sqrt E (should all be same)

Time bar (total: 4.1s)

analyze1.0ms (0%)

Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
100%100%0%0%0%0%0%1
Compiler

Compiled 10 to 8 computations (20% saved)

sample1.0s (24.3%)

Results
996.0ms8255×body256valid
0.0msbody256infinite
Bogosity

preprocess131.0ms (3.2%)

Algorithm
egg-herbie
Rules
1064×fma-neg
980×distribute-lft-out
900×fma-def
886×hypot-def
742×distribute-lft-neg-in
Problems
137×(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
119×No Errors
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01588
13156
27556
324856
4108256
5285256
6584256
7790856
Stop Event
node limit
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
(sqrt.f64 (+.f64 (pow.f64 (neg.f64 x) 2) (pow.f64 (neg.f64 x) 2)))
(neg.f64 (sqrt.f64 (+.f64 (pow.f64 (neg.f64 x) 2) (pow.f64 (neg.f64 x) 2))))
Outputs
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(hypot.f64 x x)
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(hypot.f64 x x)
(sqrt.f64 (+.f64 (pow.f64 (neg.f64 x) 2) (pow.f64 (neg.f64 x) 2)))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(hypot.f64 x x)
(neg.f64 (sqrt.f64 (+.f64 (pow.f64 (neg.f64 x) 2) (pow.f64 (neg.f64 x) 2))))
(neg.f64 (sqrt.f64 (*.f64 2 (pow.f64 (neg.f64 x) 2))))
(neg.f64 (hypot.f64 x x))
Symmetry

(abs x)

Compiler

Compiled 31 to 23 computations (25.8% saved)

eval0.0ms (0%)

Compiler

Compiled 10 to 7 computations (30% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(hypot.f64 x x)
100.0%
(hypot.f64 x x)
Compiler

Compiled 8 to 4 computations (50% saved)

localize15.0ms (0.4%)

Localize:

Found 1 expressions with local error:

NewAccuracyProgram
100.0%
(hypot.f64 x x)
Compiler

Compiled 6 to 3 computations (50% saved)

series2.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(hypot.f64 x x)
1.0ms
x
@inf
(hypot.f64 x x)
1.0ms
x
@0
(hypot.f64 x x)

rewrite164.0ms (4%)

Algorithm
batch-egg-rewrite
Rules
801×log1p-expm1-u
486×expm1-log1p-u
434×expm1-udef
434×log1p-udef
408×associate-*r*
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0613
14613
24787
354967
Stop Event
node limit
Counts
1 → 104
Calls
Call 1
Inputs
(hypot.f64 x x)
Outputs
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(+.f64 (+.f64 (/.f64 0 0) 1) -1)
(+.f64 0 (/.f64 0 0))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 0 0))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 0 0)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))))
(+.f64 (*.f64 (/.f64 0 0) (pow.f64 x 2)) (*.f64 (/.f64 0 0) (pow.f64 x 2)))
(+.f64 (*.f64 (pow.f64 x 2) (/.f64 0 0)) (*.f64 (pow.f64 x 2) (/.f64 0 0)))
(-.f64 (+.f64 (/.f64 0 0) 1) 1)
(-.f64 (/.f64 (pow.f64 x 4) 0) (/.f64 (pow.f64 x 4) 0))
(*.f64 x (*.f64 x 2))
(*.f64 x (*.f64 (*.f64 x 2) 1))
(*.f64 x (*.f64 (*.f64 x 2) (/.f64 0 0)))
(*.f64 (pow.f64 x 2) 2)
(*.f64 (pow.f64 x 2) (*.f64 (*.f64 x 2) (*.f64 x 2)))
(*.f64 (/.f64 0 0) (/.f64 0 0))
(*.f64 (/.f64 0 0) 1)
(*.f64 (/.f64 0 0) (log.f64 (E.f64)))
(*.f64 (/.f64 0 0) (pow.f64 1 1/3))
(*.f64 (/.f64 0 0) (pow.f64 1 1/2))
(*.f64 1 (/.f64 0 0))
(*.f64 (cbrt.f64 x) (cbrt.f64 (*.f64 x 2)))
(*.f64 (cbrt.f64 x) (+.f64 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (cbrt.f64 x) 5)))
(*.f64 (cbrt.f64 x) (*.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 x 2)))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (pow.f64 (cbrt.f64 x) 4) (pow.f64 (cbrt.f64 x) 4)))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (*.f64 x 2)))
(*.f64 (sqrt.f64 x) (pow.f64 (*.f64 x 2) 1/2))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x 2)))
(*.f64 (sqrt.f64 x) (+.f64 (pow.f64 x 3/2) (pow.f64 x 3/2)))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (*.f64 x 2)))
(*.f64 0 (/.f64 1 0))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (*.f64 (pow.f64 x 2) (/.f64 0 0)))
(*.f64 (pow.f64 (cbrt.f64 x) 4) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (pow.f64 x 3/2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))
(*.f64 (*.f64 2 (pow.f64 x 6)) (/.f64 1 (+.f64 0 (pow.f64 x 4))))
(*.f64 (*.f64 x 2) x)
(*.f64 (pow.f64 (cbrt.f64 x) 5) (+.f64 (cbrt.f64 x) (cbrt.f64 x)))
(*.f64 4 (pow.f64 x 4))
(*.f64 (pow.f64 1 1/3) (/.f64 0 0))
(*.f64 (pow.f64 1 1/2) (/.f64 0 0))
(*.f64 (pow.f64 2 1/2) x)
(*.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 x) 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 (*.f64 2 (sqrt.f64 x)) (pow.f64 x 3/2))
(*.f64 (*.f64 2 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (cbrt.f64 x) 4))
(*.f64 (*.f64 2 (pow.f64 (cbrt.f64 x) 4)) (pow.f64 (cbrt.f64 x) 2))
(*.f64 (*.f64 2 (pow.f64 x 3/2)) (sqrt.f64 x))
(*.f64 (*.f64 2 (pow.f64 (cbrt.f64 x) 5)) (cbrt.f64 x))
(*.f64 (*.f64 (/.f64 0 0) x) (*.f64 x 2))
(*.f64 (*.f64 (/.f64 0 0) 2) (pow.f64 x 2))
(/.f64 1 (/.f64 0 0))
(/.f64 1 (/.f64 (+.f64 0 (pow.f64 x 4)) (*.f64 2 (pow.f64 x 6))))
(/.f64 0 0)
(/.f64 (*.f64 2 (pow.f64 x 6)) (+.f64 0 (pow.f64 x 4)))
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 6))) (cbrt.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 (sqrt.f64 0) (sqrt.f64 0))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) (*.f64 2 (pow.f64 x 6))) (*.f64 (+.f64 0 (pow.f64 x 4)) (+.f64 0 (pow.f64 x 4))))
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) 0) (*.f64 (+.f64 0 (pow.f64 x 4)) 0))
(/.f64 (*.f64 0 (*.f64 2 (pow.f64 x 6))) (*.f64 0 (+.f64 0 (pow.f64 x 4))))
(/.f64 (neg.f64 (*.f64 2 (pow.f64 x 6))) (neg.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 0 0) 1) 3) 1) (+.f64 (*.f64 (+.f64 (/.f64 0 0) 1) (+.f64 (/.f64 0 0) 1)) (+.f64 1 (+.f64 (/.f64 0 0) 1))))
(/.f64 (-.f64 (*.f64 (+.f64 (/.f64 0 0) 1) (+.f64 (/.f64 0 0) 1)) 1) (+.f64 (+.f64 (/.f64 0 0) 1) 1))
(/.f64 (*.f64 (/.f64 0 0) (*.f64 2 (pow.f64 x 6))) (+.f64 0 (pow.f64 x 4)))
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) 1) (+.f64 0 (pow.f64 x 4)))
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) (/.f64 0 0)) (+.f64 0 (pow.f64 x 4)))
(/.f64 (*.f64 0 (/.f64 0 0)) 0)
(pow.f64 (/.f64 0 0) 1)
(pow.f64 (/.f64 0 0) 2)
(pow.f64 (/.f64 0 0) 1/2)
(pow.f64 (/.f64 0 0) 1/3)
(pow.f64 (/.f64 0 0) 3)
(pow.f64 (/.f64 0 0) 6)
(pow.f64 (/.f64 0 0) 5/2)
(pow.f64 (/.f64 0 0) 5)
(pow.f64 (/.f64 0 0) 3/2)
(pow.f64 (/.f64 0 0) 4/3)
(pow.f64 (/.f64 0 0) 4)
(pow.f64 (/.f64 0 0) 2/3)
(pow.f64 (/.f64 0 0) 1/6)
(pow.f64 (/.f64 0 0) 1/9)
(pow.f64 (/.f64 0 0) 1/4)
(pow.f64 (/.f64 0 0) 9)
(pow.f64 (E.f64) (log.f64 (/.f64 0 0)))
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (/.f64 0 0)) 2))) (cbrt.f64 (log.f64 (/.f64 0 0))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 0 0)))) (sqrt.f64 (log.f64 (/.f64 0 0))))
(sqrt.f64 (/.f64 0 0))
(fabs.f64 (/.f64 0 0))
(fabs.f64 (neg.f64 (/.f64 0 0)))
(log.f64 (exp.f64 (/.f64 0 0)))
(cbrt.f64 (/.f64 0 0))
(expm1.f64 (log1p.f64 (/.f64 0 0)))
(exp.f64 (log.f64 (/.f64 0 0)))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/2))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 3))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/3))
(log1p.f64 (expm1.f64 (/.f64 0 0)))
(fma.f64 x x (pow.f64 x 2))
(fma.f64 1 (pow.f64 x 2) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 4) (pow.f64 x 2))
(fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 4) (pow.f64 (cbrt.f64 x) 2) (pow.f64 x 2))
(fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (pow.f64 x 2))

simplify14.0ms (0.3%)

Algorithm
egg-herbie
Rules
78×*-commutative
60×sqr-pow
30×associate-*r*
26×associate-*l*
20×count-2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0223916
1678916
Stop Event
unsound
Counts
116 → 126
Calls
Call 1
Inputs
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 -1 (*.f64 x (sqrt.f64 2)))
(*.f64 -1 (*.f64 x (sqrt.f64 2)))
(*.f64 -1 (*.f64 x (sqrt.f64 2)))
(*.f64 -1 (*.f64 x (sqrt.f64 2)))
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(+.f64 (+.f64 (/.f64 0 0) 1) -1)
(+.f64 0 (/.f64 0 0))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 0 0))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 0 0)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))))
(+.f64 (*.f64 (/.f64 0 0) (pow.f64 x 2)) (*.f64 (/.f64 0 0) (pow.f64 x 2)))
(+.f64 (*.f64 (pow.f64 x 2) (/.f64 0 0)) (*.f64 (pow.f64 x 2) (/.f64 0 0)))
(-.f64 (+.f64 (/.f64 0 0) 1) 1)
(-.f64 (/.f64 (pow.f64 x 4) 0) (/.f64 (pow.f64 x 4) 0))
(*.f64 x (*.f64 x 2))
(*.f64 x (*.f64 (*.f64 x 2) 1))
(*.f64 x (*.f64 (*.f64 x 2) (/.f64 0 0)))
(*.f64 (pow.f64 x 2) 2)
(*.f64 (pow.f64 x 2) (*.f64 (*.f64 x 2) (*.f64 x 2)))
(*.f64 (/.f64 0 0) (/.f64 0 0))
(*.f64 (/.f64 0 0) 1)
(*.f64 (/.f64 0 0) (log.f64 (E.f64)))
(*.f64 (/.f64 0 0) (pow.f64 1 1/3))
(*.f64 (/.f64 0 0) (pow.f64 1 1/2))
(*.f64 1 (/.f64 0 0))
(*.f64 (cbrt.f64 x) (cbrt.f64 (*.f64 x 2)))
(*.f64 (cbrt.f64 x) (+.f64 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (cbrt.f64 x) 5)))
(*.f64 (cbrt.f64 x) (*.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 x 2)))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (pow.f64 (cbrt.f64 x) 4) (pow.f64 (cbrt.f64 x) 4)))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (*.f64 x 2)))
(*.f64 (sqrt.f64 x) (pow.f64 (*.f64 x 2) 1/2))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x 2)))
(*.f64 (sqrt.f64 x) (+.f64 (pow.f64 x 3/2) (pow.f64 x 3/2)))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (*.f64 x 2)))
(*.f64 0 (/.f64 1 0))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (*.f64 (pow.f64 x 2) (/.f64 0 0)))
(*.f64 (pow.f64 (cbrt.f64 x) 4) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (pow.f64 x 3/2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))
(*.f64 (*.f64 2 (pow.f64 x 6)) (/.f64 1 (+.f64 0 (pow.f64 x 4))))
(*.f64 (*.f64 x 2) x)
(*.f64 (pow.f64 (cbrt.f64 x) 5) (+.f64 (cbrt.f64 x) (cbrt.f64 x)))
(*.f64 4 (pow.f64 x 4))
(*.f64 (pow.f64 1 1/3) (/.f64 0 0))
(*.f64 (pow.f64 1 1/2) (/.f64 0 0))
(*.f64 (pow.f64 2 1/2) x)
(*.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 x) 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 (*.f64 2 (sqrt.f64 x)) (pow.f64 x 3/2))
(*.f64 (*.f64 2 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (cbrt.f64 x) 4))
(*.f64 (*.f64 2 (pow.f64 (cbrt.f64 x) 4)) (pow.f64 (cbrt.f64 x) 2))
(*.f64 (*.f64 2 (pow.f64 x 3/2)) (sqrt.f64 x))
(*.f64 (*.f64 2 (pow.f64 (cbrt.f64 x) 5)) (cbrt.f64 x))
(*.f64 (*.f64 (/.f64 0 0) x) (*.f64 x 2))
(*.f64 (*.f64 (/.f64 0 0) 2) (pow.f64 x 2))
(/.f64 1 (/.f64 0 0))
(/.f64 1 (/.f64 (+.f64 0 (pow.f64 x 4)) (*.f64 2 (pow.f64 x 6))))
(/.f64 0 0)
(/.f64 (*.f64 2 (pow.f64 x 6)) (+.f64 0 (pow.f64 x 4)))
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 6))) (cbrt.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 (sqrt.f64 0) (sqrt.f64 0))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) (*.f64 2 (pow.f64 x 6))) (*.f64 (+.f64 0 (pow.f64 x 4)) (+.f64 0 (pow.f64 x 4))))
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) 0) (*.f64 (+.f64 0 (pow.f64 x 4)) 0))
(/.f64 (*.f64 0 (*.f64 2 (pow.f64 x 6))) (*.f64 0 (+.f64 0 (pow.f64 x 4))))
(/.f64 (neg.f64 (*.f64 2 (pow.f64 x 6))) (neg.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 0 0) 1) 3) 1) (+.f64 (*.f64 (+.f64 (/.f64 0 0) 1) (+.f64 (/.f64 0 0) 1)) (+.f64 1 (+.f64 (/.f64 0 0) 1))))
(/.f64 (-.f64 (*.f64 (+.f64 (/.f64 0 0) 1) (+.f64 (/.f64 0 0) 1)) 1) (+.f64 (+.f64 (/.f64 0 0) 1) 1))
(/.f64 (*.f64 (/.f64 0 0) (*.f64 2 (pow.f64 x 6))) (+.f64 0 (pow.f64 x 4)))
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) 1) (+.f64 0 (pow.f64 x 4)))
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) (/.f64 0 0)) (+.f64 0 (pow.f64 x 4)))
(/.f64 (*.f64 0 (/.f64 0 0)) 0)
(pow.f64 (/.f64 0 0) 1)
(pow.f64 (/.f64 0 0) 2)
(pow.f64 (/.f64 0 0) 1/2)
(pow.f64 (/.f64 0 0) 1/3)
(pow.f64 (/.f64 0 0) 3)
(pow.f64 (/.f64 0 0) 6)
(pow.f64 (/.f64 0 0) 5/2)
(pow.f64 (/.f64 0 0) 5)
(pow.f64 (/.f64 0 0) 3/2)
(pow.f64 (/.f64 0 0) 4/3)
(pow.f64 (/.f64 0 0) 4)
(pow.f64 (/.f64 0 0) 2/3)
(pow.f64 (/.f64 0 0) 1/6)
(pow.f64 (/.f64 0 0) 1/9)
(pow.f64 (/.f64 0 0) 1/4)
(pow.f64 (/.f64 0 0) 9)
(pow.f64 (E.f64) (log.f64 (/.f64 0 0)))
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (/.f64 0 0)) 2))) (cbrt.f64 (log.f64 (/.f64 0 0))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 0 0)))) (sqrt.f64 (log.f64 (/.f64 0 0))))
(sqrt.f64 (/.f64 0 0))
(fabs.f64 (/.f64 0 0))
(fabs.f64 (neg.f64 (/.f64 0 0)))
(log.f64 (exp.f64 (/.f64 0 0)))
(cbrt.f64 (/.f64 0 0))
(expm1.f64 (log1p.f64 (/.f64 0 0)))
(exp.f64 (log.f64 (/.f64 0 0)))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/2))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 3))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/3))
(log1p.f64 (expm1.f64 (/.f64 0 0)))
(fma.f64 x x (pow.f64 x 2))
(fma.f64 1 (pow.f64 x 2) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 4) (pow.f64 x 2))
(fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 4) (pow.f64 (cbrt.f64 x) 2) (pow.f64 x 2))
(fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (pow.f64 x 2))
Outputs
(*.f64 x (sqrt.f64 2))
(*.f64 x -2)
(*.f64 x (sqrt.f64 2))
(*.f64 x -2)
(*.f64 x (sqrt.f64 2))
(*.f64 x -2)
(*.f64 x (sqrt.f64 2))
(*.f64 x -2)
(*.f64 x (sqrt.f64 2))
(*.f64 x -2)
(*.f64 x (sqrt.f64 2))
(*.f64 x -2)
(*.f64 x (sqrt.f64 2))
(*.f64 x -2)
(*.f64 x (sqrt.f64 2))
(*.f64 x -2)
(*.f64 -1 (*.f64 x (sqrt.f64 2)))
(*.f64 x -2)
(*.f64 -1 (*.f64 x (sqrt.f64 2)))
(*.f64 x -2)
(*.f64 -1 (*.f64 x (sqrt.f64 2)))
(*.f64 x -2)
(*.f64 -1 (*.f64 x (sqrt.f64 2)))
(*.f64 x -2)
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
-2
(+.f64 (+.f64 (/.f64 0 0) 1) -1)
-2
(+.f64 0 (/.f64 0 0))
-2
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 0 0))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 0 0)))))
-2
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))))
-2
(+.f64 (*.f64 (/.f64 0 0) (pow.f64 x 2)) (*.f64 (/.f64 0 0) (pow.f64 x 2)))
-2
(+.f64 (*.f64 (pow.f64 x 2) (/.f64 0 0)) (*.f64 (pow.f64 x 2) (/.f64 0 0)))
-2
(-.f64 (+.f64 (/.f64 0 0) 1) 1)
-2
(-.f64 (/.f64 (pow.f64 x 4) 0) (/.f64 (pow.f64 x 4) 0))
-2
(*.f64 x (*.f64 x 2))
-2
(*.f64 x (*.f64 (*.f64 x 2) 1))
-2
(*.f64 x (*.f64 (*.f64 x 2) (/.f64 0 0)))
-2
(*.f64 (pow.f64 x 2) 2)
-2
(*.f64 (pow.f64 x 2) (*.f64 (*.f64 x 2) (*.f64 x 2)))
-2
(*.f64 (/.f64 0 0) (/.f64 0 0))
-2
(*.f64 (/.f64 0 0) 1)
-2
(*.f64 (/.f64 0 0) (log.f64 (E.f64)))
-2
(*.f64 (/.f64 0 0) (pow.f64 1 1/3))
-2
(*.f64 (/.f64 0 0) (pow.f64 1 1/2))
-2
(*.f64 1 (/.f64 0 0))
-2
(*.f64 (cbrt.f64 x) (cbrt.f64 (*.f64 x 2)))
(*.f64 (cbrt.f64 x) (cbrt.f64 (*.f64 x -2)))
(*.f64 (cbrt.f64 x) (+.f64 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (cbrt.f64 x) 5)))
(*.f64 -2 (*.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x)))
(*.f64 (cbrt.f64 x) (*.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 x 2)))
(*.f64 (cbrt.f64 x) (*.f64 (*.f64 x -2) (pow.f64 (cbrt.f64 x) -2)))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (pow.f64 (cbrt.f64 x) 4) (pow.f64 (cbrt.f64 x) 4)))
(*.f64 -2 (pow.f64 (cbrt.f64 x) -2))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (*.f64 x 2)))
(*.f64 (pow.f64 (cbrt.f64 x) -2) (*.f64 (*.f64 x -2) (cbrt.f64 x)))
(*.f64 (sqrt.f64 x) (pow.f64 (*.f64 x 2) 1/2))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x -2)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x 2)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x -2)))
(*.f64 (sqrt.f64 x) (+.f64 (pow.f64 x 3/2) (pow.f64 x 3/2)))
(*.f64 -2 (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (*.f64 x 2)))
(*.f64 (sqrt.f64 x) (*.f64 (*.f64 x -2) (sqrt.f64 x)))
(*.f64 0 (/.f64 1 0))
-2
(*.f64 2 (pow.f64 x 2))
-2
(*.f64 2 (*.f64 (pow.f64 x 2) (/.f64 0 0)))
-2
(*.f64 (pow.f64 (cbrt.f64 x) 4) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 -2 (pow.f64 (cbrt.f64 x) -2))
(*.f64 (pow.f64 x 3/2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))
(*.f64 -2 (sqrt.f64 x))
(*.f64 (*.f64 2 (pow.f64 x 6)) (/.f64 1 (+.f64 0 (pow.f64 x 4))))
-2
(*.f64 (*.f64 x 2) x)
-2
(*.f64 (pow.f64 (cbrt.f64 x) 5) (+.f64 (cbrt.f64 x) (cbrt.f64 x)))
(*.f64 -2 (*.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x)))
(*.f64 4 (pow.f64 x 4))
-2
(*.f64 (pow.f64 1 1/3) (/.f64 0 0))
-2
(*.f64 (pow.f64 1 1/2) (/.f64 0 0))
-2
(*.f64 (pow.f64 2 1/2) x)
(*.f64 x -2)
(*.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 x) 2))
(*.f64 -2 (pow.f64 (cbrt.f64 x) -2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x -2)
(*.f64 (*.f64 2 (sqrt.f64 x)) (pow.f64 x 3/2))
(*.f64 -2 (sqrt.f64 x))
(*.f64 (*.f64 2 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (cbrt.f64 x) 4))
(*.f64 -2 (pow.f64 (cbrt.f64 x) -2))
(*.f64 (*.f64 2 (pow.f64 (cbrt.f64 x) 4)) (pow.f64 (cbrt.f64 x) 2))
(*.f64 -2 (pow.f64 (cbrt.f64 x) -2))
(*.f64 (*.f64 2 (pow.f64 x 3/2)) (sqrt.f64 x))
(*.f64 -2 (sqrt.f64 x))
(*.f64 (*.f64 2 (pow.f64 (cbrt.f64 x) 5)) (cbrt.f64 x))
(*.f64 -2 (*.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x)))
(*.f64 (*.f64 (/.f64 0 0) x) (*.f64 x 2))
-2
(*.f64 (*.f64 (/.f64 0 0) 2) (pow.f64 x 2))
-2
(/.f64 1 (/.f64 0 0))
-2
(/.f64 1 (/.f64 (+.f64 0 (pow.f64 x 4)) (*.f64 2 (pow.f64 x 6))))
-2
(/.f64 0 0)
-2
(/.f64 (*.f64 2 (pow.f64 x 6)) (+.f64 0 (pow.f64 x 4)))
-2
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 6))) (cbrt.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 -2 (cbrt.f64 (pow.f64 x -2)))
(/.f64 (sqrt.f64 0) (sqrt.f64 0))
-2
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 -2 (sqrt.f64 (pow.f64 x -2)))
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) (*.f64 2 (pow.f64 x 6))) (*.f64 (+.f64 0 (pow.f64 x 4)) (+.f64 0 (pow.f64 x 4))))
-2
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) 0) (*.f64 (+.f64 0 (pow.f64 x 4)) 0))
-2
(/.f64 (*.f64 0 (*.f64 2 (pow.f64 x 6))) (*.f64 0 (+.f64 0 (pow.f64 x 4))))
-2
(/.f64 (neg.f64 (*.f64 2 (pow.f64 x 6))) (neg.f64 (+.f64 0 (pow.f64 x 4))))
-2
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 0 0) 1) 3) 1) (+.f64 (*.f64 (+.f64 (/.f64 0 0) 1) (+.f64 (/.f64 0 0) 1)) (+.f64 1 (+.f64 (/.f64 0 0) 1))))
-2
(/.f64 (-.f64 (*.f64 (+.f64 (/.f64 0 0) 1) (+.f64 (/.f64 0 0) 1)) 1) (+.f64 (+.f64 (/.f64 0 0) 1) 1))
-2
(/.f64 (*.f64 (/.f64 0 0) (*.f64 2 (pow.f64 x 6))) (+.f64 0 (pow.f64 x 4)))
-2
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) 1) (+.f64 0 (pow.f64 x 4)))
-2
(/.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) (/.f64 0 0)) (+.f64 0 (pow.f64 x 4)))
-2
(/.f64 (*.f64 0 (/.f64 0 0)) 0)
-2
(pow.f64 (/.f64 0 0) 1)
-2
(pow.f64 (/.f64 0 0) 2)
-2
(pow.f64 (/.f64 0 0) 1/2)
-2
(pow.f64 (/.f64 0 0) 1/3)
-2
(pow.f64 (/.f64 0 0) 3)
-2
(pow.f64 (/.f64 0 0) 6)
-2
(pow.f64 (/.f64 0 0) 5/2)
(pow.f64 -2 5/2)
(pow.f64 (/.f64 0 0) 5)
-2
(pow.f64 (/.f64 0 0) 3/2)
-2
(pow.f64 (/.f64 0 0) 4/3)
-2
(pow.f64 (/.f64 0 0) 4)
-2
(pow.f64 (/.f64 0 0) 2/3)
-2
(pow.f64 (/.f64 0 0) 1/6)
(pow.f64 -2 1/6)
(pow.f64 (/.f64 0 0) 1/9)
(*.f64 (pow.f64 -2 1/18) (pow.f64 -2 1/18))
(pow.f64 (/.f64 0 0) 1/4)
-2
(pow.f64 (/.f64 0 0) 9)
-2
(pow.f64 (E.f64) (log.f64 (/.f64 0 0)))
-2
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (/.f64 0 0)) 2))) (cbrt.f64 (log.f64 (/.f64 0 0))))
-2
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 0 0)))) (sqrt.f64 (log.f64 (/.f64 0 0))))
-2
(sqrt.f64 (/.f64 0 0))
-2
(fabs.f64 (/.f64 0 0))
-2
(fabs.f64 (neg.f64 (/.f64 0 0)))
-2
(log.f64 (exp.f64 (/.f64 0 0)))
-2
(cbrt.f64 (/.f64 0 0))
-2
(expm1.f64 (log1p.f64 (/.f64 0 0)))
-2
(exp.f64 (log.f64 (/.f64 0 0)))
-2
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/2))
-2
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 3))
-2
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/3))
-2
(log1p.f64 (expm1.f64 (/.f64 0 0)))
-2
(fma.f64 x x (pow.f64 x 2))
-2
(fma.f64 1 (pow.f64 x 2) (pow.f64 x 2))
(pow.f64 x -2)
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 4) (pow.f64 x 2))
(+.f64 (pow.f64 (cbrt.f64 x) -2) (pow.f64 x -2))
(fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (pow.f64 x 2))
(fma.f64 (sqrt.f64 x) (pow.f64 x -2) (pow.f64 x -2))
(fma.f64 (pow.f64 (cbrt.f64 x) 4) (pow.f64 (cbrt.f64 x) 2) (pow.f64 x 2))
(+.f64 (pow.f64 (cbrt.f64 x) -2) (pow.f64 x -2))
(fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (pow.f64 x 2))
(fma.f64 (pow.f64 x -2) (sqrt.f64 x) (pow.f64 x -2))
(fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (pow.f64 x -2))

eval66.0ms (1.6%)

Compiler

Compiled 1036 to 827 computations (20.2% saved)

prune19.0ms (0.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1215126
Fresh000
Picked011
Done000
Total1216127
Accuracy
100.0%
Counts
127 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(hypot.f64 x x)
6.9%
(*.f64 (*.f64 x 2) x)
99.4%
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x 2)))
99.3%
(*.f64 (sqrt.f64 2) x)
2.3%
(*.f64 x -2)
1.7%
-2
100.0%
(hypot.f64 x x)
6.9%
(*.f64 (*.f64 x 2) x)
99.4%
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x 2)))
99.3%
(*.f64 (sqrt.f64 2) x)
2.3%
(*.f64 x -2)
1.7%
-2
Compiler

Compiled 58 to 42 computations (27.6% saved)

localize87.0ms (2.1%)

Localize:

Found 2 expressions with local error:

NewAccuracyProgram
99.4%
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x 2)))
99.3%
(*.f64 (sqrt.f64 2) x)
Compiler

Compiled 43 to 28 computations (34.9% saved)

series3.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x 2)))
0.0ms
x
@0
(*.f64 (sqrt.f64 2) x)
0.0ms
x
@inf
(*.f64 (sqrt.f64 2) x)
0.0ms
x
@-inf
(*.f64 (sqrt.f64 2) x)
0.0ms
x
@inf
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x 2)))

rewrite60.0ms (1.4%)

Algorithm
batch-egg-rewrite
Rules
1036×unpow-prod-down
744×prod-exp
642×log-prod
564×pow-prod-down
490×log1p-expm1-u
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01328
114828
2167128
Stop Event
node limit
Counts
2 → 100
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x 2)))
Outputs
(+.f64 0 (*.f64 (sqrt.f64 2) x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (*.f64 (sqrt.f64 2) x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))) (log.f64 (sqrt.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x))) 1)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(pow.f64 (exp.f64 1) (log.f64 (*.f64 (sqrt.f64 2) x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (sqrt.f64 2) x))) 2)) (cbrt.f64 (log.f64 (*.f64 (sqrt.f64 2) x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))) (sqrt.f64 (log.f64 (*.f64 (sqrt.f64 2) x))))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(log.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 2) x)) 1))
(exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 2) x)) 1) 1))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x))) 3))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 (sqrt.f64 2) x))) 1/3))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (pow.f64 x 2))) 1/2))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x))) 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (*.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (log.f64 x)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (*.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (log.f64 x)))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (*.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (log.f64 (sqrt.f64 2))))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (*.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (*.f64 (log.f64 (*.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1/2) (log.f64 (sqrt.f64 (*.f64 2 x)))))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1/2) (*.f64 (log.f64 (*.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1/2) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 x)) 1) (log.f64 (sqrt.f64 (*.f64 2 x)))))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 x)) 1) (*.f64 (log.f64 (*.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 x)) 1) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 2 x)) 1/2) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 2 x)) 1/2) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 2 x)) 1/2) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 0 (*.f64 (sqrt.f64 2) x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (*.f64 (sqrt.f64 2) x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))) (log.f64 (sqrt.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x))) 1)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(pow.f64 (exp.f64 1) (log.f64 (*.f64 (sqrt.f64 2) x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (sqrt.f64 2) x))) 2)) (cbrt.f64 (log.f64 (*.f64 (sqrt.f64 2) x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))) (sqrt.f64 (log.f64 (*.f64 (sqrt.f64 2) x))))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(log.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 2) x)) 1))
(exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 2) x)) 1) 1))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x))) 3))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 (sqrt.f64 2) x))) 1/3))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (pow.f64 x 2))) 1/2))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x))) 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (*.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (log.f64 x)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (*.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (log.f64 x)))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (*.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (log.f64 (sqrt.f64 2))))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (*.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (*.f64 (log.f64 (*.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1/2) (log.f64 (sqrt.f64 (*.f64 2 x)))))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1/2) (*.f64 (log.f64 (*.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1/2) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 x)) 1) (log.f64 (sqrt.f64 (*.f64 2 x)))))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 x)) 1) (*.f64 (log.f64 (*.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 x)) 1) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 2 x)) 1/2) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 2 x)) 1/2) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 2 x)) 1/2) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))

simplify73.0ms (1.8%)

Algorithm
egg-herbie
Rules
1386×log-prod
758×prod-exp
742×associate-*r*
672×associate-*l*
546×associate-+r+
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01462058
13121996
27081996
334391996
471421996
Stop Event
node limit
Counts
124 → 60
Calls
Call 1
Inputs
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 -1 (*.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(*.f64 -1 (*.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(*.f64 -1 (*.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(*.f64 -1 (*.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(+.f64 0 (*.f64 (sqrt.f64 2) x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (*.f64 (sqrt.f64 2) x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))) (log.f64 (sqrt.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x))) 1)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(pow.f64 (exp.f64 1) (log.f64 (*.f64 (sqrt.f64 2) x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (sqrt.f64 2) x))) 2)) (cbrt.f64 (log.f64 (*.f64 (sqrt.f64 2) x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))) (sqrt.f64 (log.f64 (*.f64 (sqrt.f64 2) x))))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(log.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 2) x)) 1))
(exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 2) x)) 1) 1))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x))) 3))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 (sqrt.f64 2) x))) 1/3))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (pow.f64 x 2))) 1/2))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x))) 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (*.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (log.f64 x)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (*.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (log.f64 x)))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (*.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (log.f64 (sqrt.f64 2))))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (*.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (*.f64 (log.f64 (*.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1/2) (log.f64 (sqrt.f64 (*.f64 2 x)))))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1/2) (*.f64 (log.f64 (*.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1/2) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 x)) 1) (log.f64 (sqrt.f64 (*.f64 2 x)))))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 x)) 1) (*.f64 (log.f64 (*.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 x)) 1) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 2 x)) 1/2) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 2 x)) 1/2) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 2 x)) 1/2) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 0 (*.f64 (sqrt.f64 2) x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (*.f64 (sqrt.f64 2) x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))) (log.f64 (sqrt.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x))) 1)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(pow.f64 (exp.f64 1) (log.f64 (*.f64 (sqrt.f64 2) x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (sqrt.f64 2) x))) 2)) (cbrt.f64 (log.f64 (*.f64 (sqrt.f64 2) x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))) (sqrt.f64 (log.f64 (*.f64 (sqrt.f64 2) x))))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(log.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 2) x)) 1))
(exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 2) x)) 1) 1))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x))) 3))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 (sqrt.f64 2) x))) 1/3))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (pow.f64 x 2))) 1/2))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x))) 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (*.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (log.f64 x)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (*.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (log.f64 x)))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (*.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (log.f64 (sqrt.f64 2))))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (*.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (*.f64 (log.f64 (*.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1/2) (log.f64 (sqrt.f64 (*.f64 2 x)))))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1/2) (*.f64 (log.f64 (*.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1/2) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 x)) 1) (log.f64 (sqrt.f64 (*.f64 2 x)))))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 x)) 1) (*.f64 (log.f64 (*.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 x)) 1) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 2 x)) 1/2) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 2 x)) 1/2) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 2 x)) 1/2) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))
Outputs
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 -1 (*.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(neg.f64 (*.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(*.f64 x (neg.f64 (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(*.f64 x (*.f64 (sqrt.f64 -2) (neg.f64 (sqrt.f64 -1))))
(*.f64 -1 (*.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(neg.f64 (*.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(*.f64 x (neg.f64 (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(*.f64 x (*.f64 (sqrt.f64 -2) (neg.f64 (sqrt.f64 -1))))
(*.f64 -1 (*.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(neg.f64 (*.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(*.f64 x (neg.f64 (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(*.f64 x (*.f64 (sqrt.f64 -2) (neg.f64 (sqrt.f64 -1))))
(*.f64 -1 (*.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(neg.f64 (*.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(*.f64 x (neg.f64 (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(*.f64 x (*.f64 (sqrt.f64 -2) (neg.f64 (sqrt.f64 -1))))
(+.f64 0 (*.f64 (sqrt.f64 2) x))
(*.f64 x (sqrt.f64 2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (*.f64 (sqrt.f64 2) x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(*.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))) 3)
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))) (log.f64 (sqrt.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))))
(*.f64 x (sqrt.f64 2))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x))) 1)
(*.f64 x (sqrt.f64 2))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(*.f64 x (sqrt.f64 2))
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(*.f64 x (sqrt.f64 2))
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(*.f64 x (sqrt.f64 2))
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(*.f64 x (sqrt.f64 2))
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(*.f64 x (sqrt.f64 2))
(pow.f64 (exp.f64 1) (log.f64 (*.f64 (sqrt.f64 2) x)))
(*.f64 x (sqrt.f64 2))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (sqrt.f64 2) x))) 2)) (cbrt.f64 (log.f64 (*.f64 (sqrt.f64 2) x))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 x (sqrt.f64 2)))) 2)) (cbrt.f64 (log.f64 (*.f64 x (sqrt.f64 2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))) (sqrt.f64 (log.f64 (*.f64 (sqrt.f64 2) x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 x (sqrt.f64 2))))) (sqrt.f64 (log.f64 (*.f64 x (sqrt.f64 2)))))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(*.f64 x (sqrt.f64 2))
(log.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))
(*.f64 x (sqrt.f64 2))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(*.f64 x (sqrt.f64 2))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 2) x)) 1))
(*.f64 x (sqrt.f64 2))
(exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 2) x)) 1) 1))
(*.f64 x (sqrt.f64 2))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x))) 3))
(*.f64 x (sqrt.f64 2))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 (sqrt.f64 2) x))) 1/3))
(*.f64 x (sqrt.f64 2))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (pow.f64 x 2))) 1/2))
(*.f64 x (sqrt.f64 2))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x))) 2))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (*.f64 (log.f64 x) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (log.f64 x)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (*.f64 (log.f64 x) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (log.f64 x)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (*.f64 (log.f64 x) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 2) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (log.f64 (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (*.f64 (log.f64 2) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (*.f64 (log.f64 (*.f64 2 x)) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1/2) (log.f64 (sqrt.f64 (*.f64 2 x)))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1/2) (*.f64 (log.f64 (*.f64 2 x)) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1/2) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 x)) 1) (log.f64 (sqrt.f64 (*.f64 2 x)))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 x)) 1) (*.f64 (log.f64 (*.f64 2 x)) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 x)) 1) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) (*.f64 (log.f64 x) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 2 x)) 1/2) (log.f64 (sqrt.f64 x))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 2 x)) 1/2) (*.f64 (log.f64 x) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 2 x)) 1/2) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1) (log.f64 (sqrt.f64 x))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1) (*.f64 (log.f64 x) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(*.f64 x (sqrt.f64 2))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))
(*.f64 x (sqrt.f64 2))
(+.f64 0 (*.f64 (sqrt.f64 2) x))
(*.f64 x (sqrt.f64 2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (*.f64 (sqrt.f64 2) x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(*.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))) 3)
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))) (log.f64 (sqrt.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))))
(*.f64 x (sqrt.f64 2))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x))) 1)
(*.f64 x (sqrt.f64 2))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(*.f64 x (sqrt.f64 2))
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(*.f64 x (sqrt.f64 2))
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(*.f64 x (sqrt.f64 2))
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(*.f64 x (sqrt.f64 2))
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(*.f64 x (sqrt.f64 2))
(pow.f64 (exp.f64 1) (log.f64 (*.f64 (sqrt.f64 2) x)))
(*.f64 x (sqrt.f64 2))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (sqrt.f64 2) x))) 2)) (cbrt.f64 (log.f64 (*.f64 (sqrt.f64 2) x))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 x (sqrt.f64 2)))) 2)) (cbrt.f64 (log.f64 (*.f64 x (sqrt.f64 2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))) (sqrt.f64 (log.f64 (*.f64 (sqrt.f64 2) x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 x (sqrt.f64 2))))) (sqrt.f64 (log.f64 (*.f64 x (sqrt.f64 2)))))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(*.f64 x (sqrt.f64 2))
(log.f64 (exp.f64 (*.f64 (sqrt.f64 2) x)))
(*.f64 x (sqrt.f64 2))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(*.f64 x (sqrt.f64 2))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 2) x)) 1))
(*.f64 x (sqrt.f64 2))
(exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 2) x)) 1) 1))
(*.f64 x (sqrt.f64 2))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x))) 3))
(*.f64 x (sqrt.f64 2))
(exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 (sqrt.f64 2) x))) 1/3))
(*.f64 x (sqrt.f64 2))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (pow.f64 x 2))) 1/2))
(*.f64 x (sqrt.f64 2))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x))) 2))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (*.f64 (log.f64 x) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (log.f64 x)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (*.f64 (log.f64 x) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (log.f64 x)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (*.f64 (log.f64 x) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 2) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (log.f64 (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (*.f64 (log.f64 2) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (*.f64 (log.f64 (*.f64 2 x)) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1/2) (log.f64 (sqrt.f64 (*.f64 2 x)))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1/2) (*.f64 (log.f64 (*.f64 2 x)) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1/2) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 x)) 1) (log.f64 (sqrt.f64 (*.f64 2 x)))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 x)) 1) (*.f64 (log.f64 (*.f64 2 x)) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 x)) 1) (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) (*.f64 (log.f64 x) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 2 x)) 1/2) (log.f64 (sqrt.f64 x))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 2 x)) 1/2) (*.f64 (log.f64 x) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (*.f64 2 x)) 1/2) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1) (log.f64 (sqrt.f64 x))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1) (*.f64 (log.f64 x) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(*.f64 x (sqrt.f64 2))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))
(*.f64 x (sqrt.f64 2))

eval15.0ms (0.4%)

Compiler

Compiled 604 to 488 computations (19.2% saved)

prune11.0ms (0.3%)

Pruning

6 alts after pruning (1 fresh and 5 done)

PrunedKeptTotal
New60060
Fresh011
Picked044
Done011
Total60666
Accuracy
100.0%
Counts
66 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(hypot.f64 x x)
6.9%
(*.f64 (*.f64 x 2) x)
99.4%
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x 2)))
99.3%
(*.f64 (sqrt.f64 2) x)
2.3%
(*.f64 x -2)
1.7%
-2
100.0%
(hypot.f64 x x)
6.9%
(*.f64 (*.f64 x 2) x)
99.4%
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x 2)))
99.3%
(*.f64 (sqrt.f64 2) x)
2.3%
(*.f64 x -2)
1.7%
-2
Compiler

Compiled 58 to 42 computations (27.6% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune4.0ms (0.1%)

Pruning

6 alts after pruning (1 fresh and 5 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done055
Total066
Accuracy
100.0%
Counts
6 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(hypot.f64 x x)
6.9%
(*.f64 (*.f64 x 2) x)
99.4%
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x 2)))
99.3%
(*.f64 (sqrt.f64 2) x)
2.3%
(*.f64 x -2)
1.7%
-2
100.0%
(hypot.f64 x x)
6.9%
(*.f64 (*.f64 x 2) x)
99.4%
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x 2)))
99.3%
(*.f64 (sqrt.f64 2) x)
2.3%
(*.f64 x -2)
1.7%
-2
Compiler

Compiled 58 to 42 computations (27.6% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune4.0ms (0.1%)

Pruning

6 alts after pruning (1 fresh and 5 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done055
Total066
Accuracy
100.0%
Counts
6 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(hypot.f64 x x)
6.9%
(*.f64 (*.f64 x 2) x)
99.4%
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x 2)))
99.3%
(*.f64 (sqrt.f64 2) x)
2.3%
(*.f64 x -2)
1.7%
-2
Compiler

Compiled 61 to 43 computations (29.5% saved)

regimes23.0ms (0.6%)

Counts
7 → 1
Calls
Call 1
Inputs
-2
(*.f64 x -2)
(*.f64 (*.f64 x 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x 2)))
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
Outputs
(hypot.f64 x x)
Calls

4 calls:

10.0ms
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
5.0ms
x
4.0ms
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
3.0ms
(pow.f64 x 2)
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
100.0%1(+.f64 (pow.f64 x 2) (pow.f64 x 2))
100.0%1(pow.f64 x 2)
Compiler

Compiled 55 to 39 computations (29.1% saved)

regimes4.0ms (0.1%)

Counts
3 → 1
Calls
Call 1
Inputs
-2
(*.f64 x -2)
(*.f64 (*.f64 x 2) x)
Outputs
(*.f64 (*.f64 x 2) x)
Calls

1 calls:

3.0ms
x
Results
AccuracySegmentsBranch
6.9%1x
Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes4.0ms (0.1%)

Counts
2 → 1
Calls
Call 1
Inputs
-2
(*.f64 x -2)
Outputs
(*.f64 x -2)
Calls

1 calls:

3.0ms
x
Results
AccuracySegmentsBranch
2.3%1x
Compiler

Compiled 7 to 5 computations (28.6% saved)

regimes3.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
-2
Outputs
-2
Calls

1 calls:

2.0ms
x
Results
AccuracySegmentsBranch
1.7%1x
Compiler

Compiled 4 to 3 computations (25% saved)

simplify2.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01143
11443
Stop Event
fuel
saturated
Calls
Call 1
Inputs
(hypot.f64 x x)
(*.f64 (*.f64 x 2) x)
(*.f64 x -2)
-2
Outputs
(hypot.f64 x x)
(*.f64 (*.f64 x 2) x)
(*.f64 x (*.f64 x 2))
(*.f64 x -2)
-2
Compiler

Compiled 16 to 11 computations (31.3% saved)

soundness2.4s (57.9%)

Rules
1064×fma-neg
980×distribute-lft-out
900×fma-def
886×hypot-def
801×log1p-expm1-u
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01588
13156
27556
324856
4108256
5285256
6584256
7790856
0613
14613
24787
354967
0223916
1678916
0223916
1678916
0613
14613
24787
354967
Stop Event
node limit
unsound
unsound
node limit
node limit
Compiler

Compiled 632 to 167 computations (73.6% saved)

end0.0ms (0%)

preprocess34.0ms (0.8%)

Remove

(abs x)

Compiler

Compiled 52 to 34 computations (34.6% saved)

Profiling

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