Details

Time bar (total: 3.3s)

analyze155.0ms (4.7%)

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
25%25%75%0%0%0%0%3
28.6%25%62.5%0%0%0%12.5%4
30.8%25%56.2%0%0%0%18.7%5
36%28.1%50%0%0%0%21.9%6
38.8%29.7%46.9%0%0%0%23.4%7
40.2%30.5%45.3%0%0%0%24.2%8
40.7%30.8%44.9%0%0%0%24.2%9
41.2%31.2%44.5%0%0%0%24.2%10
41.4%31.3%44.4%0%0%0%24.2%11
41.5%31.4%44.3%0%0%0%24.3%12
Compiler

Compiled 14 to 12 computations (14.3% saved)

sample2.1s (62.8%)

Results
1.1s2843×body1024valid
434.0ms3725×body256valid
296.0ms1407×body512valid
123.0ms281×body2048valid
5.0ms46×body256infinite
Bogosity

preprocess109.0ms (3.3%)

Algorithm
2×egg-herbie
Rules
1440×associate-/l*
1382×associate-*r*
1160×associate-/r*
968×associate-*l*
702×fma-def
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01325
12725
23625
36225
413521
534915
6123815
011
Stop Event
1×saturated
1×node limit
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
Outputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (+.f64 1 (exp.f64 x)) 1))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
Compiler

Compiled 14 to 12 computations (14.3% saved)

simplify36.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
1440×associate-/l*
1382×associate-*r*
1160×associate-/r*
968×associate-*l*
702×fma-def
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01325
12725
23625
36225
413521
534915
6123815
Stop Event
1×node limit
Counts
1 → 5
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
Outputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (+.f64 1 (exp.f64 x)) 1))
(sqrt.f64 (+.f64 1 (exp.f64 x)))

eval1.0ms (0%)

Compiler

Compiled 41 to 29 computations (29.3% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New415
Fresh101
Picked000
Done000
Total516
Accurracy
100.0%
Counts
6 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(sqrt.f64 (+.f64 1 (exp.f64 x)))
Compiler

Compiled 6 to 5 computations (16.7% saved)

localize5.0ms (0.2%)

Local Accuracy

Found 1 expressions with local accuracy:

NewAccuracyProgram
✓100.0%
(sqrt.f64 (+.f64 1 (exp.f64 x)))
Compiler

Compiled 14 to 8 computations (42.9% saved)

series1.0ms (0%)

Counts
1 → 4
Calls

3 calls:

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

rewrite177.0ms (5.4%)

Algorithm
1×batch-egg-rewrite
Rules
1470×add-sqr-sqrt
1452×*-un-lft-identity
1352×add-cube-cbrt
1340×add-cbrt-cube
1328×add-exp-log
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0815
115615
2185115
Stop Event
1×node limit
Counts
1 → 25
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 1 (exp.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (hypot.f64 1 (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (sqrt.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2))) (sqrt.f64 (-.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (exp.f64 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 1 (sqrt.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))))))

simplify70.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
1372×associate-*l*
910×fma-def
666×associate-/l*
610×times-frac
574×*-commutative
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0931011
1223837
2603733
31553645
45904633
Stop Event
1×node limit
Counts
29 → 51
Calls
Call 1
Inputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(-.f64 (+.f64 1 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) 1)
(*.f64 1 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1)
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(*.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (pow.f64 1 1/2) (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 1/2))
(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (sqrt.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(pow.f64 (+.f64 1 (exp.f64 x)) 1/2)
(pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) 2)
(pow.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) 3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
(fabs.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(log.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(expm1.f64 (log1p.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(exp.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x))))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
(exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x))) 1))
(log1p.f64 (expm1.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (*.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (*.f64 x x))) (/.f64 x (sqrt.f64 2)))))
(fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (*.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (*.f64 x x))) (sqrt.f64 2))
(fma.f64 1/2 (fma.f64 (-.f64 (/.f64 1/2 (sqrt.f64 2)) (/.f64 (/.f64 1/4 (sqrt.f64 2)) 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2))) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 x (*.f64 x 3/8)))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/6 (*.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 (+.f64 1/6 (*.f64 -1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (/.f64 (sqrt.f64 2) (pow.f64 x 3))) (*.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (*.f64 x x))) (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (*.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (*.f64 x x))) (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2))))
(fma.f64 1/2 (fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (fma.f64 (-.f64 (/.f64 1/2 (sqrt.f64 2)) (/.f64 (/.f64 1/4 (sqrt.f64 2)) 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2)))) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (fma.f64 (/.f64 3/16 (sqrt.f64 2)) (*.f64 x x) (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 7/96 (pow.f64 x 3))))))
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 (*.f64 x x) (+.f64 3/8 (*.f64 x 7/96))))))
(-.f64 (+.f64 1 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) 1)
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 1 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1)
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(*.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 3/2)
(*.f64 (pow.f64 1 1/2) (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 3/2)
(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (sqrt.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))
(/.f64 (hypot.f64 1 (pow.f64 (exp.f64 x) 3/2)) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (sqrt.f64 (-.f64 1 (exp.f64 (+.f64 x x)))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(pow.f64 (+.f64 1 (exp.f64 x)) 1/2)
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1)
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) 2)
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) 3)
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(fabs.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(expm1.f64 (log1p.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(exp.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x))))
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) 1/2)
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) 1/2)
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
(exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x))) 1))
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) 1/2)
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
(log1p.f64 (expm1.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))

eval14.0ms (0.4%)

Compiler

Compiled 685 to 517 computations (24.5% saved)

prune8.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New49251
Fresh000
Picked011
Done000
Total49352
Accurracy
100.0%
Counts
52 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶68.5%
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
✓100.0%
(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶74.1%
(sqrt.f64 2)
Compiler

Compiled 19 to 17 computations (10.5% saved)

localize2.0ms (0.1%)

Compiler

Compiled 4 to 4 computations (0% saved)

localize11.0ms (0.3%)

Local Accuracy

Found 2 expressions with local accuracy:

NewAccuracyProgram
✓100.0%
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
✓99.3%
(/.f64 x (sqrt.f64 2))
Compiler

Compiled 25 to 21 computations (16% saved)

series2.0ms (0.1%)

Counts
2 → 3
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(/.f64 x (sqrt.f64 2))
0.0ms
x
@0
(/.f64 x (sqrt.f64 2))
0.0ms
x
@-inf
(/.f64 x (sqrt.f64 2))
0.0ms
x
@0
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
0.0ms
x
@inf
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))

rewrite87.0ms (2.6%)

Algorithm
1×batch-egg-rewrite
Rules
1396×associate-*r/
968×*-commutative
892×associate-/r*
876×associate-*l/
610×associate-/l*
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01038
121634
2279234
Stop Event
1×node limit
Counts
2 → 121
Calls
Call 1
Inputs
(/.f64 x (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
Outputs
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simplify108.0ms (3.3%)

Algorithm
1×egg-herbie
Rules
1778×associate-/r*
960×associate-/l/
684×associate-/r/
414×distribute-lft-neg-in
384×distribute-rgt-neg-in
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03066608
18295990
234675890
Stop Event
1×node limit
Counts
124 → 199
Calls
Call 1
Inputs
(sqrt.f64 2)
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 x (sqrt.f64 2)))) 1)
(*.f64 x (pow.f64 2 -1/2))
(*.f64 (/.f64 x (sqrt.f64 2)) 1)
(*.f64 1 (/.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (sqrt.f64 2)))
(*.f64 (sqrt.f64 (/.f64 x (sqrt.f64 2))) (sqrt.f64 (/.f64 x (sqrt.f64 2))))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (/.f64 (cbrt.f64 x) (sqrt.f64 2)))
(*.f64 (cbrt.f64 (/.f64 x (sqrt.f64 2))) (cbrt.f64 (/.f64 x (/.f64 2 x))))
(*.f64 (cbrt.f64 (/.f64 x (sqrt.f64 2))) (/.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 2)))
(*.f64 (cbrt.f64 (/.f64 x (/.f64 2 x))) (cbrt.f64 (/.f64 x (sqrt.f64 2))))
(*.f64 (pow.f64 2 -1/2) x)
(*.f64 (neg.f64 x) (/.f64 -1 (sqrt.f64 2)))
(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 2)) (sqrt.f64 x))
(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 2)) (/.f64 (sqrt.f64 x) 1))
(*.f64 (/.f64 (cbrt.f64 x) (sqrt.f64 2)) (pow.f64 (cbrt.f64 x) 2))
(*.f64 (/.f64 (cbrt.f64 x) (sqrt.f64 2)) (/.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(*.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 x (pow.f64 2 1/4)))
(*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 x (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 x (pow.f64 2 1/4)) (/.f64 1 (pow.f64 2 1/4)))
(*.f64 (/.f64 x (cbrt.f64 (sqrt.f64 2))) (/.f64 1 (cbrt.f64 2)))
(*.f64 (/.f64 -1 (sqrt.f64 2)) (neg.f64 x))
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (sqrt.f64 2)))
(*.f64 (/.f64 (sqrt.f64 x) (cbrt.f64 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (sqrt.f64 x) (cbrt.f64 (sqrt.f64 2))) (/.f64 (sqrt.f64 x) (cbrt.f64 2)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (sqrt.f64 2)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 x) (pow.f64 2 1/4)))
(*.f64 (/.f64 (cbrt.f64 x) (pow.f64 2 1/4)) (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 2 1/4)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 x (sqrt.f64 2))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 2)) (cbrt.f64 x))
(*.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2))) (cbrt.f64 x))
(pow.f64 (/.f64 x (sqrt.f64 2)) 1)
(pow.f64 (sqrt.f64 (/.f64 x (sqrt.f64 2))) 2)
(pow.f64 (cbrt.f64 (/.f64 x (sqrt.f64 2))) 3)
(pow.f64 (pow.f64 (/.f64 x (sqrt.f64 2)) 3) 1/3)
(pow.f64 (/.f64 (sqrt.f64 2) x) -1)
(neg.f64 (/.f64 x (neg.f64 (sqrt.f64 2))))
(sqrt.f64 (/.f64 x (/.f64 2 x)))
(log.f64 (exp.f64 (/.f64 x (sqrt.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 x (sqrt.f64 2)))))
(cbrt.f64 (pow.f64 (/.f64 x (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (/.f64 x (sqrt.f64 2))))
(exp.f64 (log.f64 (/.f64 x (sqrt.f64 2))))
(log1p.f64 (expm1.f64 (/.f64 x (sqrt.f64 2))))
(-.f64 (exp.f64 (log1p.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)))) 1)
(-.f64 (exp.f64 (log1p.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))))) (-.f64 1 (sqrt.f64 2)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 2))) (-.f64 1 (*.f64 x (/.f64 1/2 (sqrt.f64 2)))))
(-.f64 (/.f64 2 (+.f64 (sqrt.f64 2) (/.f64 (*.f64 -1/2 x) (sqrt.f64 2)))) (/.f64 (/.f64 (*.f64 1/4 x) (/.f64 2 x)) (+.f64 (sqrt.f64 2) (/.f64 (*.f64 -1/2 x) (sqrt.f64 2)))))
(-.f64 (+.f64 (sqrt.f64 2) (exp.f64 (log1p.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2)))))) 1)
(-.f64 (+.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (exp.f64 (log1p.f64 (sqrt.f64 2)))) 1)
(*.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)) 1)
(*.f64 1 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)))
(*.f64 (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))))
(*.f64 (cbrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))) (pow.f64 (cbrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))) 2))
(*.f64 (pow.f64 (cbrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))) 2) (cbrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))))
(*.f64 (-.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x))) (/.f64 1 (+.f64 (sqrt.f64 2) (/.f64 (*.f64 -1/2 x) (sqrt.f64 2)))))
(*.f64 (+.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3))) (/.f64 1 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2))))))
(*.f64 (/.f64 1 (+.f64 (sqrt.f64 2) (/.f64 (*.f64 -1/2 x) (sqrt.f64 2)))) (-.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x))))
(*.f64 (/.f64 1 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2))))) (+.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3))))
(*.f64 (/.f64 (-.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x))) (-.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x)))) (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)))
(*.f64 (/.f64 (-.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x))) (-.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3)))) (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)))))
(*.f64 (/.f64 (+.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3))) (-.f64 4 (*.f64 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2))) (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2)))))) (-.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2)))))
(*.f64 (/.f64 (+.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3))) (+.f64 8 (pow.f64 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2))) 3))) (+.f64 4 (*.f64 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2))) (-.f64 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2))) 2))))
(/.f64 1 (/.f64 1 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))))
(/.f64 (-.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x))) (+.f64 (sqrt.f64 2) (/.f64 (*.f64 -1/2 x) (sqrt.f64 2))))
(/.f64 (+.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3))) (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2)))))
(/.f64 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2)))) (/.f64 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2)))) (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3)))) (/.f64 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2)))) (sqrt.f64 (+.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3))))))
(/.f64 (sqrt.f64 (-.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x)))) (/.f64 (+.f64 (sqrt.f64 2) (/.f64 (*.f64 -1/2 x) (sqrt.f64 2))) (sqrt.f64 (-.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x))))))
(/.f64 (*.f64 (cbrt.f64 (+.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3)))) (cbrt.f64 (+.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3))))) (/.f64 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2)))) (cbrt.f64 (+.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3))))))
(/.f64 (*.f64 (cbrt.f64 (-.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x)))) (cbrt.f64 (-.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x))))) (/.f64 (+.f64 (sqrt.f64 2) (/.f64 (*.f64 -1/2 x) (sqrt.f64 2))) (cbrt.f64 (-.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x))))))
(/.f64 (-.f64 (/.f64 (*.f64 1/4 x) (/.f64 2 x)) 2) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2)))
(/.f64 (-.f64 (*.f64 (pow.f64 2 3/2) (pow.f64 2 3/2)) (*.f64 (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3)) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3)))) (*.f64 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2)))) (-.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3)))))
(/.f64 (-.f64 4 (*.f64 (/.f64 (*.f64 1/4 x) (/.f64 2 x)) (/.f64 (*.f64 1/4 x) (/.f64 2 x)))) (*.f64 (+.f64 (sqrt.f64 2) (/.f64 (*.f64 -1/2 x) (sqrt.f64 2))) (+.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x)))))
(/.f64 (+.f64 (pow.f64 (pow.f64 2 3/2) 3) (pow.f64 (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3)) 3)) (*.f64 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2)))) (+.f64 (*.f64 (pow.f64 2 3/2) (pow.f64 2 3/2)) (*.f64 (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3)) (-.f64 (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3)) (pow.f64 2 3/2))))))
(/.f64 (-.f64 8 (pow.f64 (/.f64 (*.f64 1/4 x) (/.f64 2 x)) 3)) (*.f64 (+.f64 (sqrt.f64 2) (/.f64 (*.f64 -1/2 x) (sqrt.f64 2))) (+.f64 4 (*.f64 (/.f64 (*.f64 1/4 x) (/.f64 2 x)) (+.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x)))))))
(/.f64 (neg.f64 (-.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x)))) (neg.f64 (+.f64 (sqrt.f64 2) (/.f64 (*.f64 -1/2 x) (sqrt.f64 2)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3)))) (neg.f64 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2))))))
(/.f64 (*.f64 1 (-.f64 (/.f64 (*.f64 1/4 x) (/.f64 2 x)) 2)) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2)))
(/.f64 (*.f64 1 (neg.f64 (-.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x))))) (neg.f64 (+.f64 (sqrt.f64 2) (/.f64 (*.f64 -1/2 x) (sqrt.f64 2)))))
(/.f64 (*.f64 1 (neg.f64 (+.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3))))) (neg.f64 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2))))))
(/.f64 (*.f64 (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))) (sqrt.f64 (+.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3))))) (sqrt.f64 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2))))))
(/.f64 (*.f64 (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))) (sqrt.f64 (-.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x))))) (sqrt.f64 (+.f64 (sqrt.f64 2) (/.f64 (*.f64 -1/2 x) (sqrt.f64 2)))))
(/.f64 (*.f64 (pow.f64 (cbrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))) 2) (cbrt.f64 (+.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3))))) (cbrt.f64 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2))))))
(/.f64 (*.f64 (pow.f64 (cbrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))) 2) (cbrt.f64 (-.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x))))) (cbrt.f64 (+.f64 (sqrt.f64 2) (/.f64 (*.f64 -1/2 x) (sqrt.f64 2)))))
(/.f64 (*.f64 (-.f64 (/.f64 (*.f64 1/4 x) (/.f64 2 x)) 2) 1) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2)))
(/.f64 (*.f64 (neg.f64 (-.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x)))) 1) (neg.f64 (+.f64 (sqrt.f64 2) (/.f64 (*.f64 -1/2 x) (sqrt.f64 2)))))
(/.f64 (*.f64 (neg.f64 (+.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3)))) 1) (neg.f64 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2))))))
(/.f64 (*.f64 (sqrt.f64 (+.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3)))) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)))) (sqrt.f64 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2))))))
(/.f64 (*.f64 (sqrt.f64 (-.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x)))) (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)))) (sqrt.f64 (+.f64 (sqrt.f64 2) (/.f64 (*.f64 -1/2 x) (sqrt.f64 2)))))
(/.f64 (*.f64 (cbrt.f64 (+.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3)))) (pow.f64 (cbrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))) 2)) (cbrt.f64 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2))))))
(/.f64 (*.f64 (cbrt.f64 (-.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x)))) (pow.f64 (cbrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))) 2)) (cbrt.f64 (+.f64 (sqrt.f64 2) (/.f64 (*.f64 -1/2 x) (sqrt.f64 2)))))
(/.f64 (*.f64 (-.f64 4 (*.f64 (/.f64 (*.f64 1/4 x) (/.f64 2 x)) (/.f64 (*.f64 1/4 x) (/.f64 2 x)))) (/.f64 1 (+.f64 (sqrt.f64 2) (/.f64 (*.f64 -1/2 x) (sqrt.f64 2))))) (+.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x))))
(/.f64 (*.f64 (-.f64 8 (pow.f64 (/.f64 (*.f64 1/4 x) (/.f64 2 x)) 3)) (/.f64 1 (+.f64 (sqrt.f64 2) (/.f64 (*.f64 -1/2 x) (sqrt.f64 2))))) (+.f64 4 (*.f64 (/.f64 (*.f64 1/4 x) (/.f64 2 x)) (+.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x))))))
(/.f64 (*.f64 (-.f64 (*.f64 (pow.f64 2 3/2) (pow.f64 2 3/2)) (*.f64 (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3)) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3)))) (/.f64 1 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2)))))) (-.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3))))
(/.f64 (*.f64 (+.f64 (pow.f64 (pow.f64 2 3/2) 3) (pow.f64 (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3)) 3)) (/.f64 1 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2)))))) (+.f64 (*.f64 (pow.f64 2 3/2) (pow.f64 2 3/2)) (*.f64 (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3)) (-.f64 (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3)) (pow.f64 2 3/2)))))
(/.f64 (/.f64 (-.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x))) 1) (+.f64 (sqrt.f64 2) (/.f64 (*.f64 -1/2 x) (sqrt.f64 2))))
(/.f64 (/.f64 (-.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x))) (sqrt.f64 (+.f64 (sqrt.f64 2) (/.f64 (*.f64 -1/2 x) (sqrt.f64 2))))) (sqrt.f64 (+.f64 (sqrt.f64 2) (/.f64 (*.f64 -1/2 x) (sqrt.f64 2)))))
(/.f64 (/.f64 (-.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x))) (*.f64 (cbrt.f64 (+.f64 (sqrt.f64 2) (/.f64 (*.f64 -1/2 x) (sqrt.f64 2)))) (cbrt.f64 (+.f64 (sqrt.f64 2) (/.f64 (*.f64 -1/2 x) (sqrt.f64 2)))))) (cbrt.f64 (+.f64 (sqrt.f64 2) (/.f64 (*.f64 -1/2 x) (sqrt.f64 2)))))
(/.f64 (/.f64 (-.f64 2 (/.f64 (*.f64 1/4 x) (/.f64 2 x))) (+.f64 (sqrt.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2)))) (pow.f64 2 1/4))) (-.f64 (pow.f64 2 1/4) (sqrt.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))))))
(/.f64 (/.f64 (+.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3))) 1) (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2)))))
(/.f64 (/.f64 (+.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3))) (sqrt.f64 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2)))))) (sqrt.f64 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2))))))
(/.f64 (/.f64 (+.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3))) (*.f64 (cbrt.f64 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2))))) (cbrt.f64 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2))))))) (cbrt.f64 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2))))))
(pow.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)) 1)
(pow.f64 (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))) 2)
(pow.f64 (cbrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))) 3)
(pow.f64 (pow.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)) 3) 1/3)
(sqrt.f64 (pow.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)) 2))
(log.f64 (exp.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)))))
(cbrt.f64 (pow.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))))
(exp.f64 (log.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))))
(log1p.f64 (expm1.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))))
(fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(fma.f64 1 (sqrt.f64 2) (*.f64 x (/.f64 1/2 (sqrt.f64 2))))
(fma.f64 1 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2))
(fma.f64 (sqrt.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2)))) (sqrt.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2)))) (sqrt.f64 2))
(fma.f64 (pow.f64 2 1/4) (pow.f64 2 1/4) (*.f64 x (/.f64 1/2 (sqrt.f64 2))))
(fma.f64 (cbrt.f64 (/.f64 (*.f64 1/4 x) (/.f64 2 x))) (cbrt.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2)))) (sqrt.f64 2))
(fma.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2)) (*.f64 x (/.f64 1/2 (sqrt.f64 2))))
Outputs
(sqrt.f64 2)
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 x (sqrt.f64 2)))) 1)
(/.f64 x (sqrt.f64 2))
(*.f64 x (pow.f64 2 -1/2))
(*.f64 (/.f64 x (sqrt.f64 2)) 1)
(/.f64 x (sqrt.f64 2))
(*.f64 1 (/.f64 x (sqrt.f64 2)))
(/.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (sqrt.f64 2)))
(/.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 x (sqrt.f64 2))) (sqrt.f64 (/.f64 x (sqrt.f64 2))))
(/.f64 x (sqrt.f64 2))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (/.f64 (cbrt.f64 x) (sqrt.f64 2)))
(/.f64 x (sqrt.f64 2))
(*.f64 (cbrt.f64 (/.f64 x (sqrt.f64 2))) (cbrt.f64 (/.f64 x (/.f64 2 x))))
(*.f64 (cbrt.f64 (/.f64 x (sqrt.f64 2))) (cbrt.f64 (*.f64 (/.f64 x 2) x)))
(*.f64 (cbrt.f64 (/.f64 x (sqrt.f64 2))) (cbrt.f64 (*.f64 x (/.f64 x 2))))
(*.f64 (cbrt.f64 (/.f64 x (sqrt.f64 2))) (/.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 2)))
(/.f64 (cbrt.f64 (/.f64 x (sqrt.f64 2))) (/.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (/.f64 (cbrt.f64 (/.f64 x (sqrt.f64 2))) (cbrt.f64 2)) (pow.f64 (cbrt.f64 x) 2))
(*.f64 (cbrt.f64 (/.f64 x (/.f64 2 x))) (cbrt.f64 (/.f64 x (sqrt.f64 2))))
(*.f64 (cbrt.f64 (/.f64 x (sqrt.f64 2))) (cbrt.f64 (*.f64 (/.f64 x 2) x)))
(*.f64 (cbrt.f64 (/.f64 x (sqrt.f64 2))) (cbrt.f64 (*.f64 x (/.f64 x 2))))
(*.f64 (pow.f64 2 -1/2) x)
(*.f64 x (pow.f64 2 -1/2))
(*.f64 (neg.f64 x) (/.f64 -1 (sqrt.f64 2)))
(/.f64 x (sqrt.f64 2))
(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 2)) (sqrt.f64 x))
(/.f64 x (sqrt.f64 2))
(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 2)) (/.f64 (sqrt.f64 x) 1))
(/.f64 x (sqrt.f64 2))
(*.f64 (/.f64 (cbrt.f64 x) (sqrt.f64 2)) (pow.f64 (cbrt.f64 x) 2))
(/.f64 x (sqrt.f64 2))
(*.f64 (/.f64 (cbrt.f64 x) (sqrt.f64 2)) (/.f64 (pow.f64 (cbrt.f64 x) 2) 1))
(/.f64 x (sqrt.f64 2))
(*.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 x (pow.f64 2 1/4)))
(/.f64 (/.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4))
(/.f64 x (pow.f64 2 1/2))
(*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 x (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 x (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 2))
(/.f64 x (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 x (pow.f64 2 1/4)) (/.f64 1 (pow.f64 2 1/4)))
(*.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 x (pow.f64 2 1/4)))
(/.f64 (/.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4))
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(/.f64 (*.f64 1 (+.f64 (pow.f64 2 3/2) (*.f64 (pow.f64 (/.f64 x (sqrt.f64 2)) 3) 1/8))) (+.f64 2 (*.f64 x (*.f64 (/.f64 1/2 (sqrt.f64 2)) (fma.f64 x (/.f64 1/2 (sqrt.f64 2)) (neg.f64 (sqrt.f64 2)))))))
(/.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 2)) 3) 1/8 (pow.f64 2 3/2)) (fma.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) (fma.f64 x (/.f64 1/2 (sqrt.f64 2)) (neg.f64 (sqrt.f64 2))) 2))
(/.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 2)) 3) 1/8 (pow.f64 2 3/2)) (fma.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) (-.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) (sqrt.f64 2)) 2))
(/.f64 (/.f64 (+.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3))) (sqrt.f64 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2)))))) (sqrt.f64 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2))))))
(/.f64 (*.f64 1 (+.f64 (pow.f64 2 3/2) (*.f64 (pow.f64 (/.f64 x (sqrt.f64 2)) 3) 1/8))) (+.f64 2 (*.f64 x (*.f64 (/.f64 1/2 (sqrt.f64 2)) (fma.f64 x (/.f64 1/2 (sqrt.f64 2)) (neg.f64 (sqrt.f64 2)))))))
(/.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 2)) 3) 1/8 (pow.f64 2 3/2)) (fma.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) (fma.f64 x (/.f64 1/2 (sqrt.f64 2)) (neg.f64 (sqrt.f64 2))) 2))
(/.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 2)) 3) 1/8 (pow.f64 2 3/2)) (fma.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) (-.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) (sqrt.f64 2)) 2))
(/.f64 (/.f64 (+.f64 (pow.f64 2 3/2) (*.f64 1/8 (pow.f64 (/.f64 x (sqrt.f64 2)) 3))) (*.f64 (cbrt.f64 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2))))) (cbrt.f64 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2))))))) (cbrt.f64 (+.f64 2 (*.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (-.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2))))))
(/.f64 (*.f64 1 (+.f64 (pow.f64 2 3/2) (*.f64 (pow.f64 (/.f64 x (sqrt.f64 2)) 3) 1/8))) (+.f64 2 (*.f64 x (*.f64 (/.f64 1/2 (sqrt.f64 2)) (fma.f64 x (/.f64 1/2 (sqrt.f64 2)) (neg.f64 (sqrt.f64 2)))))))
(/.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 2)) 3) 1/8 (pow.f64 2 3/2)) (fma.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) (fma.f64 x (/.f64 1/2 (sqrt.f64 2)) (neg.f64 (sqrt.f64 2))) 2))
(/.f64 (fma.f64 (pow.f64 (/.f64 x (sqrt.f64 2)) 3) 1/8 (pow.f64 2 3/2)) (fma.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) (-.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) (sqrt.f64 2)) 2))
(pow.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)) 1)
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(pow.f64 (sqrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))) 2)
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(pow.f64 (cbrt.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))) 3)
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(pow.f64 (pow.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)) 3) 1/3)
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(sqrt.f64 (pow.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)) 2))
(sqrt.f64 (pow.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 2))
(fabs.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)))
(log.f64 (exp.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(log.f64 (+.f64 1 (expm1.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(cbrt.f64 (pow.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2)) 3))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(expm1.f64 (log1p.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(exp.f64 (log.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(log1p.f64 (expm1.f64 (fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(fma.f64 (/.f64 x (sqrt.f64 2)) 1/2 (sqrt.f64 2))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(fma.f64 1 (sqrt.f64 2) (*.f64 x (/.f64 1/2 (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(fma.f64 1 (*.f64 x (/.f64 1/2 (sqrt.f64 2))) (sqrt.f64 2))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(fma.f64 (sqrt.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2)))) (sqrt.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2)))) (sqrt.f64 2))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(fma.f64 (pow.f64 2 1/4) (pow.f64 2 1/4) (*.f64 x (/.f64 1/2 (sqrt.f64 2))))
(+.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2))) (pow.f64 2 1/2))
(fma.f64 (cbrt.f64 (/.f64 (*.f64 1/4 x) (/.f64 2 x))) (cbrt.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2)))) (sqrt.f64 2))
(fma.f64 (cbrt.f64 (/.f64 1/4 (/.f64 (/.f64 2 x) x))) (cbrt.f64 (*.f64 x (/.f64 1/2 (sqrt.f64 2)))) (sqrt.f64 2))
(fma.f64 (cbrt.f64 (*.f64 x (/.f64 x 8))) (cbrt.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2)))) (sqrt.f64 2))
(fma.f64 (cbrt.f64 (*.f64 x (*.f64 1/8 x))) (cbrt.f64 (*.f64 1/2 (/.f64 x (sqrt.f64 2)))) (sqrt.f64 2))
(fma.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2)) (*.f64 x (/.f64 1/2 (sqrt.f64 2))))
(fma.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2)) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))

eval117.0ms (3.5%)

Compiler

Compiled 5324 to 4668 computations (12.3% saved)

prune30.0ms (0.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1981199
Fresh000
Picked011
Done022
Total1984202
Accurracy
100.0%
Counts
202 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓68.5%
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
▶2.9%
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
✓100.0%
(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓74.1%
(sqrt.f64 2)
Compiler

Compiled 26 to 23 computations (11.5% saved)

localize7.0ms (0.2%)

Local Accuracy

Found 1 expressions with local accuracy:

NewAccuracyProgram
99.3%
(/.f64 x (sqrt.f64 2))
Compiler

Compiled 16 to 13 computations (18.8% saved)

eval13.0ms (0.4%)

Compiler

Compiled 593 to 478 computations (19.4% saved)

prune9.0ms (0.3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New53154
Fresh000
Picked011
Done033
Total53558
Accurracy
100.0%
Counts
58 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓68.5%
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
✓2.9%
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
▶2.9%
(*.f64 1/2 (*.f64 (pow.f64 2 -1/2) x))
✓100.0%
(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓74.1%
(sqrt.f64 2)
Compiler

Compiled 34 to 30 computations (11.8% saved)

localize9.0ms (0.3%)

Local Accuracy

Found 1 expressions with local accuracy:

NewAccuracyProgram
✓99.3%
(*.f64 (pow.f64 2 -1/2) x)
Compiler

Compiled 20 to 17 computations (15% saved)

series2.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(*.f64 (pow.f64 2 -1/2) x)
1.0ms
x
@0
(*.f64 (pow.f64 2 -1/2) x)
0.0ms
x
@-inf
(*.f64 (pow.f64 2 -1/2) x)

rewrite48.0ms (1.5%)

Algorithm
1×batch-egg-rewrite
Rules
1250×add-sqr-sqrt
1224×*-un-lft-identity
1148×add-cube-cbrt
1132×add-cbrt-cube
1120×add-exp-log
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0713
114611
2161711
Stop Event
1×node limit
Counts
1 → 11
Calls
Call 1
Inputs
(*.f64 (pow.f64 2 -1/2) x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (sqrt.f64 1/2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 x x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) x)))))))

simplify63.0ms (1.9%)

Algorithm
1×egg-herbie
Rules
1026×*-commutative
880×log-prod
778×associate--l+
632×distribute-rgt-in
632×distribute-lft-in
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033253
179253
2273253
31578253
44488253
56754253
Stop Event
1×node limit
Counts
23 → 12
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(-.f64 (+.f64 1 (*.f64 (sqrt.f64 1/2) x)) 1)
(pow.f64 (*.f64 (sqrt.f64 1/2) x) 1)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) x)) 2)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) x)) 3)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) x) 3) 1/3)
(sqrt.f64 (*.f64 (*.f64 x x) 1/2))
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 1/2)))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) x) 3))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) x)))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) x)))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) x)))
Outputs
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(*.f64 (sqrt.f64 1/2) x)
(-.f64 (+.f64 1 (*.f64 (sqrt.f64 1/2) x)) 1)
(*.f64 (sqrt.f64 1/2) x)
(pow.f64 (*.f64 (sqrt.f64 1/2) x) 1)
(*.f64 (sqrt.f64 1/2) x)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) x)) 2)
(*.f64 (sqrt.f64 1/2) x)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) x)) 3)
(*.f64 (sqrt.f64 1/2) x)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) x) 3) 1/3)
(*.f64 (sqrt.f64 1/2) x)
(sqrt.f64 (*.f64 (*.f64 x x) 1/2))
(*.f64 (sqrt.f64 1/2) x)
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 1/2)))
(*.f64 (sqrt.f64 1/2) x)
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) x) 3))
(*.f64 (sqrt.f64 1/2) x)
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) x)))
(*.f64 (sqrt.f64 1/2) x)
(exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) x)))
(*.f64 (sqrt.f64 1/2) x)
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) x)))
(*.f64 (sqrt.f64 1/2) x)

eval3.0ms (0.1%)

Compiler

Compiled 102 to 89 computations (12.7% saved)

prune4.0ms (0.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New10212
Fresh000
Picked101
Done134
Total12517
Accurracy
100.0%
Counts
17 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓68.5%
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
2.6%
(*.f64 1/2 (-.f64 (+.f64 1 (*.f64 (sqrt.f64 1/2) x)) 1))
2.9%
(*.f64 1/2 (*.f64 (sqrt.f64 1/2) x))
✓100.0%
(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓74.1%
(sqrt.f64 2)
Compiler

Compiled 37 to 33 computations (10.8% saved)

regimes13.0ms (0.4%)

Counts
8 → 1
Calls
Call 1
Inputs
(sqrt.f64 2)
(*.f64 1/2 (*.f64 (sqrt.f64 1/2) x))
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
(*.f64 1/2 (*.f64 (pow.f64 2 -1/2) x))
(*.f64 1/2 (-.f64 (+.f64 1 (*.f64 (sqrt.f64 1/2) x)) 1))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
Outputs
(sqrt.f64 (+.f64 1 (exp.f64 x)))
Calls

3 calls:

6.0ms
x
2.0ms
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
2.0ms
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
100.0%1(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
Compiler

Compiled 85 to 71 computations (16.5% saved)

regimes5.0ms (0.2%)

Accuracy

Total -45.9b remaining (-276.8%)

Threshold costs -45.9b (-276.8%)

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

1 calls:

4.0ms
x
Results
AccuracySegmentsBranch
74.1%1x
Compiler

Compiled 34 to 29 computations (14.7% saved)

simplify9.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
2×1-exp
2×+-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01020
11320
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 2)
Outputs
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 2)
Compiler

Compiled 9 to 8 computations (11.1% saved)

soundness94.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
1440×associate-/l*
1382×associate-*r*
1160×associate-/r*
968×associate-*l*
702×fma-def
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01325
12725
23625
36225
413521
534915
6123815
Stop Event
1×node limit
Compiler

Compiled 85 to 56 computations (34.1% saved)

end14.0ms (0.4%)

Compiler

Compiled 8 to 7 computations (12.5% saved)

Profiling

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