Details

Time bar (total: 5.4s)

analyze368.0ms (6.8%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%50%50%2
0%50%50%3
0%50%50%4
12.5%37.5%50%5
12.5%34.3%53.2%6
15.6%26.5%57.9%7
15.6%22.6%61.8%8
17.2%17.6%65.3%9
17.2%15%67.8%10
18%12.2%69.9%11
18%10.8%71.3%12
18.3%9.3%72.4%13
18.3%8.5%73.1%14
Compiler

Compiled 19 to 16 computations (15.8% saved)

sample3.2s (58.9%)

Results
1.4s8256×body128valid
1.1s1336×body1024invalid
398.0ms677×body512invalid
196.0ms1152×body128invalid
119.0ms364×body256invalid

preprocess34.0ms (0.6%)

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

Useful iterations: 0 (0.0ms)

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

Compiled 18 to 15 computations (16.7% saved)

simplify18.0ms (0.3%)

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

Useful iterations: 5 (0.0ms)

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

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Compiled 97 to 77 computations (20.6% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series69.0ms (1.3%)

Counts
3 → 48
Calls

15 calls:

TimeVariablePointExpression
29.0ms
n
@0
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
23.0ms
n
@-inf
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
8.0ms
n
@inf
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
3.0ms
k
@0
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
2.0ms
k
@-inf
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

rewrite55.0ms (1%)

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

Useful iterations: 0 (0.0ms)

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

simplify43.0ms (0.8%)

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

Useful iterations: 3 (0.0ms)

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

prune212.0ms (3.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New967103
Fresh101
Picked101
Done000
Total987105
Error
0.0b
Counts
105 → 7
Alt Table
StatusErrorProgram
0.7b
(*.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
▶0.3b
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) (sqrt.f64 (/.f64 1 k)))
0.4b
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
0.4b
(*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
0.4b
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
0.5b
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 k))
8.7b
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2) k))
Compiler

Compiled 2457 to 1677 computations (31.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series10.0ms (0.2%)

Counts
4 → 28
Calls

18 calls:

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

rewrite60.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
679×log-prod_binary64
249×expm1-udef_binary64
249×log1p-udef_binary64
228×log-pow_binary64
148×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01549
130844
2351144
Stop Event
1×node limit
Counts
4 → 93
Calls
Call 1
Inputs
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)) (sqrt.f64 (/.f64 1 k)))
(*.f64 n (PI.f64))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2))
(sqrt.f64 (/.f64 1 k))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k)))) (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 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 2 n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 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 2 n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)) 3) (pow.f64 (/.f64 1 k) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 1 k) 3/2) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 n (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64))) (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 n (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 n (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (PI.f64)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 n (PI.f64))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 n (PI.f64)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 n) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 n (PI.f64))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)))) (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (*.f64 2 (fma.f64 -1/2 k 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (*.f64 2 (fma.f64 -1/2 k 1/2)))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 (fma.f64 -1/2 k 1/2)) (pow.f64 (*.f64 n (PI.f64)) (fma.f64 -1/2 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 -1/2 k 1/2)) (pow.f64 2 (fma.f64 -1/2 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 (fma.f64 -1/2 k 1/2)) (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) 2)) (fma.f64 -1/2 k 1/2)) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (fma.f64 -1/2 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (fma.f64 -1/2 k 1/2)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))) (fma.f64 -1/2 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 n) (fma.f64 -1/2 k 1/2)) (pow.f64 (PI.f64) (fma.f64 -1/2 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (*.f64 -1/2 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (*.f64 2 (fma.f64 -1/2 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 -1/2 k 1/2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 -1/2 k 1/2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (fma.f64 -1/2 k 1/2))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2))) (cbrt.f64 (exp.f64 (pow.f64 k -1/2))))) (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 (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 (cbrt.f64 (/.f64 1 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 (pow.f64 (cbrt.f64 (pow.f64 k -2)) 1/2) (pow.f64 (cbrt.f64 (/.f64 1 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 (pow.f64 (/.f64 1 k) 3/2) 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 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 (pow.f64 (/.f64 1 k) 3/2))))) (#(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))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 k -1/2)))))))

simplify40.0ms (0.7%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
071926
1195812
2624721
33583662
Stop Event
1×node limit
Counts
121 → 111
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))))))))
Outputs
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 k))) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)))
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (+.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)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)))
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (+.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)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)))
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (+.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)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
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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))
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(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
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(+.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2) (*.f64 (sqrt.f64 2) (*.f64 k k)))) (*.f64 -1/48 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3)))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 -1/2 (sqrt.f64 2)) (*.f64 k (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (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 (*.f64 1/8 (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)) (*.f64 k k)) (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3)))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (+.f64 (*.f64 -1/48 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k 3))) (*.f64 1/8 (*.f64 k k)))) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))))

prune179.0ms (3.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1101111
Fresh066
Picked101
Done000
Total1117118
Error
0b
Counts
118 → 7
Alt Table
StatusErrorProgram
0.7b
(*.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
▶0.4b
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
0.4b
(*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
0.4b
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
0.5b
(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (*.f64 -1/2 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 (/.f64 1 k)))
0.5b
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 k))
8.7b
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2) k))
Compiler

Compiled 2619 to 1886 computations (28% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series99.0ms (1.8%)

Counts
3 → 48
Calls

18 calls:

TimeVariablePointExpression
52.0ms
n
@0
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
15.0ms
n
@-inf
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
9.0ms
n
@inf
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
7.0ms
k
@0
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
5.0ms
k
@0
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))

rewrite66.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
259×expm1-udef_binary64
259×log1p-udef_binary64
154×add-sqr-sqrt_binary64
148×pow1_binary64
146×*-un-lft-identity_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01656
134249
2388449
Stop Event
1×node limit
Counts
3 → 102
Calls
Call 1
Inputs
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))
Outputs
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(#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 2 (fma.f64 k -1/2 1/2))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 2 (fma.f64 k -1/2 1/2))) k)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 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*.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 2 (fma.f64 k -1/2 1/2)))) 1) (/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 2 (fma.f64 k -1/2 1/2)))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 2 (fma.f64 k -1/2 1/2))) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (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)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) 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) n) (*.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) 2)) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 2 (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 (PI.f64) n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))))))

simplify45.0ms (0.8%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
0681308
11901132
25911116
330841029
Stop Event
1×node limit
Counts
150 → 126
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n)))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))
(exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (*.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))
(sqrt.f64 (*.f64 n (PI.f64)))
(+.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (*.f64 k (log.f64 (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 n (PI.f64))))))
(+.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 k (log.f64 (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 1/8 (*.f64 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 n (PI.f64))) 2)) (sqrt.f64 (*.f64 n (PI.f64)))))))
(+.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/48 (*.f64 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 n (PI.f64))) 3)) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 k (log.f64 (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 1/8 (*.f64 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 n (PI.f64))) 2)) (sqrt.f64 (*.f64 n (PI.f64))))))))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
Outputs
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (+.f64 1/2 (*.f64 -1/2 k))) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (PI.f64)) (log.f64 n))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 2 (fma.f64 k -1/2 1/2))) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))))
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(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (neg.f64 (PI.f64))) (neg.f64 (log.f64 (/.f64 -1 n)))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n))))
(exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n)))))
(pow.f64 (/.f64 (neg.f64 (PI.f64)) (/.f64 -1 n)) (fma.f64 k -1/2 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 -1 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (neg.f64 (PI.f64))) (neg.f64 (log.f64 (/.f64 -1 n)))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n))))
(exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (-.f64 (log.f64 (neg.f64 (PI.f64))) (log.f64 (/.f64 -1 n)))))
(pow.f64 (/.f64 (neg.f64 (PI.f64)) (/.f64 -1 n)) (fma.f64 k -1/2 1/2))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt.f64 (*.f64 (PI.f64) n))
(+.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (*.f64 k (log.f64 (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 n (PI.f64))))))
(+.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) n)))) (sqrt.f64 (*.f64 (PI.f64) n))))
(*.f64 (+.f64 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) n)))) 1) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) n))) 1))
(+.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 k (log.f64 (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 1/8 (*.f64 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 n (PI.f64))) 2)) (sqrt.f64 (*.f64 n (PI.f64)))))))
(+.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 -1/2 (*.f64 k (*.f64 (log.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 1/8 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) 2))))))
(+.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) 2))) (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) n)))))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) 2))) (fma.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) n))) 1)))
(*.f64 (+.f64 (*.f64 (*.f64 k (log.f64 (*.f64 (PI.f64) n))) (+.f64 (*.f64 1/8 (*.f64 k (log.f64 (*.f64 (PI.f64) n)))) -1/2)) 1) (sqrt.f64 (*.f64 (PI.f64) n)))
(+.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/48 (*.f64 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 n (PI.f64))) 3)) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 k (log.f64 (*.f64 n (PI.f64)))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 1/8 (*.f64 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 n (PI.f64))) 2)) (sqrt.f64 (*.f64 n (PI.f64))))))))
(+.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 -1/48 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) 3))) (fma.f64 -1/2 (*.f64 k (*.f64 (log.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 1/8 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) 2)))))))
(+.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) 2))) (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) n)))))) (*.f64 (+.f64 (*.f64 (*.f64 -1/48 (pow.f64 k 3)) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) 3)) 1) (sqrt.f64 (*.f64 (PI.f64) n))))
(fma.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) n))) (*.f64 1/8 (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) 2)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (fma.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) 3)) 1)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 (*.f64 k (log.f64 (*.f64 (PI.f64) n))) (+.f64 (*.f64 1/8 (*.f64 k (log.f64 (*.f64 (PI.f64) n)))) -1/2)) (fma.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 (PI.f64) n)) 3)) 1)))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))

prune315.0ms (5.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1442146
Fresh156
Picked101
Done000
Total1467153
Error
0b
Counts
153 → 7
Alt Table
StatusErrorProgram
0.7b
(*.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
0.4b
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
0.5b
(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (*.f64 -1/2 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 (/.f64 1 k)))
0.5b
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 k))
8.7b
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2) k))
▶0.4b
(/.f64 1 (/.f64 1 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
0.4b
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (/.f64 (neg.f64 (PI.f64)) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
Compiler

Compiled 3822 to 2574 computations (32.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series15.0ms (0.3%)

Counts
2 → 24
Calls

12 calls:

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

rewrite60.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
259×expm1-udef_binary64
259×log1p-udef_binary64
156×add-sqr-sqrt_binary64
149×pow1_binary64
148×*-un-lft-identity_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01643
134240
2395640
Stop Event
1×node limit
Counts
2 → 85
Calls
Call 1
Inputs
(/.f64 1 (/.f64 1 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(/.f64 1 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 2 (fma.f64 k -1/2 1/2)))) (*.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 2 (fma.f64 k -1/2 1/2))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 2 (fma.f64 k -1/2 1/2))) k)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (neg.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) 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simplify31.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
443×fma-def_binary64
353×distribute-rgt-in_binary64
307×distribute-lft-in_binary64
242×exp-sum_binary64
211×associate-+l+_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
047764
1116684
2338684
31345540
Stop Event
1×node limit
Counts
109 → 95
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 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
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 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 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 (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)) (pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 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 (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)) (pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 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 (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)) (pow.f64 (exp.f64 (+.f64 1/2 (*.f64 -1/2 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 (+.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))) (+.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 (+.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))) (+.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 (+.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))) (+.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 (+.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))) (+.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 (+.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 -2 (/.f64 (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 -2 (/.f64 (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 -2 (/.f64 (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 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(/.f64 (sqrt.f64 k) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(/.f64 (sqrt.f64 k) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(/.f64 (sqrt.f64 k) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(/.f64 (sqrt.f64 k) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(/.f64 (sqrt.f64 k) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(/.f64 (sqrt.f64 k) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(/.f64 (sqrt.f64 k) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))))
(/.f64 (sqrt.f64 k) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))))
(/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(*.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (*.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 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 k) (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(*.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (*.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 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 k) (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(*.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (*.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 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 k) (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(*.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (*.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 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 k) (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 -1/2 k 1/2)))

prune282.0ms (5.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1582160
Fresh246
Picked101
Done000
Total1616167
Error
0b
Counts
167 → 6
Alt Table
StatusErrorProgram
0.4b
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
0.5b
(/.f64 1 (*.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (fma.f64 k -1/2 1/2))) (pow.f64 k 1/4)) (pow.f64 k 1/4)))
0.5b
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 k))
0.3b
(*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (fma.f64 k -1/2 1/2))) -1) (pow.f64 k -1/2))
0.5b
(*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (*.f64 -1/2 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 2 n)))) (sqrt.f64 (/.f64 1 k)))
0.4b
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (/.f64 (neg.f64 (PI.f64)) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
Compiler

Compiled 3703 to 2569 computations (30.6% saved)

regimes164.0ms (3%)

Accuracy

Total -47.8b remaining (-16599.3%)

Threshold costs -47.8b (-16599.3%)

Counts
77 → 1
Compiler

Compiled 1477 to 985 computations (33.3% saved)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Rules
3×*-commutative_binary64
1×*-lft-identity_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01520
12020
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 1 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
Outputs
(*.f64 1 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

end18.0ms (0.3%)

Stop Event
1×fuel
Compiler

Compiled 30 to 24 computations (20% saved)

Profiling

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