Details

Time bar (total: 2.5s)

analyze6.0ms (0.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%50%50%3
25%25%50%4
37.5%12.5%50%5
43.7%6.2%50%6
46.9%3.1%50%7
48.4%1.6%50%8
49.2%0.8%50%9
49.6%0.4%50%10
49.8%0.2%50%11
49.9%0.1%50%12
49.9%0%50.1%13
49.9%0%50.1%14
Compiler

Compiled 22 to 17 computations (22.7% saved)

sample1.0s (40.7%)

Results
1.0s8256×body128valid
1.0ms5×body128invalid

preprocess33.0ms (1.3%)

Algorithm
2×egg-herbie
Rules
1332×fma-def_binary64
553×distribute-rgt-in_binary64
496×unsub-neg_binary64
223×distribute-rgt-neg-out_binary64
221×distribute-lft-neg-out_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01731
14228
210926
332126
496826
5174724
6370624
011
Stop Event
1×saturated
1×node limit
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
Outputs
(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (+.f64 2 (*.f64 -6 (*.f64 v v))))))
(/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (+.f64 2 (*.f64 (*.f64 v v) -6))))
(/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))
(/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
(/.f64 (/.f64 (/.f64 4/3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))
Compiler

Compiled 21 to 16 computations (23.8% saved)

simplify25.0ms (1%)

Algorithm
1×egg-herbie
Rules
1332×fma-def_binary64
553×distribute-rgt-in_binary64
496×unsub-neg_binary64
223×distribute-rgt-neg-out_binary64
221×distribute-lft-neg-out_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01731
14228
210926
332126
496826
5174724
6370624
Stop Event
1×node limit
Counts
1 → 2
Calls
Call 1
Inputs
(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
Outputs
(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (+.f64 2 (*.f64 -6 (*.f64 v v))))))
(/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (+.f64 2 (*.f64 (*.f64 v v) -6))))
(/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))
(/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
(/.f64 (/.f64 (/.f64 4/3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
▶0.0b
(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))
1.0b
(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
Compiler

Compiled 113 to 85 computations (24.8% saved)

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
✓0.0b
(/.f64 -4/3 (fma.f64 v v -1))
✓0.0b
(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))

series10.0ms (0.4%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
2.0ms
v
@0
(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))
2.0ms
v
@inf
(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))
1.0ms
v
@-inf
(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))
1.0ms
v
@inf
(*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
1.0ms
v
@0
(*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

rewrite59.0ms (2.3%)

Algorithm
1×batch-egg-rewrite
Rules
251×expm1-udef_binary64
251×log1p-udef_binary64
205×log-pow_binary64
143×add-sqr-sqrt_binary64
134×*-un-lft-identity_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01446
129446
2367946
Stop Event
1×node limit
Counts
3 → 84
Calls
Call 1
Inputs
(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))
(/.f64 -4/3 (fma.f64 v v -1))
(*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -4/3 (/.f64 (/.f64 1 (fma.f64 v v -1)) (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -4/3 (/.f64 1 (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)) (*.f64 (PI.f64) (fma.f64 v v -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -4/3 (*.f64 (/.f64 1 (fma.f64 v v -1)) (/.f64 1 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -4/3 (fma.f64 v v -1)) (/.f64 1 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v 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2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) 2) (PI.f64)) (/.f64 (cbrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (PI.f64)) (/.f64 (sqrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (/.f64 (sqrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (/.f64 (/.f64 1 (fma.f64 v v -1)) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) 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(sqrt.f64 (fma.f64 v (*.f64 v -6) 2)) (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)) (neg.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (/.f64 -4/3 (fma.f64 v v -1)) 3) (pow.f64 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 -4/3 (fma.f64 v v -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -4/3 (/.f64 1 (fma.f64 v v -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -4/3 (fma.f64 v v -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 -4/3 (fma.f64 v v -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (pow.f64 (cbrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) 2) (cbrt.f64 (/.f64 -4/3 (fma.f64 v v -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (sqrt.f64 (/.f64 -4/3 (fma.f64 v v -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4/3 (/.f64 1 (neg.f64 (fma.f64 v v -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 v v -1)) -4/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 -4/3 (fma.f64 v v -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 -4/3 (fma.f64 v v -1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (fma.f64 v v -1) -3/4) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 16/9 (pow.f64 (fma.f64 v v -1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 -4/3 (fma.f64 v v -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 -4/3 (fma.f64 v v -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 -4/3 (fma.f64 v v -1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 -4/3 (fma.f64 v v -1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 -4/3 (fma.f64 v v -1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 -4/3 (fma.f64 v v -1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 -4/3 (fma.f64 v v -1))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (fma.f64 v (*.f64 v -6) 2) (pow.f64 (PI.f64) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (fma.f64 v (*.f64 v -6) 2) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (fma.f64 v (*.f64 v -6) 2) 3/2) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) 1))))))

simplify45.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
893×fma-def_binary64
420×times-frac_binary64
341×associate-/l*_binary64
180×distribute-rgt-in_binary64
165×distribute-lft-in_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01891656
16171582
221101515
Stop Event
1×node limit
Counts
120 → 146
Calls
Call 1
Inputs
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 2) (-.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 2) (-.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 4) (-.f64 (+.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (*.f64 (sqrt.f64 1/2) (PI.f64))))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))))
(+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 6) (-.f64 (+.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (*.f64 -1/2 (/.f64 (-.f64 27/2 (*.f64 3/4 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (*.f64 (sqrt.f64 1/2) (PI.f64)))) (*.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (*.f64 (sqrt.f64 1/2) (PI.f64)))))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 2) (-.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 4) (-.f64 (+.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (*.f64 (sqrt.f64 1/2) (PI.f64))))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))))
(*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64))))
(+.f64 (*.f64 -4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64)))))
(+.f64 (*.f64 -4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (+.f64 (*.f64 -4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64))))))
(+.f64 (*.f64 -4/3 (/.f64 (-.f64 (+.f64 (*.f64 -1/2 (/.f64 (+.f64 1/162 (*.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 (sqrt.f64 -1/6) 2)))) (*.f64 (sqrt.f64 -1/6) (PI.f64)))) (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (PI.f64)))))) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 9))) (+.f64 (*.f64 -4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (+.f64 (*.f64 -4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64)))))))
(*.f64 4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64))))
(+.f64 (*.f64 4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (*.f64 4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64)))))
(+.f64 (*.f64 4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (+.f64 (*.f64 4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (*.f64 4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64))))))
(+.f64 (*.f64 4/3 (/.f64 (-.f64 (+.f64 (*.f64 -1/2 (/.f64 (+.f64 1/162 (*.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 (sqrt.f64 -1/6) 2)))) (*.f64 (sqrt.f64 -1/6) (PI.f64)))) (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (PI.f64)))))) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 9))) (+.f64 (*.f64 4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (+.f64 (*.f64 4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (*.f64 4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64)))))))
4/3
(+.f64 4/3 (*.f64 4/3 (pow.f64 v 2)))
(+.f64 4/3 (+.f64 (*.f64 4/3 (pow.f64 v 4)) (*.f64 4/3 (pow.f64 v 2))))
(+.f64 4/3 (+.f64 (*.f64 4/3 (pow.f64 v 4)) (+.f64 (*.f64 4/3 (pow.f64 v 6)) (*.f64 4/3 (pow.f64 v 2)))))
(/.f64 -4/3 (pow.f64 v 2))
(neg.f64 (+.f64 (*.f64 4/3 (/.f64 1 (pow.f64 v 4))) (*.f64 4/3 (/.f64 1 (pow.f64 v 2)))))
(neg.f64 (+.f64 (*.f64 4/3 (/.f64 1 (pow.f64 v 2))) (+.f64 (*.f64 4/3 (/.f64 1 (pow.f64 v 4))) (*.f64 4/3 (/.f64 1 (pow.f64 v 6))))))
(neg.f64 (+.f64 (*.f64 4/3 (/.f64 1 (pow.f64 v 8))) (+.f64 (*.f64 4/3 (/.f64 1 (pow.f64 v 2))) (+.f64 (*.f64 4/3 (/.f64 1 (pow.f64 v 6))) (*.f64 4/3 (/.f64 1 (pow.f64 v 4)))))))
(/.f64 -4/3 (pow.f64 v 2))
(neg.f64 (+.f64 (*.f64 4/3 (/.f64 1 (pow.f64 v 4))) (*.f64 4/3 (/.f64 1 (pow.f64 v 2)))))
(neg.f64 (+.f64 (*.f64 4/3 (/.f64 1 (pow.f64 v 2))) (+.f64 (*.f64 4/3 (/.f64 1 (pow.f64 v 4))) (*.f64 4/3 (/.f64 1 (pow.f64 v 6))))))
(neg.f64 (+.f64 (*.f64 4/3 (/.f64 1 (pow.f64 v 8))) (+.f64 (*.f64 4/3 (/.f64 1 (pow.f64 v 2))) (+.f64 (*.f64 4/3 (/.f64 1 (pow.f64 v 6))) (*.f64 4/3 (/.f64 1 (pow.f64 v 4)))))))
(*.f64 (sqrt.f64 2) (PI.f64))
(+.f64 (*.f64 -3 (/.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (PI.f64)))
(+.f64 (*.f64 -9/2 (/.f64 (*.f64 (pow.f64 v 4) (PI.f64)) (pow.f64 (sqrt.f64 2) 3))) (+.f64 (*.f64 -3 (/.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (PI.f64))))
(+.f64 (*.f64 -9/2 (/.f64 (*.f64 (pow.f64 v 4) (PI.f64)) (pow.f64 (sqrt.f64 2) 3))) (+.f64 (*.f64 -3 (/.f64 (*.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 2))) (+.f64 (*.f64 -27/2 (/.f64 (*.f64 (pow.f64 v 6) (PI.f64)) (pow.f64 (sqrt.f64 2) 5))) (*.f64 (sqrt.f64 2) (PI.f64)))))
(*.f64 (sqrt.f64 -6) (*.f64 v (PI.f64)))
(+.f64 (/.f64 (PI.f64) (*.f64 (sqrt.f64 -6) v)) (*.f64 (sqrt.f64 -6) (*.f64 v (PI.f64))))
(+.f64 (*.f64 (sqrt.f64 -6) (*.f64 v (PI.f64))) (+.f64 (*.f64 -1/2 (/.f64 (PI.f64) (*.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3)))) (/.f64 (PI.f64) (*.f64 v (sqrt.f64 -6)))))
(+.f64 (*.f64 (sqrt.f64 -6) (*.f64 v (PI.f64))) (+.f64 (*.f64 1/2 (/.f64 (PI.f64) (*.f64 (pow.f64 (sqrt.f64 -6) 5) (pow.f64 v 5)))) (+.f64 (*.f64 -1/2 (/.f64 (PI.f64) (*.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3)))) (/.f64 (PI.f64) (*.f64 v (sqrt.f64 -6))))))
(*.f64 -1 (*.f64 v (*.f64 (sqrt.f64 -6) (PI.f64))))
(+.f64 (*.f64 -1 (*.f64 v (*.f64 (sqrt.f64 -6) (PI.f64)))) (*.f64 -1 (/.f64 (PI.f64) (*.f64 (sqrt.f64 -6) v))))
(+.f64 (*.f64 -1 (*.f64 v (*.f64 (sqrt.f64 -6) (PI.f64)))) (+.f64 (*.f64 -1 (/.f64 (PI.f64) (*.f64 (sqrt.f64 -6) v))) (*.f64 1/2 (/.f64 (PI.f64) (*.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3))))))
(+.f64 (*.f64 -1 (*.f64 v (*.f64 (sqrt.f64 -6) (PI.f64)))) (+.f64 (*.f64 -1 (/.f64 (PI.f64) (*.f64 (sqrt.f64 -6) v))) (+.f64 (*.f64 -1/2 (/.f64 (PI.f64) (*.f64 (pow.f64 (sqrt.f64 -6) 5) (pow.f64 v 5)))) (*.f64 1/2 (/.f64 (PI.f64) (*.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3)))))))
Outputs
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 2) (-.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(fma.f64 -4/3 (*.f64 (*.f64 v v) (-.f64 (neg.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 3/4 (*.f64 (sqrt.f64 1/2) (PI.f64))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (*.f64 (fma.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) -1 (/.f64 -3/4 (*.f64 (sqrt.f64 1/2) (PI.f64)))) (*.f64 -4/3 (*.f64 v v))))
(fma.f64 -4/3 (*.f64 (*.f64 v v) (-.f64 (/.f64 -3/4 (*.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (sqrt.f64 1/2) (PI.f64)))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))
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4/3
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(fma.f64 -1 (*.f64 (sqrt.f64 -6) (*.f64 (PI.f64) v)) (fma.f64 -1 (/.f64 (/.f64 (PI.f64) v) (sqrt.f64 -6)) (fma.f64 -1/2 (/.f64 (PI.f64) (*.f64 (pow.f64 v 5) (pow.f64 (sqrt.f64 -6) 5))) (/.f64 (*.f64 1/2 (PI.f64)) (*.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 3))))))
(fma.f64 -1 (fma.f64 v (*.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) v)) (fma.f64 1/2 (/.f64 (PI.f64) (*.f64 (pow.f64 v 3) (*.f64 (sqrt.f64 -6) -6))) (/.f64 (*.f64 (PI.f64) -1/2) (*.f64 (pow.f64 v 5) (pow.f64 (sqrt.f64 -6) 5)))))
(-.f64 (fma.f64 -1/2 (/.f64 (PI.f64) (*.f64 (pow.f64 v 5) (pow.f64 (sqrt.f64 -6) 5))) (*.f64 (/.f64 (PI.f64) (*.f64 (pow.f64 v 3) (sqrt.f64 -6))) -1/12)) (fma.f64 (PI.f64) (*.f64 v (sqrt.f64 -6)) (/.f64 (/.f64 (PI.f64) v) (sqrt.f64 -6))))

prune322.0ms (12.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1442146
Fresh101
Picked101
Done000
Total1462148
Error
0b
Counts
148 → 2
Alt Table
StatusErrorProgram
▶0.0b
(*.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (/.f64 (/.f64 1 (fma.f64 v v -1)) (PI.f64)))
0.0b
(*.f64 (/.f64 (sqrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (PI.f64)) (/.f64 (sqrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))
Compiler

Compiled 4189 to 3246 computations (22.5% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 1 (fma.f64 v v -1))
✓0.0b
(/.f64 (/.f64 1 (fma.f64 v v -1)) (PI.f64))
✓1.0b
(*.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (/.f64 (/.f64 1 (fma.f64 v v -1)) (PI.f64)))
✓1.0b
(/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

series8.0ms (0.3%)

Counts
4 → 48
Calls

12 calls:

TimeVariablePointExpression
1.0ms
v
@inf
(/.f64 1 (fma.f64 v v -1))
1.0ms
v
@0
(/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
1.0ms
v
@inf
(/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
1.0ms
v
@0
(/.f64 (/.f64 1 (fma.f64 v v -1)) (PI.f64))
1.0ms
v
@-inf
(/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

rewrite73.0ms (2.9%)

Algorithm
1×batch-egg-rewrite
Rules
278×expm1-udef_binary64
278×log1p-udef_binary64
162×add-sqr-sqrt_binary64
152×*-un-lft-identity_binary64
152×pow1_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01660
133757
2420657
Stop Event
1×node limit
Counts
4 → 132
Calls
Call 1
Inputs
(/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
(*.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (/.f64 (/.f64 1 (fma.f64 v v -1)) (PI.f64)))
(/.f64 (/.f64 1 (fma.f64 v v -1)) (PI.f64))
(/.f64 1 (fma.f64 v v -1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -4/3 (pow.f64 (fma.f64 v (*.f64 v -6) 2) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) (cbrt.f64 (/.f64 16/9 (fma.f64 v (*.f64 v -6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 16/9 (fma.f64 v (*.f64 v -6) 2))) (cbrt.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) (sqrt.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4/3 (/.f64 1 (neg.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 v (*.f64 v -6) 2) -1/2) -4/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)) -3/4) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 16/9 (fma.f64 v (*.f64 v -6) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 -4/3 (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)) (*.f64 (fma.f64 v v -1) (PI.f64)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -4/3 (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)) (*.f64 (fma.f64 v v -1) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -4/3 (*.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -4/3 (/.f64 (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)) (PI.f64)) (/.f64 1 (fma.f64 v v -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -4/3 (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)) (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (*.f64 (fma.f64 v v -1) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)) -3/4) (*.f64 (fma.f64 v v -1) 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#<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 -4/3 (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)) (fma.f64 v v -1))) 1) (PI.f64))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 -4/3 (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)) (fma.f64 v v -1))) (cbrt.f64 (pow.f64 (PI.f64) 2))) (cbrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 -4/3 (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)) (fma.f64 v v -1))) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 4/3 (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64)))) (neg.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 -1 (fma.f64 v v -1)) (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) (neg.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (/.f64 -1 (fma.f64 v v -1))) (neg.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 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simplify55.0ms (2.2%)

Algorithm
1×egg-herbie
Rules
701×fma-def_binary64
409×associate-/r*_binary64
298×associate-/l*_binary64
268×times-frac_binary64
184×distribute-lft-in_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01982049
16101976
219931881
Stop Event
1×node limit
Counts
180 → 206
Calls
Call 1
Inputs
(*.f64 -4/3 (sqrt.f64 1/2))
(+.f64 (*.f64 -1 (/.f64 (pow.f64 v 2) (sqrt.f64 1/2))) (*.f64 -4/3 (sqrt.f64 1/2)))
(+.f64 (*.f64 -1 (/.f64 (pow.f64 v 2) (sqrt.f64 1/2))) (+.f64 (*.f64 -2/3 (/.f64 (*.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 v 4)) (sqrt.f64 1/2))) (*.f64 -4/3 (sqrt.f64 1/2))))
(+.f64 (*.f64 -1 (/.f64 (pow.f64 v 2) (sqrt.f64 1/2))) (+.f64 (*.f64 -2/3 (/.f64 (*.f64 (pow.f64 v 6) (-.f64 27/2 (*.f64 3/4 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2))))) (sqrt.f64 1/2))) (+.f64 (*.f64 -2/3 (/.f64 (*.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 v 4)) (sqrt.f64 1/2))) (*.f64 -4/3 (sqrt.f64 1/2)))))
(*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) v))
(+.f64 (*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) v)) (*.f64 1/27 (/.f64 1 (*.f64 (pow.f64 v 3) (sqrt.f64 -1/6)))))
(+.f64 (*.f64 1/27 (/.f64 1 (*.f64 (pow.f64 v 3) (sqrt.f64 -1/6)))) (+.f64 (*.f64 2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (pow.f64 v 5) (sqrt.f64 -1/6)))) (*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) v))))
(+.f64 (*.f64 1/27 (/.f64 1 (*.f64 (pow.f64 v 3) (sqrt.f64 -1/6)))) (+.f64 (*.f64 2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (pow.f64 v 5) (sqrt.f64 -1/6)))) (+.f64 (*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) v)) (*.f64 2/3 (/.f64 (+.f64 (*.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 (sqrt.f64 -1/6) 2))) 1/162) (*.f64 (pow.f64 v 7) (sqrt.f64 -1/6)))))))
(*.f64 4/3 (/.f64 (sqrt.f64 -1/6) v))
(-.f64 (*.f64 4/3 (/.f64 (sqrt.f64 -1/6) v)) (*.f64 1/27 (/.f64 1 (*.f64 (pow.f64 v 3) (sqrt.f64 -1/6)))))
(-.f64 (+.f64 (*.f64 -2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (pow.f64 v 5) (sqrt.f64 -1/6)))) (*.f64 4/3 (/.f64 (sqrt.f64 -1/6) v))) (*.f64 1/27 (/.f64 1 (*.f64 (pow.f64 v 3) (sqrt.f64 -1/6)))))
(-.f64 (+.f64 (*.f64 -2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (pow.f64 v 5) (sqrt.f64 -1/6)))) (+.f64 (*.f64 4/3 (/.f64 (sqrt.f64 -1/6) v)) (*.f64 -2/3 (/.f64 (+.f64 (*.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 (sqrt.f64 -1/6) 2))) 1/162) (*.f64 (pow.f64 v 7) (sqrt.f64 -1/6)))))) (*.f64 1/27 (/.f64 1 (*.f64 (pow.f64 v 3) (sqrt.f64 -1/6)))))
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 2) (-.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 2) (-.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 4) (-.f64 (+.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (*.f64 (sqrt.f64 1/2) (PI.f64))))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))))
(+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 6) (-.f64 (+.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (*.f64 -1/2 (/.f64 (-.f64 27/2 (*.f64 3/4 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (*.f64 (sqrt.f64 1/2) (PI.f64)))) (*.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (*.f64 (sqrt.f64 1/2) (PI.f64)))))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 2) (-.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 4) (-.f64 (+.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (*.f64 (sqrt.f64 1/2) (PI.f64))))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))))
(*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64))))
(+.f64 (*.f64 -4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64)))))
(+.f64 (*.f64 -4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (+.f64 (*.f64 -4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64))))))
(+.f64 (*.f64 -4/3 (/.f64 (-.f64 (+.f64 (*.f64 -1/2 (/.f64 (+.f64 1/162 (*.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 (sqrt.f64 -1/6) 2)))) (*.f64 (sqrt.f64 -1/6) (PI.f64)))) (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (PI.f64)))))) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 9))) (+.f64 (*.f64 -4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (+.f64 (*.f64 -4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64)))))))
(*.f64 4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64))))
(+.f64 (*.f64 4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (*.f64 4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64)))))
(+.f64 (*.f64 4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (+.f64 (*.f64 4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (*.f64 4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64))))))
(+.f64 (*.f64 4/3 (/.f64 (-.f64 (+.f64 (*.f64 -1/2 (/.f64 (+.f64 1/162 (*.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 (sqrt.f64 -1/6) 2)))) (*.f64 (sqrt.f64 -1/6) (PI.f64)))) (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (PI.f64)))))) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 9))) (+.f64 (*.f64 4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (+.f64 (*.f64 4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (*.f64 4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64)))))))
(/.f64 -1 (PI.f64))
(-.f64 (*.f64 -1 (/.f64 (pow.f64 v 2) (PI.f64))) (/.f64 1 (PI.f64)))
(-.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 v 4) (PI.f64))) (*.f64 -1 (/.f64 (pow.f64 v 2) (PI.f64)))) (/.f64 1 (PI.f64)))
(-.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 v 6) (PI.f64))) (+.f64 (*.f64 -1 (/.f64 (pow.f64 v 4) (PI.f64))) (*.f64 -1 (/.f64 (pow.f64 v 2) (PI.f64))))) (/.f64 1 (PI.f64)))
(/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64)))
(+.f64 (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))) (/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64))))
(+.f64 (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64))) (/.f64 1 (*.f64 (pow.f64 v 6) (PI.f64)))))
(+.f64 (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (pow.f64 v 8) (PI.f64))) (/.f64 1 (*.f64 (pow.f64 v 6) (PI.f64))))))
(/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64)))
(+.f64 (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))) (/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64))))
(+.f64 (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64))) (/.f64 1 (*.f64 (pow.f64 v 6) (PI.f64)))))
(+.f64 (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (pow.f64 v 8) (PI.f64))) (/.f64 1 (*.f64 (pow.f64 v 6) (PI.f64))))))
-1
(-.f64 (*.f64 -1 (pow.f64 v 2)) 1)
(-.f64 (+.f64 (*.f64 -1 (pow.f64 v 2)) (*.f64 -1 (pow.f64 v 4))) 1)
(-.f64 (+.f64 (*.f64 -1 (pow.f64 v 2)) (+.f64 (*.f64 -1 (pow.f64 v 6)) (*.f64 -1 (pow.f64 v 4)))) 1)
(/.f64 1 (pow.f64 v 2))
(+.f64 (/.f64 1 (pow.f64 v 4)) (/.f64 1 (pow.f64 v 2)))
(+.f64 (/.f64 1 (pow.f64 v 4)) (+.f64 (/.f64 1 (pow.f64 v 6)) (/.f64 1 (pow.f64 v 2))))
(+.f64 (/.f64 1 (pow.f64 v 4)) (+.f64 (/.f64 1 (pow.f64 v 6)) (+.f64 (/.f64 1 (pow.f64 v 2)) (/.f64 1 (pow.f64 v 8)))))
(/.f64 1 (pow.f64 v 2))
(+.f64 (/.f64 1 (pow.f64 v 4)) (/.f64 1 (pow.f64 v 2)))
(+.f64 (/.f64 1 (pow.f64 v 4)) (+.f64 (/.f64 1 (pow.f64 v 6)) (/.f64 1 (pow.f64 v 2))))
(+.f64 (/.f64 1 (pow.f64 v 4)) (+.f64 (/.f64 1 (pow.f64 v 6)) (+.f64 (/.f64 1 (pow.f64 v 2)) (/.f64 1 (pow.f64 v 8)))))
Outputs
(*.f64 -4/3 (sqrt.f64 1/2))
(+.f64 (*.f64 -1 (/.f64 (pow.f64 v 2) (sqrt.f64 1/2))) (*.f64 -4/3 (sqrt.f64 1/2)))
(fma.f64 -1 (/.f64 (*.f64 v v) (sqrt.f64 1/2)) (*.f64 -4/3 (sqrt.f64 1/2)))
(-.f64 (*.f64 -4/3 (sqrt.f64 1/2)) (/.f64 v (/.f64 (sqrt.f64 1/2) v)))
(-.f64 (*.f64 -4/3 (sqrt.f64 1/2)) (*.f64 (/.f64 v (sqrt.f64 1/2)) v))
(+.f64 (*.f64 -1 (/.f64 (pow.f64 v 2) (sqrt.f64 1/2))) (+.f64 (*.f64 -2/3 (/.f64 (*.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 v 4)) (sqrt.f64 1/2))) (*.f64 -4/3 (sqrt.f64 1/2))))
(fma.f64 -1 (/.f64 (*.f64 v v) (sqrt.f64 1/2)) (fma.f64 -2/3 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (/.f64 (sqrt.f64 1/2) (pow.f64 v 4))) (*.f64 -4/3 (sqrt.f64 1/2))))
(-.f64 (fma.f64 -4/3 (sqrt.f64 1/2) (/.f64 (*.f64 (*.f64 -2/3 (pow.f64 v 4)) (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2))) (sqrt.f64 1/2))) (/.f64 v (/.f64 (sqrt.f64 1/2) v)))
(-.f64 (fma.f64 -4/3 (sqrt.f64 1/2) (*.f64 -2/3 (*.f64 (/.f64 (pow.f64 v 4) (sqrt.f64 1/2)) (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2))))) (*.f64 (/.f64 v (sqrt.f64 1/2)) v))
(+.f64 (*.f64 -1 (/.f64 (pow.f64 v 2) (sqrt.f64 1/2))) (+.f64 (*.f64 -2/3 (/.f64 (*.f64 (pow.f64 v 6) (-.f64 27/2 (*.f64 3/4 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2))))) (sqrt.f64 1/2))) (+.f64 (*.f64 -2/3 (/.f64 (*.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 v 4)) (sqrt.f64 1/2))) (*.f64 -4/3 (sqrt.f64 1/2)))))
(fma.f64 -1 (/.f64 (*.f64 v v) (sqrt.f64 1/2)) (fma.f64 -2/3 (/.f64 (*.f64 (pow.f64 v 6) (+.f64 27/2 (*.f64 -3/4 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2))))) (sqrt.f64 1/2)) (fma.f64 -2/3 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (/.f64 (sqrt.f64 1/2) (pow.f64 v 4))) (*.f64 -4/3 (sqrt.f64 1/2)))))
(-.f64 (fma.f64 -2/3 (*.f64 (/.f64 (pow.f64 v 6) (sqrt.f64 1/2)) (+.f64 27/2 (*.f64 (-.f64 9 (/.f64 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2) 1/2)) -3/4))) (fma.f64 -4/3 (sqrt.f64 1/2) (/.f64 (*.f64 (*.f64 -2/3 (pow.f64 v 4)) (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2))) (sqrt.f64 1/2)))) (/.f64 v (/.f64 (sqrt.f64 1/2) v)))
(-.f64 (fma.f64 -4/3 (sqrt.f64 1/2) (fma.f64 -2/3 (*.f64 (/.f64 (pow.f64 v 4) (sqrt.f64 1/2)) (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2))) (/.f64 (*.f64 -45/8 (pow.f64 v 6)) (sqrt.f64 1/2)))) (*.f64 (/.f64 v (sqrt.f64 1/2)) v))
(*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) v))
(+.f64 (*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) v)) (*.f64 1/27 (/.f64 1 (*.f64 (pow.f64 v 3) (sqrt.f64 -1/6)))))
(fma.f64 -4/3 (/.f64 (sqrt.f64 -1/6) v) (/.f64 1/27 (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3))))
(+.f64 (*.f64 1/27 (/.f64 1 (*.f64 (pow.f64 v 3) (sqrt.f64 -1/6)))) (+.f64 (*.f64 2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (pow.f64 v 5) (sqrt.f64 -1/6)))) (*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) v))))
(+.f64 (/.f64 1/27 (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3))) (fma.f64 2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 5))) (*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) v))))
(+.f64 (/.f64 1/27 (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3))) (fma.f64 -4/3 (/.f64 (sqrt.f64 -1/6) v) (/.f64 (+.f64 1/81 (*.f64 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2) 2/3)) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 5)))))
(+.f64 (/.f64 1/27 (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3))) (fma.f64 -4/3 (/.f64 (sqrt.f64 -1/6) v) (/.f64 (fma.f64 2/3 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2) 1/81) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 5)))))
(+.f64 (*.f64 1/27 (/.f64 1 (*.f64 (pow.f64 v 3) (sqrt.f64 -1/6)))) (+.f64 (*.f64 2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (pow.f64 v 5) (sqrt.f64 -1/6)))) (+.f64 (*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) v)) (*.f64 2/3 (/.f64 (+.f64 (*.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 (sqrt.f64 -1/6) 2))) 1/162) (*.f64 (pow.f64 v 7) (sqrt.f64 -1/6)))))))
(+.f64 (/.f64 1/27 (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3))) (fma.f64 2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 5))) (fma.f64 -4/3 (/.f64 (sqrt.f64 -1/6) v) (*.f64 2/3 (/.f64 (fma.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 (sqrt.f64 -1/6) 2)) 1/162) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 7)))))))
(+.f64 (/.f64 1/27 (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3))) (fma.f64 2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 5))) (fma.f64 -4/3 (/.f64 (sqrt.f64 -1/6) v) (*.f64 (/.f64 2/3 (sqrt.f64 -1/6)) (/.f64 (fma.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) -1/6) 1/162) (pow.f64 v 7))))))
(+.f64 (/.f64 1/27 (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3))) (fma.f64 -4/3 (/.f64 (sqrt.f64 -1/6) v) (*.f64 (/.f64 2/3 (sqrt.f64 -1/6)) (+.f64 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 v 5)) (/.f64 (+.f64 (*.f64 -1/6 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2))) 1/162) (pow.f64 v 7))))))
(*.f64 4/3 (/.f64 (sqrt.f64 -1/6) v))
(*.f64 (/.f64 (sqrt.f64 -1/6) v) 4/3)
(-.f64 (*.f64 4/3 (/.f64 (sqrt.f64 -1/6) v)) (*.f64 1/27 (/.f64 1 (*.f64 (pow.f64 v 3) (sqrt.f64 -1/6)))))
(-.f64 (*.f64 (/.f64 (sqrt.f64 -1/6) v) 4/3) (/.f64 1/27 (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3))))
(fma.f64 (/.f64 (sqrt.f64 -1/6) v) 4/3 (/.f64 -1/27 (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3))))
(-.f64 (+.f64 (*.f64 -2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (pow.f64 v 5) (sqrt.f64 -1/6)))) (*.f64 4/3 (/.f64 (sqrt.f64 -1/6) v))) (*.f64 1/27 (/.f64 1 (*.f64 (pow.f64 v 3) (sqrt.f64 -1/6)))))
(-.f64 (fma.f64 -2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 5))) (*.f64 (/.f64 (sqrt.f64 -1/6) v) 4/3)) (/.f64 1/27 (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3))))
(fma.f64 -2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 5))) (fma.f64 (/.f64 (sqrt.f64 -1/6) v) 4/3 (/.f64 -1/27 (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3)))))
(-.f64 (+.f64 (*.f64 -2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (pow.f64 v 5) (sqrt.f64 -1/6)))) (+.f64 (*.f64 4/3 (/.f64 (sqrt.f64 -1/6) v)) (*.f64 -2/3 (/.f64 (+.f64 (*.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 (sqrt.f64 -1/6) 2))) 1/162) (*.f64 (pow.f64 v 7) (sqrt.f64 -1/6)))))) (*.f64 1/27 (/.f64 1 (*.f64 (pow.f64 v 3) (sqrt.f64 -1/6)))))
(-.f64 (fma.f64 -2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 5))) (fma.f64 4/3 (/.f64 (sqrt.f64 -1/6) v) (*.f64 -2/3 (/.f64 (fma.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 (sqrt.f64 -1/6) 2)) 1/162) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 7)))))) (/.f64 1/27 (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3))))
(+.f64 (fma.f64 -2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 5))) (fma.f64 -2/3 (/.f64 (fma.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) -1/6) 1/162) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 7))) (*.f64 (/.f64 (sqrt.f64 -1/6) v) 4/3))) (/.f64 -1/27 (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3))))
(+.f64 (fma.f64 (/.f64 (sqrt.f64 -1/6) v) 4/3 (*.f64 (/.f64 -2/3 (sqrt.f64 -1/6)) (+.f64 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 v 5)) (/.f64 (+.f64 (*.f64 -1/6 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2))) 1/162) (pow.f64 v 7))))) (/.f64 -1/27 (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3))))
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 2) (-.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(fma.f64 -4/3 (*.f64 (*.f64 v v) (-.f64 (neg.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 3/4 (*.f64 (sqrt.f64 1/2) (PI.f64))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(fma.f64 (*.f64 -4/3 (*.f64 v v)) (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 -3/4 (*.f64 (sqrt.f64 1/2) (PI.f64)))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(fma.f64 -4/3 (*.f64 v (*.f64 v (-.f64 (/.f64 -3/4 (*.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (sqrt.f64 1/2) (PI.f64))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 2) (-.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 4) (-.f64 (+.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (*.f64 (sqrt.f64 1/2) (PI.f64))))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))))
(fma.f64 -4/3 (*.f64 (*.f64 v v) (-.f64 (neg.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 3/4 (*.f64 (sqrt.f64 1/2) (PI.f64))))) (fma.f64 -4/3 (*.f64 (pow.f64 v 4) (-.f64 (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (*.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (*.f64 (sqrt.f64 1/2) (PI.f64))))) (/.f64 3/4 (*.f64 (sqrt.f64 1/2) (PI.f64))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))))
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(fma.f64 4/3 (/.f64 (-.f64 (fma.f64 -1/2 (/.f64 (fma.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 (sqrt.f64 -1/6) 2)) 1/162) (*.f64 (sqrt.f64 -1/6) (PI.f64))) (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (PI.f64)))))) (/.f64 1/36 (*.f64 (sqrt.f64 -1/6) (PI.f64)))) (pow.f64 v 9)) (fma.f64 4/3 (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (-.f64 (*.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (PI.f64)))) (/.f64 1/36 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7)) (*.f64 4/3 (+.f64 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 1/36 (*.f64 (sqrt.f64 -1/6) (PI.f64)))) (pow.f64 v 5)) (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64)))))))
(fma.f64 4/3 (/.f64 (+.f64 (fma.f64 -1/2 (/.f64 (fma.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) -1/6) 1/162) (*.f64 (sqrt.f64 -1/6) (PI.f64))) (fma.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (PI.f64))) (/.f64 (sqrt.f64 -1/6) (PI.f64)))) (/.f64 -1/36 (*.f64 (sqrt.f64 -1/6) (PI.f64)))) (pow.f64 v 9)) (*.f64 4/3 (+.f64 (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (fma.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (PI.f64))) (/.f64 -1/36 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7)) (+.f64 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64))) (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -1/36 (*.f64 (sqrt.f64 -1/6) (PI.f64)))) (pow.f64 v 5))))))
(*.f64 4/3 (+.f64 (+.f64 (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (+.f64 (/.f64 (fma.f64 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2) -1/2 -1/108) (*.f64 (sqrt.f64 -1/6) (PI.f64))) (/.f64 -1/36 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7)) (+.f64 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64))) (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 (/.f64 1/36 (sqrt.f64 -1/6)) (PI.f64))) (pow.f64 v 5)))) (/.f64 (+.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 (/.f64 -1/2 (sqrt.f64 -1/6)) (+.f64 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (PI.f64)) (/.f64 (+.f64 (*.f64 -1/6 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2))) 1/162) (PI.f64))))) (/.f64 -1/36 (*.f64 (sqrt.f64 -1/6) (PI.f64)))) (pow.f64 v 9))))
(/.f64 -1 (PI.f64))
(-.f64 (*.f64 -1 (/.f64 (pow.f64 v 2) (PI.f64))) (/.f64 1 (PI.f64)))
(-.f64 (/.f64 (neg.f64 (*.f64 v v)) (PI.f64)) (/.f64 1 (PI.f64)))
(fma.f64 -1 (/.f64 (*.f64 v v) (PI.f64)) (/.f64 -1 (PI.f64)))
(-.f64 (/.f64 -1 (PI.f64)) (*.f64 (/.f64 v (PI.f64)) v))
(-.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 v 4) (PI.f64))) (*.f64 -1 (/.f64 (pow.f64 v 2) (PI.f64)))) (/.f64 1 (PI.f64)))
(-.f64 (*.f64 -1 (+.f64 (/.f64 (pow.f64 v 4) (PI.f64)) (/.f64 (*.f64 v v) (PI.f64)))) (/.f64 1 (PI.f64)))
(fma.f64 -1 (+.f64 (/.f64 (*.f64 v v) (PI.f64)) (/.f64 (pow.f64 v 4) (PI.f64))) (/.f64 -1 (PI.f64)))
(-.f64 (/.f64 -1 (PI.f64)) (+.f64 (*.f64 (/.f64 v (PI.f64)) v) (/.f64 (pow.f64 v 4) (PI.f64))))
(-.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 v 6) (PI.f64))) (+.f64 (*.f64 -1 (/.f64 (pow.f64 v 4) (PI.f64))) (*.f64 -1 (/.f64 (pow.f64 v 2) (PI.f64))))) (/.f64 1 (PI.f64)))
(-.f64 (fma.f64 -1 (/.f64 (pow.f64 v 6) (PI.f64)) (*.f64 -1 (+.f64 (/.f64 (pow.f64 v 4) (PI.f64)) (/.f64 (*.f64 v v) (PI.f64))))) (/.f64 1 (PI.f64)))
(+.f64 (-.f64 (-.f64 (/.f64 (*.f64 v (neg.f64 v)) (PI.f64)) (/.f64 (pow.f64 v 4) (PI.f64))) (/.f64 (pow.f64 v 6) (PI.f64))) (/.f64 -1 (PI.f64)))
(-.f64 (-.f64 (/.f64 -1 (PI.f64)) (+.f64 (*.f64 (/.f64 v (PI.f64)) v) (/.f64 (pow.f64 v 4) (PI.f64)))) (/.f64 (pow.f64 v 6) (PI.f64)))
(/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64)))
(/.f64 1 (*.f64 (*.f64 v v) (PI.f64)))
(/.f64 1 (*.f64 v (*.f64 v (PI.f64))))
(+.f64 (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))) (/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64))))
(+.f64 (/.f64 1 (*.f64 (*.f64 v v) (PI.f64))) (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))))
(+.f64 (/.f64 1 (*.f64 v (*.f64 v (PI.f64)))) (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))))
(+.f64 (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64))) (/.f64 1 (*.f64 (pow.f64 v 6) (PI.f64)))))
(+.f64 (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (*.f64 v v) (PI.f64))) (/.f64 1 (*.f64 (pow.f64 v 6) (PI.f64)))))
(+.f64 (/.f64 1 (*.f64 v (*.f64 v (PI.f64)))) (+.f64 (/.f64 (/.f64 1 (PI.f64)) (pow.f64 v 6)) (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64)))))
(+.f64 (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (pow.f64 v 8) (PI.f64))) (/.f64 1 (*.f64 (pow.f64 v 6) (PI.f64))))))
(+.f64 (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (*.f64 v v) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (pow.f64 v 6) (PI.f64))) (/.f64 1 (*.f64 (PI.f64) (pow.f64 v 8))))))
(+.f64 (+.f64 (/.f64 1 (*.f64 v (*.f64 v (PI.f64)))) (/.f64 (/.f64 1 (PI.f64)) (pow.f64 v 8))) (+.f64 (/.f64 (/.f64 1 (PI.f64)) (pow.f64 v 6)) (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64)))))
(+.f64 (+.f64 (/.f64 1 (*.f64 v (*.f64 v (PI.f64)))) (/.f64 1 (*.f64 (PI.f64) (pow.f64 v 8)))) (+.f64 (/.f64 (/.f64 1 (PI.f64)) (pow.f64 v 6)) (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64)))))
(/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64)))
(/.f64 1 (*.f64 (*.f64 v v) (PI.f64)))
(/.f64 1 (*.f64 v (*.f64 v (PI.f64))))
(+.f64 (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))) (/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64))))
(+.f64 (/.f64 1 (*.f64 (*.f64 v v) (PI.f64))) (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))))
(+.f64 (/.f64 1 (*.f64 v (*.f64 v (PI.f64)))) (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))))
(+.f64 (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64))) (/.f64 1 (*.f64 (pow.f64 v 6) (PI.f64)))))
(+.f64 (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (*.f64 v v) (PI.f64))) (/.f64 1 (*.f64 (pow.f64 v 6) (PI.f64)))))
(+.f64 (/.f64 1 (*.f64 v (*.f64 v (PI.f64)))) (+.f64 (/.f64 (/.f64 1 (PI.f64)) (pow.f64 v 6)) (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64)))))
(+.f64 (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (pow.f64 v 8) (PI.f64))) (/.f64 1 (*.f64 (pow.f64 v 6) (PI.f64))))))
(+.f64 (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (*.f64 v v) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (pow.f64 v 6) (PI.f64))) (/.f64 1 (*.f64 (PI.f64) (pow.f64 v 8))))))
(+.f64 (+.f64 (/.f64 1 (*.f64 v (*.f64 v (PI.f64)))) (/.f64 (/.f64 1 (PI.f64)) (pow.f64 v 8))) (+.f64 (/.f64 (/.f64 1 (PI.f64)) (pow.f64 v 6)) (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64)))))
(+.f64 (+.f64 (/.f64 1 (*.f64 v (*.f64 v (PI.f64)))) (/.f64 1 (*.f64 (PI.f64) (pow.f64 v 8)))) (+.f64 (/.f64 (/.f64 1 (PI.f64)) (pow.f64 v 6)) (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64)))))
-1
(-.f64 (*.f64 -1 (pow.f64 v 2)) 1)
(fma.f64 -1 (*.f64 v v) -1)
(fma.f64 v (neg.f64 v) -1)
(-.f64 (+.f64 (*.f64 -1 (pow.f64 v 2)) (*.f64 -1 (pow.f64 v 4))) 1)
(+.f64 (*.f64 -1 (+.f64 (*.f64 v v) (pow.f64 v 4))) -1)
(fma.f64 -1 (fma.f64 v v (pow.f64 v 4)) -1)
(-.f64 -1 (fma.f64 v v (pow.f64 v 4)))
(-.f64 (+.f64 (*.f64 -1 (pow.f64 v 2)) (+.f64 (*.f64 -1 (pow.f64 v 6)) (*.f64 -1 (pow.f64 v 4)))) 1)
(+.f64 (fma.f64 -1 (*.f64 v v) (fma.f64 -1 (pow.f64 v 6) (neg.f64 (pow.f64 v 4)))) -1)
(fma.f64 -1 (*.f64 v v) (fma.f64 -1 (+.f64 (pow.f64 v 4) (pow.f64 v 6)) -1))
(fma.f64 -1 (fma.f64 v v (+.f64 (pow.f64 v 4) (pow.f64 v 6))) -1)
(/.f64 1 (pow.f64 v 2))
(/.f64 1 (*.f64 v v))
(+.f64 (/.f64 1 (pow.f64 v 4)) (/.f64 1 (pow.f64 v 2)))
(+.f64 (/.f64 1 (*.f64 v v)) (/.f64 1 (pow.f64 v 4)))
(+.f64 (/.f64 1 (pow.f64 v 4)) (+.f64 (/.f64 1 (pow.f64 v 6)) (/.f64 1 (pow.f64 v 2))))
(+.f64 (/.f64 1 (pow.f64 v 4)) (+.f64 (/.f64 1 (*.f64 v v)) (/.f64 1 (pow.f64 v 6))))
(+.f64 (/.f64 1 (pow.f64 v 6)) (+.f64 (/.f64 1 (*.f64 v v)) (/.f64 1 (pow.f64 v 4))))
(+.f64 (/.f64 1 (*.f64 v v)) (+.f64 (/.f64 1 (pow.f64 v 4)) (/.f64 1 (pow.f64 v 6))))
(+.f64 (/.f64 1 (pow.f64 v 4)) (+.f64 (/.f64 1 (pow.f64 v 6)) (+.f64 (/.f64 1 (pow.f64 v 2)) (/.f64 1 (pow.f64 v 8)))))
(+.f64 (/.f64 1 (pow.f64 v 4)) (+.f64 (/.f64 1 (pow.f64 v 6)) (+.f64 (/.f64 1 (*.f64 v v)) (/.f64 1 (pow.f64 v 8)))))
(+.f64 (+.f64 (/.f64 1 (*.f64 v v)) (/.f64 1 (pow.f64 v 6))) (+.f64 (/.f64 1 (pow.f64 v 8)) (/.f64 1 (pow.f64 v 4))))
(+.f64 (/.f64 1 (pow.f64 v 4)) (+.f64 (/.f64 1 (*.f64 v v)) (+.f64 (/.f64 1 (pow.f64 v 6)) (/.f64 1 (pow.f64 v 8)))))
(/.f64 1 (pow.f64 v 2))
(/.f64 1 (*.f64 v v))
(+.f64 (/.f64 1 (pow.f64 v 4)) (/.f64 1 (pow.f64 v 2)))
(+.f64 (/.f64 1 (*.f64 v v)) (/.f64 1 (pow.f64 v 4)))
(+.f64 (/.f64 1 (pow.f64 v 4)) (+.f64 (/.f64 1 (pow.f64 v 6)) (/.f64 1 (pow.f64 v 2))))
(+.f64 (/.f64 1 (pow.f64 v 4)) (+.f64 (/.f64 1 (*.f64 v v)) (/.f64 1 (pow.f64 v 6))))
(+.f64 (/.f64 1 (pow.f64 v 6)) (+.f64 (/.f64 1 (*.f64 v v)) (/.f64 1 (pow.f64 v 4))))
(+.f64 (/.f64 1 (*.f64 v v)) (+.f64 (/.f64 1 (pow.f64 v 4)) (/.f64 1 (pow.f64 v 6))))
(+.f64 (/.f64 1 (pow.f64 v 4)) (+.f64 (/.f64 1 (pow.f64 v 6)) (+.f64 (/.f64 1 (pow.f64 v 2)) (/.f64 1 (pow.f64 v 8)))))
(+.f64 (/.f64 1 (pow.f64 v 4)) (+.f64 (/.f64 1 (pow.f64 v 6)) (+.f64 (/.f64 1 (*.f64 v v)) (/.f64 1 (pow.f64 v 8)))))
(+.f64 (+.f64 (/.f64 1 (*.f64 v v)) (/.f64 1 (pow.f64 v 6))) (+.f64 (/.f64 1 (pow.f64 v 8)) (/.f64 1 (pow.f64 v 4))))
(+.f64 (/.f64 1 (pow.f64 v 4)) (+.f64 (/.f64 1 (*.f64 v v)) (+.f64 (/.f64 1 (pow.f64 v 6)) (/.f64 1 (pow.f64 v 8)))))

prune477.0ms (18.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New2051206
Fresh101
Picked011
Done000
Total2062208
Error
0b
Counts
208 → 2
Alt Table
StatusErrorProgram
▶0.0b
(/.f64 -4/3 (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)) (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64)))))
✓0.0b
(*.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (/.f64 (/.f64 1 (fma.f64 v v -1)) (PI.f64)))
Compiler

Compiled 5653 to 4415 computations (21.9% saved)

localize12.0ms (0.5%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64)))
✓0.0b
(/.f64 -4/3 (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)) (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64)))))
✓0.0b
(*.f64 (fma.f64 v v -1) (PI.f64))

series5.0ms (0.2%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
1.0ms
v
@inf
(*.f64 (fma.f64 v v -1) (PI.f64))
1.0ms
v
@0
(*.f64 (fma.f64 v v -1) (PI.f64))
1.0ms
v
@-inf
(*.f64 (fma.f64 v v -1) (PI.f64))
1.0ms
v
@inf
(/.f64 -4/3 (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)) (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64)))))
1.0ms
v
@0
(/.f64 -4/3 (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)) (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64)))))

rewrite60.0ms (2.4%)

Algorithm
1×batch-egg-rewrite
Rules
270×expm1-udef_binary64
270×log1p-udef_binary64
160×add-sqr-sqrt_binary64
150×*-un-lft-identity_binary64
150×pow1_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01648
133445
2400845
Stop Event
1×node limit
Counts
3 → 84
Calls
Call 1
Inputs
(*.f64 (fma.f64 v v -1) (PI.f64))
(/.f64 -4/3 (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)) (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64)))))
(/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 v v) (PI.f64)) (*.f64 -1 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (PI.f64) (*.f64 v v)) (*.f64 (PI.f64) -1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (fma.f64 v v -1) (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (/.f64 -1 (*.f64 (fma.f64 v v -1) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 v v -1) (/.f64 1 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (PI.f64) (/.f64 1 (fma.f64 v v -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (*.f64 (fma.f64 v v -1) (PI.f64))) 2) (/.f64 1 (cbrt.f64 (*.f64 (fma.f64 v v -1) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 (fma.f64 v v -1) (PI.f64))) (pow.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 v v -1) (neg.f64 (PI.f64))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 (cbrt.f64 (pow.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) -2))) (/.f64 1 (cbrt.f64 (*.f64 (fma.f64 v v -1) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 (pow.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) -1/2)) (pow.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (fma.f64 v v -1) (PI.f64))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (fma.f64 v v -1) (PI.f64))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (PI.f64)) (fma.f64 v v -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (fma.f64 v v -1) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (fma.f64 v v -1) 3) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (fma.f64 v v -1) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (fma.f64 v v -1) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (fma.f64 v v -1) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (fma.f64 v v -1) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (fma.f64 v v -1) (PI.f64))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (neg.f64 (log.f64 (*.f64 (fma.f64 v v -1) (PI.f64))))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 -4/3 (*.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -4/3 (/.f64 (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 -4/3 (*.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64))) (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -4/3 (*.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 -4/3 (*.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))) (cbrt.f64 (/.f64 16/9 (*.f64 (fma.f64 v (*.f64 v -6) 2) (pow.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 16/9 (*.f64 (fma.f64 v (*.f64 v -6) 2) (pow.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) 2)))) (cbrt.f64 (/.f64 -4/3 (*.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 -4/3 (*.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))) (sqrt.f64 (/.f64 -4/3 (*.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4/3 (/.f64 1 (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)) (*.f64 (fma.f64 v v -1) (neg.f64 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) -4/3)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -4/3 (neg.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) (/.f64 -1 (*.f64 (fma.f64 v v -1) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) 1) (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (cbrt.f64 (pow.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) -2))) (/.f64 1 (cbrt.f64 (*.f64 (fma.f64 v v -1) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (pow.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) -1/2)) (pow.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 -4/3 (*.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 -4/3 (*.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 -4/3 (*.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 -4/3 (*.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)) (/.f64 -4/3 (*.f64 (fma.f64 v v -1) (PI.f64)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 16/9 (*.f64 (fma.f64 v (*.f64 v -6) 2) (pow.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 -4/3 (*.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 -4/3 (*.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 -4/3 (*.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 -4/3 (*.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 -4/3 (*.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 -4/3 (*.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 -4/3 (*.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 -1 (*.f64 (fma.f64 v v -1) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (*.f64 (fma.f64 v v -1) (PI.f64)))) (cbrt.f64 (pow.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) -2)) (/.f64 1 (cbrt.f64 (*.f64 (fma.f64 v v -1) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) -1/2) (pow.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 v v -1)) (pow.f64 (PI.f64) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 v v -1)) (/.f64 1 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) -1) (/.f64 1 (fma.f64 v v -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (fma.f64 v v -1) (PI.f64))) 2) -1) (pow.f64 (cbrt.f64 (*.f64 (fma.f64 v v -1) (PI.f64))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 (fma.f64 v v -1) (PI.f64))) -1) (pow.f64 (sqrt.f64 (*.f64 (fma.f64 v v -1) (PI.f64))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (*.f64 (fma.f64 v v -1) (PI.f64)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (fma.f64 v v -1) (PI.f64)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (*.f64 (fma.f64 v v -1) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (fma.f64 v v -1) (PI.f64))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (*.f64 (fma.f64 v v -1) (PI.f64)))) 1))))))

simplify43.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
436×fma-def_binary64
309×associate-*l*_binary64
307×associate-*r*_binary64
270×associate-/r*_binary64
181×associate-/l*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01371474
14251425
213861350
Stop Event
1×node limit
Counts
120 → 129
Calls
Call 1
Inputs
(*.f64 -1 (PI.f64))
(+.f64 (*.f64 -1 (PI.f64)) (*.f64 (pow.f64 v 2) (PI.f64)))
(+.f64 (*.f64 -1 (PI.f64)) (*.f64 (pow.f64 v 2) (PI.f64)))
(+.f64 (*.f64 -1 (PI.f64)) (*.f64 (pow.f64 v 2) (PI.f64)))
(*.f64 (pow.f64 v 2) (PI.f64))
(+.f64 (*.f64 -1 (PI.f64)) (*.f64 (pow.f64 v 2) (PI.f64)))
(+.f64 (*.f64 -1 (PI.f64)) (*.f64 (pow.f64 v 2) (PI.f64)))
(+.f64 (*.f64 -1 (PI.f64)) (*.f64 (pow.f64 v 2) (PI.f64)))
(*.f64 (pow.f64 v 2) (PI.f64))
(+.f64 (*.f64 -1 (PI.f64)) (*.f64 (pow.f64 v 2) (PI.f64)))
(+.f64 (*.f64 -1 (PI.f64)) (*.f64 (pow.f64 v 2) (PI.f64)))
(+.f64 (*.f64 -1 (PI.f64)) (*.f64 (pow.f64 v 2) (PI.f64)))
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 2) (-.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 2) (-.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 4) (-.f64 (+.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (*.f64 (sqrt.f64 1/2) (PI.f64))))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))))
(+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 6) (-.f64 (+.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (*.f64 -1/2 (/.f64 (-.f64 27/2 (*.f64 3/4 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (*.f64 (sqrt.f64 1/2) (PI.f64)))) (*.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (*.f64 (sqrt.f64 1/2) (PI.f64)))))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 2) (-.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 4) (-.f64 (+.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (*.f64 (sqrt.f64 1/2) (PI.f64))))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))))
(*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64))))
(+.f64 (*.f64 -4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64)))))
(+.f64 (*.f64 -4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (+.f64 (*.f64 -4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64))))))
(+.f64 (*.f64 -4/3 (/.f64 (-.f64 (+.f64 (*.f64 -1/2 (/.f64 (+.f64 1/162 (*.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 (sqrt.f64 -1/6) 2)))) (*.f64 (sqrt.f64 -1/6) (PI.f64)))) (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (PI.f64)))))) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 9))) (+.f64 (*.f64 -4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (+.f64 (*.f64 -4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64)))))))
(*.f64 4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64))))
(+.f64 (*.f64 4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (*.f64 4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64)))))
(+.f64 (*.f64 4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (+.f64 (*.f64 4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (*.f64 4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64))))))
(+.f64 (*.f64 4/3 (/.f64 (-.f64 (+.f64 (*.f64 -1/2 (/.f64 (+.f64 1/162 (*.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 (sqrt.f64 -1/6) 2)))) (*.f64 (sqrt.f64 -1/6) (PI.f64)))) (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (PI.f64)))))) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 9))) (+.f64 (*.f64 4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (+.f64 (*.f64 4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (*.f64 4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64)))))))
(/.f64 -1 (PI.f64))
(-.f64 (*.f64 -1 (/.f64 (pow.f64 v 2) (PI.f64))) (/.f64 1 (PI.f64)))
(-.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 v 4) (PI.f64))) (*.f64 -1 (/.f64 (pow.f64 v 2) (PI.f64)))) (/.f64 1 (PI.f64)))
(-.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 v 6) (PI.f64))) (+.f64 (*.f64 -1 (/.f64 (pow.f64 v 4) (PI.f64))) (*.f64 -1 (/.f64 (pow.f64 v 2) (PI.f64))))) (/.f64 1 (PI.f64)))
(/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64)))
(+.f64 (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))) (/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64))))
(+.f64 (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64))) (/.f64 1 (*.f64 (pow.f64 v 6) (PI.f64)))))
(+.f64 (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (pow.f64 v 8) (PI.f64))) (/.f64 1 (*.f64 (pow.f64 v 6) (PI.f64))))))
(/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64)))
(+.f64 (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))) (/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64))))
(+.f64 (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64))) (/.f64 1 (*.f64 (pow.f64 v 6) (PI.f64)))))
(+.f64 (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (pow.f64 v 8) (PI.f64))) (/.f64 1 (*.f64 (pow.f64 v 6) (PI.f64))))))
Outputs
(*.f64 -1 (PI.f64))
(neg.f64 (PI.f64))
(+.f64 (*.f64 -1 (PI.f64)) (*.f64 (pow.f64 v 2) (PI.f64)))
(*.f64 (PI.f64) (+.f64 -1 (*.f64 v v)))
(*.f64 (PI.f64) (fma.f64 v v -1))
(+.f64 (*.f64 -1 (PI.f64)) (*.f64 (pow.f64 v 2) (PI.f64)))
(*.f64 (PI.f64) (+.f64 -1 (*.f64 v v)))
(*.f64 (PI.f64) (fma.f64 v v -1))
(+.f64 (*.f64 -1 (PI.f64)) (*.f64 (pow.f64 v 2) (PI.f64)))
(*.f64 (PI.f64) (+.f64 -1 (*.f64 v v)))
(*.f64 (PI.f64) (fma.f64 v v -1))
(*.f64 (pow.f64 v 2) (PI.f64))
(*.f64 (PI.f64) (*.f64 v v))
(+.f64 (*.f64 -1 (PI.f64)) (*.f64 (pow.f64 v 2) (PI.f64)))
(*.f64 (PI.f64) (+.f64 -1 (*.f64 v v)))
(*.f64 (PI.f64) (fma.f64 v v -1))
(+.f64 (*.f64 -1 (PI.f64)) (*.f64 (pow.f64 v 2) (PI.f64)))
(*.f64 (PI.f64) (+.f64 -1 (*.f64 v v)))
(*.f64 (PI.f64) (fma.f64 v v -1))
(+.f64 (*.f64 -1 (PI.f64)) (*.f64 (pow.f64 v 2) (PI.f64)))
(*.f64 (PI.f64) (+.f64 -1 (*.f64 v v)))
(*.f64 (PI.f64) (fma.f64 v v -1))
(*.f64 (pow.f64 v 2) (PI.f64))
(*.f64 (PI.f64) (*.f64 v v))
(+.f64 (*.f64 -1 (PI.f64)) (*.f64 (pow.f64 v 2) (PI.f64)))
(*.f64 (PI.f64) (+.f64 -1 (*.f64 v v)))
(*.f64 (PI.f64) (fma.f64 v v -1))
(+.f64 (*.f64 -1 (PI.f64)) (*.f64 (pow.f64 v 2) (PI.f64)))
(*.f64 (PI.f64) (+.f64 -1 (*.f64 v v)))
(*.f64 (PI.f64) (fma.f64 v v -1))
(+.f64 (*.f64 -1 (PI.f64)) (*.f64 (pow.f64 v 2) (PI.f64)))
(*.f64 (PI.f64) (+.f64 -1 (*.f64 v v)))
(*.f64 (PI.f64) (fma.f64 v v -1))
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(/.f64 (*.f64 4/3 (sqrt.f64 1/2)) (PI.f64))
(+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 2) (-.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(fma.f64 -4/3 (*.f64 (*.f64 v v) (-.f64 (neg.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 3/4 (*.f64 (PI.f64) (sqrt.f64 1/2))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (*.f64 (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 -3/4 (*.f64 (PI.f64) (sqrt.f64 1/2)))) (*.f64 (*.f64 v v) -4/3)))
(fma.f64 (*.f64 v v) (*.f64 (-.f64 (/.f64 -3/4 (*.f64 (PI.f64) (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/2) (PI.f64))) -4/3) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 2) (-.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 4) (-.f64 (+.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (*.f64 (sqrt.f64 1/2) (PI.f64))))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))))
(fma.f64 -4/3 (*.f64 (*.f64 v v) (-.f64 (neg.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 3/4 (*.f64 (PI.f64) (sqrt.f64 1/2))))) (fma.f64 -4/3 (*.f64 (pow.f64 v 4) (-.f64 (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (*.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (*.f64 (PI.f64) (sqrt.f64 1/2))))) (/.f64 3/4 (*.f64 (PI.f64) (sqrt.f64 1/2))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))))
(fma.f64 -4/3 (*.f64 v (*.f64 v (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 -3/4 (*.f64 (PI.f64) (sqrt.f64 1/2)))))) (fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (*.f64 (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (*.f64 (PI.f64) (sqrt.f64 1/2))) (/.f64 -3/4 (*.f64 (PI.f64) (sqrt.f64 1/2))))) (*.f64 -4/3 (pow.f64 v 4)))))
(fma.f64 -4/3 (fma.f64 v (*.f64 v (-.f64 (/.f64 -3/4 (*.f64 (PI.f64) (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/2) (PI.f64)))) (*.f64 (pow.f64 v 4) (fma.f64 (/.f64 -1/2 (PI.f64)) (-.f64 (/.f64 9/2 (sqrt.f64 1/2)) (/.f64 (/.f64 9/16 (sqrt.f64 1/2)) 1/2)) (-.f64 (/.f64 -3/4 (*.f64 (PI.f64) (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/2) (PI.f64)))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 6) (-.f64 (+.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (*.f64 -1/2 (/.f64 (-.f64 27/2 (*.f64 3/4 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (*.f64 (sqrt.f64 1/2) (PI.f64)))) (*.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (*.f64 (sqrt.f64 1/2) (PI.f64)))))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 2) (-.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (*.f64 -4/3 (*.f64 (pow.f64 v 4) (-.f64 (+.f64 (*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (*.f64 (sqrt.f64 1/2) (PI.f64))))) (*.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))))
(fma.f64 -4/3 (*.f64 (pow.f64 v 6) (-.f64 (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (*.f64 -1/2 (+.f64 (/.f64 (-.f64 27/2 (*.f64 3/4 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (*.f64 (PI.f64) (sqrt.f64 1/2))) (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (*.f64 (PI.f64) (sqrt.f64 1/2)))))) (/.f64 3/4 (*.f64 (PI.f64) (sqrt.f64 1/2))))) (fma.f64 -4/3 (*.f64 (*.f64 v v) (-.f64 (neg.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 3/4 (*.f64 (PI.f64) (sqrt.f64 1/2))))) (fma.f64 -4/3 (*.f64 (pow.f64 v 4) (-.f64 (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (*.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (*.f64 (PI.f64) (sqrt.f64 1/2))))) (/.f64 3/4 (*.f64 (PI.f64) (sqrt.f64 1/2))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))))
(fma.f64 -4/3 (*.f64 (pow.f64 v 6) (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 -1/2 (+.f64 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (*.f64 (PI.f64) (sqrt.f64 1/2))) (/.f64 (-.f64 27/2 (/.f64 3/4 (/.f64 1/2 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2))))) (*.f64 (PI.f64) (sqrt.f64 1/2)))) (/.f64 -3/4 (*.f64 (PI.f64) (sqrt.f64 1/2)))))) (fma.f64 -4/3 (*.f64 v (*.f64 v (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 -3/4 (*.f64 (PI.f64) (sqrt.f64 1/2)))))) (fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (*.f64 (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (*.f64 (PI.f64) (sqrt.f64 1/2))) (/.f64 -3/4 (*.f64 (PI.f64) (sqrt.f64 1/2))))) (*.f64 -4/3 (pow.f64 v 4))))))
(fma.f64 (+.f64 (*.f64 (/.f64 -1/2 (sqrt.f64 1/2)) (+.f64 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (PI.f64)) (/.f64 135/16 (PI.f64)))) (-.f64 (/.f64 -3/4 (*.f64 (PI.f64) (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/2) (PI.f64)))) (*.f64 -4/3 (pow.f64 v 6)) (fma.f64 -4/3 (fma.f64 v (*.f64 v (-.f64 (/.f64 -3/4 (*.f64 (PI.f64) (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/2) (PI.f64)))) (*.f64 (pow.f64 v 4) (fma.f64 (/.f64 -1/2 (PI.f64)) (-.f64 (/.f64 9/2 (sqrt.f64 1/2)) (/.f64 (/.f64 9/16 (sqrt.f64 1/2)) 1/2)) (-.f64 (/.f64 -3/4 (*.f64 (PI.f64) (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/2) (PI.f64)))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))))
(*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64))))
(*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (PI.f64) (pow.f64 v 3))))
(*.f64 -4/3 (/.f64 (/.f64 (sqrt.f64 -1/6) (pow.f64 v 3)) (PI.f64)))
(+.f64 (*.f64 -4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64)))))
(*.f64 -4/3 (+.f64 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 1/36 (*.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5)) (/.f64 (sqrt.f64 -1/6) (*.f64 (PI.f64) (pow.f64 v 3)))))
(*.f64 -4/3 (+.f64 (/.f64 (/.f64 (sqrt.f64 -1/6) (pow.f64 v 3)) (PI.f64)) (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -1/36 (*.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5))))
(fma.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (PI.f64) (pow.f64 v 3))) (/.f64 (fma.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 1/27 (*.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5)))
(+.f64 (*.f64 -4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (+.f64 (*.f64 -4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (*.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (*.f64 1/36 (/.f64 1 (*.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (*.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64))))))
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(+.f64 (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64))) (/.f64 1 (*.f64 (pow.f64 v 6) (PI.f64)))))
(+.f64 (/.f64 1 (*.f64 (PI.f64) (pow.f64 v 4))) (+.f64 (/.f64 1 (*.f64 (PI.f64) (*.f64 v v))) (/.f64 1 (*.f64 (PI.f64) (pow.f64 v 6)))))
(+.f64 (/.f64 1 (*.f64 (PI.f64) (*.f64 v v))) (+.f64 (/.f64 1 (*.f64 (PI.f64) (pow.f64 v 4))) (/.f64 (/.f64 1 (PI.f64)) (pow.f64 v 6))))
(+.f64 (/.f64 1 (*.f64 (PI.f64) (*.f64 v v))) (+.f64 (/.f64 1 (*.f64 (PI.f64) (pow.f64 v 4))) (/.f64 1 (*.f64 (PI.f64) (pow.f64 v 6)))))
(+.f64 (/.f64 1 (*.f64 (pow.f64 v 4) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (pow.f64 v 2) (PI.f64))) (+.f64 (/.f64 1 (*.f64 (pow.f64 v 8) (PI.f64))) (/.f64 1 (*.f64 (pow.f64 v 6) (PI.f64))))))
(+.f64 (/.f64 1 (*.f64 (PI.f64) (pow.f64 v 4))) (+.f64 (/.f64 1 (*.f64 (PI.f64) (*.f64 v v))) (+.f64 (/.f64 1 (*.f64 (PI.f64) (pow.f64 v 6))) (/.f64 1 (*.f64 (PI.f64) (pow.f64 v 8))))))
(+.f64 (/.f64 1 (*.f64 (PI.f64) (*.f64 v v))) (+.f64 (+.f64 (/.f64 (/.f64 1 (PI.f64)) (pow.f64 v 6)) (/.f64 (/.f64 1 (PI.f64)) (pow.f64 v 8))) (/.f64 1 (*.f64 (PI.f64) (pow.f64 v 4)))))
(+.f64 (/.f64 1 (*.f64 (PI.f64) (*.f64 v v))) (+.f64 (+.f64 (/.f64 1 (*.f64 (PI.f64) (pow.f64 v 6))) (/.f64 1 (*.f64 (PI.f64) (pow.f64 v 8)))) (/.f64 1 (*.f64 (PI.f64) (pow.f64 v 4)))))

prune208.0ms (8.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New1290129
Fresh000
Picked011
Done011
Total1292131
Error
0b
Counts
131 → 2
Alt Table
StatusErrorProgram
✓0.0b
(/.f64 -4/3 (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)) (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64)))))
✓0.0b
(*.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (/.f64 (/.f64 1 (fma.f64 v v -1)) (PI.f64)))
Compiler

Compiled 3647 to 2844 computations (22% saved)

regimes17.0ms (0.7%)

Accuracy

Total -1.0b remaining (-25358.5%)

Threshold costs -1.0b (-25358.5%)

Counts
5 → 1
Calls
Call 1
Inputs
(/.f64 -4/3 (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)) (/.f64 1 (*.f64 (fma.f64 v v -1) (PI.f64)))))
(*.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (/.f64 (/.f64 1 (fma.f64 v v -1)) (PI.f64)))
(*.f64 (/.f64 (sqrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (PI.f64)) (/.f64 (sqrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))
(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))
(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
Outputs
(*.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (/.f64 (/.f64 1 (fma.f64 v v -1)) (PI.f64)))
Results
4.0ms0.0bv
2.0ms0.0b(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
2.0ms0.0b(*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))))
5.0ms0.0b(*.f64 v v)
Compiler

Compiled 144 to 104 computations (27.8% saved)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
2×*-commutative_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01627
12027
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (/.f64 (/.f64 1 (fma.f64 v v -1)) (PI.f64)))
Outputs
(*.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (/.f64 (/.f64 1 (fma.f64 v v -1)) (PI.f64)))

end20.0ms (0.8%)

Stop Event
1×done
Compiler

Compiled 38 to 30 computations (21.1% saved)

Profiling

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