.f64 (*.f64 (/.f64 1 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))
(if (<=.f64 k 4020129755448055/44601490397061246283071436545296723011960832) (*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(if (<=.f64 k 50999999999999999567744448016011272031221976631549659212880425833347650933505257117270677784475721244741093108897650448040809853591262051510853270765568) (*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 3) 1/6))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))))
(/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))))
(pow.f64 (/.f64 k (/.f64 n (/.f64 1/2 (PI.f64)))) -1/2)
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k 1/2)))
(sqrt.f64 (/.f64 n (*.f64 (/.f64 1/2 (PI.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))
(*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (-.f64 1 k) 2)))
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (-.f64 1 k) 2)) (pow.f64 k -1/2))
(/.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 4020129755448055/44601490397061246283071436545296723011960832) (*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (sqrt.f64 (*.f64 (/.f64 1 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))
(if (<=.f64 k 4020129755448055/44601490397061246283071436545296723011960832) (*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 (*.f64 (/.f64 1 k) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))))
(if (<=.f64 k 4020129755448055/44601490397061246283071436545296723011960832) (*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(if (<=.f64 k 4020129755448055/44601490397061246283071436545296723011960832) (*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)))
(if (<=.f64 k 50999999999999999567744448016011272031221976631549659212880425833347650933505257117270677784475721244741093108897650448040809853591262051510853270765568) (*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 3) 1/6))
(if (<=.f64 k 50999999999999999567744448016011272031221976631549659212880425833347650933505257117270677784475721244741093108897650448040809853591262051510853270765568) (*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (/.f64 (PI.f64) k))) 3) 1/6))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(*.f64 (pow.f64 k -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))
(*.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))))
(/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 k (/.f64 1/2 (PI.f64)))))
(pow.f64 (/.f64 k (/.f64 n (/.f64 1/2 (PI.f64)))) -1/2)
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (*.f64 k 1/2)))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2)))
(sqrt.f64 (/.f64 n (*.f64 (/.f64 1/2 (PI.f64)) k)))
(sqrt.f64 (/.f64 n (*.f64 k (/.f64 1/2 (PI.f64)))))
Compiler

Compiled 269 to 212 computations (21.2% saved)

soundness119.0ms (1%)

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

Useful iterations: 5 (0.0ms)

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

Compiled 350 to 293 computations (16.3% saved)

end243.0ms (2.1%)

Compiler

Compiled 239 to 158 computations (33.9% saved)

Profiling

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