Details

Time bar (total: 4.8s)

analyze350.0ms (7.3%)

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

Compiled 19 to 16 computations (15.8% saved)

sample3.3s (69.3%)

Results
1.4s8256×body128valid
1.2s1386×body1024invalid
405.0ms671×body512invalid
189.0ms1120×body128invalid
124.0ms370×body256invalid

preprocess35.0ms (0.7%)

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

Useful iterations: 0 (0.0ms)

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

Compiled 18 to 15 computations (16.7% saved)

simplify17.0ms (0.4%)

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

Useful iterations: 5 (0.0ms)

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

eval1.0ms (0%)

Compiler

Compiled 31 to 23 computations (25.8% saved)

prune3.0ms (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
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 66 to 54 computations (18.2% saved)

localize11.0ms (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 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
✓0.2b
(*.f64 (PI.f64) n)

series65.0ms (1.3%)

Counts
3 → 48
Calls

15 calls:

TimeVariablePointExpression
24.0ms
n
@0
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
19.0ms
n
@-inf
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
12.0ms
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))
1.0ms
k
@-inf
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

rewrite62.0ms (1.3%)

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

simplify42.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
392×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
33626845
Stop Event
1×node limit
Counts
130 → 101
Calls
Call 1
Inputs
(*.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))
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
Outputs
(*.f64 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))
(*.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 (PI.f64) 2)) (log.f64 n))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 n (*.f64 (PI.f64) 2)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (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 (PI.f64) 2)) (log.f64 n))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 n (*.f64 (PI.f64) 2)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (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 (PI.f64) 2)) (log.f64 n))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 n (*.f64 (PI.f64) 2)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (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 (PI.f64) 2)) (log.f64 n))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 n (*.f64 (PI.f64) 2)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (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 (PI.f64) 2)) (log.f64 n))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 n (*.f64 (PI.f64) 2)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (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 (PI.f64) 2)) (log.f64 n))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 n (*.f64 (PI.f64) 2)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (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 (PI.f64) 2)) (log.f64 n))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 n (*.f64 (PI.f64) 2)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (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 (PI.f64) 2)) (log.f64 n))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 n (*.f64 (PI.f64) 2)))) (sqrt.f64 (/.f64 1 k)))
(*.f64 (pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (fma.f64 -1/2 k 1/2)) (sqrt.f64 (/.f64 1 k)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 -1/2 k 1/2)))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 n (*.f64 (PI.f64) 2))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 n (*.f64 (PI.f64) 2))))
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(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 n (*.f64 (PI.f64) 2))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 n (*.f64 (PI.f64) 2))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 n (*.f64 (PI.f64) 2))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 n (*.f64 (PI.f64) 2))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (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))))))
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(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 n (*.f64 (PI.f64) 2))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(pow.f64 (*.f64 -2 (/.f64 (PI.f64) (/.f64 -1 n))) (fma.f64 -1/2 k 1/2))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 k (log.f64 (*.f64 (*.f64 n (PI.f64)) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 -1/2 (sqrt.f64 2)) (*.f64 k (log.f64 (*.f64 n (*.f64 (PI.f64) 2)))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (+.f64 (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) 2)) (*.f64 -1/2 k)) 1) (sqrt.f64 2)))
(*.f64 (+.f64 (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) 2)) (*.f64 -1/2 k)) 1) (*.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)))))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 k (log.f64 (*.f64 (*.f64 n (PI.f64)) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 1/8 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k k)) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) 2)) 2))))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) 2))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) 2))) 2) (*.f64 (*.f64 k (sqrt.f64 2)) k))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 (*.f64 n (PI.f64)) 2))))) (fma.f64 (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 k k))) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) 2)) 2) (sqrt.f64 2))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) 2)) 2) (*.f64 k k))) (+.f64 (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) 2)) (*.f64 -1/2 k)) 1))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 k (log.f64 (*.f64 (*.f64 n (PI.f64)) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))) (fma.f64 1/8 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k k)) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) 2)) 2))) (*.f64 -1/48 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 3)) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) 2)) 3)))))))
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) 2))) 2) (*.f64 (*.f64 k (sqrt.f64 2)) k))) (*.f64 -1/48 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) 2))) 3)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 -1/2 (sqrt.f64 2)) (*.f64 k (log.f64 (*.f64 n (*.f64 (PI.f64) 2))))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) 2)) 3))) (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) 2)) 2) (*.f64 k k))))) (*.f64 (+.f64 (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) 2)) (*.f64 -1/2 k)) 1) (sqrt.f64 2))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) 2)) 2) (+.f64 (*.f64 -1/48 (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) 2)) (pow.f64 k 3))) (*.f64 1/8 (*.f64 k k))))) (*.f64 (+.f64 (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) 2)) (*.f64 -1/2 k)) 1) (sqrt.f64 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 (PI.f64) 2)) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 n (*.f64 (PI.f64) 2))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (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 (PI.f64) 2)) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 n (*.f64 (PI.f64) 2))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (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 (PI.f64) 2)) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 n (*.f64 (PI.f64) 2))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (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 (PI.f64) 2)) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 n (*.f64 (PI.f64) 2))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (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 (PI.f64) 2)) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 n (*.f64 (PI.f64) 2))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (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 (PI.f64) 2)) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 n (*.f64 (PI.f64) 2))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (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 (PI.f64) 2)) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 n (*.f64 (PI.f64) 2))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (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 (PI.f64) 2)) (log.f64 n)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (log.f64 (*.f64 n (*.f64 (PI.f64) 2))))
(pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (fma.f64 -1/2 k 1/2))

eval42.0ms (0.9%)

Compiler

Compiled 2138 to 1428 computations (33.2% saved)

prune39.0ms (0.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New947101
Fresh011
Picked101
Done000
Total958103
Error
0.0b
Counts
103 → 8
Alt Table
Click to see full alt table
StatusErrorProgram
0.4b
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) -1)
0.3b
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))
0.5b
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
▶0.3b
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 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)))
0.8b
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))
21.9b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) 2)) 2) (+.f64 (*.f64 -1/48 (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) 2)) (pow.f64 k 3))) (*.f64 1/8 (*.f64 k k))))) (*.f64 (+.f64 (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) 2)) (*.f64 -1/2 k)) 1) (sqrt.f64 2)))) (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)))
Compiler

Compiled 412 to 322 computations (21.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series24.0ms (0.5%)

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

rewrite63.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
256×expm1-udef_binary64
256×log1p-udef_binary64
251×log-pow_binary64
146×add-sqr-sqrt_binary64
142×pow1_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01475
129857
2381453
Stop Event
1×node limit
Counts
4 → 103
Calls
Call 1
Inputs
(*.f64 (PI.f64) (*.f64 n 2))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) (sqrt.f64 k))
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))))
Outputs
((#(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 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 2) 1/2)))) (#(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 sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 2))))) (#(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 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 (PI.f64) 3) (pow.f64 (*.f64 n 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 n 2) 3) (pow.f64 (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 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 log1p.f64 (expm1.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))
((#(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 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (/.f64 1 (sqrt.f64 (/.f64 k (*.f64 2 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (*.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 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (pow.f64 k -1/2)))))) (#(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 1 (/.f64 (pow.f64 (*.f64 2 (*.f64 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(#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (*.f64 (sqrt.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 (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) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) 1) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 1) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (sqrt.f64 k)) (sqrt.f64 (*.f64 2 (*.f64 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(*.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 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 log1p.f64 (expm1.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 (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 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (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 n 2)) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 n 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) 1/2) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x 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 log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) 3) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2) (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 2 (*.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 2 (*.f64 (PI.f64) n)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))))))

simplify45.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
540×distribute-lft-out_binary64
366×associate-*r*_binary64
354×associate-*l*_binary64
198×distribute-rgt-out_binary64
184×fma-def_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
041598
1122572
2409513
32665502
44203495
Stop Event
1×node limit
Counts
127 → 114
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 (*.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 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))) (*.f64 (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 -1/2 k)) 1) (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 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (*.f64 k k)) (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 (pow.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 2) (*.f64 k k)))))))
(*.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 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (*.f64 k k)) (sqrt.f64 2))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (*.f64 k k))) (+.f64 (*.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 -1/2 (*.f64 1/8 (*.f64 k (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 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 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (*.f64 k k)) (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 (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 2) (*.f64 k k)))) (*.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 (*.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))) (sqrt.f64 2)) (sqrt.f64 2))))
(*.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 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (*.f64 k k))) (*.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 1/8 (*.f64 k k)) (*.f64 -1/48 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k 3)))))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) (+.f64 -1/2 (*.f64 1/8 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (*.f64 (*.f64 -1/48 (pow.f64 k 3)) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))))
(*.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)))

eval52.0ms (1.1%)

Compiler

Compiled 2878 to 1794 computations (37.7% saved)

prune54.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1275132
Fresh437
Picked101
Done000
Total1328140
Error
0b
Counts
140 → 8
Alt Table
Click to see full alt table
StatusErrorProgram
10.4b
(*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (/.f64 1 (sqrt.f64 (/.f64 k (*.f64 2 (*.f64 (PI.f64) n))))))
0.3b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (sqrt.f64 k)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
0.4b
(/.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)))) (sqrt.f64 k))
0.8b
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))
0.4b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/4)))
0.4b
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) -1)
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)))
▶0.2b
(*.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (pow.f64 k -1/2)))
Compiler

Compiled 370 to 280 computations (24.3% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series13.0ms (0.3%)

Counts
3 → 12
Calls

15 calls:

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

rewrite65.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
784×log-prod_binary64
255×expm1-udef_binary64
255×log1p-udef_binary64
251×log-pow_binary64
146×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01462
129850
2361450
Stop Event
1×node limit
Counts
3 → 68
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (pow.f64 k -1/2)))
(sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))
(*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (pow.f64 k -1/2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))) (pow.f64 k -1/2))) (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))) (pow.f64 k -1/2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))) (pow.f64 k -1/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 3/2) (pow.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) k) k) -1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) k) k) -1/2) 3) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 k -1/2))))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) (cbrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))))) (#(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 n (*.f64 2 (PI.f64))) 1/4) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (PI.f64)) 1/2) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))
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simplify26.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
846×fma-def_binary64
308×distribute-rgt-in_binary64
283×exp-prod_binary64
259×exp-sum_binary64
253×distribute-lft-in_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
037352
193348
2249348
3740320
42139276
Stop Event
1×node limit
Counts
80 → 73
Calls
Call 1
Inputs
(*.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 (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 (*.f64 2 (*.f64 n (PI.f64))) (*.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 (*.f64 2 (*.f64 n (PI.f64))) (*.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 (*.f64 2 (*.f64 n (PI.f64))) (*.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 (*.f64 2 (*.f64 n (PI.f64))) (*.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 (*.f64 2 (*.f64 n (PI.f64))) (*.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 (*.f64 2 (*.f64 n (PI.f64))) (*.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 (*.f64 2 (*.f64 n (PI.f64))) (*.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 (*.f64 2 (*.f64 n (PI.f64))) (*.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 (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 k (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (pow.f64 (/.f64 -1 n) (neg.f64 k)) (pow.f64 (*.f64 (PI.f64) -2) k)) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (pow.f64 (/.f64 (*.f64 -2 (PI.f64)) (/.f64 -1 n)) 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 (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 k (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (pow.f64 (/.f64 -1 n) (neg.f64 k)) (pow.f64 (*.f64 (PI.f64) -2) k)) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (pow.f64 (/.f64 (*.f64 -2 (PI.f64)) (/.f64 -1 n)) 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 (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 k (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (pow.f64 (/.f64 -1 n) (neg.f64 k)) (pow.f64 (*.f64 (PI.f64) -2) k)) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (pow.f64 (/.f64 (*.f64 -2 (PI.f64)) (/.f64 -1 n)) 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 (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 k (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (pow.f64 (/.f64 -1 n) (neg.f64 k)) (pow.f64 (*.f64 (PI.f64) -2) k)) -1/2))
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (pow.f64 (/.f64 (*.f64 -2 (PI.f64)) (/.f64 -1 n)) k) -1/2))

eval53.0ms (1.1%)

Compiler

Compiled 2625 to 1761 computations (32.9% saved)

prune45.0ms (0.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1101111
Fresh257
Picked011
Done000
Total1127119
Error
0b
Counts
119 → 7
Alt Table
Click to see full alt table
StatusErrorProgram
0.4b
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) -1)
0.4b
(*.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 (sqrt.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) k) k) -1/2)) 2))
10.4b
(*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (/.f64 1 (sqrt.f64 (/.f64 k (*.f64 2 (*.f64 (PI.f64) n))))))
▶0.4b
(/.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)))) (sqrt.f64 k))
0.8b
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))
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)))
✓0.2b
(*.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (pow.f64 k -1/2)))
Compiler

Compiled 300 to 232 computations (22.7% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series56.0ms (1.2%)

Counts
4 → 16
Calls

21 calls:

TimeVariablePointExpression
40.0ms
k
@0
(*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
2.0ms
n
@-inf
(*.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))))
2.0ms
n
@-inf
(/.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)))) (sqrt.f64 k))
1.0ms
n
@0
(/.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)))) (sqrt.f64 k))
1.0ms
k
@inf
(/.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)))) (sqrt.f64 k))

rewrite72.0ms (1.5%)

Algorithm
1×batch-egg-rewrite
Rules
310×log1p-udef_binary64
177×add-sqr-sqrt_binary64
175×associate-*r*_binary64
172×*-un-lft-identity_binary64
172×pow1_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01887
136775
2455475
Stop Event
1×node limit
Counts
4 → 95
Calls
Call 1
Inputs
(*.f64 k (log.f64 (*.f64 2 (*.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 n (PI.f64))
(/.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)))) (sqrt.f64 k))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (log.f64 2) k) (*.f64 (log.f64 (*.f64 n (PI.f64))) k))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 k (log.f64 2)) (*.f64 k (log.f64 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (-.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3) (pow.f64 k 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (-.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (*.f64 2 (pow.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (sqrt.f64 2) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2)) 3) (pow.f64 (*.f64 n (PI.f64)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 n (PI.f64)) 3/2) (pow.f64 (*.f64 (sqrt.f64 2) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2) (sqrt.f64 (*.f64 2 (*.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 (sqrt.f64 (*.f64 n (PI.f64))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (PI.f64)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (PI.f64)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 n (PI.f64)) 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 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 expm1.f64 (log1p.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 log1p.f64 (expm1.f64 (*.f64 n (PI.f64))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (*.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2) (sqrt.f64 (*.f64 n (PI.f64)))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 2) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2)) (/.f64 1 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 2) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2)) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 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simplify30.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
374×associate-*r*_binary64
349×associate-*l*_binary64
220×associate-+l+_binary64
214×associate-+r+_binary64
212×fma-def_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
057442
1169396
2489369
33029358
Stop Event
1×node limit
Counts
111 → 108
Calls
Call 1
Inputs
(*.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(*.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(*.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(*.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(*.f64 k (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 k (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 k (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 k (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 k (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))
(*.f64 k (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))
(*.f64 k (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))
(*.f64 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 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(*.f64 k (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(*.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(*.f64 k (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(*.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(*.f64 k (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(*.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(*.f64 k (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(*.f64 k (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(*.f64 k (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(*.f64 k (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(*.f64 k (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(*.f64 k (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(*.f64 k (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(*.f64 k (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 k (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(*.f64 k (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(*.f64 k (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))
(*.f64 k (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(*.f64 k (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(*.f64 k (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))
(*.f64 k (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(*.f64 k (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(*.f64 k (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))
(*.f64 k (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(*.f64 k (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(*.f64 k (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))
(*.f64 k (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(*.f64 k (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 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 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2))))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (+.f64 (*.f64 (*.f64 -1/2 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1) (sqrt.f64 2)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (+.f64 1 (*.f64 (*.f64 -1/2 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (sqrt.f64 2)))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 1/8 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)))))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 (PI.f64) n))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 k k))) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 1/8 (*.f64 k k)) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2))) (*.f64 (+.f64 (*.f64 (*.f64 -1/2 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1) (sqrt.f64 2))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (+.f64 (+.f64 1 (*.f64 (*.f64 -1/2 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (*.f64 (*.f64 1/8 (*.f64 k k)) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 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 (sqrt.f64 2) (*.f64 (*.f64 k k) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)))) (*.f64 -1/48 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3))))))))
(+.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 k k))) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2)))))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3))) (*.f64 (*.f64 1/8 (*.f64 k k)) (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2)))) (*.f64 (+.f64 (*.f64 (*.f64 -1/2 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1) (sqrt.f64 2))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) 2) (+.f64 (*.f64 -1/48 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 3))) (*.f64 1/8 (*.f64 k k)))) (*.f64 (*.f64 -1/2 k) (log.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))

eval56.0ms (1.2%)

Compiler

Compiled 3213 to 1888 computations (41.2% saved)

prune45.0ms (0.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1204124
Fresh415
Picked011
Done011
Total1247131
Error
0b
Counts
131 → 7
Alt Table
Click to see full alt table
StatusErrorProgram
0.3b
(*.f64 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2)) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))
10.4b
(*.f64 (*.f64 (sqrt.f64 2) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2)) (/.f64 1 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))
✓0.4b
(/.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)))) (sqrt.f64 k))
12.1b
(sqrt.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) (*.f64 2 (pow.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2) 2))) k))
0.3b
(*.f64 (*.f64 (sqrt.f64 2) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 k -1/2)))
0.4b
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) -1)
✓0.2b
(*.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (pow.f64 k -1/2)))
Compiler

Compiled 153 to 114 computations (25.5% saved)

regimes49.0ms (1%)

Accuracy

Total -34.0b remaining (-14714.7%)

Threshold costs -34.0b (-14714.7%)

Counts
19 → 1
Calls
Call 1
Inputs
(*.f64 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2)) (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (*.f64 (sqrt.f64 2) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2)) (/.f64 1 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))
(sqrt.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) (*.f64 2 (pow.f64 (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2) 2))) k))
(*.f64 (*.f64 (sqrt.f64 2) (pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) k) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 k -1/2)))
(*.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 (sqrt.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) k) k) -1/2)) 2))
(*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (/.f64 1 (sqrt.f64 (/.f64 k (*.f64 2 (*.f64 (PI.f64) n))))))
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (sqrt.f64 k)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))
(/.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)))) (sqrt.f64 k))
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/4)))
(*.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (pow.f64 k -1/2)))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) -1)
(*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) (sqrt.f64 k))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) 2)) 2) (+.f64 (*.f64 -1/48 (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) 2)) (pow.f64 k 3))) (*.f64 1/8 (*.f64 k k))))) (*.f64 (+.f64 (*.f64 (log.f64 (*.f64 (*.f64 n (PI.f64)) 2)) (*.f64 -1/2 k)) 1) (sqrt.f64 2)))) (sqrt.f64 k))
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
Outputs
(*.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (pow.f64 k -1/2)))
Results
TimeErrorSegmentsBranch
11.0ms0.2b1k
10.0ms0.2b1n
6.0ms0.2b1(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
11.0ms0.2b1(*.f64 (*.f64 2 (PI.f64)) n)
Compiler

Compiled 444 to 289 computations (34.9% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01432
11932
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (pow.f64 k -1/2)))
Outputs
(*.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (pow.f64 k -1/2)))

end20.0ms (0.4%)

Stop Event
1×fuel
Compiler

Compiled 44 to 32 computations (27.3% saved)

Profiling

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