Details

Time bar (total: 4.4s)

analyze158.0ms (3.6%)

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 (47.6%)

Results
1.1s2766×body1024valid
468.0ms3819×body256valid
289.0ms1371×body512valid
137.0ms300×body2048valid
6.0ms54×body256infinite
0.0ms2×body256unsamplable
Bogosity

preprocess154.0ms (3.5%)

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)

simplify33.0ms (0.8%)

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)))

eval27.0ms (0.6%)

Compiler

Compiled 41 to 29 computations (29.3% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New325
Fresh101
Picked000
Done000
Total426
Error
0.0b
Counts
6 → 2
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.0b
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
▶0.0b
(sqrt.f64 (+.f64 1 (exp.f64 x)))
Compiler

Compiled 15 to 11 computations (26.7% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiled 14 to 8 computations (42.9% saved)

series1.0ms (0%)

Counts
2 → 8
Calls

6 calls:

TimeVariablePointExpression
1.0ms
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)))
0.0ms
x
@0
(+.f64 1 (exp.f64 x))
0.0ms
x
@inf
(+.f64 1 (exp.f64 x))

rewrite60.0ms (1.4%)

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
0826
115626
2185126
Stop Event
1×node limit
Counts
2 → 61
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(+.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)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 1 (exp.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (exp.f64 x))) (/.f64 (pow.f64 (exp.f64 x) 2) (-.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (exp.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (hypot.f64 1 (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (*.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) (cbrt.f64 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (/.f64 1 (-.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (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 (*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (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 1 (/.f64 (-.f64 1 (exp.f64 x)) (-.f64 1 (pow.f64 (exp.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))) (+.f64 1 (pow.f64 (exp.f64 x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (-.f64 1 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (+.f64 (pow.f64 (exp.f64 x) 2) (-.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2))) (neg.f64 (-.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (neg.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (exp.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (exp.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) 1)))))

simplify60.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
1420×associate-/l*
1052×distribute-lft-in
994×distribute-rgt-in
800×associate-/r*
730×*-commutative
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01602019
13841767
213171463
336441417
Stop Event
1×node limit
Counts
69 → 102
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))))))
2
(+.f64 2 x)
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(-.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)))))
(-.f64 (+.f64 1 (+.f64 1 (exp.f64 x))) 1)
(-.f64 (/.f64 1 (-.f64 1 (exp.f64 x))) (/.f64 (pow.f64 (exp.f64 x) 2) (-.f64 1 (exp.f64 x))))
(*.f64 1 (+.f64 1 (exp.f64 x)))
(*.f64 (+.f64 1 (exp.f64 x)) 1)
(*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (*.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (/.f64 1 (-.f64 1 (exp.f64 x))))
(*.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))
(*.f64 (*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(*.f64 (*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (cbrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(/.f64 1 (/.f64 (-.f64 1 (exp.f64 x)) (-.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 1 (/.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))) (+.f64 1 (pow.f64 (exp.f64 x) 3))))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (-.f64 1 (exp.f64 x)))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (+.f64 (pow.f64 (exp.f64 x) 2) (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (expm1.f64 x))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2))) (neg.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (neg.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (neg.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))
(pow.f64 (+.f64 1 (exp.f64 x)) 1)
(pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 2)
(pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2) 1/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3) 1/3)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2))
(log.f64 (exp.f64 (+.f64 1 (exp.f64 x))))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 x))))
(exp.f64 (log1p.f64 (exp.f64 x)))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1))
(log1p.f64 (expm1.f64 (+.f64 1 (exp.f64 x))))
(fma.f64 1 (exp.f64 x) 1)
(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) 1)
(fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) 1)
Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
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(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 2 (expm1.f64 x))

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
✓0.0b
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
Compiler

Compiled 26 to 6 computations (76.9% saved)

series2.0ms (0%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
1.0ms
x
@-inf
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
0.0ms
x
@0
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
0.0ms
x
@-inf
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
0.0ms
x
@inf
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))

rewrite83.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
1872×add-sqr-sqrt
1854×*-un-lft-identity
1734×add-cube-cbrt
1716×add-cbrt-cube
186×pow1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0946
118646
2251846
Stop Event
1×node limit
Counts
2 → 69
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4) (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (sqrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (/.f64 1 (expm1.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2) 1/2) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (sqrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 x)) (/.f64 1 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 (+.f64 x x)) (/.f64 1 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4) (*.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4) (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2) (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (*.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (expm1.f64 x)) (expm1.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (neg.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4)) (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (/.f64 (expm1.f64 (+.f64 x x)) (sqrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (expm1.f64 (+.f64 x x)) (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) 1) (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (sqrt.f64 (expm1.f64 x))) (/.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (expm1.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))))))

simplify81.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
790×associate-*r/
696×+-commutative
636×*-commutative
606×distribute-lft-in
594×distribute-rgt-in
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01992811
14662639
217172619
367792619
Stop Event
1×node limit
Counts
93 → 104
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))))))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1)))
2
(+.f64 2 x)
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))) 1)
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 1)
(*.f64 1 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(*.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4) (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (/.f64 1 (expm1.f64 x))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (sqrt.f64 (expm1.f64 x))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (/.f64 1 (expm1.f64 x)) 1/2))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2) 1/2) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 1/2))
(/.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
(/.f64 1 (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 (+.f64 x x)))))
(/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/2)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 1)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4) 2)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) 3)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3/2) 1/3)
(fabs.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(exp.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 1/2))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) 1))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) 1)
(-.f64 (/.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 x)) (/.f64 1 (expm1.f64 x)))
(*.f64 (expm1.f64 (+.f64 x x)) (/.f64 1 (expm1.f64 x)))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1)
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(*.f64 1 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(*.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4) (*.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4) (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (expm1.f64 x))))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2) (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (*.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (expm1.f64 x))))
(*.f64 (/.f64 1 (expm1.f64 x)) (expm1.f64 (+.f64 x x)))
(*.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (neg.f64 (expm1.f64 x))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4)) (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(*.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (/.f64 (expm1.f64 (+.f64 x x)) (sqrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (expm1.f64 (+.f64 x x)) (cbrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) 1) (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (expm1.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (cbrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (expm1.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (sqrt.f64 (expm1.f64 x))) (/.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 3)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 2) 1/2)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3) 1/3)
(pow.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))) -1)
(neg.f64 (/.f64 (expm1.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 2))
(log.f64 (exp.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(exp.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(exp.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 1))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.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 (/.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))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
2
(+.f64 2 x)
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 2 (fma.f64 1/2 (*.f64 x x) x))
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(fma.f64 1/6 (pow.f64 x 3) (+.f64 2 (fma.f64 1/2 (*.f64 x x) x)))
(+.f64 (fma.f64 1/2 (*.f64 x x) x) (fma.f64 1/6 (pow.f64 x 3) 2))
(+.f64 2 (fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) x)))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))) 1)
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 1)
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(*.f64 1 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(*.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4) (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (/.f64 1 (expm1.f64 x))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x)))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (/.f64 1 (expm1.f64 x)) 1/2))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (/.f64 1 (expm1.f64 x))))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(*.f64 (fabs.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) (sqrt.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (sqrt.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2) 1/2) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(*.f64 (fabs.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) (sqrt.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (sqrt.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(/.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
(/.f64 1 (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 (+.f64 x x)))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x)))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x)))
(pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/2)
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 1)
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(pow.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4) 2)
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) 3)
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(pow.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3/2) 1/3)
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3/2))
(fabs.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(exp.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 1/2))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) 1))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) 1)
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(-.f64 (/.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 x)) (/.f64 1 (expm1.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (expm1.f64 (+.f64 x x)) (/.f64 1 (expm1.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1)
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 1 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4) (*.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4) (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (*.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) 4))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2) (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (*.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (/.f64 1 (expm1.f64 x)) (expm1.f64 (+.f64 x x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (neg.f64 (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4)) (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1/4))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (*.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))) 4))
(*.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (/.f64 (expm1.f64 (+.f64 x x)) (sqrt.f64 (expm1.f64 x))))
(/.f64 (/.f64 (expm1.f64 (+.f64 x x)) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (*.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (expm1.f64 (+.f64 x x)) (cbrt.f64 (expm1.f64 x))))
(/.f64 (/.f64 (expm1.f64 (+.f64 x x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (expm1.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) 1) (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (expm1.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (cbrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (expm1.f64 (+.f64 x x)) (cbrt.f64 (expm1.f64 x))))
(/.f64 (/.f64 (expm1.f64 (+.f64 x x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (expm1.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (expm1.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (sqrt.f64 (expm1.f64 x))) (/.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (/.f64 (expm1.f64 (+.f64 x x)) (sqrt.f64 (expm1.f64 x))))
(/.f64 (/.f64 (expm1.f64 (+.f64 x x)) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (*.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)))
(/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 1)
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 2)
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 3)
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(pow.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 2) 1/2)
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(pow.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3) 1/3)
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(pow.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))) -1)
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(neg.f64 (/.f64 (expm1.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 2))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(log.f64 (exp.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(exp.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(exp.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))

eval50.0ms (1.1%)

Compiler

Compiled 2842 to 1534 computations (46% saved)

prune25.0ms (0.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New2024206
Fresh000
Picked101
Done101
Total2044208
Error
0b
Counts
208 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.0b
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
▶19.2b
(sqrt.f64 (+.f64 2 x))
▶15.6b
(sqrt.f64 2)
▶0.7b
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
Compiler

Compiled 21 to 18 computations (14.3% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.7b
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
Compiler

Compiled 19 to 9 computations (52.6% saved)

series47.0ms (1.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
29.0ms
x
@inf
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
16.0ms
x
@-inf
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
1.0ms
x
@0
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))

rewrite51.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
1454×add-sqr-sqrt
1438×*-un-lft-identity
1332×add-cube-cbrt
1314×add-cbrt-cube
1296×add-exp-log
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0919
117215
2187515
Stop Event
1×node limit
Counts
1 → 21
Calls
Call 1
Inputs
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (expm1.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (+.f64 (exp.f64 x) 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 (exp.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 (exp.f64 x) 1) 1/4) (pow.f64 (+.f64 (exp.f64 x) 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) (cbrt.f64 (+.f64 (exp.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (exp.f64 x) 1)) (cbrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (exp.f64 x) 1) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (exp.f64 x) 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/2) (log1p.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))) (sqrt.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (*.f64 (log1p.f64 (exp.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (cbrt.f64 (*.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 2) 1/4))) (cbrt.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (+.f64 (exp.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))))))

simplify62.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
1186×fma-def
1036×associate-*r*
788×associate-*l*
672×distribute-rgt-in
672×distribute-lft-in
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
072685
1163681
2558669
32623641
45826641
Stop Event
1×node limit
Counts
33 → 40
Calls
Call 1
Inputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/4 (*.f64 (sqrt.f64 2) x)))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/32 (*.f64 (sqrt.f64 2) (pow.f64 x 2))) (*.f64 1/4 (*.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/32 (*.f64 (sqrt.f64 2) (pow.f64 x 2))) (+.f64 (*.f64 7/384 (*.f64 (sqrt.f64 2) (pow.f64 x 3))) (*.f64 1/4 (*.f64 (sqrt.f64 2) x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(+.f64 1 (expm1.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 (exp.f64 x) 1))) 1)
(*.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 1)
(*.f64 1 (sqrt.f64 (+.f64 (exp.f64 x) 1)))
(*.f64 (pow.f64 (+.f64 (exp.f64 x) 1) 1/4) (pow.f64 (+.f64 (exp.f64 x) 1) 1/4))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) (cbrt.f64 (+.f64 (exp.f64 x) 1)))
(*.f64 (cbrt.f64 (+.f64 (exp.f64 x) 1)) (cbrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))
(pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 1)
(pow.f64 (pow.f64 (+.f64 (exp.f64 x) 1) 1/4) 2)
(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) 3)
(pow.f64 (pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 3) 1/3)
(pow.f64 (+.f64 (exp.f64 x) 1) 1/2)
(pow.f64 (exp.f64 1/2) (log1p.f64 (exp.f64 x)))
(pow.f64 (exp.f64 (sqrt.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))) (sqrt.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)))
(pow.f64 (exp.f64 1) (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
(pow.f64 (exp.f64 (cbrt.f64 (*.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 2) 1/4))) (cbrt.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)))
(sqrt.f64 (+.f64 (exp.f64 x) 1))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))
(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 3))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))
Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/4 (*.f64 (sqrt.f64 2) x)))
(fma.f64 1/4 (*.f64 (sqrt.f64 2) x) (sqrt.f64 2))
(fma.f64 (sqrt.f64 2) (*.f64 1/4 x) (sqrt.f64 2))
(*.f64 (fma.f64 1/4 x 1) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/32 (*.f64 (sqrt.f64 2) (pow.f64 x 2))) (*.f64 1/4 (*.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (fma.f64 3/32 (*.f64 (sqrt.f64 2) (*.f64 x x)) (*.f64 1/4 (*.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (fma.f64 1/4 (*.f64 (sqrt.f64 2) x) (*.f64 3/32 (*.f64 (sqrt.f64 2) (*.f64 x x)))))
(+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 1/4 x) (*.f64 x (*.f64 x 3/32)))))
(fma.f64 (sqrt.f64 2) (*.f64 x (+.f64 1/4 (*.f64 x 3/32))) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 3/32 (*.f64 (sqrt.f64 2) (pow.f64 x 2))) (+.f64 (*.f64 7/384 (*.f64 (sqrt.f64 2) (pow.f64 x 3))) (*.f64 1/4 (*.f64 (sqrt.f64 2) x)))))
(+.f64 (sqrt.f64 2) (fma.f64 3/32 (*.f64 (sqrt.f64 2) (*.f64 x x)) (fma.f64 7/384 (*.f64 (sqrt.f64 2) (pow.f64 x 3)) (*.f64 1/4 (*.f64 (sqrt.f64 2) x)))))
(+.f64 (sqrt.f64 2) (fma.f64 3/32 (*.f64 (sqrt.f64 2) (*.f64 x x)) (fma.f64 1/4 (*.f64 (sqrt.f64 2) x) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 x 3) 7/384)))))
(+.f64 (sqrt.f64 2) (fma.f64 (pow.f64 x 3) (*.f64 (sqrt.f64 2) 7/384) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 1/4 x) (*.f64 x (*.f64 x 3/32))))))
(fma.f64 (sqrt.f64 2) (*.f64 (*.f64 x x) (+.f64 3/32 (*.f64 7/384 x))) (*.f64 (fma.f64 1/4 x 1) (sqrt.f64 2)))
(fma.f64 (*.f64 x x) (*.f64 (sqrt.f64 2) (+.f64 3/32 (*.f64 7/384 x))) (*.f64 (fma.f64 1/4 x 1) (sqrt.f64 2)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(+.f64 1 (expm1.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 (exp.f64 x) 1))) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 1 (sqrt.f64 (+.f64 (exp.f64 x) 1)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (pow.f64 (+.f64 (exp.f64 x) 1) 1/4) (pow.f64 (+.f64 (exp.f64 x) 1) 1/4))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) (cbrt.f64 (+.f64 (exp.f64 x) 1)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (cbrt.f64 (+.f64 (exp.f64 x) 1)) (cbrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (pow.f64 (+.f64 (exp.f64 x) 1) 1/4) 2)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))) 3)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 3) 1/3)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (+.f64 (exp.f64 x) 1) 1/2)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (exp.f64 1/2) (log1p.f64 (exp.f64 x)))
(pow.f64 (exp.f64 (sqrt.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))) (sqrt.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)))
(pow.f64 (exp.f64 1) (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
(pow.f64 (E.f64) (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
(pow.f64 (exp.f64 (cbrt.f64 (*.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 2) 1/4))) (cbrt.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)))
(pow.f64 (exp.f64 (cbrt.f64 (*.f64 1/4 (pow.f64 (log1p.f64 (exp.f64 x)) 2)))) (cbrt.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)))
(sqrt.f64 (+.f64 (exp.f64 x) 1))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1)) 3))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 (exp.f64 x) 1))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))

localize2.0ms (0%)

Compiler

Compiled 4 to 4 computations (0% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (+.f64 2 x))
Compiler

Compiled 10 to 7 computations (30% saved)

series1.0ms (0%)

Counts
1 → 4
Calls

3 calls:

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

rewrite49.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
1482×add-sqr-sqrt
1458×*-un-lft-identity
1368×add-cube-cbrt
1358×add-cbrt-cube
1348×add-exp-log
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
114811
2181011
Stop Event
1×node limit
Counts
1 → 24
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 2 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 2 x) 1/4) (pow.f64 (+.f64 2 x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 2 x)) (cbrt.f64 (sqrt.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 x))) (cbrt.f64 (+.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 2 x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 2 x)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 2 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 8 (pow.f64 x 3))) (sqrt.f64 (+.f64 4 (*.f64 x (-.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 4 (*.f64 x x))) (sqrt.f64 (-.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 2 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 2 x) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 2 x) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 2 x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 2 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 2 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 2 x))))))))

simplify55.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
1128×associate-*r*
968×associate-*l*
764×associate-/l*
682×fma-def
672×times-frac
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
087800
1191672
2505560
31419516
46085516
Stop Event
1×node limit
Counts
28 → 45
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 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
(*.f64 (sqrt.f64 (+.f64 2 x)) 1)
(*.f64 1 (sqrt.f64 (+.f64 2 x)))
(*.f64 (pow.f64 (+.f64 2 x) 1/4) (pow.f64 (+.f64 2 x) 1/4))
(*.f64 (cbrt.f64 (+.f64 2 x)) (cbrt.f64 (sqrt.f64 (+.f64 2 x))))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 x))) (cbrt.f64 (+.f64 2 x)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 2 x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 2 x)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 2 x)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 2 x)) 1/2))
(/.f64 (sqrt.f64 (+.f64 8 (pow.f64 x 3))) (sqrt.f64 (+.f64 4 (*.f64 x (-.f64 x 2)))))
(/.f64 (sqrt.f64 (-.f64 4 (*.f64 x x))) (sqrt.f64 (-.f64 2 x)))
(pow.f64 (+.f64 2 x) 1/2)
(pow.f64 (sqrt.f64 (+.f64 2 x)) 1)
(pow.f64 (pow.f64 (+.f64 2 x) 1/4) 2)
(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 x))) 3)
(pow.f64 (pow.f64 (+.f64 2 x) 3/2) 1/3)
(fabs.f64 (sqrt.f64 (+.f64 2 x)))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))
(cbrt.f64 (pow.f64 (+.f64 2 x) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 2 x))))
(exp.f64 (log.f64 (sqrt.f64 (+.f64 2 x))))
(exp.f64 (*.f64 (log.f64 (+.f64 2 x)) 1/2))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 2 x))) 1))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 2 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 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 -1/8 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 2) 3)) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)) (*.f64 -1/16 (/.f64 (*.f64 x x) (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 -1/16 (/.f64 x (/.f64 (sqrt.f64 2) x)) (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (/.f64 x -16))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 -1/8 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 2) 3)) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (*.f64 -1/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)))
(fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 -1/16 (/.f64 x (/.f64 (sqrt.f64 2) x)) (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (/.f64 x -16)))))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(*.f64 (sqrt.f64 (+.f64 2 x)) 1)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(*.f64 1 (sqrt.f64 (+.f64 2 x)))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(*.f64 (pow.f64 (+.f64 2 x) 1/4) (pow.f64 (+.f64 2 x) 1/4))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(*.f64 (cbrt.f64 (+.f64 2 x)) (cbrt.f64 (sqrt.f64 (+.f64 2 x))))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 x))) (cbrt.f64 (+.f64 2 x)))
(*.f64 (cbrt.f64 (+.f64 2 x)) (cbrt.f64 (sqrt.f64 (+.f64 2 x))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 2 x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 2 x))) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))
(*.f64 (cbrt.f64 (+.f64 2 x)) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))
(pow.f64 (cbrt.f64 (+.f64 2 x)) 3/2)
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 2 x)))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 2 x)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 2 x)) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 2 x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 2 x))) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))
(*.f64 (cbrt.f64 (+.f64 2 x)) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))
(pow.f64 (cbrt.f64 (+.f64 2 x)) 3/2)
(/.f64 (sqrt.f64 (+.f64 8 (pow.f64 x 3))) (sqrt.f64 (+.f64 4 (*.f64 x (-.f64 x 2)))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 3) 8)) (sqrt.f64 (+.f64 4 (*.f64 x (+.f64 x -2)))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 3) 8)) (sqrt.f64 (fma.f64 x (+.f64 x -2) 4)))
(/.f64 (sqrt.f64 (-.f64 4 (*.f64 x x))) (sqrt.f64 (-.f64 2 x)))
(pow.f64 (+.f64 2 x) 1/2)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(pow.f64 (sqrt.f64 (+.f64 2 x)) 1)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(pow.f64 (pow.f64 (+.f64 2 x) 1/4) 2)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 x))) 3)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(pow.f64 (pow.f64 (+.f64 2 x) 3/2) 1/3)
(cbrt.f64 (pow.f64 (+.f64 2 x) 3/2))
(fabs.f64 (sqrt.f64 (+.f64 2 x)))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(cbrt.f64 (pow.f64 (+.f64 2 x) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 2 x))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(exp.f64 (log.f64 (sqrt.f64 (+.f64 2 x))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(exp.f64 (*.f64 (log.f64 (+.f64 2 x)) 1/2))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 2 x))) 1))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 2 x))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
Compiler

Compiled 14 to 8 computations (42.9% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@0
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
0.0ms
x
@inf
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
0.0ms
x
@-inf
(sqrt.f64 (+.f64 2 (expm1.f64 x)))

rewrite50.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
1636×add-sqr-sqrt
1612×*-un-lft-identity
1510×add-cube-cbrt
1498×add-cbrt-cube
160×pow1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0815
116515
2200315
Stop Event
1×node limit
Counts
1 → 25
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (-.f64 (exp.f64 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 (exp.f64 x) -1) 1/4) (pow.f64 (-.f64 (exp.f64 x) -1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1))) (cbrt.f64 (-.f64 (exp.f64 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (exp.f64 x) -1)) (cbrt.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (exp.f64 x) -1)) 2)) (sqrt.f64 (cbrt.f64 (-.f64 (exp.f64 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (-.f64 (exp.f64 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 (exp.f64 x) -1)) 2) 1/2) (pow.f64 (cbrt.f64 (-.f64 (exp.f64 x) -1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 8 (pow.f64 (expm1.f64 x) 3))) (sqrt.f64 (+.f64 4 (*.f64 (expm1.f64 x) (-.f64 (expm1.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 4 (pow.f64 (expm1.f64 x) 2))) (sqrt.f64 (-.f64 2 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (exp.f64 x) -1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (exp.f64 x) -1) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (exp.f64 x) -1) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) -1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (-.f64 (exp.f64 x) -1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1))))))))

simplify58.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
846×fma-def
734×associate-+r+
732×associate-/l*
642×associate-+l+
626×times-frac
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0100957
1226877
2620857
31690773
45663761
Stop Event
1×node limit
Counts
37 → 48
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))))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1)))) 1)
(*.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1)) 1)
(*.f64 1 (sqrt.f64 (-.f64 (exp.f64 x) -1)))
(*.f64 (pow.f64 (-.f64 (exp.f64 x) -1) 1/4) (pow.f64 (-.f64 (exp.f64 x) -1) 1/4))
(*.f64 (cbrt.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1))) (cbrt.f64 (-.f64 (exp.f64 x) -1)))
(*.f64 (cbrt.f64 (-.f64 (exp.f64 x) -1)) (cbrt.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (exp.f64 x) -1)) 2)) (sqrt.f64 (cbrt.f64 (-.f64 (exp.f64 x) -1))))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (-.f64 (exp.f64 x) -1)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 (exp.f64 x) -1)) 2) 1/2) (pow.f64 (cbrt.f64 (-.f64 (exp.f64 x) -1)) 1/2))
(/.f64 (sqrt.f64 (+.f64 8 (pow.f64 (expm1.f64 x) 3))) (sqrt.f64 (+.f64 4 (*.f64 (expm1.f64 x) (-.f64 (expm1.f64 x) 2)))))
(/.f64 (sqrt.f64 (-.f64 4 (pow.f64 (expm1.f64 x) 2))) (sqrt.f64 (-.f64 2 (expm1.f64 x))))
(pow.f64 (-.f64 (exp.f64 x) -1) 1/2)
(pow.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1)) 1)
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) -1) 1/4) 2)
(pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1))) 3)
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) -1) 3/2) 1/3)
(fabs.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1)))
(log.f64 (exp.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1)))))
(cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) -1) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1))))
(exp.f64 (log.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1))))
(exp.f64 (*.f64 (log.f64 (-.f64 (exp.f64 x) -1)) 1/2))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1))) 1))
(log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1))))
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 (*.f64 (*.f64 x x) (+.f64 3/8 (*.f64 x 7/96))) x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1)))) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1)) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 1 (sqrt.f64 (-.f64 (exp.f64 x) -1)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (pow.f64 (-.f64 (exp.f64 x) -1) 1/4) (pow.f64 (-.f64 (exp.f64 x) -1) 1/4))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (cbrt.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1))) (cbrt.f64 (-.f64 (exp.f64 x) -1)))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (-.f64 (exp.f64 x) -1)) (cbrt.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1))))
(*.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 (exp.f64 x) -1)) 2)) (sqrt.f64 (cbrt.f64 (-.f64 (exp.f64 x) -1))))
(*.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) (sqrt.f64 (-.f64 (exp.f64 x) -1)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 (exp.f64 x) -1)) 2) 1/2) (pow.f64 (cbrt.f64 (-.f64 (exp.f64 x) -1)) 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 8 (pow.f64 (expm1.f64 x) 3))) (sqrt.f64 (+.f64 4 (*.f64 (expm1.f64 x) (-.f64 (expm1.f64 x) 2)))))
(/.f64 (sqrt.f64 (+.f64 8 (pow.f64 (expm1.f64 x) 3))) (sqrt.f64 (+.f64 4 (*.f64 (expm1.f64 x) (+.f64 (expm1.f64 x) -2)))))
(/.f64 (sqrt.f64 (+.f64 8 (pow.f64 (expm1.f64 x) 3))) (sqrt.f64 (fma.f64 (expm1.f64 x) (+.f64 (expm1.f64 x) -2) 4)))
(/.f64 (sqrt.f64 (-.f64 4 (pow.f64 (expm1.f64 x) 2))) (sqrt.f64 (-.f64 2 (expm1.f64 x))))
(pow.f64 (-.f64 (exp.f64 x) -1) 1/2)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1)) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) -1) 1/4) 2)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1))) 3)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) -1) 3/2) 1/3)
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(fabs.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (exp.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) -1) 3/2))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(exp.f64 (log.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(exp.f64 (*.f64 (log.f64 (-.f64 (exp.f64 x) -1)) 1/2))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1))) 1))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 (exp.f64 x) -1))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))

eval58.0ms (1.3%)

Compiler

Compiled 1659 to 1315 computations (20.7% saved)

prune49.0ms (1.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1312133
Fresh000
Picked011
Done123
Total1325137
Error
0b
Counts
137 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
▶19.2b
(pow.f64 (pow.f64 (+.f64 2 x) 3/2) 1/3)
▶19.9b
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
✓0.0b
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
✓19.2b
(sqrt.f64 (+.f64 2 x))
✓15.6b
(sqrt.f64 2)
Compiler

Compiled 31 to 27 computations (12.9% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 2 x))
✓0.7b
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
Compiler

Compiled 25 to 20 computations (20% saved)

series0.0ms (0%)

Counts
1 → 4
Calls

3 calls:

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

rewrite74.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
1450×associate-*r/
1116×associate-*l/
848×distribute-lft-in
812×*-commutative
312×associate-/r*
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01023
122311
2300611
Stop Event
1×node limit
Counts
1 → 118
Calls
Call 1
Inputs
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (sqrt.f64 (+.f64 2 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 2 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 2 x)) (*.f64 (pow.f64 1 1/2) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (+.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 1 (sqrt.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 1 1/2) 1) (*.f64 (pow.f64 1 1/2) (+.f64 (sqrt.f64 (+.f64 2 x)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 1 1/2) (+.f64 (sqrt.f64 (+.f64 2 x)) -1)) (*.f64 (pow.f64 1 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 1 1/2) (+.f64 1 (sqrt.f64 (+.f64 2 x)))) (*.f64 (pow.f64 1 1/2) -1))))) 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egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 (sqrt.f64 (+.f64 2 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) -1)))))

simplify115.0ms (2.6%)

Algorithm
1×egg-herbie
Rules
1704×associate-/l*
1266×associate-/r*
1016×associate-*r/
986×associate-+r+
852×*-commutative
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03166662
18816418
231916382
Stop Event
1×node limit
Counts
122 → 186
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 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 2 x)) -1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(+.f64 (sqrt.f64 (+.f64 2 x)) (*.f64 (pow.f64 1 1/2) 0))
(+.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) -1)
(+.f64 0 (sqrt.f64 (+.f64 2 x)))
(+.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1) 1)
(+.f64 -1 (+.f64 1 (sqrt.f64 (+.f64 2 x))))
(+.f64 (*.f64 (pow.f64 1 1/2) 1) (*.f64 (pow.f64 1 1/2) (+.f64 (sqrt.f64 (+.f64 2 x)) -1)))
(+.f64 (*.f64 (pow.f64 1 1/2) (+.f64 (sqrt.f64 (+.f64 2 x)) -1)) (*.f64 (pow.f64 1 1/2) 1))
(+.f64 (*.f64 (pow.f64 1 1/2) (+.f64 1 (sqrt.f64 (+.f64 2 x)))) (*.f64 (pow.f64 1 1/2) -1))
(+.f64 (*.f64 (pow.f64 1 1/2) -1) (*.f64 (pow.f64 1 1/2) (+.f64 1 (sqrt.f64 (+.f64 2 x)))))
(*.f64 1 (sqrt.f64 (+.f64 2 x)))
(*.f64 (sqrt.f64 (+.f64 2 x)) 1)
(*.f64 (sqrt.f64 (+.f64 2 x)) (pow.f64 1 1/2))
(*.f64 (pow.f64 (+.f64 2 x) 1/4) (pow.f64 (+.f64 2 x) 1/4))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 x))) (cbrt.f64 (+.f64 2 x)))
(*.f64 (cbrt.f64 (+.f64 2 x)) (cbrt.f64 (sqrt.f64 (+.f64 2 x))))
(*.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1) (/.f64 1 (+.f64 2 (sqrt.f64 (+.f64 2 x)))))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x))))))
(*.f64 (sqrt.f64 (cbrt.f64 (+.f64 2 x))) (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 2 x) 2))))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 2 x) 2))) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))
(*.f64 (+.f64 1 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4))) (-.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) 1))
(*.f64 (-.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) 1) (+.f64 1 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4))))
(*.f64 (/.f64 1 (+.f64 2 (sqrt.f64 (+.f64 2 x)))) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1))
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x))))) (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 2 x)))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 2 x) 2)) 1/2) (pow.f64 (cbrt.f64 (+.f64 2 x)) 1/2))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 2 x)) 1/2) (pow.f64 (cbrt.f64 (pow.f64 (+.f64 2 x) 2)) 1/2))
(*.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1)) (sqrt.f64 (+.f64 2 x)))
(*.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1) (-.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2))) (-.f64 0 (sqrt.f64 (+.f64 2 x))))
(*.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1) (+.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3))) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (-.f64 0 (sqrt.f64 (+.f64 2 x)))))
(*.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)) (-.f64 (*.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2)) (*.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x))) (+.f64 2 (sqrt.f64 (+.f64 2 x)))))) (-.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x)))))
(*.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)) (+.f64 (pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) 3) (pow.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x))) 3))) (+.f64 (*.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2)) (-.f64 (*.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x))) (+.f64 2 (sqrt.f64 (+.f64 2 x)))) (*.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x)))))))
(/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 2 x))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (-.f64 1 (*.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) -1))) (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3))))
(/.f64 (sqrt.f64 (+.f64 2 x)) 1)
(/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1) (+.f64 2 (sqrt.f64 (+.f64 2 x))))
(/.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x))) (/.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x))) (sqrt.f64 (+.f64 2 x))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (-.f64 1 (*.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) -1))))
(/.f64 (sqrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3))) (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x)))) (sqrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)))))
(/.f64 (sqrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3))) (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (-.f64 1 (*.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) -1))) (sqrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)))))
(/.f64 (sqrt.f64 (-.f64 4 (*.f64 x x))) (sqrt.f64 (-.f64 2 x)))
(/.f64 (sqrt.f64 (+.f64 8 (pow.f64 x 3))) (sqrt.f64 (+.f64 4 (*.f64 x (-.f64 x 2)))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1)) (/.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x))) (sqrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1))))
(/.f64 (*.f64 (cbrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3))) (cbrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)))) (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x)))) (cbrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)))))
(/.f64 (*.f64 (cbrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3))) (cbrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)))) (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (-.f64 1 (*.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) -1))) (cbrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)))))
(/.f64 (*.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1)) (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1))) (/.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x))) (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1))))
(/.f64 (-.f64 1 (*.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))) (-.f64 2 (sqrt.f64 (+.f64 2 x))))
(/.f64 (-.f64 (*.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2)) 1) (*.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x))) (+.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2))))
(/.f64 (-.f64 (*.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)) 1) (*.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x)))) (+.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3))))
(/.f64 (-.f64 (*.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)) 1) (*.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (-.f64 1 (*.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) -1))) (+.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1)) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) 3) 1) (*.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x))) (+.f64 (*.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2)) (+.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2)))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3) 3) 1) (*.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x)))) (+.f64 (*.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)) (+.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3) 3) 1) (*.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (-.f64 1 (*.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) -1))) (+.f64 (*.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)) (+.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1)) (neg.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (neg.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3))) (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x))))))
(/.f64 (*.f64 1 (sqrt.f64 (-.f64 4 (*.f64 x x)))) (sqrt.f64 (-.f64 2 x)))
(/.f64 (*.f64 1 (sqrt.f64 (+.f64 8 (pow.f64 x 3)))) (sqrt.f64 (+.f64 4 (*.f64 x (-.f64 x 2)))))
(/.f64 (*.f64 1 (-.f64 1 (*.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1)))) (-.f64 2 (sqrt.f64 (+.f64 2 x))))
(/.f64 (*.f64 1 (+.f64 1 (pow.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1) 3))) (+.f64 1 (-.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1)) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))))
(/.f64 (*.f64 1 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1))) (neg.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (*.f64 1 (neg.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)))) (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x))))))
(/.f64 (*.f64 (pow.f64 (+.f64 2 x) 1/4) (sqrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)))) (sqrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x))))))
(/.f64 (*.f64 (pow.f64 (+.f64 2 x) 1/4) (sqrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1))) (sqrt.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 x))) (cbrt.f64 (-.f64 4 (*.f64 x x)))) (cbrt.f64 (-.f64 2 x)))
(/.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 x))) (cbrt.f64 (+.f64 8 (pow.f64 x 3)))) (cbrt.f64 (+.f64 4 (*.f64 x (-.f64 x 2)))))
(/.f64 (*.f64 (cbrt.f64 (+.f64 2 x)) (cbrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)))) (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x))))))
(/.f64 (*.f64 (cbrt.f64 (+.f64 2 x)) (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1))) (cbrt.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (*.f64 (pow.f64 1 1/2) 1) (/.f64 1 (sqrt.f64 (+.f64 2 x))))
(/.f64 (*.f64 (pow.f64 1 1/2) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1)) (+.f64 2 (sqrt.f64 (+.f64 2 x))))
(/.f64 (*.f64 (pow.f64 1 1/2) (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3))) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (*.f64 (pow.f64 1 1/2) (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3))) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (-.f64 1 (*.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) -1))))
(/.f64 (*.f64 (pow.f64 1 1/2) (sqrt.f64 (-.f64 4 (*.f64 x x)))) (sqrt.f64 (-.f64 2 x)))
(/.f64 (*.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 8 (pow.f64 x 3)))) (sqrt.f64 (+.f64 4 (*.f64 x (-.f64 x 2)))))
(/.f64 (*.f64 (pow.f64 1 1/2) (-.f64 1 (*.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1)))) (-.f64 2 (sqrt.f64 (+.f64 2 x))))
(/.f64 (*.f64 (pow.f64 1 1/2) (+.f64 1 (pow.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1) 3))) (+.f64 1 (-.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1)) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))))
(/.f64 (*.f64 (pow.f64 1 1/2) (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1))) (neg.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (*.f64 (pow.f64 1 1/2) (neg.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)))) (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x))))))
(/.f64 (*.f64 (sqrt.f64 (-.f64 4 (*.f64 x x))) 1) (sqrt.f64 (-.f64 2 x)))
(/.f64 (*.f64 (sqrt.f64 (+.f64 8 (pow.f64 x 3))) 1) (sqrt.f64 (+.f64 4 (*.f64 x (-.f64 x 2)))))
(/.f64 (*.f64 (-.f64 1 (*.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))) 1) (-.f64 2 (sqrt.f64 (+.f64 2 x))))
(/.f64 (*.f64 (+.f64 1 (pow.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1) 3)) 1) (+.f64 1 (-.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1)) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))))
(/.f64 (*.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1)) 1) (neg.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (*.f64 (neg.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3))) 1) (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x))))))
(/.f64 (*.f64 (sqrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3))) (pow.f64 (+.f64 2 x) 1/4)) (sqrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x))))))
(/.f64 (*.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1)) (pow.f64 (+.f64 2 x) 1/4)) (sqrt.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (*.f64 (cbrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3))) (cbrt.f64 (+.f64 2 x))) (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x))))))
(/.f64 (*.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1)) (cbrt.f64 (+.f64 2 x))) (cbrt.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (*.f64 (cbrt.f64 (-.f64 4 (*.f64 x x))) (cbrt.f64 (sqrt.f64 (+.f64 2 x)))) (cbrt.f64 (-.f64 2 x)))
(/.f64 (*.f64 (cbrt.f64 (+.f64 8 (pow.f64 x 3))) (cbrt.f64 (sqrt.f64 (+.f64 2 x)))) (cbrt.f64 (+.f64 4 (*.f64 x (-.f64 x 2)))))
(/.f64 (*.f64 (-.f64 (*.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2)) 1) (/.f64 1 (+.f64 2 (sqrt.f64 (+.f64 2 x))))) (+.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2)))
(/.f64 (*.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) 3) 1) (/.f64 1 (+.f64 2 (sqrt.f64 (+.f64 2 x))))) (+.f64 (*.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2)) (+.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2))))
(/.f64 (*.f64 (-.f64 (*.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)) 1) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x)))))) (+.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)))
(/.f64 (*.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3) 3) 1) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x)))))) (+.f64 (*.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)) (+.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3))))
(/.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1) 1) (+.f64 2 (sqrt.f64 (+.f64 2 x))))
(/.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1) (sqrt.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x))))) (sqrt.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1) (*.f64 (cbrt.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x)))) (cbrt.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x)))))) (cbrt.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)) 1) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)) (sqrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x)))))) (sqrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x))))))
(/.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)) (*.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x))))) (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x))))))) (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x))))))
(pow.f64 (+.f64 2 x) 1/2)
(pow.f64 (sqrt.f64 (+.f64 2 x)) 1)
(pow.f64 (pow.f64 (+.f64 2 x) 1/4) 2)
(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 x))) 3)
(pow.f64 (pow.f64 (+.f64 2 x) 3/2) 1/3)
(sqrt.f64 (+.f64 2 x))
(fabs.f64 (sqrt.f64 (+.f64 2 x)))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 2 x)))))
(cbrt.f64 (pow.f64 (+.f64 2 x) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 2 x))))
(exp.f64 (log.f64 (sqrt.f64 (+.f64 2 x))))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 2 x))))
(fma.f64 1 (+.f64 1 (sqrt.f64 (+.f64 2 x))) -1)
(fma.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) -1)
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) -1)
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 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 -1/8 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 2) 3)) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (*.f64 -1/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))))
(+.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)) (/.f64 (/.f64 (*.f64 x x) -16) (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 -1/8 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 2) 3)) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (*.f64 -1/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (/.f64 (/.f64 (*.f64 x x) -16) (sqrt.f64 2)))))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 2 x)) -1))
(sqrt.f64 (+.f64 2 x))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(+.f64 (sqrt.f64 (+.f64 2 x)) (*.f64 (pow.f64 1 1/2) 0))
(sqrt.f64 (+.f64 2 x))
(+.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) -1)
(sqrt.f64 (+.f64 2 x))
(+.f64 0 (sqrt.f64 (+.f64 2 x)))
(sqrt.f64 (+.f64 2 x))
(+.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1) 1)
(sqrt.f64 (+.f64 2 x))
(+.f64 -1 (+.f64 1 (sqrt.f64 (+.f64 2 x))))
(sqrt.f64 (+.f64 2 x))
(+.f64 (*.f64 (pow.f64 1 1/2) 1) (*.f64 (pow.f64 1 1/2) (+.f64 (sqrt.f64 (+.f64 2 x)) -1)))
(sqrt.f64 (+.f64 2 x))
(+.f64 (*.f64 (pow.f64 1 1/2) (+.f64 (sqrt.f64 (+.f64 2 x)) -1)) (*.f64 (pow.f64 1 1/2) 1))
(sqrt.f64 (+.f64 2 x))
(+.f64 (*.f64 (pow.f64 1 1/2) (+.f64 1 (sqrt.f64 (+.f64 2 x)))) (*.f64 (pow.f64 1 1/2) -1))
(sqrt.f64 (+.f64 2 x))
(+.f64 (*.f64 (pow.f64 1 1/2) -1) (*.f64 (pow.f64 1 1/2) (+.f64 1 (sqrt.f64 (+.f64 2 x)))))
(sqrt.f64 (+.f64 2 x))
(*.f64 1 (sqrt.f64 (+.f64 2 x)))
(sqrt.f64 (+.f64 2 x))
(*.f64 (sqrt.f64 (+.f64 2 x)) 1)
(sqrt.f64 (+.f64 2 x))
(*.f64 (sqrt.f64 (+.f64 2 x)) (pow.f64 1 1/2))
(sqrt.f64 (+.f64 2 x))
(*.f64 (pow.f64 (+.f64 2 x) 1/4) (pow.f64 (+.f64 2 x) 1/4))
(sqrt.f64 (+.f64 2 x))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 x))) (cbrt.f64 (+.f64 2 x)))
(*.f64 (cbrt.f64 (+.f64 2 x)) (cbrt.f64 (sqrt.f64 (+.f64 2 x))))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 x))) (cbrt.f64 (+.f64 2 x)))
(*.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1) (/.f64 1 (+.f64 2 (sqrt.f64 (+.f64 2 x)))))
(sqrt.f64 (+.f64 2 x))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x))))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (+.f64 2 (sqrt.f64 (+.f64 2 x)))) (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)) (+.f64 (sqrt.f64 (+.f64 2 x)) (+.f64 2 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2))))
(/.f64 (-.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)) (-.f64 (-.f64 -2 (sqrt.f64 (+.f64 2 x))) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2)))
(*.f64 (sqrt.f64 (cbrt.f64 (+.f64 2 x))) (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 2 x) 2))))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 2 x) 2))) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 2 x) 2))) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))
(*.f64 (+.f64 1 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4))) (-.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) 1))
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(sqrt.f64 (+.f64 2 x))
(exp.f64 (log.f64 (sqrt.f64 (+.f64 2 x))))
(sqrt.f64 (+.f64 2 x))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 2 x))))
(sqrt.f64 (+.f64 2 x))
(fma.f64 1 (+.f64 1 (sqrt.f64 (+.f64 2 x))) -1)
(sqrt.f64 (+.f64 2 x))
(fma.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) -1)
(*.f64 (+.f64 1 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4))) (+.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) -1))
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) -1)
(sqrt.f64 (+.f64 2 x))

localize10.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(pow.f64 (+.f64 2 x) 3/2)
Compiler

Compiled 20 to 16 computations (20% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(pow.f64 (+.f64 2 x) 3/2)
0.0ms
x
@inf
(pow.f64 (+.f64 2 x) 3/2)
0.0ms
x
@0
(pow.f64 (+.f64 2 x) 3/2)

rewrite69.0ms (1.6%)

Algorithm
1×batch-egg-rewrite
Rules
1512×add-sqr-sqrt
1478×*-un-lft-identity
1400×add-cube-cbrt
1390×add-cbrt-cube
1380×add-exp-log
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0713
115713
2189513
Stop Event
1×node limit
Counts
1 → 16
Calls
Call 1
Inputs
(pow.f64 (+.f64 2 x) 3/2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 2 x) (cbrt.f64 (pow.f64 (+.f64 2 x) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 2 x) 3/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (+.f64 2 x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 2 x) 3/4) (pow.f64 (+.f64 2 x) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 2 x) 3/2)) (+.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 3/2) (pow.f64 (+.f64 2 x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 2 x)) 3/2) (pow.f64 (sqrt.f64 (+.f64 2 x)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 2 x)) 2) 3/2) (pow.f64 (cbrt.f64 (+.f64 2 x)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 2 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (+.f64 2 x) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (+.f64 2 x) 3/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (+.f64 2 x) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 3/2 (log.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3/2 (log.f64 (+.f64 2 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (+.f64 2 x) 3/2)))))))

simplify82.0ms (1.9%)

Algorithm
1×egg-herbie
Rules
1404×fma-def
910×unswap-sqr
750×*-commutative
638×times-frac
574×distribute-lft-in
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0951152
12301052
2579824
31813694
46827678
Stop Event
1×node limit
Counts
28 → 76
Calls
Call 1
Inputs
(sqrt.f64 8)
(+.f64 (*.f64 3/4 (*.f64 (sqrt.f64 8) x)) (sqrt.f64 8))
(+.f64 (*.f64 3/4 (*.f64 (sqrt.f64 8) x)) (+.f64 (*.f64 3/32 (*.f64 (sqrt.f64 8) (pow.f64 x 2))) (sqrt.f64 8)))
(+.f64 (*.f64 -1/128 (*.f64 (sqrt.f64 8) (pow.f64 x 3))) (+.f64 (*.f64 3/4 (*.f64 (sqrt.f64 8) x)) (+.f64 (*.f64 3/32 (*.f64 (sqrt.f64 8) (pow.f64 x 2))) (sqrt.f64 8))))
(sqrt.f64 (pow.f64 x 3))
(+.f64 (*.f64 3 (sqrt.f64 x)) (sqrt.f64 (pow.f64 x 3)))
(+.f64 (*.f64 3 (sqrt.f64 x)) (+.f64 (sqrt.f64 (pow.f64 x 3)) (*.f64 3/2 (sqrt.f64 (/.f64 1 x)))))
(+.f64 (*.f64 3 (sqrt.f64 x)) (+.f64 (sqrt.f64 (pow.f64 x 3)) (+.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/2 (sqrt.f64 (/.f64 1 x))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(+.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 3 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (*.f64 3 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(+.f64 (*.f64 -1/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (*.f64 3 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))))
(-.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) 1)
(*.f64 (+.f64 2 x) (cbrt.f64 (pow.f64 (+.f64 2 x) 3/2)))
(*.f64 (pow.f64 (+.f64 2 x) 3/2) 1)
(*.f64 1 (pow.f64 (+.f64 2 x) 3/2))
(*.f64 (pow.f64 (+.f64 2 x) 3/4) (pow.f64 (+.f64 2 x) 3/4))
(*.f64 (cbrt.f64 (pow.f64 (+.f64 2 x) 3/2)) (+.f64 2 x))
(*.f64 (pow.f64 1 3/2) (pow.f64 (+.f64 2 x) 3/2))
(*.f64 (pow.f64 (sqrt.f64 (+.f64 2 x)) 3/2) (pow.f64 (sqrt.f64 (+.f64 2 x)) 3/2))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 2 x)) 2) 3/2) (pow.f64 (cbrt.f64 (+.f64 2 x)) 3/2))
(sqrt.f64 (pow.f64 (+.f64 2 x) 3))
(log.f64 (exp.f64 (pow.f64 (+.f64 2 x) 3/2)))
(cbrt.f64 (pow.f64 (pow.f64 (+.f64 2 x) 3/2) 3))
(expm1.f64 (log1p.f64 (pow.f64 (+.f64 2 x) 3/2)))
(exp.f64 (*.f64 3/2 (log.f64 (+.f64 2 x))))
(exp.f64 (*.f64 (*.f64 3/2 (log.f64 (+.f64 2 x))) 1))
(log1p.f64 (expm1.f64 (pow.f64 (+.f64 2 x) 3/2)))
Outputs
(sqrt.f64 8)
(+.f64 (*.f64 3/4 (*.f64 (sqrt.f64 8) x)) (sqrt.f64 8))
(fma.f64 3/4 (*.f64 (sqrt.f64 8) x) (sqrt.f64 8))
(*.f64 (+.f64 (*.f64 3/4 x) 1) (sqrt.f64 8))
(*.f64 (sqrt.f64 8) (fma.f64 3/4 x 1))
(+.f64 (*.f64 3/4 (*.f64 (sqrt.f64 8) x)) (+.f64 (*.f64 3/32 (*.f64 (sqrt.f64 8) (pow.f64 x 2))) (sqrt.f64 8)))
(fma.f64 3/4 (*.f64 (sqrt.f64 8) x) (fma.f64 3/32 (*.f64 (sqrt.f64 8) (*.f64 x x)) (sqrt.f64 8)))
(+.f64 (sqrt.f64 8) (*.f64 (sqrt.f64 8) (+.f64 (*.f64 3/4 x) (*.f64 x (*.f64 x 3/32)))))
(fma.f64 (sqrt.f64 8) (*.f64 x (+.f64 3/4 (*.f64 x 3/32))) (sqrt.f64 8))
(*.f64 (+.f64 (*.f64 x (+.f64 3/4 (*.f64 x 3/32))) 1) (sqrt.f64 8))
(+.f64 (*.f64 -1/128 (*.f64 (sqrt.f64 8) (pow.f64 x 3))) (+.f64 (*.f64 3/4 (*.f64 (sqrt.f64 8) x)) (+.f64 (*.f64 3/32 (*.f64 (sqrt.f64 8) (pow.f64 x 2))) (sqrt.f64 8))))
(fma.f64 -1/128 (*.f64 (sqrt.f64 8) (pow.f64 x 3)) (fma.f64 3/4 (*.f64 (sqrt.f64 8) x) (fma.f64 3/32 (*.f64 (sqrt.f64 8) (*.f64 x x)) (sqrt.f64 8))))
(+.f64 (fma.f64 (sqrt.f64 8) (*.f64 x (*.f64 x 3/32)) (sqrt.f64 8)) (*.f64 (sqrt.f64 8) (+.f64 (*.f64 3/4 x) (*.f64 -1/128 (pow.f64 x 3)))))
(fma.f64 (sqrt.f64 8) (*.f64 x (+.f64 3/4 (*.f64 x 3/32))) (*.f64 (sqrt.f64 8) (fma.f64 -1/128 (pow.f64 x 3) 1)))
(*.f64 (sqrt.f64 8) (+.f64 (fma.f64 3/4 x 1) (*.f64 (*.f64 x x) (+.f64 3/32 (*.f64 x -1/128)))))
(sqrt.f64 (pow.f64 x 3))
(pow.f64 x 3/2)
(+.f64 (*.f64 3 (sqrt.f64 x)) (sqrt.f64 (pow.f64 x 3)))
(fma.f64 3 (sqrt.f64 x) (sqrt.f64 (pow.f64 x 3)))
(fma.f64 3 (sqrt.f64 x) (pow.f64 x 3/2))
(*.f64 (sqrt.f64 x) (+.f64 3 x))
(+.f64 (*.f64 3 (sqrt.f64 x)) (+.f64 (sqrt.f64 (pow.f64 x 3)) (*.f64 3/2 (sqrt.f64 (/.f64 1 x)))))
(+.f64 (fma.f64 3 (sqrt.f64 x) (sqrt.f64 (pow.f64 x 3))) (*.f64 3/2 (sqrt.f64 (/.f64 1 x))))
(fma.f64 3 (sqrt.f64 x) (fma.f64 3/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 (pow.f64 x 3))))
(fma.f64 3 (sqrt.f64 x) (fma.f64 3/2 (sqrt.f64 (/.f64 1 x)) (pow.f64 x 3/2)))
(fma.f64 3/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 x) (+.f64 3 x)))
(+.f64 (*.f64 3 (sqrt.f64 x)) (+.f64 (sqrt.f64 (pow.f64 x 3)) (+.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/2 (sqrt.f64 (/.f64 1 x))))))
(+.f64 (fma.f64 3 (sqrt.f64 x) (sqrt.f64 (pow.f64 x 3))) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 3/2 (sqrt.f64 (/.f64 1 x)))))
(+.f64 (fma.f64 3 (sqrt.f64 x) (sqrt.f64 (pow.f64 x 3))) (fma.f64 3/2 (sqrt.f64 (/.f64 1 x)) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(fma.f64 3 (sqrt.f64 x) (fma.f64 3/2 (sqrt.f64 (/.f64 1 x)) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (pow.f64 x 3/2))))
(fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 3 (sqrt.f64 x) (fma.f64 3/2 (sqrt.f64 (/.f64 1 x)) (pow.f64 x 3/2))))
(fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 3/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 x) (+.f64 3 x))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))
(*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))
(pow.f64 (exp.f64 3/2) (log.f64 x))
(+.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 3 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 3 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x)))
(fma.f64 3 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(fma.f64 3 (/.f64 (pow.f64 (/.f64 -1 x) -3/2) (/.f64 x (pow.f64 -1 3/2))) (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)))
(*.f64 (+.f64 (/.f64 3 x) 1) (pow.f64 (exp.f64 3/2) (log.f64 x)))
(*.f64 (+.f64 1 (/.f64 3 x)) (pow.f64 (exp.f64 3/2) (log.f64 x)))
(+.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (*.f64 3 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(+.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x)) (*.f64 3 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x))))
(+.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (fma.f64 3 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (*.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)))))
(fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) (*.f64 (/.f64 (pow.f64 (/.f64 -1 x) -3/2) (/.f64 x (pow.f64 -1 3/2))) (+.f64 3 (/.f64 3/2 x))))
(fma.f64 (/.f64 (pow.f64 (exp.f64 3/2) (log.f64 x)) x) (+.f64 3 (/.f64 3/2 x)) (pow.f64 (exp.f64 3/2) (log.f64 x)))
(*.f64 (pow.f64 (exp.f64 3/2) (log.f64 x)) (+.f64 (/.f64 3 x) (+.f64 1 (/.f64 (/.f64 3/2 x) x))))
(+.f64 (*.f64 -1/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (*.f64 3 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))))
(fma.f64 -1/2 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 3)) (+.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x)) (*.f64 3 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x)))))
(+.f64 (fma.f64 3 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (*.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)))) (fma.f64 -1/2 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)) (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))
(fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) (fma.f64 -1/2 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) (pow.f64 x 3)) (*.f64 (/.f64 (pow.f64 (/.f64 -1 x) -3/2) (/.f64 x (pow.f64 -1 3/2))) (+.f64 3 (/.f64 3/2 x)))))
(+.f64 (pow.f64 (exp.f64 3/2) (log.f64 x)) (*.f64 (/.f64 (pow.f64 (exp.f64 3/2) (log.f64 x)) x) (+.f64 (/.f64 3/2 x) (+.f64 3 (/.f64 -1/2 (*.f64 x x))))))
(-.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) 1)
(+.f64 1 (-.f64 (pow.f64 (+.f64 x 2) 3/2) 1))
(+.f64 (pow.f64 (+.f64 x 2) 3/2) 0)
(pow.f64 (+.f64 x 2) 3/2)
(*.f64 (+.f64 2 x) (cbrt.f64 (pow.f64 (+.f64 2 x) 3/2)))
(*.f64 (+.f64 x 2) (cbrt.f64 (pow.f64 (+.f64 x 2) 3/2)))
(*.f64 (pow.f64 (+.f64 2 x) 3/2) 1)
(+.f64 1 (-.f64 (pow.f64 (+.f64 x 2) 3/2) 1))
(+.f64 (pow.f64 (+.f64 x 2) 3/2) 0)
(pow.f64 (+.f64 x 2) 3/2)
(*.f64 1 (pow.f64 (+.f64 2 x) 3/2))
(+.f64 1 (-.f64 (pow.f64 (+.f64 x 2) 3/2) 1))
(+.f64 (pow.f64 (+.f64 x 2) 3/2) 0)
(pow.f64 (+.f64 x 2) 3/2)
(*.f64 (pow.f64 (+.f64 2 x) 3/4) (pow.f64 (+.f64 2 x) 3/4))
(+.f64 1 (-.f64 (pow.f64 (+.f64 x 2) 3/2) 1))
(+.f64 (pow.f64 (+.f64 x 2) 3/2) 0)
(pow.f64 (+.f64 x 2) 3/2)
(*.f64 (cbrt.f64 (pow.f64 (+.f64 2 x) 3/2)) (+.f64 2 x))
(*.f64 (+.f64 x 2) (cbrt.f64 (pow.f64 (+.f64 x 2) 3/2)))
(*.f64 (pow.f64 1 3/2) (pow.f64 (+.f64 2 x) 3/2))
(+.f64 1 (-.f64 (pow.f64 (+.f64 x 2) 3/2) 1))
(+.f64 (pow.f64 (+.f64 x 2) 3/2) 0)
(pow.f64 (+.f64 x 2) 3/2)
(*.f64 (pow.f64 (sqrt.f64 (+.f64 2 x)) 3/2) (pow.f64 (sqrt.f64 (+.f64 2 x)) 3/2))
(pow.f64 (sqrt.f64 (+.f64 x 2)) 3)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 2 x)) 2) 3/2) (pow.f64 (cbrt.f64 (+.f64 2 x)) 3/2))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 2)) 2) 3/2) (pow.f64 (cbrt.f64 (+.f64 x 2)) 3/2))
(sqrt.f64 (pow.f64 (+.f64 2 x) 3))
(+.f64 1 (-.f64 (pow.f64 (+.f64 x 2) 3/2) 1))
(+.f64 (pow.f64 (+.f64 x 2) 3/2) 0)
(pow.f64 (+.f64 x 2) 3/2)
(log.f64 (exp.f64 (pow.f64 (+.f64 2 x) 3/2)))
(+.f64 1 (-.f64 (pow.f64 (+.f64 x 2) 3/2) 1))
(+.f64 (pow.f64 (+.f64 x 2) 3/2) 0)
(pow.f64 (+.f64 x 2) 3/2)
(cbrt.f64 (pow.f64 (pow.f64 (+.f64 2 x) 3/2) 3))
(+.f64 1 (-.f64 (pow.f64 (+.f64 x 2) 3/2) 1))
(+.f64 (pow.f64 (+.f64 x 2) 3/2) 0)
(pow.f64 (+.f64 x 2) 3/2)
(expm1.f64 (log1p.f64 (pow.f64 (+.f64 2 x) 3/2)))
(+.f64 1 (-.f64 (pow.f64 (+.f64 x 2) 3/2) 1))
(+.f64 (pow.f64 (+.f64 x 2) 3/2) 0)
(pow.f64 (+.f64 x 2) 3/2)
(exp.f64 (*.f64 3/2 (log.f64 (+.f64 2 x))))
(+.f64 1 (-.f64 (pow.f64 (+.f64 x 2) 3/2) 1))
(+.f64 (pow.f64 (+.f64 x 2) 3/2) 0)
(pow.f64 (+.f64 x 2) 3/2)
(exp.f64 (*.f64 (*.f64 3/2 (log.f64 (+.f64 2 x))) 1))
(+.f64 1 (-.f64 (pow.f64 (+.f64 x 2) 3/2) 1))
(+.f64 (pow.f64 (+.f64 x 2) 3/2) 0)
(pow.f64 (+.f64 x 2) 3/2)
(log1p.f64 (expm1.f64 (pow.f64 (+.f64 2 x) 3/2)))
(+.f64 1 (-.f64 (pow.f64 (+.f64 x 2) 3/2) 1))
(+.f64 (pow.f64 (+.f64 x 2) 3/2) 0)
(pow.f64 (+.f64 x 2) 3/2)

eval234.0ms (5.3%)

Compiler

Compiled 7006 to 6092 computations (13% saved)

prune70.0ms (1.6%)

Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New3061307
Fresh000
Picked011
Done134
Total3075312
Error
0b
Counts
312 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
✓19.2b
(pow.f64 (pow.f64 (+.f64 2 x) 3/2) 1/3)
▶16.3b
(-.f64 (+.f64 1 (sqrt.f64 2)) 1)
✓0.0b
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
✓19.2b
(sqrt.f64 (+.f64 2 x))
✓15.6b
(sqrt.f64 2)
Compiler

Compiled 29 to 26 computations (10.3% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓1.0b
(-.f64 (+.f64 1 (sqrt.f64 2)) 1)
Compiler

Compiled 15 to 15 computations (0% saved)

series0.0ms (0%)

Counts
1 → 0

rewrite54.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
1504×add-sqr-sqrt
1480×*-un-lft-identity
1398×add-cube-cbrt
1386×add-cbrt-cube
1378×add-exp-log
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0817
11745
221985
Stop Event
1×node limit
Counts
1 → 40
Calls
Call 1
Inputs
(-.f64 (+.f64 1 (sqrt.f64 2)) 1)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (sqrt.f64 2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (+.f64 (sqrt.f64 2) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (sqrt.f64 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (sqrt.f64 2) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 1 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 1/4) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (sqrt.f64 2) 2) (sqrt.f64 2)) (/.f64 1 (+.f64 (sqrt.f64 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (+.f64 (sqrt.f64 2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (hypot.f64 1 (pow.f64 2 1/4)) 1) (-.f64 (hypot.f64 1 (pow.f64 2 1/4)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (sqrt.f64 2) 2) (*.f64 (+.f64 (sqrt.f64 2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (+.f64 (sqrt.f64 2) 2)) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (sqrt.f64 2) 2) (sqrt.f64 2)) (+.f64 (sqrt.f64 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (sqrt.f64 2) 2) (sqrt.f64 2)) (-.f64 (+.f64 1 (sqrt.f64 2)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (+.f64 (sqrt.f64 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (-.f64 1 (*.f64 (+.f64 1 (sqrt.f64 2)) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (+.f64 (sqrt.f64 2) -1) (+.f64 (sqrt.f64 2) -1))) (-.f64 1 (+.f64 (sqrt.f64 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 (sqrt.f64 2) -1) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 (sqrt.f64 2) -1) (+.f64 (sqrt.f64 2) -1)) (+.f64 (sqrt.f64 2) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (+.f64 (sqrt.f64 2) 2) (sqrt.f64 2))) (neg.f64 (+.f64 (sqrt.f64 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (+.f64 (sqrt.f64 2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 2 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 2 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 2 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 2)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 2 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 (sqrt.f64 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (pow.f64 2 1/4)) (hypot.f64 1 (pow.f64 2 1/4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 2))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 2))) -1)))))

simplify41.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
1428×associate-*r*
1244×associate-*l*
980×distribute-lft-in
978×fma-def
792×distribute-rgt-in
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
097748
1240682
21050640
Stop Event
1×node limit
Counts
40 → 48
Calls
Call 1
Inputs
(+.f64 1 (+.f64 (sqrt.f64 2) -1))
(+.f64 1 (*.f64 (+.f64 (sqrt.f64 2) -1) 1))
(+.f64 (+.f64 1 (sqrt.f64 2)) -1)
(+.f64 (sqrt.f64 2) 0)
(+.f64 (+.f64 (sqrt.f64 2) -1) 1)
(+.f64 -1 (+.f64 1 (sqrt.f64 2)))
(*.f64 1 (sqrt.f64 2))
(*.f64 (sqrt.f64 2) 1)
(*.f64 (pow.f64 2 1/4) (pow.f64 2 1/4))
(*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 2))
(*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2)))
(*.f64 (*.f64 (+.f64 (sqrt.f64 2) 2) (sqrt.f64 2)) (/.f64 1 (+.f64 (sqrt.f64 2) 2)))
(*.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (+.f64 (sqrt.f64 2) 2))))
(*.f64 (+.f64 (hypot.f64 1 (pow.f64 2 1/4)) 1) (-.f64 (hypot.f64 1 (pow.f64 2 1/4)) 1))
(/.f64 1 (/.f64 (+.f64 (sqrt.f64 2) 2) (*.f64 (+.f64 (sqrt.f64 2) 2) (sqrt.f64 2))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (+.f64 (sqrt.f64 2) 2)) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1)))
(/.f64 (*.f64 (+.f64 (sqrt.f64 2) 2) (sqrt.f64 2)) (+.f64 (sqrt.f64 2) 2))
(/.f64 (*.f64 (+.f64 (sqrt.f64 2) 2) (sqrt.f64 2)) (-.f64 (+.f64 1 (sqrt.f64 2)) -1))
(/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (+.f64 (sqrt.f64 2) 2)))
(/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (-.f64 1 (*.f64 (+.f64 1 (sqrt.f64 2)) -1))))
(/.f64 (-.f64 1 (*.f64 (+.f64 (sqrt.f64 2) -1) (+.f64 (sqrt.f64 2) -1))) (-.f64 1 (+.f64 (sqrt.f64 2) -1)))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (sqrt.f64 2) -1) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 (sqrt.f64 2) -1) (+.f64 (sqrt.f64 2) -1)) (+.f64 (sqrt.f64 2) -1))))
(/.f64 (neg.f64 (*.f64 (+.f64 (sqrt.f64 2) 2) (sqrt.f64 2))) (neg.f64 (+.f64 (sqrt.f64 2) 2)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (+.f64 (sqrt.f64 2) 2))))
(pow.f64 2 1/2)
(pow.f64 (sqrt.f64 2) 1)
(pow.f64 (pow.f64 2 1/4) 2)
(pow.f64 (cbrt.f64 (sqrt.f64 2)) 3)
(pow.f64 (pow.f64 2 3/2) 1/3)
(sqrt.f64 2)
(log.f64 (exp.f64 (sqrt.f64 2)))
(cbrt.f64 (pow.f64 2 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 2)))
(exp.f64 (log.f64 (sqrt.f64 2)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1))
(exp.f64 (*.f64 (log.f64 2) 1/2))
(log1p.f64 (expm1.f64 (sqrt.f64 2)))
(fma.f64 1 (+.f64 1 (sqrt.f64 2)) -1)
(fma.f64 (hypot.f64 1 (pow.f64 2 1/4)) (hypot.f64 1 (pow.f64 2 1/4)) -1)
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 2))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 2))) -1)
Outputs
(+.f64 1 (+.f64 (sqrt.f64 2) -1))
(sqrt.f64 2)
(+.f64 1 (*.f64 (+.f64 (sqrt.f64 2) -1) 1))
(sqrt.f64 2)
(+.f64 (+.f64 1 (sqrt.f64 2)) -1)
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) 0)
(sqrt.f64 2)
(+.f64 (+.f64 (sqrt.f64 2) -1) 1)
(sqrt.f64 2)
(+.f64 -1 (+.f64 1 (sqrt.f64 2)))
(sqrt.f64 2)
(*.f64 1 (sqrt.f64 2))
(sqrt.f64 2)
(*.f64 (sqrt.f64 2) 1)
(sqrt.f64 2)
(*.f64 (pow.f64 2 1/4) (pow.f64 2 1/4))
(sqrt.f64 2)
(*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 2))
(*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2)))
(*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 2))
(*.f64 (*.f64 (+.f64 (sqrt.f64 2) 2) (sqrt.f64 2)) (/.f64 1 (+.f64 (sqrt.f64 2) 2)))
(sqrt.f64 2)
(*.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (+.f64 (sqrt.f64 2) 2))))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (/.f64 1 (+.f64 (+.f64 2 (sqrt.f64 2)) (pow.f64 (+.f64 1 (sqrt.f64 2)) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (+.f64 2 (+.f64 (sqrt.f64 2) (pow.f64 (+.f64 1 (sqrt.f64 2)) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (+.f64 (+.f64 2 (pow.f64 2 3/2)) (+.f64 (sqrt.f64 2) 3)))
(*.f64 (+.f64 (hypot.f64 1 (pow.f64 2 1/4)) 1) (-.f64 (hypot.f64 1 (pow.f64 2 1/4)) 1))
(*.f64 (+.f64 1 (hypot.f64 1 (pow.f64 2 1/4))) (+.f64 (hypot.f64 1 (pow.f64 2 1/4)) -1))
(fma.f64 (hypot.f64 1 (pow.f64 2 1/4)) (hypot.f64 1 (pow.f64 2 1/4)) -1)
(/.f64 1 (/.f64 (+.f64 (sqrt.f64 2) 2) (*.f64 (+.f64 (sqrt.f64 2) 2) (sqrt.f64 2))))
(sqrt.f64 2)
(/.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (+.f64 (sqrt.f64 2) 2)) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1)))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (/.f64 1 (+.f64 (+.f64 2 (sqrt.f64 2)) (pow.f64 (+.f64 1 (sqrt.f64 2)) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (+.f64 2 (+.f64 (sqrt.f64 2) (pow.f64 (+.f64 1 (sqrt.f64 2)) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (+.f64 (+.f64 2 (pow.f64 2 3/2)) (+.f64 (sqrt.f64 2) 3)))
(/.f64 (*.f64 (+.f64 (sqrt.f64 2) 2) (sqrt.f64 2)) (+.f64 (sqrt.f64 2) 2))
(sqrt.f64 2)
(/.f64 (*.f64 (+.f64 (sqrt.f64 2) 2) (sqrt.f64 2)) (-.f64 (+.f64 1 (sqrt.f64 2)) -1))
(sqrt.f64 2)
(/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (+.f64 (sqrt.f64 2) 2)))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (/.f64 1 (+.f64 (+.f64 2 (sqrt.f64 2)) (pow.f64 (+.f64 1 (sqrt.f64 2)) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (+.f64 2 (+.f64 (sqrt.f64 2) (pow.f64 (+.f64 1 (sqrt.f64 2)) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (+.f64 (+.f64 2 (pow.f64 2 3/2)) (+.f64 (sqrt.f64 2) 3)))
(/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (-.f64 1 (*.f64 (+.f64 1 (sqrt.f64 2)) -1))))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (/.f64 1 (+.f64 (+.f64 2 (sqrt.f64 2)) (pow.f64 (+.f64 1 (sqrt.f64 2)) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (+.f64 2 (+.f64 (sqrt.f64 2) (pow.f64 (+.f64 1 (sqrt.f64 2)) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (+.f64 (+.f64 2 (pow.f64 2 3/2)) (+.f64 (sqrt.f64 2) 3)))
(/.f64 (-.f64 1 (*.f64 (+.f64 (sqrt.f64 2) -1) (+.f64 (sqrt.f64 2) -1))) (-.f64 1 (+.f64 (sqrt.f64 2) -1)))
(/.f64 (+.f64 1 (*.f64 (+.f64 (sqrt.f64 2) -1) (-.f64 1 (sqrt.f64 2)))) (-.f64 2 (sqrt.f64 2)))
(/.f64 (+.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 2) -2)) (-.f64 2 (sqrt.f64 2)))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (sqrt.f64 2) -1) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 (sqrt.f64 2) -1) (+.f64 (sqrt.f64 2) -1)) (+.f64 (sqrt.f64 2) -1))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (sqrt.f64 2) -1) 3)) (+.f64 1 (*.f64 (+.f64 (sqrt.f64 2) -1) (-.f64 (+.f64 (sqrt.f64 2) -1) 1))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (sqrt.f64 2) -1) 3)) (fma.f64 (+.f64 (sqrt.f64 2) -1) (+.f64 (sqrt.f64 2) -2) 1))
(/.f64 (neg.f64 (*.f64 (+.f64 (sqrt.f64 2) 2) (sqrt.f64 2))) (neg.f64 (+.f64 (sqrt.f64 2) 2)))
(sqrt.f64 2)
(/.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (+.f64 (sqrt.f64 2) 2))))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (/.f64 1 (+.f64 (+.f64 2 (sqrt.f64 2)) (pow.f64 (+.f64 1 (sqrt.f64 2)) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (+.f64 2 (+.f64 (sqrt.f64 2) (pow.f64 (+.f64 1 (sqrt.f64 2)) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (+.f64 (+.f64 2 (pow.f64 2 3/2)) (+.f64 (sqrt.f64 2) 3)))
(pow.f64 2 1/2)
(sqrt.f64 2)
(pow.f64 (sqrt.f64 2) 1)
(sqrt.f64 2)
(pow.f64 (pow.f64 2 1/4) 2)
(sqrt.f64 2)
(pow.f64 (cbrt.f64 (sqrt.f64 2)) 3)
(sqrt.f64 2)
(pow.f64 (pow.f64 2 3/2) 1/3)
(cbrt.f64 (pow.f64 2 3/2))
(sqrt.f64 2)
(log.f64 (exp.f64 (sqrt.f64 2)))
(sqrt.f64 2)
(cbrt.f64 (pow.f64 2 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 2)))
(sqrt.f64 2)
(exp.f64 (log.f64 (sqrt.f64 2)))
(sqrt.f64 2)
(exp.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1))
(sqrt.f64 2)
(exp.f64 (*.f64 (log.f64 2) 1/2))
(sqrt.f64 2)
(log1p.f64 (expm1.f64 (sqrt.f64 2)))
(sqrt.f64 2)
(fma.f64 1 (+.f64 1 (sqrt.f64 2)) -1)
(sqrt.f64 2)
(fma.f64 (hypot.f64 1 (pow.f64 2 1/4)) (hypot.f64 1 (pow.f64 2 1/4)) -1)
(*.f64 (+.f64 1 (hypot.f64 1 (pow.f64 2 1/4))) (+.f64 (hypot.f64 1 (pow.f64 2 1/4)) -1))
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 2))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 2))) -1)
(sqrt.f64 2)

eval13.0ms (0.3%)

Compiler

Compiled 533 to 533 computations (0% saved)

prune18.0ms (0.4%)

Pruning

5 alts after pruning (0 fresh and 5 done)

PrunedKeptTotal
New48048
Fresh000
Picked011
Done044
Total48553
Error
0b
Counts
53 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
✓19.2b
(pow.f64 (pow.f64 (+.f64 2 x) 3/2) 1/3)
✓16.3b
(-.f64 (+.f64 1 (sqrt.f64 2)) 1)
✓0.0b
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
✓19.2b
(sqrt.f64 (+.f64 2 x))
✓15.6b
(sqrt.f64 2)
Compiler

Compiled 29 to 26 computations (10.3% saved)

regimes12.0ms (0.3%)

Counts
10 → 1
Calls
Call 1
Inputs
(sqrt.f64 2)
(sqrt.f64 (+.f64 2 x))
(-.f64 (+.f64 1 (sqrt.f64 2)) 1)
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(pow.f64 (pow.f64 (+.f64 2 x) 3/2) 1/3)
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
Outputs
(sqrt.f64 (+.f64 2 (expm1.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
ErrorSegmentsBranch
0.0b1x
0.0b1(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
0.0b1(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
Compiler

Compiled 91 to 72 computations (20.9% saved)

regimes28.0ms (0.6%)

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

1 calls:

27.0ms
x
Results
ErrorSegmentsBranch
0.0b1x
Compiler

Compiled 28 to 24 computations (14.3% saved)

regimes5.0ms (0.1%)

Accuracy

Total -4.6b remaining (-29.6%)

Threshold costs -4.6b (-29.6%)

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

1 calls:

4.0ms
x
Results
ErrorSegmentsBranch
15.6b1x
Compiler

Compiled 23 to 20 computations (13% saved)

simplify4.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01335
11735
Stop Event
1×done
1×saturated
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 2)
Outputs
(sqrt.f64 (+.f64 2 (expm1.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 2)
Compiler

Compiled 15 to 13 computations (13.3% saved)

soundness183.0ms (4.2%)

Algorithm
2×egg-herbie
Rules
1440×associate-/l*
1420×associate-/l*
1382×associate-*r*
1160×associate-/r*
1052×distribute-lft-in
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01325
12725
23625
36225
413521
534915
6123815
01602019
13841767
213171463
336441417
Stop Event
1×node limit
1×node limit
Compiler

Compiled 178 to 117 computations (34.3% saved)

end19.0ms (0.4%)

Compiler

Compiled 13 to 11 computations (15.4% saved)

Profiling

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