Details

Time bar (total: 2.3s)

analyze5.0ms (0.2%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
0%0%75%0%0%25%0%3
40%25%37.5%0%0%37.5%0%4
66.7%37.5%18.7%0%0%43.7%0%5
82.4%43.7%9.4%0%0%46.9%0%6
90.9%46.9%4.7%0%0%48.4%0%7
95.4%48.4%2.3%0%0%49.2%0%8
97.7%49.2%1.2%0%0%49.6%0%9
98.8%49.6%0.6%0%0%49.8%0%10
99.4%49.8%0.3%0%0%49.9%0%11
99.7%49.9%0.1%0%0%49.9%0%12
Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.0s (44.1%)

Results
1.0s8256×body256valid
1.0ms15×body256invalid
Bogosity

preprocess65.0ms (2.8%)

Algorithm
2×egg-herbie
Rules
448×fma-def
400×associate--l-
288×associate--r-
258×associate-+l-
216×associate-*r*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01233
12133
22733
33833
46033
58733
612833
721133
839333
964933
1093733
11124533
12177333
13220533
14270233
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
Outputs
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
Compiler

Compiled 13 to 11 computations (15.4% saved)

simplify106.0ms (4.5%)

Algorithm
1×egg-herbie
Rules
448×fma-def
400×associate--l-
288×associate--r-
258×associate-+l-
216×associate-*r*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01233
12133
22733
33833
46033
58733
612833
721133
839333
964933
1093733
11124533
12177333
13220533
14270233
Stop Event
1×saturated
Counts
1 → 1
Calls
Call 1
Inputs
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
Outputs
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))

eval1.0ms (0.1%)

Compiler

Compiled 12 to 10 computations (16.7% saved)

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.0b
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
Compiler

Compiled 12 to 10 computations (16.7% saved)

localize30.0ms (1.3%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
✓0.0b
(/.f64 (-.f64 1 x) (+.f64 1 x))
Compiler

Compiled 45 to 34 computations (24.4% saved)

series2.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
0.0ms
x
@-inf
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0ms
x
@inf
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0ms
x
@inf
(/.f64 (-.f64 1 x) (+.f64 1 x))
0.0ms
x
@0
(/.f64 (-.f64 1 x) (+.f64 1 x))
0.0ms
x
@0
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))

rewrite72.0ms (3.1%)

Algorithm
1×batch-egg-rewrite
Rules
1636×associate-/r*
1154×associate-/l*
978×associate-/r/
904×*-commutative
538×associate-/l/
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0942
119342
2263642
Stop Event
1×node limit
Counts
2 → 134
Calls
Call 1
Inputs
(/.f64 (-.f64 1 x) (+.f64 1 x))
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
Outputs
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log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))))))

simplify91.0ms (3.9%)

Algorithm
1×egg-herbie
Rules
1560×associate-*r/
1310×associate-*l/
652×associate-+l+
590×+-commutative
564×associate-+r+
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03846184
110635692
239985486
Stop Event
1×node limit
Counts
158 → 258
Calls
Call 1
Inputs
1
(+.f64 1 (*.f64 -2 x))
(+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 1 (*.f64 -2 x)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 -2 x) (*.f64 -2 (pow.f64 x 3)))))
-1
(-.f64 (*.f64 2 (/.f64 1 x)) 1)
(-.f64 (*.f64 2 (/.f64 1 x)) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 2 (/.f64 1 (pow.f64 x 3)))) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
-1
(-.f64 (*.f64 2 (/.f64 1 x)) 1)
(-.f64 (*.f64 2 (/.f64 1 x)) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 2 (/.f64 1 (pow.f64 x 3)))) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
1
(+.f64 1 (*.f64 -1 x))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x)))
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))))
(sqrt.f64 -1)
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1))
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (+.f64 (sqrt.f64 -1) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (*.f64 (sqrt.f64 -1) (pow.f64 x 2))))))
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (+.f64 (sqrt.f64 -1) (+.f64 (*.f64 1/2 (/.f64 (-.f64 2 (*.f64 -1 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (pow.f64 (sqrt.f64 -1) 2)))) (*.f64 (sqrt.f64 -1) (pow.f64 x 3)))) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))))
(sqrt.f64 -1)
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1))
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (+.f64 (sqrt.f64 -1) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (*.f64 (sqrt.f64 -1) (pow.f64 x 2))))))
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (+.f64 (*.f64 1/2 (/.f64 (+.f64 2 (+.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)) (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))))) (*.f64 (sqrt.f64 -1) (pow.f64 x 3)))) (+.f64 (sqrt.f64 -1) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))))
(+.f64 (/.f64 1 (+.f64 1 x)) (neg.f64 (/.f64 x (+.f64 1 x))))
(+.f64 (/.f64 1 (+.f64 1 x)) (*.f64 1 (neg.f64 (/.f64 x (+.f64 1 x)))))
(+.f64 (/.f64 1 (+.f64 1 x)) (*.f64 (/.f64 1 (+.f64 1 x)) (neg.f64 x)))
(+.f64 (/.f64 1 (+.f64 1 x)) (*.f64 (neg.f64 (/.f64 x (+.f64 1 x))) 1))
(+.f64 (/.f64 1 (+.f64 1 x)) (*.f64 (neg.f64 x) (/.f64 1 (+.f64 1 x))))
(+.f64 (neg.f64 (/.f64 x (+.f64 1 x))) (/.f64 1 (+.f64 1 x)))
(+.f64 (*.f64 (/.f64 1 (+.f64 1 x)) (neg.f64 x)) (/.f64 1 (+.f64 1 x)))
(+.f64 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) 1) (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (-.f64 (*.f64 x x) x)))
(+.f64 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (-.f64 (*.f64 x x) x)) (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) 1))
(+.f64 (*.f64 (neg.f64 x) (/.f64 1 (+.f64 1 x))) (/.f64 1 (+.f64 1 x)))
(+.f64 (*.f64 1 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))) (*.f64 (-.f64 (*.f64 x x) x) (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))))
(+.f64 (*.f64 (-.f64 (*.f64 x x) x) (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))) (*.f64 1 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))))
(-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 x (+.f64 1 x)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 1)
(*.f64 1 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(*.f64 (-.f64 1 x) (/.f64 1 (+.f64 1 x)))
(*.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1)
(*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(*.f64 (sqrt.f64 (-.f64 1 x)) (/.f64 (sqrt.f64 (-.f64 1 x)) (+.f64 1 x)))
(*.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1/4) (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1/4)))
(*.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (/.f64 (cbrt.f64 (-.f64 1 x)) (+.f64 1 x)))
(*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(*.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 2))
(*.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))
(*.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 2) (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(*.f64 (/.f64 1 (+.f64 1 x)) (-.f64 1 x))
(*.f64 (+.f64 (-.f64 1 x) (*.f64 x x)) (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))))
(*.f64 (+.f64 -1 x) (/.f64 1 (-.f64 -1 x)))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1/4)) (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1/4))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))) (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (/.f64 (-.f64 1 x) (cbrt.f64 (+.f64 1 x))))
(*.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
(*.f64 (/.f64 (-.f64 1 x) (cbrt.f64 (+.f64 1 x))) (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)))
(*.f64 (/.f64 1 (-.f64 1 (*.f64 x x))) (pow.f64 (-.f64 1 x) 2))
(*.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3))) (*.f64 (-.f64 1 x) (+.f64 (-.f64 1 x) (*.f64 x x))))
(*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (-.f64 1 x) (*.f64 x x)))
(*.f64 (/.f64 1 (-.f64 -1 x)) (+.f64 -1 x))
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (+.f64 1 x)) (sqrt.f64 (-.f64 1 x)))
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (/.f64 (sqrt.f64 (-.f64 1 x)) (cbrt.f64 (+.f64 1 x))))
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (cbrt.f64 (+.f64 1 x))) (/.f64 (sqrt.f64 (-.f64 1 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) 1) (/.f64 (cbrt.f64 (-.f64 1 x)) (+.f64 1 x)))
(*.f64 (/.f64 (cbrt.f64 (-.f64 1 x)) (+.f64 1 x)) (pow.f64 (cbrt.f64 (-.f64 1 x)) 2))
(*.f64 (/.f64 (cbrt.f64 (-.f64 1 x)) (+.f64 1 x)) (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) 1))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (sqrt.f64 (+.f64 1 x))) (/.f64 (cbrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))
(*.f64 (/.f64 (cbrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (sqrt.f64 (+.f64 1 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2) (+.f64 1 x)) (cbrt.f64 (-.f64 1 x)))
(*.f64 (/.f64 (-.f64 1 (*.f64 x x)) (*.f64 (-.f64 1 (*.f64 x x)) (-.f64 1 (*.f64 x x)))) (pow.f64 (-.f64 1 x) 2))
(*.f64 (/.f64 (-.f64 1 x) (neg.f64 (-.f64 1 (*.f64 x x)))) (+.f64 -1 x))
(*.f64 (/.f64 (-.f64 1 x) (neg.f64 (+.f64 1 (pow.f64 x 3)))) (neg.f64 (+.f64 (-.f64 1 x) (*.f64 x x))))
(*.f64 (/.f64 1 (/.f64 (+.f64 1 x) (pow.f64 (cbrt.f64 (-.f64 1 x)) 2))) (cbrt.f64 (-.f64 1 x)))
(*.f64 (/.f64 (-.f64 1 x) (/.f64 (-.f64 1 (*.f64 x x)) (sqrt.f64 (-.f64 1 x)))) (sqrt.f64 (-.f64 1 x)))
(*.f64 (/.f64 (-.f64 1 x) (/.f64 (-.f64 1 (*.f64 x x)) (pow.f64 (cbrt.f64 (-.f64 1 x)) 2))) (cbrt.f64 (-.f64 1 x)))
(*.f64 (/.f64 (-.f64 1 x) (-.f64 (*.f64 x x) 1)) (-.f64 x 1))
(*.f64 (/.f64 (-.f64 1 (*.f64 x x)) (*.f64 (+.f64 1 (pow.f64 x 3)) (+.f64 1 (pow.f64 x 3)))) (*.f64 (+.f64 (-.f64 1 x) (*.f64 x x)) (+.f64 (-.f64 1 x) (*.f64 x x))))
(*.f64 (/.f64 (-.f64 1 (*.f64 x x)) (*.f64 (-.f64 1 (*.f64 x x)) (+.f64 1 (pow.f64 x 3)))) (*.f64 (-.f64 1 x) (+.f64 (-.f64 1 x) (*.f64 x x))))
(*.f64 (/.f64 (+.f64 -1 x) (neg.f64 (-.f64 1 (*.f64 x x)))) (-.f64 1 x))
(*.f64 (/.f64 (+.f64 -1 x) (neg.f64 (+.f64 1 (pow.f64 x 3)))) (+.f64 (-.f64 1 x) (*.f64 x x)))
(*.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (sqrt.f64 (-.f64 1 x))) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 (-.f64 1 x) (*.f64 x x))))
(*.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (sqrt.f64 (-.f64 1 x))) (sqrt.f64 (-.f64 1 (*.f64 x x)))) (sqrt.f64 (-.f64 1 x)))
(*.f64 (/.f64 (*.f64 (/.f64 1 (+.f64 1 x)) (-.f64 1 (pow.f64 x 3))) (-.f64 1 (*.f64 (fma.f64 x x x) (fma.f64 x x x)))) (-.f64 1 (fma.f64 x x x)))
(*.f64 (/.f64 (*.f64 (/.f64 1 (+.f64 1 x)) (-.f64 1 (pow.f64 x 3))) (+.f64 1 (pow.f64 (fma.f64 x x x) 3))) (-.f64 (+.f64 1 (*.f64 (fma.f64 x x x) (fma.f64 x x x))) (fma.f64 x x x)))
(*.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 (-.f64 1 x) (*.f64 x x))))
(*.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (-.f64 1 (*.f64 x x)))) (sqrt.f64 (-.f64 1 x)))
(*.f64 (/.f64 (/.f64 (-.f64 1 x) (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (cbrt.f64 (+.f64 1 (pow.f64 x 3)))) (cbrt.f64 (+.f64 (-.f64 1 x) (*.f64 x x))))
(*.f64 (/.f64 (/.f64 (-.f64 1 x) (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (cbrt.f64 (-.f64 1 (*.f64 x x)))) (cbrt.f64 (-.f64 1 x)))
(*.f64 (/.f64 (-.f64 (+.f64 1 x) (fma.f64 x x x)) (*.f64 (+.f64 1 (pow.f64 x 3)) (+.f64 1 (pow.f64 x 3)))) (*.f64 (+.f64 (-.f64 1 x) (*.f64 x x)) (+.f64 (-.f64 1 x) (*.f64 x x))))
(*.f64 (/.f64 (-.f64 (+.f64 1 x) (fma.f64 x x x)) (*.f64 (-.f64 1 (*.f64 x x)) (-.f64 1 (*.f64 x x)))) (pow.f64 (-.f64 1 x) 2))
(*.f64 (/.f64 (-.f64 (+.f64 1 x) (fma.f64 x x x)) (*.f64 (+.f64 1 x) (-.f64 1 (*.f64 x x)))) (-.f64 1 x))
(*.f64 (/.f64 (-.f64 (+.f64 1 x) (fma.f64 x x x)) (*.f64 (+.f64 1 x) (+.f64 1 (pow.f64 x 3)))) (+.f64 (-.f64 1 x) (*.f64 x x)))
(*.f64 (/.f64 (-.f64 (+.f64 1 x) (fma.f64 x x x)) (*.f64 (-.f64 1 (*.f64 x x)) (+.f64 1 (pow.f64 x 3)))) (*.f64 (-.f64 1 x) (+.f64 (-.f64 1 x) (*.f64 x x))))
(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1)
(pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 2)
(pow.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 3)
(pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 2) 1/2)
(pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3) 1/3)
(pow.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)) -1)
(neg.f64 (/.f64 (-.f64 1 x) (-.f64 -1 x)))
(sqrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 2))
(log.f64 (exp.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3))
(cbrt.f64 (/.f64 (pow.f64 (-.f64 1 x) 3) (pow.f64 (+.f64 1 x) 3)))
(expm1.f64 (log1p.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(exp.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))
(log1p.f64 (expm1.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))) 1)
(*.f64 1 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 1)
(*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (pow.f64 1 1/2))
(*.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))
(*.f64 (sqrt.f64 (-.f64 1 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
(*.f64 (sqrt.f64 (-.f64 1 x)) (pow.f64 (/.f64 1 (+.f64 1 x)) 1/2))
(*.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1/4) (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1/4))
(*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(*.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(*.f64 (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 2)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (sqrt.f64 (-.f64 1 x)))
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (-.f64 1 x)))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(*.f64 (pow.f64 (/.f64 1 (+.f64 1 x)) 1/2) (sqrt.f64 (-.f64 1 x)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 2) 1/2) (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 1/2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 1/2) (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 2) 1/2))
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (-.f64 1 (*.f64 x x)))) (sqrt.f64 (-.f64 1 x)))
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 (-.f64 1 x) (*.f64 x x))))
(/.f64 1 (sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))
(/.f64 1 (/.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (-.f64 1 x))))
(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
(/.f64 (cbrt.f64 (-.f64 1 x)) (/.f64 (sqrt.f64 (+.f64 1 x)) (cbrt.f64 (sqrt.f64 (-.f64 1 x)))))
(/.f64 (sqrt.f64 (+.f64 -1 x)) (sqrt.f64 (-.f64 -1 x)))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 (fma.f64 x x x)))))
(/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 x))) (/.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (sqrt.f64 (-.f64 1 x)))))
(/.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 x)) 2)) (/.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (cbrt.f64 (-.f64 1 x)))))
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 1 x))) (neg.f64 (sqrt.f64 (+.f64 1 x))))
(/.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (cbrt.f64 (+.f64 1 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 x))))
(/.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
(/.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1/2)
(pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 1)
(pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1/4) 2)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) 3)
(pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2) 1/3)
(fabs.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))
(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(exp.f64 (*.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)) 1/2))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
Outputs
1
(+.f64 1 (*.f64 -2 x))
(fma.f64 -2 x 1)
(+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 1 (*.f64 -2 x)))
(fma.f64 2 (*.f64 x x) (+.f64 1 (*.f64 -2 x)))
(fma.f64 2 (*.f64 x x) (fma.f64 -2 x 1))
(+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 -2 x) (*.f64 -2 (pow.f64 x 3)))))
(fma.f64 2 (*.f64 x x) (+.f64 1 (*.f64 -2 (+.f64 x (pow.f64 x 3)))))
(fma.f64 2 (*.f64 x x) (fma.f64 -2 (+.f64 x (pow.f64 x 3)) 1))
-1
(-.f64 (*.f64 2 (/.f64 1 x)) 1)
(+.f64 (/.f64 2 x) -1)
(+.f64 -1 (/.f64 2 x))
(-.f64 (*.f64 2 (/.f64 1 x)) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (/.f64 2 x) (+.f64 1 (/.f64 2 (*.f64 x x))))
(+.f64 (/.f64 2 x) (-.f64 -1 (/.f64 2 (*.f64 x x))))
(+.f64 -1 (+.f64 (/.f64 2 x) (/.f64 -2 (*.f64 x x))))
(-.f64 (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 2 (/.f64 1 (pow.f64 x 3)))) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 2 (pow.f64 x 3)) (+.f64 1 (/.f64 2 (*.f64 x x)))))
(+.f64 -1 (+.f64 (/.f64 -2 (*.f64 x x)) (+.f64 (/.f64 2 x) (/.f64 2 (pow.f64 x 3)))))
-1
(-.f64 (*.f64 2 (/.f64 1 x)) 1)
(+.f64 (/.f64 2 x) -1)
(+.f64 -1 (/.f64 2 x))
(-.f64 (*.f64 2 (/.f64 1 x)) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (/.f64 2 x) (+.f64 1 (/.f64 2 (*.f64 x x))))
(+.f64 (/.f64 2 x) (-.f64 -1 (/.f64 2 (*.f64 x x))))
(+.f64 -1 (+.f64 (/.f64 2 x) (/.f64 -2 (*.f64 x x))))
(-.f64 (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 2 (/.f64 1 (pow.f64 x 3)))) (+.f64 1 (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 2 (pow.f64 x 3)) (+.f64 1 (/.f64 2 (*.f64 x x)))))
(+.f64 -1 (+.f64 (/.f64 -2 (*.f64 x x)) (+.f64 (/.f64 2 x) (/.f64 2 (pow.f64 x 3)))))
1
(+.f64 1 (*.f64 -1 x))
(-.f64 1 x)
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x)))
(+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x)))
(+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))
(+.f64 (*.f64 x (*.f64 x 1/2)) (-.f64 1 x))
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))))
(+.f64 1 (fma.f64 -1/2 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(+.f64 1 (-.f64 (fma.f64 (pow.f64 x 3) -1/2 (*.f64 x (*.f64 x 1/2))) x))
(+.f64 1 (-.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2))) x))
(sqrt.f64 -1)
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1))
(+.f64 (sqrt.f64 -1) (/.f64 1 (*.f64 x (sqrt.f64 -1))))
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (+.f64 (sqrt.f64 -1) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (*.f64 (sqrt.f64 -1) (pow.f64 x 2))))))
(+.f64 (+.f64 (sqrt.f64 -1) (/.f64 1 (*.f64 x (sqrt.f64 -1)))) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (*.f64 (sqrt.f64 -1) (*.f64 x x)))))
(+.f64 (/.f64 1 (*.f64 x (sqrt.f64 -1))) (fma.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (*.f64 x (*.f64 x (sqrt.f64 -1)))) (sqrt.f64 -1)))
(+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 (*.f64 x (sqrt.f64 -1))) (/.f64 (/.f64 -1/2 (sqrt.f64 -1)) (*.f64 x x))))
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (+.f64 (sqrt.f64 -1) (+.f64 (*.f64 1/2 (/.f64 (-.f64 2 (*.f64 -1 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (pow.f64 (sqrt.f64 -1) 2)))) (*.f64 (sqrt.f64 -1) (pow.f64 x 3)))) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))))
(+.f64 (+.f64 (sqrt.f64 -1) (/.f64 1 (*.f64 x (sqrt.f64 -1)))) (fma.f64 1/2 (/.f64 (-.f64 2 (neg.f64 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (pow.f64 (sqrt.f64 -1) 2)))) (*.f64 (pow.f64 x 3) (sqrt.f64 -1))) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (*.f64 (sqrt.f64 -1) (*.f64 x x))))))
(+.f64 (/.f64 1 (*.f64 x (sqrt.f64 -1))) (+.f64 (sqrt.f64 -1) (fma.f64 1/2 (/.f64 (+.f64 2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) -1)) (*.f64 (pow.f64 x 3) (sqrt.f64 -1))) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (*.f64 x (*.f64 x (sqrt.f64 -1))))))))
(+.f64 (sqrt.f64 -1) (+.f64 (/.f64 (/.f64 -1/2 (sqrt.f64 -1)) (*.f64 x x)) (+.f64 (/.f64 1 (*.f64 x (sqrt.f64 -1))) (/.f64 1/2 (*.f64 (pow.f64 x 3) (sqrt.f64 -1))))))
(sqrt.f64 -1)
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1))
(+.f64 (sqrt.f64 -1) (/.f64 1 (*.f64 x (sqrt.f64 -1))))
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (+.f64 (sqrt.f64 -1) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (*.f64 (sqrt.f64 -1) (pow.f64 x 2))))))
(+.f64 (+.f64 (sqrt.f64 -1) (/.f64 1 (*.f64 x (sqrt.f64 -1)))) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (*.f64 (sqrt.f64 -1) (*.f64 x x)))))
(+.f64 (/.f64 1 (*.f64 x (sqrt.f64 -1))) (fma.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (*.f64 x (*.f64 x (sqrt.f64 -1)))) (sqrt.f64 -1)))
(+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 (*.f64 x (sqrt.f64 -1))) (/.f64 (/.f64 -1/2 (sqrt.f64 -1)) (*.f64 x x))))
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (+.f64 (*.f64 1/2 (/.f64 (+.f64 2 (+.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)) (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))))) (*.f64 (sqrt.f64 -1) (pow.f64 x 3)))) (+.f64 (sqrt.f64 -1) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))))
(+.f64 (+.f64 (sqrt.f64 -1) (/.f64 1 (*.f64 x (sqrt.f64 -1)))) (fma.f64 1/2 (/.f64 (-.f64 2 (neg.f64 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (pow.f64 (sqrt.f64 -1) 2)))) (*.f64 (pow.f64 x 3) (sqrt.f64 -1))) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (*.f64 (sqrt.f64 -1) (*.f64 x x))))))
(+.f64 (/.f64 1 (*.f64 x (sqrt.f64 -1))) (+.f64 (sqrt.f64 -1) (fma.f64 1/2 (/.f64 (+.f64 2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) -1)) (*.f64 (pow.f64 x 3) (sqrt.f64 -1))) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (*.f64 x (*.f64 x (sqrt.f64 -1))))))))
(+.f64 (sqrt.f64 -1) (+.f64 (/.f64 (/.f64 -1/2 (sqrt.f64 -1)) (*.f64 x x)) (+.f64 (/.f64 1 (*.f64 x (sqrt.f64 -1))) (/.f64 1/2 (*.f64 (pow.f64 x 3) (sqrt.f64 -1))))))
(+.f64 (/.f64 1 (+.f64 1 x)) (neg.f64 (/.f64 x (+.f64 1 x))))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(+.f64 (/.f64 1 (+.f64 1 x)) (*.f64 1 (neg.f64 (/.f64 x (+.f64 1 x)))))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(+.f64 (/.f64 1 (+.f64 1 x)) (*.f64 (/.f64 1 (+.f64 1 x)) (neg.f64 x)))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(+.f64 (/.f64 1 (+.f64 1 x)) (*.f64 (neg.f64 (/.f64 x (+.f64 1 x))) 1))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(+.f64 (/.f64 1 (+.f64 1 x)) (*.f64 (neg.f64 x) (/.f64 1 (+.f64 1 x))))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(+.f64 (neg.f64 (/.f64 x (+.f64 1 x))) (/.f64 1 (+.f64 1 x)))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(+.f64 (*.f64 (/.f64 1 (+.f64 1 x)) (neg.f64 x)) (/.f64 1 (+.f64 1 x)))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(+.f64 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) 1) (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (-.f64 (*.f64 x x) x)))
(*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (-.f64 (*.f64 x x) x) 1))
(*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (fma.f64 x x (-.f64 1 x)))
(/.f64 (fma.f64 x x (-.f64 1 x)) (/.f64 (+.f64 1 (pow.f64 x 3)) (-.f64 1 x)))
(+.f64 (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (-.f64 (*.f64 x x) x)) (*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) 1))
(*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (-.f64 (*.f64 x x) x) 1))
(*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (fma.f64 x x (-.f64 1 x)))
(/.f64 (fma.f64 x x (-.f64 1 x)) (/.f64 (+.f64 1 (pow.f64 x 3)) (-.f64 1 x)))
(+.f64 (*.f64 (neg.f64 x) (/.f64 1 (+.f64 1 x))) (/.f64 1 (+.f64 1 x)))
(/.f64 (-.f64 1 x) (+.f64 1 x))
(+.f64 (*.f64 1 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))) (*.f64 (-.f64 (*.f64 x x) x) (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))))
(*.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3))) (+.f64 (-.f64 (*.f64 x x) x) 1))
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(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
(exp.f64 (*.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)) 1/2))
(pow.f64 (exp.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))) 1/2)
(sqrt.f64 (exp.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))

eval95.0ms (4.1%)

Compiler

Compiled 5494 to 4225 computations (23.1% saved)

prune36.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2544258
Fresh000
Picked011
Done000
Total2545259
Error
0b
Counts
259 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
▶0b
(*.f64 2 (atan.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (-.f64 1 (*.f64 x x))))))
▶0.4b
(*.f64 2 (atan.f64 (-.f64 1 x)))
▶0.1b
(*.f64 2 (atan.f64 (+.f64 1 (-.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2))) x))))
▶0.2b
(*.f64 2 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))))
✓0.0b
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
Compiler

Compiled 63 to 50 computations (20.6% saved)

localize18.0ms (0.8%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))
Compiler

Compiled 51 to 35 computations (31.4% saved)

series0.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@-inf
(atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))
0.0ms
x
@0
(atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))
0.0ms
x
@inf
(atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))

rewrite63.0ms (2.7%)

Algorithm
1×batch-egg-rewrite
Rules
1044×*-commutative
838×associate-*r/
668×distribute-lft-in
660×distribute-rgt-in
600×associate-*l/
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01129
123629
2303129
Stop Event
1×node limit
Counts
1 → 17
Calls
Call 1
Inputs
(atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))) (sqrt.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))) (pow.f64 (cbrt.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))) 2) (cbrt.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))))))))

simplify71.0ms (3%)

Algorithm
1×egg-herbie
Rules
810×*-commutative
800×associate-*r*
600×associate-*l*
568×distribute-lft-in
496×distribute-rgt-in
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
052841
1105725
2412609
32177609
45254609
57682609
Stop Event
1×node limit
Counts
29 → 22
Calls
Call 1
Inputs
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))))
(atan.f64 (+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))))
(atan.f64 (+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))))
(atan.f64 (+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))))
(-.f64 (exp.f64 (log1p.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))))) 1)
(*.f64 1 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))))
(*.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))) 1)
(*.f64 (sqrt.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))) (sqrt.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))))
(*.f64 (cbrt.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))) (pow.f64 (cbrt.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))) 2))
(*.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))) 2) (cbrt.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))))
(pow.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))) 1)
(pow.f64 (sqrt.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))) 2)
(pow.f64 (cbrt.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))) 3)
(pow.f64 (pow.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))) 3) 1/3)
(sqrt.f64 (pow.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))) 2))
(log.f64 (exp.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))))
(log.f64 (+.f64 1 (expm1.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))))))
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))) 3))
(expm1.f64 (log1p.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))))
(exp.f64 (log.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))))
(log1p.f64 (expm1.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))))
Outputs
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(atan.f64 (-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) x))
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(atan.f64 (+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))))
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(atan.f64 (+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))))
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(atan.f64 (+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))))
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(atan.f64 (+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x))))
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(-.f64 (exp.f64 (log1p.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))))) 1)
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(*.f64 1 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))))
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(*.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))) 1)
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(*.f64 (sqrt.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))) (sqrt.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))))
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(*.f64 (cbrt.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))) (pow.f64 (cbrt.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))) 2))
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(*.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))) 2) (cbrt.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))))
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(pow.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))) 1)
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(pow.f64 (sqrt.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))) 2)
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(pow.f64 (cbrt.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))) 3)
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(pow.f64 (pow.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))) 3) 1/3)
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(sqrt.f64 (pow.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))) 2))
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(log.f64 (exp.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))))
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(log.f64 (+.f64 1 (expm1.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))))))
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))) 3))
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(expm1.f64 (log1p.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))))
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(exp.f64 (log.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))))
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))
(log1p.f64 (expm1.f64 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x)))))
(atan.f64 (+.f64 1 (fma.f64 1/2 (*.f64 x x) (neg.f64 x))))
(atan.f64 (-.f64 (fma.f64 1/2 (*.f64 x x) 1) x))
(atan.f64 (fma.f64 x (fma.f64 1/2 x -1) 1))

localize26.0ms (1.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2)))
Compiler

Compiled 80 to 51 computations (36.3% saved)

series1.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@0
(*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2)))
0.0ms
x
@inf
(*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2)))
0.0ms
x
@-inf
(*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2)))

rewrite63.0ms (2.7%)

Algorithm
1×batch-egg-rewrite
Rules
1998×add-sqr-sqrt
1968×*-un-lft-identity
1848×add-cube-cbrt
1826×add-cbrt-cube
192×pow1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0925
119921
2257221
Stop Event
1×node limit
Counts
1 → 24
Calls
Call 1
Inputs
(*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 x 1/2)) (*.f64 -1/2 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 -1/2 (pow.f64 x 3)) (*.f64 x (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x (*.f64 x 1/2)) 1) (*.f64 (*.f64 -1/2 (pow.f64 x 3)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 x x) (-.f64 1/4 (*.f64 (*.f64 x x) 1/4))) (+.f64 1/2 (*.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 x x) (+.f64 1/8 (*.f64 -1/8 (pow.f64 x 3)))) (+.f64 1/4 (-.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 -1/4 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/4 (*.f64 (*.f64 x x) 1/4)) (*.f64 x x)) (+.f64 1/2 (*.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1/8 (*.f64 -1/8 (pow.f64 x 3))) (*.f64 x x)) (+.f64 1/4 (-.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 -1/4 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x 1/2)) (*.f64 x (*.f64 x 1/2))) (*.f64 (*.f64 -1/2 (pow.f64 x 3)) (*.f64 -1/2 (pow.f64 x 3)))) (-.f64 (*.f64 x (*.f64 x 1/2)) (*.f64 -1/2 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x (*.f64 x 1/2)) 3) (pow.f64 (*.f64 -1/2 (pow.f64 x 3)) 3)) (+.f64 (*.f64 (*.f64 x (*.f64 x 1/2)) (*.f64 x (*.f64 x 1/2))) (-.f64 (*.f64 (*.f64 -1/2 (pow.f64 x 3)) (*.f64 -1/2 (pow.f64 x 3))) (*.f64 (*.f64 x (*.f64 x 1/2)) (*.f64 -1/2 (pow.f64 x 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (+.f64 1/2 (*.f64 x -1/2)) 2) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 x) x) (+.f64 1/2 (*.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) 1/2 (*.f64 -1/2 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (*.f64 x x) (*.f64 -1/2 (pow.f64 x 3)))))))

simplify58.0ms (2.5%)

Algorithm
1×egg-herbie
Rules
938×associate-+r+
930×associate-+l+
694×distribute-lft-out
662×fma-def
624×associate-/l/
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0931164
1283938
21231896
34265886
Stop Event
1×node limit
Counts
36 → 44
Calls
Call 1
Inputs
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (*.f64 -1/2 (pow.f64 x 3)) (*.f64 1/2 (pow.f64 x 2)))
(+.f64 (*.f64 -1/2 (pow.f64 x 3)) (*.f64 1/2 (pow.f64 x 2)))
(+.f64 (*.f64 -1/2 (pow.f64 x 3)) (*.f64 1/2 (pow.f64 x 2)))
(*.f64 -1/2 (pow.f64 x 3))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/2 (pow.f64 x 3)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/2 (pow.f64 x 3)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/2 (pow.f64 x 3)))
(*.f64 -1/2 (pow.f64 x 3))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/2 (pow.f64 x 3)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/2 (pow.f64 x 3)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/2 (pow.f64 x 3)))
(+.f64 (*.f64 x (*.f64 x 1/2)) (*.f64 -1/2 (pow.f64 x 3)))
(+.f64 (*.f64 -1/2 (pow.f64 x 3)) (*.f64 x (*.f64 x 1/2)))
(+.f64 (*.f64 (*.f64 x (*.f64 x 1/2)) 1) (*.f64 (*.f64 -1/2 (pow.f64 x 3)) 1))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2))))) 1)
(/.f64 (*.f64 (*.f64 x x) (-.f64 1/4 (*.f64 (*.f64 x x) 1/4))) (+.f64 1/2 (*.f64 1/2 x)))
(/.f64 (*.f64 (*.f64 x x) (+.f64 1/8 (*.f64 -1/8 (pow.f64 x 3)))) (+.f64 1/4 (-.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 -1/4 x))))
(/.f64 (*.f64 (-.f64 1/4 (*.f64 (*.f64 x x) 1/4)) (*.f64 x x)) (+.f64 1/2 (*.f64 1/2 x)))
(/.f64 (*.f64 (+.f64 1/8 (*.f64 -1/8 (pow.f64 x 3))) (*.f64 x x)) (+.f64 1/4 (-.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 -1/4 x))))
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x 1/2)) (*.f64 x (*.f64 x 1/2))) (*.f64 (*.f64 -1/2 (pow.f64 x 3)) (*.f64 -1/2 (pow.f64 x 3)))) (-.f64 (*.f64 x (*.f64 x 1/2)) (*.f64 -1/2 (pow.f64 x 3))))
(/.f64 (+.f64 (pow.f64 (*.f64 x (*.f64 x 1/2)) 3) (pow.f64 (*.f64 -1/2 (pow.f64 x 3)) 3)) (+.f64 (*.f64 (*.f64 x (*.f64 x 1/2)) (*.f64 x (*.f64 x 1/2))) (-.f64 (*.f64 (*.f64 -1/2 (pow.f64 x 3)) (*.f64 -1/2 (pow.f64 x 3))) (*.f64 (*.f64 x (*.f64 x 1/2)) (*.f64 -1/2 (pow.f64 x 3))))))
(pow.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2))) 1)
(pow.f64 (*.f64 x (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 2)
(pow.f64 (cbrt.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2)))) 3)
(pow.f64 (pow.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2))) 3) 1/3)
(sqrt.f64 (*.f64 (pow.f64 (+.f64 1/2 (*.f64 x -1/2)) 2) (pow.f64 x 4)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 x) x) (+.f64 1/2 (*.f64 x -1/2))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2))))))
(cbrt.f64 (pow.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2))) 3))
(expm1.f64 (log1p.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2)))))
(exp.f64 (log.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2)))))
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2)))) 1))
(log1p.f64 (expm1.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2)))))
(fma.f64 (*.f64 x x) 1/2 (*.f64 -1/2 (pow.f64 x 3)))
(fma.f64 1/2 (*.f64 x x) (*.f64 -1/2 (pow.f64 x 3)))
Outputs
(*.f64 1/2 (pow.f64 x 2))
(*.f64 1/2 (*.f64 x x))
(+.f64 (*.f64 -1/2 (pow.f64 x 3)) (*.f64 1/2 (pow.f64 x 2)))
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(+.f64 (*.f64 -1/2 (pow.f64 x 3)) (*.f64 1/2 (pow.f64 x 2)))
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(+.f64 (*.f64 -1/2 (pow.f64 x 3)) (*.f64 1/2 (pow.f64 x 2)))
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(*.f64 -1/2 (pow.f64 x 3))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/2 (pow.f64 x 3)))
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/2 (pow.f64 x 3)))
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/2 (pow.f64 x 3)))
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(*.f64 -1/2 (pow.f64 x 3))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/2 (pow.f64 x 3)))
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/2 (pow.f64 x 3)))
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/2 (pow.f64 x 3)))
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(+.f64 (*.f64 x (*.f64 x 1/2)) (*.f64 -1/2 (pow.f64 x 3)))
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(+.f64 (*.f64 -1/2 (pow.f64 x 3)) (*.f64 x (*.f64 x 1/2)))
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(+.f64 (*.f64 (*.f64 x (*.f64 x 1/2)) 1) (*.f64 (*.f64 -1/2 (pow.f64 x 3)) 1))
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2))))) 1)
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(/.f64 (*.f64 (*.f64 x x) (-.f64 1/4 (*.f64 (*.f64 x x) 1/4))) (+.f64 1/2 (*.f64 1/2 x)))
(/.f64 (-.f64 1/4 (*.f64 (*.f64 x x) 1/4)) (/.f64 (+.f64 1/2 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (*.f64 x x) (fma.f64 1/2 x 1/2)) (+.f64 1/4 (*.f64 (*.f64 x x) -1/4)))
(*.f64 (fma.f64 x (*.f64 x -1/4) 1/4) (/.f64 x (/.f64 (fma.f64 1/2 x 1/2) x)))
(*.f64 (fma.f64 x (*.f64 x -1/4) 1/4) (*.f64 (/.f64 x (fma.f64 1/2 x 1/2)) x))
(/.f64 (*.f64 (*.f64 x x) (+.f64 1/8 (*.f64 -1/8 (pow.f64 x 3)))) (+.f64 1/4 (-.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 -1/4 x))))
(/.f64 (*.f64 x x) (/.f64 (+.f64 1/4 (+.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 1/4 x))) (+.f64 1/8 (*.f64 (pow.f64 x 3) -1/8))))
(/.f64 x (/.f64 (+.f64 1/4 (*.f64 x (-.f64 (*.f64 x 1/4) -1/4))) (*.f64 x (fma.f64 (pow.f64 x 3) -1/8 1/8))))
(*.f64 (*.f64 x x) (/.f64 (fma.f64 (pow.f64 x 3) -1/8 1/8) (fma.f64 x (fma.f64 x 1/4 1/4) 1/4)))
(/.f64 (*.f64 (-.f64 1/4 (*.f64 (*.f64 x x) 1/4)) (*.f64 x x)) (+.f64 1/2 (*.f64 1/2 x)))
(/.f64 (-.f64 1/4 (*.f64 (*.f64 x x) 1/4)) (/.f64 (+.f64 1/2 (*.f64 1/2 x)) (*.f64 x x)))
(*.f64 (/.f64 (*.f64 x x) (fma.f64 1/2 x 1/2)) (+.f64 1/4 (*.f64 (*.f64 x x) -1/4)))
(*.f64 (fma.f64 x (*.f64 x -1/4) 1/4) (/.f64 x (/.f64 (fma.f64 1/2 x 1/2) x)))
(*.f64 (fma.f64 x (*.f64 x -1/4) 1/4) (*.f64 (/.f64 x (fma.f64 1/2 x 1/2)) x))
(/.f64 (*.f64 (+.f64 1/8 (*.f64 -1/8 (pow.f64 x 3))) (*.f64 x x)) (+.f64 1/4 (-.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 -1/4 x))))
(/.f64 (*.f64 x x) (/.f64 (+.f64 1/4 (+.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 1/4 x))) (+.f64 1/8 (*.f64 (pow.f64 x 3) -1/8))))
(/.f64 x (/.f64 (+.f64 1/4 (*.f64 x (-.f64 (*.f64 x 1/4) -1/4))) (*.f64 x (fma.f64 (pow.f64 x 3) -1/8 1/8))))
(*.f64 (*.f64 x x) (/.f64 (fma.f64 (pow.f64 x 3) -1/8 1/8) (fma.f64 x (fma.f64 x 1/4 1/4) 1/4)))
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x 1/2)) (*.f64 x (*.f64 x 1/2))) (*.f64 (*.f64 -1/2 (pow.f64 x 3)) (*.f64 -1/2 (pow.f64 x 3)))) (-.f64 (*.f64 x (*.f64 x 1/2)) (*.f64 -1/2 (pow.f64 x 3))))
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(/.f64 (+.f64 (pow.f64 (*.f64 x (*.f64 x 1/2)) 3) (pow.f64 (*.f64 -1/2 (pow.f64 x 3)) 3)) (+.f64 (*.f64 (*.f64 x (*.f64 x 1/2)) (*.f64 x (*.f64 x 1/2))) (-.f64 (*.f64 (*.f64 -1/2 (pow.f64 x 3)) (*.f64 -1/2 (pow.f64 x 3))) (*.f64 (*.f64 x (*.f64 x 1/2)) (*.f64 -1/2 (pow.f64 x 3))))))
(/.f64 (+.f64 (pow.f64 (*.f64 1/2 (*.f64 x x)) 3) (*.f64 -1/8 (pow.f64 (pow.f64 x 3) 3))) (fma.f64 (*.f64 1/2 (*.f64 x x)) (*.f64 1/2 (*.f64 x x)) (*.f64 (*.f64 -1/2 (pow.f64 x 3)) (-.f64 (*.f64 -1/2 (pow.f64 x 3)) (*.f64 1/2 (*.f64 x x))))))
(/.f64 (fma.f64 -1/8 (pow.f64 (pow.f64 x 3) 3) (*.f64 1/8 (pow.f64 x 6))) (fma.f64 (*.f64 -1/2 (pow.f64 x 3)) (fma.f64 -1/2 (pow.f64 x 3) (*.f64 -1/2 (*.f64 x x))) (*.f64 1/4 (pow.f64 x 4))))
(/.f64 (fma.f64 1/8 (pow.f64 x 6) (*.f64 -1/8 (pow.f64 (pow.f64 x 3/2) 6))) (fma.f64 1/4 (pow.f64 x 6) (fma.f64 x (*.f64 1/4 (pow.f64 x 4)) (*.f64 1/4 (pow.f64 x 4)))))
(/.f64 (*.f64 (pow.f64 x 6) (+.f64 (pow.f64 (*.f64 x -1/2) 3) 1/8)) (fma.f64 1/4 (pow.f64 x 6) (*.f64 (*.f64 1/4 (pow.f64 x 4)) (+.f64 x 1))))
(pow.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2))) 1)
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(pow.f64 (*.f64 x (sqrt.f64 (+.f64 1/2 (*.f64 x -1/2)))) 2)
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(pow.f64 (cbrt.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2)))) 3)
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(pow.f64 (pow.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2))) 3) 1/3)
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(sqrt.f64 (*.f64 (pow.f64 (+.f64 1/2 (*.f64 x -1/2)) 2) (pow.f64 x 4)))
(sqrt.f64 (*.f64 (pow.f64 (fma.f64 x -1/2 1/2) 2) (pow.f64 x 4)))
(fabs.f64 (*.f64 x (*.f64 x (fma.f64 x -1/2 1/2))))
(log.f64 (pow.f64 (pow.f64 (exp.f64 x) x) (+.f64 1/2 (*.f64 x -1/2))))
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2))))))
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(cbrt.f64 (pow.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2))) 3))
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(expm1.f64 (log1p.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2)))))
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(exp.f64 (log.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2)))))
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2)))) 1))
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(log1p.f64 (expm1.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2)))))
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(fma.f64 (*.f64 x x) 1/2 (*.f64 -1/2 (pow.f64 x 3)))
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))
(fma.f64 1/2 (*.f64 x x) (*.f64 -1/2 (pow.f64 x 3)))
(fma.f64 -1/2 (pow.f64 x 3) (*.f64 1/2 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 x -1/2 1/2)))

localize7.0ms (0.3%)

Compiler

Compiled 17 to 13 computations (23.5% saved)

localize19.0ms (0.8%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (-.f64 1 (*.f64 x x)))
Compiler

Compiled 55 to 33 computations (40% saved)

series1.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0ms
x
@0
(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0ms
x
@-inf
(sqrt.f64 (-.f64 1 (*.f64 x x)))

rewrite51.0ms (2.2%)

Algorithm
1×batch-egg-rewrite
Rules
1534×add-sqr-sqrt
1512×*-un-lft-identity
1410×add-cube-cbrt
1400×add-cbrt-cube
1394×add-exp-log
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0817
116317
2200617
Stop Event
1×node limit
Counts
1 → 24
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (cbrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 2) 1/2) (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 6))) (sqrt.f64 (+.f64 1 (+.f64 (*.f64 x x) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (*.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (*.f64 x (neg.f64 x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))))))

simplify74.0ms (3.2%)

Algorithm
1×egg-herbie
Rules
998×associate-/r/
738×*-commutative
716×associate--r+
680×unswap-sqr
596×associate-*r/
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01121318
12751170
27901042
32409994
46659994
Stop Event
1×node limit
Counts
36 → 86
Calls
Call 1
Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (*.f64 -1/8 (pow.f64 x 4))))
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/16 (pow.f64 x 6)) (*.f64 -1/8 (pow.f64 x 4)))))
(*.f64 (sqrt.f64 -1) x)
(+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x)) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(-.f64 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(*.f64 -1 (*.f64 (sqrt.f64 -1) x))
(-.f64 (*.f64 -1 (*.f64 (sqrt.f64 -1) x)) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (*.f64 -1 (*.f64 (sqrt.f64 -1) x))) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (*.f64 -1 (*.f64 (sqrt.f64 -1) x))) (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x)))))
(-.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1)
(*.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)
(*.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4))
(*.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (cbrt.f64 (-.f64 1 (*.f64 x x))))
(*.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 x x)))))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (-.f64 1 (*.f64 x x))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 2) 1/2) (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 1/2))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 6))) (sqrt.f64 (+.f64 1 (+.f64 (*.f64 x x) (pow.f64 x 4)))))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (*.f64 x x))))
(pow.f64 (-.f64 1 (*.f64 x x)) 1/2)
(pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)
(pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) 2)
(pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 3)
(pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2) 1/3)
(fabs.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(log.f64 (exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(exp.f64 (log.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(exp.f64 (*.f64 (log1p.f64 (*.f64 x (neg.f64 x))) 1/2))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1))
(log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
Outputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1/2 (*.f64 x x)))
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (*.f64 -1/8 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (*.f64 x x) (*.f64 -1/8 (pow.f64 x 4))))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 -1/8 (pow.f64 x 4) 1))
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (+.f64 (*.f64 -1/16 (pow.f64 x 6)) (*.f64 -1/8 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (*.f64 x x) (fma.f64 -1/16 (pow.f64 x 6) (*.f64 -1/8 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (*.f64 x x) (fma.f64 -1/8 (pow.f64 x 4) (*.f64 -1/16 (pow.f64 x 6)))))
(+.f64 1 (fma.f64 -1/8 (pow.f64 x 4) (fma.f64 -1/16 (pow.f64 x 6) (*.f64 x (*.f64 -1/2 x)))))
(+.f64 (fma.f64 -1/2 (*.f64 x x) 1) (fma.f64 -1/8 (pow.f64 x 4) (*.f64 -1/16 (pow.f64 x 6))))
(*.f64 (sqrt.f64 -1) x)
(*.f64 x (sqrt.f64 -1))
(+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))
(+.f64 (*.f64 x (sqrt.f64 -1)) (/.f64 1/2 (*.f64 x (sqrt.f64 -1))))
(fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1)))
(fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 (sqrt.f64 -1)) x))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x)) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(+.f64 (/.f64 1/2 (*.f64 x (sqrt.f64 -1))) (-.f64 (*.f64 x (sqrt.f64 -1)) (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(-.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1))) (/.f64 (/.f64 1/8 (pow.f64 x 3)) (neg.f64 (sqrt.f64 -1))))
(+.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 -1)) (fma.f64 x (sqrt.f64 -1) (/.f64 1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3)))))
(+.f64 (/.f64 (/.f64 1/2 (sqrt.f64 -1)) x) (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/8 (pow.f64 x 3)) (sqrt.f64 -1))))
(-.f64 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(+.f64 (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))) (+.f64 (/.f64 1/2 (*.f64 x (sqrt.f64 -1))) (-.f64 (*.f64 x (sqrt.f64 -1)) (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))))
(+.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1))) (-.f64 (/.f64 (/.f64 1/16 (pow.f64 x 5)) (pow.f64 (sqrt.f64 -1) 5)) (/.f64 (/.f64 1/8 (pow.f64 x 3)) (neg.f64 (sqrt.f64 -1)))))
(+.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 -1)) (-.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (/.f64 (/.f64 -1/8 (sqrt.f64 -1)) (pow.f64 x 3))))
(-.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (*.f64 (/.f64 (/.f64 -1 x) (sqrt.f64 -1)) (+.f64 (/.f64 1/8 (*.f64 x x)) 1/2)))
(-.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (*.f64 (/.f64 (/.f64 -1 x) (sqrt.f64 -1)) (+.f64 1/2 (/.f64 1/8 (*.f64 x x)))))
(*.f64 -1 (*.f64 (sqrt.f64 -1) x))
(neg.f64 (*.f64 x (sqrt.f64 -1)))
(*.f64 x (neg.f64 (sqrt.f64 -1)))
(-.f64 (*.f64 -1 (*.f64 (sqrt.f64 -1) x)) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))))
(-.f64 (neg.f64 (*.f64 x (sqrt.f64 -1))) (/.f64 1/2 (*.f64 x (sqrt.f64 -1))))
(neg.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1))))
(-.f64 (/.f64 (/.f64 -1/2 x) (sqrt.f64 -1)) (*.f64 x (sqrt.f64 -1)))
(-.f64 (/.f64 -1/2 (*.f64 x (sqrt.f64 -1))) (*.f64 x (sqrt.f64 -1)))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (*.f64 -1 (*.f64 (sqrt.f64 -1) x))) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x))))
(+.f64 (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))) (-.f64 (neg.f64 (*.f64 x (sqrt.f64 -1))) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))))
(fma.f64 1/8 (/.f64 (/.f64 -1 (sqrt.f64 -1)) (pow.f64 x 3)) (neg.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1)))))
(-.f64 (/.f64 (/.f64 -1/8 (sqrt.f64 -1)) (pow.f64 x 3)) (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1))))
(-.f64 (/.f64 (/.f64 -1/8 (sqrt.f64 -1)) (pow.f64 x 3)) (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 (sqrt.f64 -1)) x)))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (*.f64 -1 (*.f64 (sqrt.f64 -1) x))) (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (*.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) x)))))
(-.f64 (+.f64 (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))) (neg.f64 (*.f64 x (sqrt.f64 -1)))) (+.f64 (/.f64 1/2 (*.f64 x (sqrt.f64 -1))) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))))
(-.f64 (fma.f64 1/8 (/.f64 (/.f64 -1 (sqrt.f64 -1)) (pow.f64 x 3)) (neg.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1))))) (/.f64 (/.f64 1/16 (pow.f64 x 5)) (pow.f64 (sqrt.f64 -1) 5)))
(+.f64 (-.f64 (/.f64 (/.f64 -1/8 (sqrt.f64 -1)) (pow.f64 x 3)) (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1)))) (/.f64 -1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))))
(-.f64 (*.f64 (/.f64 (/.f64 -1 x) (sqrt.f64 -1)) (+.f64 (/.f64 1/8 (*.f64 x x)) 1/2)) (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))))
(-.f64 (*.f64 (/.f64 (/.f64 -1 x) (sqrt.f64 -1)) (+.f64 1/2 (/.f64 1/8 (*.f64 x x)))) (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))))
(-.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(*.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(*.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(*.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (cbrt.f64 (-.f64 1 (*.f64 x x))))
(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (neg.f64 x) 1))) (cbrt.f64 (fma.f64 x (neg.f64 x) 1)))
(*.f64 (cbrt.f64 (sqrt.f64 (neg.f64 (fma.f64 x x -1)))) (cbrt.f64 (neg.f64 (fma.f64 x x -1))))
(*.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(*.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (cbrt.f64 (-.f64 1 (*.f64 x x))))
(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (neg.f64 x) 1))) (cbrt.f64 (fma.f64 x (neg.f64 x) 1)))
(*.f64 (cbrt.f64 (sqrt.f64 (neg.f64 (fma.f64 x x -1)))) (cbrt.f64 (neg.f64 (fma.f64 x x -1))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 x x)))))
(*.f64 (fabs.f64 (cbrt.f64 (-.f64 1 (*.f64 x x)))) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 x x)))))
(*.f64 (cbrt.f64 (fma.f64 x (neg.f64 x) 1)) (sqrt.f64 (cbrt.f64 (fma.f64 x (neg.f64 x) 1))))
(pow.f64 (cbrt.f64 (neg.f64 (fma.f64 x x -1))) 3/2)
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (-.f64 1 (*.f64 x x))))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 2) 1/2) (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 x x)))))
(*.f64 (fabs.f64 (cbrt.f64 (-.f64 1 (*.f64 x x)))) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 x x)))))
(*.f64 (cbrt.f64 (fma.f64 x (neg.f64 x) 1)) (sqrt.f64 (cbrt.f64 (fma.f64 x (neg.f64 x) 1))))
(pow.f64 (cbrt.f64 (neg.f64 (fma.f64 x x -1))) 3/2)
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 6))) (sqrt.f64 (+.f64 1 (+.f64 (*.f64 x x) (pow.f64 x 4)))))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 6))) (sqrt.f64 (+.f64 1 (fma.f64 x x (pow.f64 x 4)))))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (*.f64 x x))))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (hypot.f64 1 x))
(pow.f64 (-.f64 1 (*.f64 x x)) 1/2)
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) 2)
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 3)
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2) 1/3)
(cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2))
(cbrt.f64 (pow.f64 (fma.f64 x (neg.f64 x) 1) 3/2))
(cbrt.f64 (pow.f64 (neg.f64 (fma.f64 x x -1)) 3/2))
(fabs.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(log.f64 (exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2))
(cbrt.f64 (pow.f64 (fma.f64 x (neg.f64 x) 1) 3/2))
(cbrt.f64 (pow.f64 (neg.f64 (fma.f64 x x -1)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(exp.f64 (log.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(exp.f64 (*.f64 (log1p.f64 (*.f64 x (neg.f64 x))) 1/2))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))

eval57.0ms (2.5%)

Compiler

Compiled 3233 to 2531 computations (21.7% saved)

prune21.0ms (0.9%)

Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New1511152
Fresh000
Picked011
Done134
Total1525157
Error
0b
Counts
157 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.1b
(*.f64 2 (atan.f64 (/.f64 (-.f64 1 x) (+.f64 1 (*.f64 -1/2 (*.f64 x x))))))
✓0b
(*.f64 2 (atan.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (-.f64 1 (*.f64 x x))))))
✓0.4b
(*.f64 2 (atan.f64 (-.f64 1 x)))
✓0.2b
(*.f64 2 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))))
✓0.0b
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
Compiler

Compiled 61 to 49 computations (19.7% saved)

localize20.0ms (0.8%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 -1/2 (*.f64 x x))
Compiler

Compiled 60 to 38 computations (36.7% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@inf
(*.f64 -1/2 (*.f64 x x))
0.0ms
x
@0
(*.f64 -1/2 (*.f64 x x))
0.0ms
x
@-inf
(*.f64 -1/2 (*.f64 x x))

rewrite47.0ms (2%)

Algorithm
1×batch-egg-rewrite
Rules
1076×add-sqr-sqrt
1058×*-un-lft-identity
1006×pow1
986×add-cube-cbrt
978×add-cbrt-cube
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0613
112213
2140913
Stop Event
1×node limit
Counts
1 → 11
Calls
Call 1
Inputs
(*.f64 -1/2 (*.f64 x x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 -1/2 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/2 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 -1/2 (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 -1/2 (*.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/4 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 -1/2 (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -1/2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 -1/2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -1/2 (*.f64 x x))))))))

simplify39.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
1470×distribute-rgt-in
1446×distribute-lft-in
1164×log-prod
760×associate-*r*
704×associate-+r+
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
038299
193299
2347299
31912299
Stop Event
1×node limit
Counts
23 → 14
Calls
Call 1
Inputs
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(-.f64 (+.f64 1 (*.f64 -1/2 (*.f64 x x))) 1)
(pow.f64 (*.f64 -1/2 (*.f64 x x)) 1)
(pow.f64 (*.f64 x (sqrt.f64 -1/2)) 2)
(pow.f64 (cbrt.f64 (*.f64 -1/2 (*.f64 x x))) 3)
(pow.f64 (pow.f64 (*.f64 -1/2 (*.f64 x x)) 3) 1/3)
(sqrt.f64 (*.f64 1/4 (pow.f64 x 4)))
(log.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x)))
(cbrt.f64 (pow.f64 (*.f64 -1/2 (*.f64 x x)) 3))
(expm1.f64 (log1p.f64 (*.f64 -1/2 (*.f64 x x))))
(exp.f64 (log.f64 (*.f64 -1/2 (*.f64 x x))))
(log1p.f64 (expm1.f64 (*.f64 -1/2 (*.f64 x x))))
Outputs
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (*.f64 x x))
(*.f64 x (*.f64 -1/2 x))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (*.f64 x x))
(*.f64 x (*.f64 -1/2 x))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (*.f64 x x))
(*.f64 x (*.f64 -1/2 x))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (*.f64 x x))
(*.f64 x (*.f64 -1/2 x))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (*.f64 x x))
(*.f64 x (*.f64 -1/2 x))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (*.f64 x x))
(*.f64 x (*.f64 -1/2 x))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (*.f64 x x))
(*.f64 x (*.f64 -1/2 x))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (*.f64 x x))
(*.f64 x (*.f64 -1/2 x))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (*.f64 x x))
(*.f64 x (*.f64 -1/2 x))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (*.f64 x x))
(*.f64 x (*.f64 -1/2 x))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (*.f64 x x))
(*.f64 x (*.f64 -1/2 x))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (*.f64 x x))
(*.f64 x (*.f64 -1/2 x))
(-.f64 (+.f64 1 (*.f64 -1/2 (*.f64 x x))) 1)
(*.f64 -1/2 (*.f64 x x))
(*.f64 x (*.f64 -1/2 x))
(pow.f64 (*.f64 -1/2 (*.f64 x x)) 1)
(*.f64 -1/2 (*.f64 x x))
(*.f64 x (*.f64 -1/2 x))
(pow.f64 (*.f64 x (sqrt.f64 -1/2)) 2)
(*.f64 -1/2 (*.f64 x x))
(*.f64 x (*.f64 -1/2 x))
(pow.f64 (cbrt.f64 (*.f64 -1/2 (*.f64 x x))) 3)
(*.f64 -1/2 (*.f64 x x))
(*.f64 x (*.f64 -1/2 x))
(pow.f64 (pow.f64 (*.f64 -1/2 (*.f64 x x)) 3) 1/3)
(*.f64 -1/2 (*.f64 x x))
(*.f64 x (*.f64 -1/2 x))
(sqrt.f64 (*.f64 1/4 (pow.f64 x 4)))
(*.f64 -1/2 (*.f64 x x))
(*.f64 x (*.f64 -1/2 x))
(log.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x)))
(*.f64 -1/2 (*.f64 x x))
(*.f64 x (*.f64 -1/2 x))
(cbrt.f64 (pow.f64 (*.f64 -1/2 (*.f64 x x)) 3))
(*.f64 -1/2 (*.f64 x x))
(*.f64 x (*.f64 -1/2 x))
(expm1.f64 (log1p.f64 (*.f64 -1/2 (*.f64 x x))))
(*.f64 -1/2 (*.f64 x x))
(*.f64 x (*.f64 -1/2 x))
(exp.f64 (log.f64 (*.f64 -1/2 (*.f64 x x))))
(*.f64 -1/2 (*.f64 x x))
(*.f64 x (*.f64 -1/2 x))
(log1p.f64 (expm1.f64 (*.f64 -1/2 (*.f64 x x))))
(*.f64 -1/2 (*.f64 x x))
(*.f64 x (*.f64 -1/2 x))

eval4.0ms (0.2%)

Compiler

Compiled 223 to 175 computations (21.5% saved)

prune4.0ms (0.2%)

Pruning

5 alts after pruning (0 fresh and 5 done)

PrunedKeptTotal
New14014
Fresh000
Picked011
Done044
Total14519
Error
0b
Counts
19 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
✓0.1b
(*.f64 2 (atan.f64 (/.f64 (-.f64 1 x) (+.f64 1 (*.f64 -1/2 (*.f64 x x))))))
✓0b
(*.f64 2 (atan.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (-.f64 1 (*.f64 x x))))))
✓0.4b
(*.f64 2 (atan.f64 (-.f64 1 x)))
✓0.2b
(*.f64 2 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))))
✓0.0b
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
Compiler

Compiled 61 to 49 computations (19.7% saved)

regimes15.0ms (0.7%)

Counts
6 → 1
Calls
Call 1
Inputs
(*.f64 2 (atan.f64 (-.f64 1 x)))
(*.f64 2 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))))
(*.f64 2 (atan.f64 (/.f64 (-.f64 1 x) (+.f64 1 (*.f64 -1/2 (*.f64 x x))))))
(*.f64 2 (atan.f64 (+.f64 1 (-.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2))) x))))
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(*.f64 2 (atan.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (-.f64 1 (*.f64 x x))))))
Outputs
(*.f64 2 (atan.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (-.f64 1 (*.f64 x x))))))
Calls

5 calls:

4.0ms
x
3.0ms
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
2.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
2.0ms
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
2.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
Results
ErrorSegmentsBranch
0b1x
0b1(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
0b1(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
0b1(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0b1(/.f64 (-.f64 1 x) (+.f64 1 x))
Compiler

Compiled 114 to 87 computations (23.7% saved)

regimes14.0ms (0.6%)

Counts
5 → 1
Calls
Call 1
Inputs
(*.f64 2 (atan.f64 (-.f64 1 x)))
(*.f64 2 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))))
(*.f64 2 (atan.f64 (/.f64 (-.f64 1 x) (+.f64 1 (*.f64 -1/2 (*.f64 x x))))))
(*.f64 2 (atan.f64 (+.f64 1 (-.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2))) x))))
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
Outputs
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
Calls

5 calls:

4.0ms
x
2.0ms
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
2.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
2.0ms
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
2.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
Results
ErrorSegmentsBranch
0.0b1x
0.0b1(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
0.0b1(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
0.0b1(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0b1(/.f64 (-.f64 1 x) (+.f64 1 x))
Compiler

Compiled 101 to 78 computations (22.8% saved)

regimes5.0ms (0.2%)

Counts
4 → 1
Calls
Call 1
Inputs
(*.f64 2 (atan.f64 (-.f64 1 x)))
(*.f64 2 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))))
(*.f64 2 (atan.f64 (/.f64 (-.f64 1 x) (+.f64 1 (*.f64 -1/2 (*.f64 x x))))))
(*.f64 2 (atan.f64 (+.f64 1 (-.f64 (*.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/2))) x))))
Outputs
(*.f64 2 (atan.f64 (/.f64 (-.f64 1 x) (+.f64 1 (*.f64 -1/2 (*.f64 x x))))))
Calls

1 calls:

3.0ms
x
Results
ErrorSegmentsBranch
0.1b1x
Compiler

Compiled 51 to 38 computations (25.5% saved)

regimes4.0ms (0.2%)

Accuracy

Total -0.2b remaining (-85.5%)

Threshold costs -0.2b (-85.5%)

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

1 calls:

3.0ms
x
Results
ErrorSegmentsBranch
0.2b1x
Compiler

Compiled 21 to 16 computations (23.8% saved)

simplify7.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
22×*-commutative
18×+-commutative
8×sub-neg
4×neg-mul-1
4×cancel-sign-sub-inv
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033165
153165
263165
367165
469165
Stop Event
1×done
1×saturated
Calls
Call 1
Inputs
(*.f64 2 (atan.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(*.f64 2 (atan.f64 (/.f64 (-.f64 1 x) (+.f64 1 (*.f64 -1/2 (*.f64 x x))))))
(*.f64 2 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))))
(*.f64 2 (atan.f64 (-.f64 1 x)))
Outputs
(*.f64 2 (atan.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (-.f64 1 (*.f64 x x))))))
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
(*.f64 2 (atan.f64 (/.f64 (-.f64 1 x) (+.f64 1 (*.f64 -1/2 (*.f64 x x))))))
(*.f64 2 (atan.f64 (/.f64 (-.f64 1 x) (+.f64 1 (*.f64 (*.f64 x x) -1/2)))))
(*.f64 2 (atan.f64 (+.f64 1 (-.f64 (*.f64 x (*.f64 x 1/2)) x))))
(*.f64 2 (atan.f64 (-.f64 1 x)))
Compiler

Compiled 61 to 49 computations (19.7% saved)

soundness71.0ms (3%)

Algorithm
1×egg-herbie
Rules
1560×associate-*r/
1310×associate-*l/
652×associate-+l+
590×+-commutative
564×associate-+r+
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03846184
110635692
239985486
Stop Event
1×node limit
Compiler

Compiled 52 to 39 computations (25% saved)

end39.0ms (1.7%)

Compiler

Compiled 57 to 44 computations (22.8% saved)

Profiling

Loading profile data...