Details

Time bar (total: 4.7s)

analyze210.0ms (4.5%)

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)

sample2.2s (47.7%)

Results
1.3s2805×body1024valid
516.0ms3857×body256valid
277.0ms1328×body512valid
120.0ms266×body2048valid
5.0ms46×body256infinite
0.0ms3×body256unsamplable
Bogosity

preprocess75.0ms (1.6%)

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)

simplify34.0ms (0.7%)

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

Useful iterations: 5 (0.0ms)

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

eval1.0ms (0%)

Compiler

Compiled 41 to 29 computations (29.3% saved)

prune16.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New325
Fresh101
Picked000
Done000
Total426
Error
0.01%
Counts
6 → 2
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.02%
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
▶0.02%
(sqrt.f64 (+.f64 1 (exp.f64 x)))
Compiler

Compiled 15 to 11 computations (26.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.01%
(+.f64 1 (exp.f64 x))
✓0.02%
(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 (1.3%)

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)))))

simplify64.0ms (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))

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.01%
(expm1.f64 (+.f64 x x))
✓0.02%
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
✓0.02%
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
Compiler

Compiled 26 to 6 computations (76.9% saved)

series2.0ms (0.1%)

Counts
3 → 36
Calls

9 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
@0
(expm1.f64 (+.f64 x x))

rewrite73.0ms (1.6%)

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
0957
118657
2251857
Stop Event
1×node limit
Counts
3 → 89
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(expm1.f64 (+.f64 x 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))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (exp.f64 2) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (exp.f64 2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 (+.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (expm1.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (cbrt.f64 (expm1.f64 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (pow.f64 (exp.f64 2) x) (pow.f64 (exp.f64 2) x)) 1) (+.f64 (pow.f64 (exp.f64 2) x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 2) x) 3) 1) (+.f64 (*.f64 (pow.f64 (exp.f64 2) x) (pow.f64 (exp.f64 2) x)) (+.f64 1 (*.f64 (pow.f64 (exp.f64 2) x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (expm1.f64 (+.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (expm1.f64 (+.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (expm1.f64 (+.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (expm1.f64 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (expm1.f64 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (expm1.f64 (+.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (expm1.f64 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (expm1.f64 (+.f64 x x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (expm1.f64 (+.f64 x x))))))))

simplify69.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
1638×associate-*l/
1518×associate-/l*
932×*-commutative
862×associate-/r*
818×distribute-lft-in
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02463349
15743151
226053151
Stop Event
1×node limit
Counts
125 → 144
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 2 x)
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 2 x))
(+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 (*.f64 4/3 (pow.f64 x 3)) (*.f64 2 x)))
(+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 (*.f64 2/3 (pow.f64 x 4)) (+.f64 (*.f64 4/3 (pow.f64 x 3)) (*.f64 2 x))))
(-.f64 (exp.f64 (*.f64 2 x)) 1)
(-.f64 (exp.f64 (*.f64 2 x)) 1)
(-.f64 (exp.f64 (*.f64 2 x)) 1)
(-.f64 (exp.f64 (*.f64 2 x)) 1)
(-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1)
(-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1)
(-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1)
(-.f64 (exp.f64 (neg.f64 (*.f64 -2 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))))
(+.f64 (pow.f64 (exp.f64 2) x) -1)
(-.f64 (pow.f64 (exp.f64 2) x) 1)
(*.f64 (expm1.f64 (+.f64 x x)) 1)
(*.f64 1 (expm1.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 (+.f64 x x))))
(*.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (cbrt.f64 (expm1.f64 (+.f64 x x))))
(/.f64 (-.f64 (*.f64 (pow.f64 (exp.f64 2) x) (pow.f64 (exp.f64 2) x)) 1) (+.f64 (pow.f64 (exp.f64 2) x) 1))
(/.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 2) x) 3) 1) (+.f64 (*.f64 (pow.f64 (exp.f64 2) x) (pow.f64 (exp.f64 2) x)) (+.f64 1 (*.f64 (pow.f64 (exp.f64 2) x) 1))))
(pow.f64 (expm1.f64 (+.f64 x x)) 1)
(pow.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) 2)
(pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 3)
(pow.f64 (pow.f64 (expm1.f64 (+.f64 x x)) 3) 1/3)
(sqrt.f64 (pow.f64 (expm1.f64 (+.f64 x x)) 2))
(log.f64 (exp.f64 (expm1.f64 (+.f64 x x))))
(log.f64 (+.f64 1 (expm1.f64 (expm1.f64 (+.f64 x x)))))
(cbrt.f64 (pow.f64 (expm1.f64 (+.f64 x x)) 3))
(exp.f64 (log.f64 (expm1.f64 (+.f64 x x))))
(exp.f64 (*.f64 (log.f64 (expm1.f64 (+.f64 x x))) 1))
(log1p.f64 (expm1.f64 (expm1.f64 (+.f64 x 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 (+.f64 (/.f64 x (sqrt.f64 2)) (*.f64 (*.f64 x x) (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (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))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (*.f64 (*.f64 x x) (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)))) (*.f64 (/.f64 7/192 (sqrt.f64 2)) (pow.f64 x 3))))
(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 (-.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 2 x)
(+.f64 x x)
(+.f64 (*.f64 2 (pow.f64 x 2)) (*.f64 2 x))
(*.f64 2 (+.f64 (*.f64 x x) x))
(*.f64 2 (fma.f64 x x x))
(+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 (*.f64 4/3 (pow.f64 x 3)) (*.f64 2 x)))
(fma.f64 2 (*.f64 x x) (fma.f64 4/3 (pow.f64 x 3) (+.f64 x x)))
(+.f64 (*.f64 2 (fma.f64 x x x)) (*.f64 (pow.f64 x 3) 4/3))
(+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 (*.f64 2/3 (pow.f64 x 4)) (+.f64 (*.f64 4/3 (pow.f64 x 3)) (*.f64 2 x))))
(fma.f64 2 (*.f64 x x) (fma.f64 2/3 (pow.f64 x 4) (fma.f64 4/3 (pow.f64 x 3) (+.f64 x x))))
(+.f64 (fma.f64 2/3 (pow.f64 x 4) (*.f64 (pow.f64 x 3) 4/3)) (*.f64 2 (fma.f64 x x x)))
(+.f64 (*.f64 2 (fma.f64 x x x)) (fma.f64 2/3 (pow.f64 x 4) (*.f64 (pow.f64 x 3) 4/3)))
(-.f64 (exp.f64 (*.f64 2 x)) 1)
(expm1.f64 (+.f64 x x))
(-.f64 (exp.f64 (*.f64 2 x)) 1)
(expm1.f64 (+.f64 x x))
(-.f64 (exp.f64 (*.f64 2 x)) 1)
(expm1.f64 (+.f64 x x))
(-.f64 (exp.f64 (*.f64 2 x)) 1)
(expm1.f64 (+.f64 x x))
(-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1)
(expm1.f64 (+.f64 x x))
(-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1)
(expm1.f64 (+.f64 x x))
(-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1)
(expm1.f64 (+.f64 x x))
(-.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) 1)
(expm1.f64 (+.f64 x 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))))
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(expm1.f64 (+.f64 x x))
(exp.f64 (log.f64 (expm1.f64 (+.f64 x x))))
(expm1.f64 (+.f64 x x))
(exp.f64 (*.f64 (log.f64 (expm1.f64 (+.f64 x x))) 1))
(expm1.f64 (+.f64 x x))
(log1p.f64 (expm1.f64 (expm1.f64 (+.f64 x x))))
(expm1.f64 (+.f64 x x))

eval64.0ms (1.4%)

Compiler

Compiled 3427 to 1865 computations (45.6% saved)

prune29.0ms (0.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2424246
Fresh000
Picked101
Done011
Total2435248
Error
0%
Counts
248 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
▶34.91%
(sqrt.f64 (/.f64 (*.f64 2 (+.f64 (*.f64 x x) x)) (expm1.f64 x)))
▶34.77%
(sqrt.f64 (+.f64 2 x))
✓0.02%
(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶28.43%
(sqrt.f64 2)
▶0.96%
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
Compiler

Compiled 33 to 26 computations (21.2% saved)

localize12.0ms (0.3%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.02%
(log1p.f64 (exp.f64 x))
✓0.95%
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
Compiler

Compiled 19 to 9 computations (52.6% saved)

series43.0ms (0.9%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
23.0ms
x
@inf
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
19.0ms
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))
0.0ms
x
@0
(log1p.f64 (exp.f64 x))
0.0ms
x
@inf
(log1p.f64 (exp.f64 x))

rewrite60.0ms (1.3%)

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
0928
117224
2187524
Stop Event
1×node limit
Counts
2 → 37
Calls
Call 1
Inputs
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
(log1p.f64 (exp.f64 x))
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))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (log1p.f64 (exp.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log1p.f64 (exp.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log1p.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log1p.f64 (exp.f64 x))) (sqrt.f64 (log1p.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log1p.f64 (exp.f64 x))) (pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 x))) 2) (cbrt.f64 (log1p.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log1p.f64 (exp.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log1p.f64 (exp.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 (exp.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log1p.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log1p.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (log1p.f64 (exp.f64 x))) 1))))))

simplify53.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
1222×distribute-lft-in
1208×distribute-rgt-in
1166×fma-def
766×unswap-sqr
700×*-commutative
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0110987
1242983
2991971
32729935
Stop Event
1×node limit
Counts
61 → 73
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)))
(log.f64 2)
(+.f64 (*.f64 1/2 x) (log.f64 2))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (log.f64 2)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -1/192 (pow.f64 x 4)) (log.f64 2))))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.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))))
(-.f64 (+.f64 1 (log1p.f64 (exp.f64 x))) 1)
(*.f64 (log1p.f64 (exp.f64 x)) 1)
(*.f64 1 (log1p.f64 (exp.f64 x)))
(*.f64 (sqrt.f64 (log1p.f64 (exp.f64 x))) (sqrt.f64 (log1p.f64 (exp.f64 x))))
(*.f64 (cbrt.f64 (log1p.f64 (exp.f64 x))) (pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 x))) 2) (cbrt.f64 (log1p.f64 (exp.f64 x))))
(pow.f64 (log1p.f64 (exp.f64 x)) 1)
(pow.f64 (sqrt.f64 (log1p.f64 (exp.f64 x))) 2)
(pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 x))) 3)
(pow.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) 1/3)
(sqrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 2))
(log.f64 (+.f64 (exp.f64 x) 1))
(cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3))
(expm1.f64 (log1p.f64 (log1p.f64 (exp.f64 x))))
(exp.f64 (log.f64 (log1p.f64 (exp.f64 x))))
(exp.f64 (*.f64 (log.f64 (log1p.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 (sqrt.f64 2) (fma.f64 1/4 x 1))
(+.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 (sqrt.f64 2) (*.f64 (*.f64 x x) 3/32))))
(+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 1/4 x) (*.f64 3/32 (*.f64 x x)))))
(fma.f64 (sqrt.f64 2) (fma.f64 3/32 (*.f64 x x) (*.f64 1/4 x)) (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 (fma.f64 (sqrt.f64 2) (*.f64 1/4 x) (sqrt.f64 2)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 3/32 (*.f64 x x)) (*.f64 7/384 (pow.f64 x 3)))))
(fma.f64 (sqrt.f64 2) (fma.f64 7/384 (pow.f64 x 3) (*.f64 3/32 (*.f64 x x))) (*.f64 (sqrt.f64 2) (fma.f64 1/4 x 1)))
(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)))
(log.f64 2)
(+.f64 (*.f64 1/2 x) (log.f64 2))
(fma.f64 1/2 x (log.f64 2))
(fma.f64 x 1/2 (log.f64 2))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (log.f64 2)))
(fma.f64 1/8 (*.f64 x x) (fma.f64 1/2 x (log.f64 2)))
(fma.f64 (*.f64 x x) 1/8 (fma.f64 x 1/2 (log.f64 2)))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x 1/8) (log.f64 2)))
(fma.f64 x (fma.f64 x 1/8 1/2) (log.f64 2))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -1/192 (pow.f64 x 4)) (log.f64 2))))
(fma.f64 1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 -1/192 (pow.f64 x 4) (log.f64 2))))
(fma.f64 (*.f64 x x) 1/8 (fma.f64 x 1/2 (fma.f64 -1/192 (pow.f64 x 4) (log.f64 2))))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x 1/8) (fma.f64 -1/192 (pow.f64 x 4) (log.f64 2))))
(fma.f64 x (fma.f64 x 1/8 1/2) (fma.f64 -1/192 (pow.f64 x 4) (log.f64 2)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(+.f64 1 (expm1.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)))
(+.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x)))))
(-.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 (sqrt.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x))))) (sqrt.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x)))))
(pow.f64 (exp.f64 1) (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
(pow.f64 (E.f64) (*.f64 1/2 (log1p.f64 (exp.f64 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)))
(pow.f64 (exp.f64 (cbrt.f64 (*.f64 1/4 (pow.f64 (log1p.f64 (exp.f64 x)) 2)))) (cbrt.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x)))))
(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)))
(-.f64 (+.f64 1 (log1p.f64 (exp.f64 x))) 1)
(log1p.f64 (exp.f64 x))
(*.f64 (log1p.f64 (exp.f64 x)) 1)
(log1p.f64 (exp.f64 x))
(*.f64 1 (log1p.f64 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(*.f64 (sqrt.f64 (log1p.f64 (exp.f64 x))) (sqrt.f64 (log1p.f64 (exp.f64 x))))
(log1p.f64 (exp.f64 x))
(*.f64 (cbrt.f64 (log1p.f64 (exp.f64 x))) (pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 x))) 2))
(log1p.f64 (exp.f64 x))
(*.f64 (pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 x))) 2) (cbrt.f64 (log1p.f64 (exp.f64 x))))
(log1p.f64 (exp.f64 x))
(pow.f64 (log1p.f64 (exp.f64 x)) 1)
(log1p.f64 (exp.f64 x))
(pow.f64 (sqrt.f64 (log1p.f64 (exp.f64 x))) 2)
(log1p.f64 (exp.f64 x))
(pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 x))) 3)
(log1p.f64 (exp.f64 x))
(pow.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) 1/3)
(log1p.f64 (exp.f64 x))
(sqrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 2))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 (exp.f64 x) 1))
(log1p.f64 (exp.f64 x))
(cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3))
(log1p.f64 (exp.f64 x))
(expm1.f64 (log1p.f64 (log1p.f64 (exp.f64 x))))
(log1p.f64 (exp.f64 x))
(exp.f64 (log.f64 (log1p.f64 (exp.f64 x))))
(log1p.f64 (exp.f64 x))
(exp.f64 (*.f64 (log.f64 (log1p.f64 (exp.f64 x))) 1))
(log1p.f64 (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
✓0.03%
(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))

rewrite85.0ms (1.8%)

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))))))))

simplify69.0ms (1.5%)

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))

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.03%
(sqrt.f64 (/.f64 (*.f64 2 (+.f64 (*.f64 x x) x)) (expm1.f64 x)))
✓0.04%
(/.f64 (*.f64 2 (+.f64 (*.f64 x x) x)) (expm1.f64 x))
✓0.05%
(+.f64 (*.f64 x x) x)
Compiler

Compiled 41 to 14 computations (65.9% saved)

series3.0ms (0.1%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(sqrt.f64 (/.f64 (*.f64 2 (+.f64 (*.f64 x x) x)) (expm1.f64 x)))
1.0ms
x
@inf
(sqrt.f64 (/.f64 (*.f64 2 (+.f64 (*.f64 x x) x)) (expm1.f64 x)))
1.0ms
x
@-inf
(/.f64 (*.f64 2 (+.f64 (*.f64 x x) x)) (expm1.f64 x))
0.0ms
x
@inf
(/.f64 (*.f64 2 (+.f64 (*.f64 x x) x)) (expm1.f64 x))
0.0ms
x
@inf
(+.f64 (*.f64 x x) x)

rewrite123.0ms (2.6%)

Algorithm
1×batch-egg-rewrite
Rules
1872×associate-/r*
1360×associate-/l*
746×distribute-lft-in
580×associate-/r/
320×associate-/l/
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01163
124263
2340563
Stop Event
1×node limit
Counts
3 → 191
Calls
Call 1
Inputs
(+.f64 (*.f64 x x) x)
(/.f64 (*.f64 2 (+.f64 (*.f64 x x) x)) (expm1.f64 x))
(sqrt.f64 (/.f64 (*.f64 2 (+.f64 (*.f64 x x) x)) (expm1.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 x 1) (-.f64 1 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x x))) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x 4) (-.f64 (*.f64 x x) x)) (/.f64 (*.f64 x x) (-.f64 (*.f64 x x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 x (exp.f64 (log1p.f64 (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 x x) (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 x (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x x x)) (pow.f64 (cbrt.f64 (fma.f64 x x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x x x)) 2) (cbrt.f64 (fma.f64 x x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x 4) (*.f64 x x)) (/.f64 (/.f64 1 x) (-.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 3) (pow.f64 x 6)) (/.f64 1 (+.f64 (*.f64 x x) (-.f64 (pow.f64 x 4) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 x 1) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 x 1) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 x 1) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 x) (-.f64 x 1)) (-.f64 (pow.f64 x 4) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (*.f64 x x) (-.f64 (pow.f64 x 4) (pow.f64 x 3)))) (+.f64 (pow.f64 x 3) (pow.f64 x 6)))))) 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(sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))))))))))

simplify167.0ms (3.6%)

Algorithm
1×egg-herbie
Rules
760×+-commutative
734×associate-*r*
632×associate-+r+
594×associate-*l*
536×*-commutative
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
05367555
114177173
260027045
Stop Event
1×node limit
Counts
227 → 328
Calls
Call 1
Inputs
x
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) x)
2
(+.f64 2 x)
(+.f64 2 (+.f64 (*.f64 -5/6 (pow.f64 x 2)) x))
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 2 (+.f64 (*.f64 -5/6 (pow.f64 x 2)) x)))
(*.f64 2 (/.f64 (pow.f64 x 2) (-.f64 (exp.f64 x) 1)))
(+.f64 (*.f64 2 (/.f64 x (-.f64 (exp.f64 x) 1))) (*.f64 2 (/.f64 (pow.f64 x 2) (-.f64 (exp.f64 x) 1))))
(+.f64 (*.f64 2 (/.f64 x (-.f64 (exp.f64 x) 1))) (*.f64 2 (/.f64 (pow.f64 x 2) (-.f64 (exp.f64 x) 1))))
(+.f64 (*.f64 2 (/.f64 x (-.f64 (exp.f64 x) 1))) (*.f64 2 (/.f64 (pow.f64 x 2) (-.f64 (exp.f64 x) 1))))
(*.f64 2 (/.f64 (pow.f64 x 2) (-.f64 (exp.f64 x) 1)))
(+.f64 (*.f64 2 (/.f64 x (-.f64 (exp.f64 x) 1))) (*.f64 2 (/.f64 (pow.f64 x 2) (-.f64 (exp.f64 x) 1))))
(+.f64 (*.f64 2 (/.f64 x (-.f64 (exp.f64 x) 1))) (*.f64 2 (/.f64 (pow.f64 x 2) (-.f64 (exp.f64 x) 1))))
(+.f64 (*.f64 2 (/.f64 x (-.f64 (exp.f64 x) 1))) (*.f64 2 (/.f64 (pow.f64 x 2) (-.f64 (exp.f64 x) 1))))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/4 (*.f64 (sqrt.f64 2) x)))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/4 (*.f64 (sqrt.f64 2) x)) (*.f64 -23/96 (*.f64 (sqrt.f64 2) (pow.f64 x 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/4 (*.f64 (sqrt.f64 2) x)) (+.f64 (*.f64 13/128 (*.f64 (sqrt.f64 2) (pow.f64 x 3))) (*.f64 -23/96 (*.f64 (sqrt.f64 2) (pow.f64 x 2))))))
(*.f64 (*.f64 (sqrt.f64 2) x) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1))))
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1))))) (*.f64 (*.f64 (sqrt.f64 2) x) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1)))))
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) x) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1)))) (*.f64 -1/8 (*.f64 (/.f64 (sqrt.f64 2) x) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1)))))))
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1))))) (+.f64 (*.f64 1/16 (*.f64 (/.f64 (sqrt.f64 2) (pow.f64 x 2)) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) x) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1)))) (*.f64 -1/8 (*.f64 (/.f64 (sqrt.f64 2) x) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1))))))))
(*.f64 -1 (*.f64 (*.f64 (sqrt.f64 2) x) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1)))))
(+.f64 (*.f64 -1 (*.f64 (*.f64 (sqrt.f64 2) x) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1))))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1))))))
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(exp.f64 (log.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))) 1))
(log1p.f64 (expm1.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))))) 1)
(*.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))) 1)
(*.f64 1 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))))
(*.f64 (pow.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))) 1/4) (pow.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))) 1/4))
(*.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) 2)) (sqrt.f64 (/.f64 1 (expm1.f64 x))))
(*.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) 2)) (/.f64 1 (sqrt.f64 (expm1.f64 x))))
(*.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) 2)) (pow.f64 (/.f64 1 (expm1.f64 x)) 1/2))
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))))) (cbrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))))
(*.f64 (cbrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))) (cbrt.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))))))
(*.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (*.f64 (fma.f64 x x x) 2)))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))) 1/2))
(/.f64 1 (sqrt.f64 (*.f64 (expm1.f64 x) (/.f64 1/2 (fma.f64 x x x)))))
(/.f64 1 (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (*.f64 (fma.f64 x x x) 2))))
(/.f64 1 (/.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (fma.f64 x x x))) (sqrt.f64 2)))
(/.f64 (hypot.f64 x (sqrt.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 2)))
(/.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (expm1.f64 x) (fma.f64 x x x))))
(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (expm1.f64 x)) (hypot.f64 x (sqrt.f64 x))))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) 2)) (sqrt.f64 (expm1.f64 x)))
(/.f64 (cbrt.f64 (*.f64 (fma.f64 x x x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) 2)))))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) -2)) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) 2))) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) 2)))))
(/.f64 (sqrt.f64 (sqrt.f64 2)) (/.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (fma.f64 x x x))) (sqrt.f64 (sqrt.f64 2))))
(/.f64 (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 (fma.f64 x x x) 2) 4))) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (cbrt.f64 (*.f64 (fma.f64 x x x) 2)))))
(/.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (/.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (fma.f64 x x x))) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) 2))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) 2)) 1) (sqrt.f64 (expm1.f64 x)))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) 2)) (cbrt.f64 (expm1.f64 x))) (cbrt.f64 (sqrt.f64 (expm1.f64 x))))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) 2)) (sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))) (sqrt.f64 (cbrt.f64 (expm1.f64 x))))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) 2)) (sqrt.f64 (sqrt.f64 (expm1.f64 x)))) (sqrt.f64 (sqrt.f64 (expm1.f64 x))))
(pow.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))) 1/2)
(pow.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))) 1)
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))) 1/4) 2)
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))))) 3)
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))) 3/2) 1/3)
(fabs.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))))))
(cbrt.f64 (pow.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))))))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))) 1/2))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))))) 1))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))))))
Outputs
x
(+.f64 (pow.f64 x 2) x)
(fma.f64 x x x)
(+.f64 (pow.f64 x 2) x)
(fma.f64 x x x)
(+.f64 (pow.f64 x 2) x)
(fma.f64 x x x)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) x)
(fma.f64 x x x)
(+.f64 (pow.f64 x 2) x)
(fma.f64 x x x)
(+.f64 (pow.f64 x 2) x)
(fma.f64 x x x)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) x)
(fma.f64 x x x)
(+.f64 (pow.f64 x 2) x)
(fma.f64 x x x)
(+.f64 (pow.f64 x 2) x)
(fma.f64 x x x)
2
(+.f64 2 x)
(+.f64 x 2)
(+.f64 2 (+.f64 (*.f64 -5/6 (pow.f64 x 2)) x))
(+.f64 2 (fma.f64 -5/6 (*.f64 x x) x))
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 2 (+.f64 (*.f64 -5/6 (pow.f64 x 2)) x)))
(fma.f64 1/6 (pow.f64 x 3) (+.f64 2 (fma.f64 -5/6 (*.f64 x x) x)))
(+.f64 (fma.f64 -5/6 (*.f64 x x) x) (fma.f64 1/6 (pow.f64 x 3) 2))
(*.f64 2 (/.f64 (pow.f64 x 2) (-.f64 (exp.f64 x) 1)))
(*.f64 (*.f64 x x) (/.f64 2 (expm1.f64 x)))
(/.f64 2 (/.f64 (expm1.f64 x) (*.f64 x x)))
(+.f64 (*.f64 2 (/.f64 x (-.f64 (exp.f64 x) 1))) (*.f64 2 (/.f64 (pow.f64 x 2) (-.f64 (exp.f64 x) 1))))
(/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x))
(/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x)))
(+.f64 (*.f64 2 (/.f64 x (-.f64 (exp.f64 x) 1))) (*.f64 2 (/.f64 (pow.f64 x 2) (-.f64 (exp.f64 x) 1))))
(/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x))
(/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x)))
(+.f64 (*.f64 2 (/.f64 x (-.f64 (exp.f64 x) 1))) (*.f64 2 (/.f64 (pow.f64 x 2) (-.f64 (exp.f64 x) 1))))
(/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x))
(/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x)))
(*.f64 2 (/.f64 (pow.f64 x 2) (-.f64 (exp.f64 x) 1)))
(*.f64 (*.f64 x x) (/.f64 2 (expm1.f64 x)))
(/.f64 2 (/.f64 (expm1.f64 x) (*.f64 x x)))
(+.f64 (*.f64 2 (/.f64 x (-.f64 (exp.f64 x) 1))) (*.f64 2 (/.f64 (pow.f64 x 2) (-.f64 (exp.f64 x) 1))))
(/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x))
(/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x)))
(+.f64 (*.f64 2 (/.f64 x (-.f64 (exp.f64 x) 1))) (*.f64 2 (/.f64 (pow.f64 x 2) (-.f64 (exp.f64 x) 1))))
(/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x))
(/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x)))
(+.f64 (*.f64 2 (/.f64 x (-.f64 (exp.f64 x) 1))) (*.f64 2 (/.f64 (pow.f64 x 2) (-.f64 (exp.f64 x) 1))))
(/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x))
(/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x)))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/4 (*.f64 (sqrt.f64 2) x)))
(+.f64 (sqrt.f64 2) (*.f64 1/4 (*.f64 x (sqrt.f64 2))))
(fma.f64 1/4 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/4 (*.f64 (sqrt.f64 2) x)) (*.f64 -23/96 (*.f64 (sqrt.f64 2) (pow.f64 x 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 1/4 (*.f64 x (sqrt.f64 2)) (*.f64 (*.f64 -23/96 (sqrt.f64 2)) (*.f64 x x))))
(+.f64 (fma.f64 1/4 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) (*.f64 (sqrt.f64 2) (*.f64 (*.f64 x x) -23/96)))
(+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 1/4 x) (*.f64 -23/96 (*.f64 x x)))))
(+.f64 (sqrt.f64 2) (+.f64 (*.f64 1/4 (*.f64 (sqrt.f64 2) x)) (+.f64 (*.f64 13/128 (*.f64 (sqrt.f64 2) (pow.f64 x 3))) (*.f64 -23/96 (*.f64 (sqrt.f64 2) (pow.f64 x 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/4 (*.f64 x (sqrt.f64 2)) (fma.f64 13/128 (*.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 (*.f64 -23/96 (sqrt.f64 2)) (*.f64 x x)))))
(+.f64 (fma.f64 1/4 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) (fma.f64 -23/96 (*.f64 x (*.f64 x (sqrt.f64 2))) (*.f64 (pow.f64 x 3) (*.f64 (sqrt.f64 2) 13/128))))
(+.f64 (fma.f64 1/4 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (*.f64 x x) -23/96) (*.f64 (pow.f64 x 3) 13/128))))
(*.f64 (*.f64 (sqrt.f64 2) x) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1))))
(*.f64 (sqrt.f64 2) (*.f64 x (sqrt.f64 (/.f64 1 (expm1.f64 x)))))
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1))))) (*.f64 (*.f64 (sqrt.f64 2) x) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1)))))
(fma.f64 1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (expm1.f64 x)))) (*.f64 (sqrt.f64 2) (*.f64 x (sqrt.f64 (/.f64 1 (expm1.f64 x))))))
(*.f64 (sqrt.f64 (/.f64 1 (expm1.f64 x))) (+.f64 (*.f64 x (sqrt.f64 2)) (*.f64 (sqrt.f64 2) 1/2)))
(*.f64 (sqrt.f64 (/.f64 1 (expm1.f64 x))) (*.f64 (sqrt.f64 2) (+.f64 1/2 x)))
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) x) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1)))) (*.f64 -1/8 (*.f64 (/.f64 (sqrt.f64 2) x) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1)))))))
(fma.f64 1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (expm1.f64 x)))) (fma.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (expm1.f64 x))) (*.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 1 (expm1.f64 x))) (/.f64 (sqrt.f64 2) x)))))
(fma.f64 1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (expm1.f64 x)))) (*.f64 (sqrt.f64 (/.f64 1 (expm1.f64 x))) (+.f64 (*.f64 x (sqrt.f64 2)) (*.f64 -1/8 (/.f64 (sqrt.f64 2) x)))))
(*.f64 (sqrt.f64 (/.f64 1 (expm1.f64 x))) (+.f64 (*.f64 (sqrt.f64 2) (+.f64 1/2 x)) (*.f64 -1/8 (/.f64 (sqrt.f64 2) x))))
(+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1))))) (+.f64 (*.f64 1/16 (*.f64 (/.f64 (sqrt.f64 2) (pow.f64 x 2)) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) x) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1)))) (*.f64 -1/8 (*.f64 (/.f64 (sqrt.f64 2) x) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1))))))))
(fma.f64 1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (expm1.f64 x)))) (fma.f64 1/16 (*.f64 (sqrt.f64 (/.f64 1 (expm1.f64 x))) (/.f64 (sqrt.f64 2) (*.f64 x x))) (fma.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (expm1.f64 x))) (*.f64 -1/8 (*.f64 (sqrt.f64 (/.f64 1 (expm1.f64 x))) (/.f64 (sqrt.f64 2) x))))))
(+.f64 (*.f64 (sqrt.f64 (/.f64 1 (expm1.f64 x))) (+.f64 (*.f64 x (sqrt.f64 2)) (*.f64 -1/8 (/.f64 (sqrt.f64 2) x)))) (*.f64 (sqrt.f64 (/.f64 1 (expm1.f64 x))) (+.f64 (*.f64 (sqrt.f64 2) 1/2) (*.f64 1/16 (/.f64 (sqrt.f64 2) (*.f64 x x))))))
(*.f64 (sqrt.f64 (/.f64 1 (expm1.f64 x))) (+.f64 (+.f64 (*.f64 x (sqrt.f64 2)) (*.f64 -1/8 (/.f64 (sqrt.f64 2) x))) (+.f64 (*.f64 1/16 (/.f64 (sqrt.f64 2) (*.f64 x x))) (*.f64 (sqrt.f64 2) 1/2))))
(*.f64 -1 (*.f64 (*.f64 (sqrt.f64 2) x) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1)))))
(neg.f64 (*.f64 (sqrt.f64 2) (*.f64 x (sqrt.f64 (/.f64 1 (expm1.f64 x))))))
(*.f64 (*.f64 x (sqrt.f64 2)) (neg.f64 (sqrt.f64 (/.f64 1 (expm1.f64 x)))))
(+.f64 (*.f64 -1 (*.f64 (*.f64 (sqrt.f64 2) x) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1))))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1))))))
(fma.f64 -1 (*.f64 (sqrt.f64 2) (*.f64 x (sqrt.f64 (/.f64 1 (expm1.f64 x))))) (*.f64 (*.f64 -1/2 (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (expm1.f64 x)))))
(*.f64 (sqrt.f64 (/.f64 1 (expm1.f64 x))) (+.f64 (*.f64 (neg.f64 x) (sqrt.f64 2)) (*.f64 (sqrt.f64 2) -1/2)))
(*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (expm1.f64 x)))) (-.f64 -1/2 x))
(+.f64 (*.f64 -1 (*.f64 (*.f64 (sqrt.f64 2) x) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1))))) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1))))) (*.f64 1/8 (*.f64 (/.f64 (sqrt.f64 2) x) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1)))))))
(fma.f64 -1 (*.f64 (sqrt.f64 2) (*.f64 x (sqrt.f64 (/.f64 1 (expm1.f64 x))))) (fma.f64 -1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (expm1.f64 x)))) (*.f64 (*.f64 (sqrt.f64 (/.f64 1 (expm1.f64 x))) (/.f64 (sqrt.f64 2) x)) 1/8)))
(-.f64 (*.f64 (sqrt.f64 (/.f64 1 (expm1.f64 x))) (+.f64 (*.f64 (sqrt.f64 2) -1/2) (/.f64 (*.f64 1/8 (sqrt.f64 2)) x))) (*.f64 (sqrt.f64 2) (*.f64 x (sqrt.f64 (/.f64 1 (expm1.f64 x))))))
(*.f64 (sqrt.f64 (/.f64 1 (expm1.f64 x))) (+.f64 (*.f64 (sqrt.f64 2) (+.f64 -1/2 (neg.f64 x))) (/.f64 (*.f64 1/8 (sqrt.f64 2)) x)))
(+.f64 (*.f64 -1/16 (*.f64 (/.f64 (sqrt.f64 2) (pow.f64 x 2)) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1))))) (+.f64 (*.f64 -1 (*.f64 (*.f64 (sqrt.f64 2) x) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1))))) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1))))) (*.f64 1/8 (*.f64 (/.f64 (sqrt.f64 2) x) (sqrt.f64 (/.f64 1 (-.f64 (exp.f64 x) 1))))))))
(fma.f64 -1/16 (*.f64 (sqrt.f64 (/.f64 1 (expm1.f64 x))) (/.f64 (sqrt.f64 2) (*.f64 x x))) (fma.f64 -1 (*.f64 (sqrt.f64 2) (*.f64 x (sqrt.f64 (/.f64 1 (expm1.f64 x))))) (fma.f64 -1/2 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (expm1.f64 x)))) (*.f64 (*.f64 (sqrt.f64 (/.f64 1 (expm1.f64 x))) (/.f64 (sqrt.f64 2) x)) 1/8))))
(+.f64 (*.f64 (sqrt.f64 (/.f64 1 (expm1.f64 x))) (+.f64 (*.f64 (sqrt.f64 2) -1/2) (/.f64 (*.f64 1/8 (sqrt.f64 2)) x))) (*.f64 (sqrt.f64 (/.f64 1 (expm1.f64 x))) (+.f64 (*.f64 (/.f64 (sqrt.f64 2) (*.f64 x x)) -1/16) (*.f64 (neg.f64 x) (sqrt.f64 2)))))
(*.f64 (sqrt.f64 (/.f64 1 (expm1.f64 x))) (+.f64 (+.f64 (/.f64 (*.f64 1/8 (sqrt.f64 2)) x) (*.f64 (sqrt.f64 2) -1/2)) (+.f64 (*.f64 (neg.f64 x) (sqrt.f64 2)) (*.f64 (/.f64 (sqrt.f64 2) (*.f64 x x)) -1/16))))
(-.f64 (+.f64 x 1) (-.f64 1 (*.f64 x x)))
(fma.f64 x x x)
(-.f64 (exp.f64 (log1p.f64 (fma.f64 x x x))) 1)
(fma.f64 x x x)
(-.f64 (exp.f64 (log1p.f64 (*.f64 x x))) (-.f64 1 x))
(+.f64 x (expm1.f64 (log1p.f64 (*.f64 x x))))
(-.f64 (/.f64 (pow.f64 x 4) (-.f64 (*.f64 x x) x)) (/.f64 (*.f64 x x) (-.f64 (*.f64 x x) x)))
(fma.f64 x x x)
(-.f64 (+.f64 x (exp.f64 (log1p.f64 (*.f64 x x)))) 1)
(-.f64 (exp.f64 (log1p.f64 (*.f64 x x))) (-.f64 1 x))
(+.f64 x (expm1.f64 (log1p.f64 (*.f64 x x))))
(-.f64 (+.f64 (*.f64 x x) (+.f64 x 1)) 1)
(fma.f64 x x x)
(*.f64 x (+.f64 x 1))
(fma.f64 x x x)
(*.f64 (fma.f64 x x x) 1)
(fma.f64 x x x)
(*.f64 1 (fma.f64 x x x))
(fma.f64 x x x)
(*.f64 (hypot.f64 x (sqrt.f64 x)) (hypot.f64 x (sqrt.f64 x)))
(pow.f64 (hypot.f64 x (sqrt.f64 x)) 2)
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(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))))) 1)
(sqrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))))
(*.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))) 1)
(sqrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))))
(*.f64 1 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))))
(sqrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))))
(*.f64 (pow.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))) 1/4) (pow.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))) 1/4))
(sqrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))))
(*.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) 2)) (sqrt.f64 (/.f64 1 (expm1.f64 x))))
(*.f64 (sqrt.f64 (/.f64 1 (expm1.f64 x))) (sqrt.f64 (*.f64 2 (fma.f64 x x x))))
(*.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) 2)) (/.f64 1 (sqrt.f64 (expm1.f64 x))))
(*.f64 (sqrt.f64 (*.f64 2 (fma.f64 x x x))) (/.f64 1 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (*.f64 2 (fma.f64 x x x))) (sqrt.f64 (expm1.f64 x)))
(*.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) 2)) (pow.f64 (/.f64 1 (expm1.f64 x)) 1/2))
(*.f64 (sqrt.f64 (/.f64 1 (expm1.f64 x))) (sqrt.f64 (*.f64 2 (fma.f64 x x x))))
(*.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))))) (cbrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))))
(*.f64 (cbrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x))) (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x)))))
(*.f64 (cbrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x)))) (cbrt.f64 (sqrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))))))
(*.f64 (cbrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))) (cbrt.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))))))
(*.f64 (cbrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x))) (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x)))))
(*.f64 (cbrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x)))) (cbrt.f64 (sqrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x)))))
(*.f64 (fabs.f64 (cbrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))))) (sqrt.f64 (cbrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))))))
(*.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (*.f64 (fma.f64 x x x) 2)))
(*.f64 (sqrt.f64 (*.f64 2 (fma.f64 x x x))) (/.f64 1 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (*.f64 2 (fma.f64 x x x))) (sqrt.f64 (expm1.f64 x)))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))))
(sqrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x)))))
(*.f64 (fabs.f64 (cbrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))))) (sqrt.f64 (cbrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))))))
(/.f64 1 (sqrt.f64 (*.f64 (expm1.f64 x) (/.f64 1/2 (fma.f64 x x x)))))
(/.f64 1 (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (*.f64 (fma.f64 x x x) 2))))
(*.f64 (sqrt.f64 (*.f64 2 (fma.f64 x x x))) (/.f64 1 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (*.f64 2 (fma.f64 x x x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 1 (/.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (fma.f64 x x x))) (sqrt.f64 2)))
(*.f64 (/.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) (fma.f64 x x x)))) (sqrt.f64 2))
(/.f64 (*.f64 1 (sqrt.f64 2)) (sqrt.f64 (/.f64 (expm1.f64 x) (fma.f64 x x x))))
(/.f64 (hypot.f64 x (sqrt.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 2)))
(/.f64 (*.f64 (hypot.f64 x (sqrt.f64 x)) (sqrt.f64 2)) (sqrt.f64 (expm1.f64 x)))
(/.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (expm1.f64 x) (fma.f64 x x x))))
(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (expm1.f64 x)) (hypot.f64 x (sqrt.f64 x))))
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (expm1.f64 x))) (hypot.f64 x (sqrt.f64 x)))
(*.f64 (hypot.f64 x (sqrt.f64 x)) (/.f64 (sqrt.f64 2) (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) 2)) (sqrt.f64 (expm1.f64 x)))
(*.f64 (sqrt.f64 (*.f64 2 (fma.f64 x x x))) (/.f64 1 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (*.f64 2 (fma.f64 x x x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (cbrt.f64 (*.f64 (fma.f64 x x x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) 2)))))
(*.f64 (/.f64 (cbrt.f64 (*.f64 2 (fma.f64 x x x))) (sqrt.f64 (expm1.f64 x))) (cbrt.f64 (sqrt.f64 (*.f64 2 (fma.f64 x x x)))))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) -2)) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) 2))) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) 2)))))
(*.f64 (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (fma.f64 x x x)))) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (sqrt.f64 (*.f64 2 (fma.f64 x x x)))))
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (fma.f64 x x x)))) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (fma.f64 x x x)))) (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (sqrt.f64 2)) (/.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (fma.f64 x x x))) (sqrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (/.f64 (expm1.f64 x) (fma.f64 x x x)))) (sqrt.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 (sqrt.f64 2)) (/.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (/.f64 (expm1.f64 x) (fma.f64 x x x)))))
(/.f64 (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 (fma.f64 x x x) 2) 4))) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (cbrt.f64 (*.f64 (fma.f64 x x x) 2)))))
(*.f64 (/.f64 (sqrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 (fma.f64 x x x) 2)))) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (cbrt.f64 (*.f64 2 (fma.f64 x x x)))))
(*.f64 (sqrt.f64 (cbrt.f64 (*.f64 2 (fma.f64 x x x)))) (/.f64 (sqrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 (fma.f64 x x x) 2)))) (sqrt.f64 (expm1.f64 x))))
(/.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (/.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (fma.f64 x x x))) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (/.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (fma.f64 x x x))) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (sqrt.f64 (/.f64 (expm1.f64 x) (fma.f64 x x x)))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) 2))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (fma.f64 x x x)))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(*.f64 1 (/.f64 (sqrt.f64 (*.f64 2 (fma.f64 x x x))) (sqrt.f64 (expm1.f64 x))))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) 2)) 1) (sqrt.f64 (expm1.f64 x)))
(*.f64 (sqrt.f64 (*.f64 2 (fma.f64 x x x))) (/.f64 1 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (*.f64 2 (fma.f64 x x x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) 2)) (cbrt.f64 (expm1.f64 x))) (cbrt.f64 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (*.f64 2 (fma.f64 x x x))) (*.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 x))) (cbrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (*.f64 2 (fma.f64 x x x))) (*.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 (sqrt.f64 (expm1.f64 x)))))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) 2)) (sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))) (sqrt.f64 (cbrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (*.f64 2 (fma.f64 x x x))) (*.f64 (sqrt.f64 (cbrt.f64 (expm1.f64 x))) (sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))))
(/.f64 (sqrt.f64 (*.f64 2 (fma.f64 x x x))) (*.f64 (fabs.f64 (cbrt.f64 (expm1.f64 x))) (sqrt.f64 (cbrt.f64 (expm1.f64 x)))))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) 2)) (sqrt.f64 (sqrt.f64 (expm1.f64 x)))) (sqrt.f64 (sqrt.f64 (expm1.f64 x))))
(*.f64 (sqrt.f64 (*.f64 2 (fma.f64 x x x))) (/.f64 1 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (*.f64 2 (fma.f64 x x x))) (sqrt.f64 (expm1.f64 x)))
(pow.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))) 1/2)
(sqrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))))
(pow.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))) 1)
(sqrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))))
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))) 1/4) 2)
(sqrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))))
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))))) 3)
(sqrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))))
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))) 3/2) 1/3)
(cbrt.f64 (pow.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x)) 3/2))
(cbrt.f64 (pow.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))) 3/2))
(fabs.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))))
(sqrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))))))
(sqrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))))))
(sqrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))))
(cbrt.f64 (pow.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))) 3/2))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x)) 3/2))
(cbrt.f64 (pow.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))))))
(sqrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))))))
(sqrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x)))) 1/2))
(sqrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))))) 1))
(sqrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 2 (/.f64 (fma.f64 x x x) (expm1.f64 x))))))
(sqrt.f64 (/.f64 (*.f64 2 (fma.f64 x x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 2 (/.f64 (expm1.f64 x) (fma.f64 x x x))))

eval164.0ms (3.5%)

Compiler

Compiled 7888 to 4720 computations (40.2% saved)

prune113.0ms (2.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New4451446
Fresh000
Picked101
Done134
Total4474451
Error
0%
Counts
451 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
▶35.71%
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
✓34.77%
(sqrt.f64 (+.f64 2 x))
✓0.02%
(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓28.43%
(sqrt.f64 2)
Compiler

Compiled 23 to 20 computations (13% saved)

localize13.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.03%
(sqrt.f64 (+.f64 2 x))
✓0.03%
(+.f64 1 (sqrt.f64 (+.f64 2 x)))
✓0.99%
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
Compiler

Compiled 25 to 20 computations (20% saved)

series1.0ms (0%)

Counts
2 → 8
Calls

6 calls:

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

rewrite87.0ms (1.8%)

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
01040
122328
2300628
Stop Event
1×node limit
Counts
2 → 197
Calls
Call 1
Inputs
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
(+.f64 1 (sqrt.f64 (+.f64 2 x)))
Outputs
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2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (sqrt.f64 (+.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 2 x) 1/4) (pow.f64 (+.f64 2 x) 1/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 2 x)) (cbrt.f64 (sqrt.f64 (+.f64 2 x))) 1)))))

simplify134.0ms (2.8%)

Algorithm
1×egg-herbie
Rules
1188×associate-+r-
1084×+-commutative
1000×associate-+l-
808×associate--l+
568×distribute-lft-in
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
050810645
1143410089
2559810063
Stop Event
1×node limit
Counts
205 → 313
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 (sqrt.f64 2) 1)
(+.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 1 (+.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 1 (+.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))))
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(/.f64 (*.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) (sqrt.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)))) (sqrt.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x))))))
(/.f64 (*.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) (sqrt.f64 (-.f64 -1 x))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 2) (cbrt.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)))) (cbrt.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x))))))
(/.f64 (*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 2) (cbrt.f64 (-.f64 -1 x))) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (*.f64 (+.f64 1 x) 1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))
(/.f64 (*.f64 (neg.f64 (-.f64 -1 x)) 1) (neg.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (*.f64 (neg.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2))) 1) (neg.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x))))))
(/.f64 (*.f64 (sqrt.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2))) (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4))) (sqrt.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x))))))
(/.f64 (*.f64 (sqrt.f64 (-.f64 -1 x)) (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (*.f64 (cbrt.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2))) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 2)) (cbrt.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x))))))
(/.f64 (*.f64 (cbrt.f64 (-.f64 -1 x)) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 2)) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (*.f64 (-.f64 1 (pow.f64 (+.f64 2 x) 2)) (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 2 x))))) (+.f64 3 x))
(/.f64 (*.f64 (-.f64 1 (pow.f64 (+.f64 2 x) 3)) (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 2 x))))) (+.f64 1 (+.f64 (+.f64 2 x) (pow.f64 (+.f64 2 x) 2))))
(/.f64 (*.f64 (+.f64 1 (pow.f64 (pow.f64 (+.f64 2 x) 3/2) 3)) (/.f64 1 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x)))))) (+.f64 1 (-.f64 (pow.f64 (+.f64 2 x) 3) (pow.f64 (+.f64 2 x) 3/2))))
(/.f64 (*.f64 (-.f64 1 (pow.f64 (+.f64 2 x) 3)) (/.f64 1 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x)))))) (-.f64 1 (pow.f64 (+.f64 2 x) 3/2)))
(/.f64 (/.f64 (-.f64 -1 x) 1) (-.f64 1 (sqrt.f64 (+.f64 2 x))))
(/.f64 (/.f64 (+.f64 1 x) 1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))
(/.f64 (/.f64 (-.f64 -1 x) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (/.f64 (-.f64 -1 x) (*.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))))) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (/.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) 1) (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x)))))
(/.f64 (/.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) (sqrt.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x)))))) (sqrt.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x))))))
(/.f64 (/.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) (*.f64 (cbrt.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x))))) (cbrt.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x))))))) (cbrt.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x))))))
(/.f64 (/.f64 (+.f64 1 x) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1)))
(/.f64 (/.f64 (+.f64 1 x) (*.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1)) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1)))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1)))
(/.f64 (/.f64 (+.f64 1 x) (+.f64 1 (pow.f64 (+.f64 2 x) 1/4))) (-.f64 (pow.f64 (+.f64 2 x) 1/4) 1))
(pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
(pow.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) 2)
(pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 3)
(pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3) 1/3)
(sqrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2))
(log.f64 (exp.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))))
(log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))))))
(cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3))
(expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))))
(exp.f64 (log1p.f64 (sqrt.f64 (+.f64 2 x))))
(log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))))
(fma.f64 1 (sqrt.f64 (+.f64 2 x)) 1)
(fma.f64 (pow.f64 (+.f64 2 x) 1/4) (pow.f64 (+.f64 2 x) 1/4) 1)
(fma.f64 (cbrt.f64 (+.f64 2 x)) (cbrt.f64 (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 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)) (*.f64 -1/16 (/.f64 (*.f64 x 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 (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 (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)) (*.f64 -1/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) 1)
(+.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (+.f64 (sqrt.f64 2) 1) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1)
(+.f64 (sqrt.f64 2) (+.f64 1 (+.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 (fma.f64 -1/8 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 2) 3)) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))) 1))
(+.f64 (+.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)) (*.f64 -1/16 (/.f64 (*.f64 x x) (sqrt.f64 2)))) 1)
(+.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)) (+.f64 (*.f64 -1/16 (/.f64 (*.f64 x x) (sqrt.f64 2))) 1))
(+.f64 (sqrt.f64 2) (+.f64 1 (+.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) (+.f64 (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))))) 1))
(+.f64 (+.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))) 1)
(+.f64 (+.f64 (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)) (*.f64 -1/16 (/.f64 (*.f64 x x) (sqrt.f64 2))))) 1)
(+.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 2 (+.f64 (sqrt.f64 (+.f64 2 x)) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2))))
(/.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 (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))
(*.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 -1 (pow.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) 2))
(*.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 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4))) (+.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) -1))
(+.f64 -1 (pow.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) 2))
(*.f64 (/.f64 1 (+.f64 2 (sqrt.f64 (+.f64 2 x)))) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) -1))
(sqrt.f64 (+.f64 2 x))
(*.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 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 2 (+.f64 (sqrt.f64 (+.f64 2 x)) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2))))
(/.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 (pow.f64 1 1/2) (sqrt.f64 (+.f64 2 x)))
(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 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 2 x) 2))) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 2 x)) 1/2) (pow.f64 (cbrt.f64 (pow.f64 (+.f64 2 x) 2)) 1/2))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 2 x) 2))) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))
(*.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)))
(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 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2)) (-.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2))) (neg.f64 (sqrt.f64 (+.f64 2 x))))
(/.f64 (+.f64 (+.f64 2 x) (*.f64 2 (sqrt.f64 (+.f64 2 x)))) (/.f64 (-.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2)) (neg.f64 (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))) 2)) (+.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3))) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (neg.f64 (sqrt.f64 (+.f64 2 x)))))
(*.f64 (/.f64 (+.f64 (+.f64 2 x) (*.f64 2 (sqrt.f64 (+.f64 2 x)))) (+.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3))) (-.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2) (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 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 4) (*.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 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 4) (*.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 (/.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 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 4) (*.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x))) (-.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x))) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2)))))
(*.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3)) (+.f64 (pow.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x))) 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 6))) (fma.f64 (+.f64 2 (sqrt.f64 (+.f64 2 x))) (+.f64 2 (-.f64 (sqrt.f64 (+.f64 2 x)) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2))) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 4)))
(/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 2 x))))
(sqrt.f64 (+.f64 2 x))
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(*.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 3/4)) (/.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 3/4)) (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x)))))
(/.f64 (sqrt.f64 (-.f64 -1 x)) (/.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x))) (sqrt.f64 (-.f64 -1 x))))
(*.f64 (/.f64 (sqrt.f64 (-.f64 -1 x)) (-.f64 1 (sqrt.f64 (+.f64 2 x)))) (sqrt.f64 (-.f64 -1 x)))
(*.f64 (sqrt.f64 (-.f64 -1 x)) (/.f64 (sqrt.f64 (-.f64 -1 x)) (-.f64 1 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (*.f64 (cbrt.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2))) (cbrt.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)))) (/.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x)))) (cbrt.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)))))
(/.f64 (cbrt.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2))) (/.f64 (/.f64 (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x))) (cbrt.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)))) (cbrt.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)))))
(/.f64 (cbrt.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2))) (/.f64 (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x))) (*.f64 (cbrt.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2))) (cbrt.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2))))))
(/.f64 (*.f64 (cbrt.f64 (-.f64 -1 x)) (cbrt.f64 (-.f64 -1 x))) (/.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x))) (cbrt.f64 (-.f64 -1 x))))
(/.f64 (cbrt.f64 (-.f64 -1 x)) (/.f64 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x))) (cbrt.f64 (-.f64 -1 x))) (cbrt.f64 (-.f64 -1 x))))
(*.f64 (cbrt.f64 (-.f64 -1 x)) (/.f64 (cbrt.f64 (-.f64 -1 x)) (/.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x))) (cbrt.f64 (-.f64 -1 x)))))
(/.f64 (+.f64 1 x) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))
(/.f64 (+.f64 x 1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))
(/.f64 (-.f64 1 (pow.f64 (+.f64 2 x) 2)) (*.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x))) (+.f64 3 x)))
(/.f64 (-.f64 1 (pow.f64 (+.f64 2 x) 2)) (*.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x))) (+.f64 x 3)))
(/.f64 (+.f64 1 (pow.f64 (pow.f64 (+.f64 2 x) 3/2) 3)) (*.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x)))) (+.f64 1 (-.f64 (pow.f64 (+.f64 2 x) 3) (pow.f64 (+.f64 2 x) 3/2)))))
(/.f64 (+.f64 1 (pow.f64 (pow.f64 (+.f64 2 x) 3/2) 3)) (*.f64 (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x))) (+.f64 1 (-.f64 (pow.f64 (+.f64 2 x) 3) (pow.f64 (+.f64 2 x) 3/2)))))
(/.f64 (+.f64 1 (pow.f64 (pow.f64 (+.f64 2 x) 3/2) 3)) (*.f64 (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x))) (+.f64 (pow.f64 (+.f64 2 x) 3) (-.f64 1 (pow.f64 (+.f64 2 x) 3/2)))))
(/.f64 (+.f64 1 (pow.f64 (pow.f64 (+.f64 2 x) 3/2) 3)) (*.f64 (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x))) (+.f64 (-.f64 1 (pow.f64 (+.f64 2 x) 3/2)) (pow.f64 (+.f64 2 x) 3))))
(/.f64 (-.f64 1 (pow.f64 (+.f64 2 x) 3)) (*.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x)))) (-.f64 1 (pow.f64 (+.f64 2 x) 3/2))))
(/.f64 (-.f64 1 (pow.f64 (+.f64 2 x) 3)) (*.f64 (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x))) (-.f64 1 (pow.f64 (+.f64 2 x) 3/2))))
(/.f64 (/.f64 (-.f64 1 (pow.f64 (+.f64 2 x) 3)) (-.f64 1 (pow.f64 (+.f64 2 x) 3/2))) (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x))))
(/.f64 (-.f64 1 (pow.f64 (+.f64 2 x) 3)) (*.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x))) (+.f64 1 (+.f64 (+.f64 2 x) (pow.f64 (+.f64 2 x) 2)))))
(/.f64 (/.f64 (-.f64 1 (pow.f64 (+.f64 2 x) 3)) (-.f64 1 (sqrt.f64 (+.f64 2 x)))) (+.f64 1 (+.f64 2 (+.f64 x (pow.f64 (+.f64 2 x) 2)))))
(/.f64 (/.f64 (-.f64 1 (pow.f64 (+.f64 2 x) 3)) (+.f64 3 (+.f64 x (pow.f64 (+.f64 2 x) 2)))) (-.f64 1 (sqrt.f64 (+.f64 2 x))))
(/.f64 (neg.f64 (-.f64 -1 x)) (neg.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (+.f64 x 1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))
(/.f64 (neg.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2))) (neg.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x))))))
(*.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) (/.f64 1 (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x)))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x))))
(/.f64 (*.f64 1 (+.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))
(/.f64 (+.f64 x 1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))
(/.f64 (*.f64 1 (neg.f64 (-.f64 -1 x))) (neg.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (+.f64 x 1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))
(/.f64 (*.f64 1 (neg.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)))) (neg.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x))))))
(*.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) (/.f64 1 (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x)))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x))))
(/.f64 (*.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) (sqrt.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)))) (sqrt.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x))))))
(/.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) (/.f64 (sqrt.f64 (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x)))) (sqrt.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)))))
(*.f64 (/.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) (sqrt.f64 (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x))))) (hypot.f64 1 (pow.f64 (+.f64 2 x) 3/4)))
(/.f64 (*.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) (sqrt.f64 (-.f64 -1 x))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) (/.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))) (sqrt.f64 (-.f64 -1 x))))
(/.f64 (*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 2) (cbrt.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)))) (cbrt.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x))))))
(/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 2) (/.f64 (cbrt.f64 (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x)))) (cbrt.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 2) (cbrt.f64 (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x))))) (cbrt.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2))))
(/.f64 (*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 2) (cbrt.f64 (-.f64 -1 x))) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 2) (/.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))) (cbrt.f64 (-.f64 -1 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 2) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x))))) (cbrt.f64 (-.f64 -1 x)))
(/.f64 (*.f64 (+.f64 1 x) 1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))
(/.f64 (+.f64 x 1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))
(/.f64 (*.f64 (neg.f64 (-.f64 -1 x)) 1) (neg.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (+.f64 x 1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))
(/.f64 (*.f64 (neg.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2))) 1) (neg.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x))))))
(*.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) (/.f64 1 (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x)))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x))))
(/.f64 (*.f64 (sqrt.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2))) (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4))) (sqrt.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x))))))
(/.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) (/.f64 (sqrt.f64 (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x)))) (sqrt.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)))))
(*.f64 (/.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) (sqrt.f64 (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x))))) (hypot.f64 1 (pow.f64 (+.f64 2 x) 3/4)))
(/.f64 (*.f64 (sqrt.f64 (-.f64 -1 x)) (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) (/.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))) (sqrt.f64 (-.f64 -1 x))))
(/.f64 (*.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) (sqrt.f64 (-.f64 -1 x))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (*.f64 (cbrt.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2))) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 2)) (cbrt.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x))))))
(/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 2) (/.f64 (cbrt.f64 (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x)))) (cbrt.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 2) (cbrt.f64 (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x))))) (cbrt.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2))))
(/.f64 (*.f64 (cbrt.f64 (-.f64 -1 x)) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 2)) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))))
(/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 2) (/.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))) (cbrt.f64 (-.f64 -1 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 2) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x))))) (cbrt.f64 (-.f64 -1 x)))
(/.f64 (*.f64 (-.f64 1 (pow.f64 (+.f64 2 x) 2)) (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 2 x))))) (+.f64 3 x))
(/.f64 (-.f64 1 (pow.f64 (+.f64 2 x) 2)) (*.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x))) (+.f64 x 3)))
(/.f64 (*.f64 (-.f64 1 (pow.f64 (+.f64 2 x) 3)) (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 2 x))))) (+.f64 1 (+.f64 (+.f64 2 x) (pow.f64 (+.f64 2 x) 2))))
(/.f64 (/.f64 (-.f64 1 (pow.f64 (+.f64 2 x) 3)) (-.f64 1 (sqrt.f64 (+.f64 2 x)))) (+.f64 1 (+.f64 2 (+.f64 x (pow.f64 (+.f64 2 x) 2)))))
(/.f64 (/.f64 (-.f64 1 (pow.f64 (+.f64 2 x) 3)) (+.f64 3 (+.f64 x (pow.f64 (+.f64 2 x) 2)))) (-.f64 1 (sqrt.f64 (+.f64 2 x))))
(/.f64 (*.f64 (+.f64 1 (pow.f64 (pow.f64 (+.f64 2 x) 3/2) 3)) (/.f64 1 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x)))))) (+.f64 1 (-.f64 (pow.f64 (+.f64 2 x) 3) (pow.f64 (+.f64 2 x) 3/2))))
(/.f64 (+.f64 1 (pow.f64 (pow.f64 (+.f64 2 x) 3/2) 3)) (*.f64 (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x))) (+.f64 1 (-.f64 (pow.f64 (+.f64 2 x) 3) (pow.f64 (+.f64 2 x) 3/2)))))
(/.f64 (+.f64 1 (pow.f64 (pow.f64 (+.f64 2 x) 3/2) 3)) (*.f64 (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x))) (+.f64 (pow.f64 (+.f64 2 x) 3) (-.f64 1 (pow.f64 (+.f64 2 x) 3/2)))))
(/.f64 (+.f64 1 (pow.f64 (pow.f64 (+.f64 2 x) 3/2) 3)) (*.f64 (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x))) (+.f64 (-.f64 1 (pow.f64 (+.f64 2 x) 3/2)) (pow.f64 (+.f64 2 x) 3))))
(/.f64 (*.f64 (-.f64 1 (pow.f64 (+.f64 2 x) 3)) (/.f64 1 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x)))))) (-.f64 1 (pow.f64 (+.f64 2 x) 3/2)))
(/.f64 (-.f64 1 (pow.f64 (+.f64 2 x) 3)) (*.f64 (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x))) (-.f64 1 (pow.f64 (+.f64 2 x) 3/2))))
(/.f64 (/.f64 (-.f64 1 (pow.f64 (+.f64 2 x) 3)) (-.f64 1 (pow.f64 (+.f64 2 x) 3/2))) (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x))))
(/.f64 (/.f64 (-.f64 -1 x) 1) (-.f64 1 (sqrt.f64 (+.f64 2 x))))
(*.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 2 x)))) (-.f64 -1 x))
(/.f64 (-.f64 -1 x) (-.f64 1 (sqrt.f64 (+.f64 2 x))))
(/.f64 (/.f64 (+.f64 1 x) 1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))
(/.f64 (+.f64 x 1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))
(/.f64 (/.f64 (-.f64 -1 x) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))))
(*.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 2 x)))) (-.f64 -1 x))
(/.f64 (-.f64 -1 x) (-.f64 1 (sqrt.f64 (+.f64 2 x))))
(/.f64 (/.f64 (-.f64 -1 x) (*.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))))) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x)))))
(*.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 2 x)))) (-.f64 -1 x))
(/.f64 (-.f64 -1 x) (-.f64 1 (sqrt.f64 (+.f64 2 x))))
(/.f64 (/.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) 1) (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x)))))
(*.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) (/.f64 1 (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x)))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x))))
(/.f64 (/.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) (sqrt.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x)))))) (sqrt.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x))))))
(*.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) (/.f64 1 (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x)))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x))))
(/.f64 (/.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) (*.f64 (cbrt.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x))))) (cbrt.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x))))))) (cbrt.f64 (+.f64 3 (-.f64 x (sqrt.f64 (+.f64 2 x))))))
(*.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) (/.f64 1 (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x)))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 2 x) 3/2)) (-.f64 (+.f64 x 3) (sqrt.f64 (+.f64 2 x))))
(/.f64 (/.f64 (+.f64 1 x) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1)))
(/.f64 (+.f64 x 1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))
(/.f64 (/.f64 (+.f64 1 x) (*.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1)) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1)))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 2 x)) -1)))
(/.f64 (+.f64 x 1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))
(/.f64 (/.f64 (+.f64 1 x) (+.f64 1 (pow.f64 (+.f64 2 x) 1/4))) (-.f64 (pow.f64 (+.f64 2 x) 1/4) 1))
(/.f64 (+.f64 x 1) (+.f64 (sqrt.f64 (+.f64 2 x)) -1))
(pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
(+.f64 1 (sqrt.f64 (+.f64 2 x)))
(pow.f64 (hypot.f64 1 (pow.f64 (+.f64 2 x) 1/4)) 2)
(pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))) 3)
(+.f64 1 (sqrt.f64 (+.f64 2 x)))
(pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3) 1/3)
(+.f64 1 (sqrt.f64 (+.f64 2 x)))
(sqrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 2))
(fabs.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))))
(log.f64 (exp.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))))
(+.f64 1 (sqrt.f64 (+.f64 2 x)))
(log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))))))
(+.f64 1 (sqrt.f64 (+.f64 2 x)))
(cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 3))
(+.f64 1 (sqrt.f64 (+.f64 2 x)))
(expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))))
(+.f64 1 (sqrt.f64 (+.f64 2 x)))
(exp.f64 (log1p.f64 (sqrt.f64 (+.f64 2 x))))
(log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x)))))
(+.f64 1 (sqrt.f64 (+.f64 2 x)))
(fma.f64 1 (sqrt.f64 (+.f64 2 x)) 1)
(+.f64 1 (sqrt.f64 (+.f64 2 x)))
(fma.f64 (pow.f64 (+.f64 2 x) 1/4) (pow.f64 (+.f64 2 x) 1/4) 1)
(+.f64 1 (sqrt.f64 (+.f64 2 x)))
(fma.f64 (cbrt.f64 (+.f64 2 x)) (cbrt.f64 (sqrt.f64 (+.f64 2 x))) 1)
(fma.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 x))) (cbrt.f64 (+.f64 2 x)) 1)

eval247.0ms (5.2%)

Compiler

Compiled 8431 to 7336 computations (13% saved)

prune52.0ms (1.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New3571358
Fresh000
Picked011
Done033
Total3575362
Error
0%
Counts
362 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
▶29.36%
(-.f64 (+.f64 (sqrt.f64 2) 1) 1)
✓35.71%
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
✓34.77%
(sqrt.f64 (+.f64 2 x))
✓0.02%
(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓28.43%
(sqrt.f64 2)
Compiler

Compiled 30 to 27 computations (10% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓1.56%
(-.f64 (+.f64 (sqrt.f64 2) 1) 1)
Compiler

Compiled 15 to 15 computations (0% saved)

series0.0ms (0%)

Counts
1 → 0

rewrite57.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
1462×add-sqr-sqrt
1438×*-un-lft-identity
1356×add-cube-cbrt
1348×add-cbrt-cube
1338×add-exp-log
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0811
11755
221835
Stop Event
1×node limit
Counts
1 → 44
Calls
Call 1
Inputs
(-.f64 (+.f64 (sqrt.f64 2) 1) 1)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (sqrt.f64 2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (sqrt.f64 2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 (sqrt.f64 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 2))))) (#(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 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) 1))))) (#(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 (cbrt.f64 2) (*.f64 (cbrt.f64 (sqrt.f64 2)) 1))))) (#(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 (sqrt.f64 2) 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 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 2 (-.f64 (sqrt.f64 2) 0))))) (#(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 (sqrt.f64 2) 1) 2) (+.f64 (sqrt.f64 2) 2)) (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 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 (sqrt.f64 2) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 2 3/2) (+.f64 2 (-.f64 0 (*.f64 (sqrt.f64 2) 0))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3) -1) (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 2) (+.f64 (sqrt.f64 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3) -1) (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 2) (-.f64 1 (*.f64 (+.f64 (sqrt.f64 2) 1) -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 (sqrt.f64 2) 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 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 (sqrt.f64 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (sqrt.f64 2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 2 1/4) (pow.f64 2 1/4) 0)))) (#(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 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 2) 1)) 2) (cbrt.f64 (+.f64 (sqrt.f64 2) 1)) -1)))))

simplify82.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
1150×distribute-rgt-out
968×associate-*r*
842×associate-*l*
706×distribute-lft-in
658×times-frac
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
099688
1227638
2895618
36734608
Stop Event
1×node limit
Counts
44 → 51
Calls
Call 1
Inputs
(+.f64 (sqrt.f64 2) 0)
(+.f64 1 (+.f64 (sqrt.f64 2) -1))
(+.f64 (+.f64 (sqrt.f64 2) 1) -1)
(+.f64 0 (sqrt.f64 2))
(+.f64 -1 (+.f64 (sqrt.f64 2) 1))
(*.f64 (sqrt.f64 2) 1)
(*.f64 1 (sqrt.f64 2))
(*.f64 (pow.f64 2 1/4) (pow.f64 2 1/4))
(*.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) 1))
(*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 2))
(*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2)))
(*.f64 (cbrt.f64 2) (*.f64 (cbrt.f64 (sqrt.f64 2)) 1))
(*.f64 (*.f64 (+.f64 (sqrt.f64 2) 2) (sqrt.f64 2)) (/.f64 1 (+.f64 (sqrt.f64 2) 2)))
(*.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 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 2 (-.f64 (sqrt.f64 2) 0))
(/.f64 1 (/.f64 (+.f64 (sqrt.f64 2) 2) (*.f64 (+.f64 (sqrt.f64 2) 2) (sqrt.f64 2))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 2) (+.f64 (sqrt.f64 2) 2)) (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 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 (sqrt.f64 2) 1) -1))
(/.f64 (pow.f64 2 3/2) (+.f64 2 (-.f64 0 (*.f64 (sqrt.f64 2) 0))))
(/.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3) -1) (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 2) (+.f64 (sqrt.f64 2) 2)))
(/.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3) -1) (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 2) (-.f64 1 (*.f64 (+.f64 (sqrt.f64 2) 1) -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 (sqrt.f64 2) 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 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 (sqrt.f64 2) 0)
(fma.f64 1 (+.f64 (sqrt.f64 2) 1) -1)
(fma.f64 (pow.f64 2 1/4) (pow.f64 2 1/4) 0)
(fma.f64 (hypot.f64 1 (pow.f64 2 1/4)) (hypot.f64 1 (pow.f64 2 1/4)) -1)
(fma.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2)) 0)
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 2) 1)) 2) (cbrt.f64 (+.f64 (sqrt.f64 2) 1)) -1)
Outputs
(+.f64 (sqrt.f64 2) 0)
(sqrt.f64 2)
(+.f64 1 (+.f64 (sqrt.f64 2) -1))
(sqrt.f64 2)
(+.f64 (+.f64 (sqrt.f64 2) 1) -1)
(sqrt.f64 2)
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(+.f64 -1 (+.f64 (sqrt.f64 2) 1))
(sqrt.f64 2)
(*.f64 (sqrt.f64 2) 1)
(sqrt.f64 2)
(*.f64 1 (sqrt.f64 2))
(sqrt.f64 2)
(*.f64 (pow.f64 2 1/4) (pow.f64 2 1/4))
(sqrt.f64 2)
(*.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) 1))
(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 (cbrt.f64 2) (*.f64 (cbrt.f64 (sqrt.f64 2)) 1))
(*.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 (sqrt.f64 2) 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 2) (+.f64 (sqrt.f64 2) 2))))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3)) (/.f64 1 (+.f64 (+.f64 2 (sqrt.f64 2)) (pow.f64 (+.f64 (sqrt.f64 2) 1) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3)) (+.f64 2 (+.f64 (sqrt.f64 2) (pow.f64 (+.f64 (sqrt.f64 2) 1) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3)) (+.f64 (+.f64 2 (pow.f64 2 3/2)) (+.f64 (sqrt.f64 2) 3)))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3)) (+.f64 3 (*.f64 (sqrt.f64 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 2 (-.f64 (sqrt.f64 2) 0))
(/.f64 2 (sqrt.f64 2))
(/.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 (sqrt.f64 2) 1) 2) (+.f64 (sqrt.f64 2) 2)) (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3) -1)))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3)) (/.f64 1 (+.f64 (+.f64 2 (sqrt.f64 2)) (pow.f64 (+.f64 (sqrt.f64 2) 1) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3)) (+.f64 2 (+.f64 (sqrt.f64 2) (pow.f64 (+.f64 (sqrt.f64 2) 1) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3)) (+.f64 (+.f64 2 (pow.f64 2 3/2)) (+.f64 (sqrt.f64 2) 3)))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3)) (+.f64 3 (*.f64 (sqrt.f64 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 (sqrt.f64 2) 1) -1))
(sqrt.f64 2)
(/.f64 (pow.f64 2 3/2) (+.f64 2 (-.f64 0 (*.f64 (sqrt.f64 2) 0))))
(/.f64 (pow.f64 2 3/2) 2)
(/.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3) -1) (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 2) (+.f64 (sqrt.f64 2) 2)))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3)) (/.f64 1 (+.f64 (+.f64 2 (sqrt.f64 2)) (pow.f64 (+.f64 (sqrt.f64 2) 1) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3)) (+.f64 2 (+.f64 (sqrt.f64 2) (pow.f64 (+.f64 (sqrt.f64 2) 1) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3)) (+.f64 (+.f64 2 (pow.f64 2 3/2)) (+.f64 (sqrt.f64 2) 3)))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3)) (+.f64 3 (*.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 2) 3))))
(/.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3) -1) (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 2) (-.f64 1 (*.f64 (+.f64 (sqrt.f64 2) 1) -1))))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3)) (/.f64 1 (+.f64 (+.f64 2 (sqrt.f64 2)) (pow.f64 (+.f64 (sqrt.f64 2) 1) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3)) (+.f64 2 (+.f64 (sqrt.f64 2) (pow.f64 (+.f64 (sqrt.f64 2) 1) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3)) (+.f64 (+.f64 2 (pow.f64 2 3/2)) (+.f64 (sqrt.f64 2) 3)))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3)) (+.f64 3 (*.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 2) 3))))
(/.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 (sqrt.f64 2) 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 2) 1) 2) (+.f64 (sqrt.f64 2) 2))))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3)) (/.f64 1 (+.f64 (+.f64 2 (sqrt.f64 2)) (pow.f64 (+.f64 (sqrt.f64 2) 1) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3)) (+.f64 2 (+.f64 (sqrt.f64 2) (pow.f64 (+.f64 (sqrt.f64 2) 1) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3)) (+.f64 (+.f64 2 (pow.f64 2 3/2)) (+.f64 (sqrt.f64 2) 3)))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 (sqrt.f64 2) 1) 3)) (+.f64 3 (*.f64 (sqrt.f64 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 (sqrt.f64 2) 0)
(sqrt.f64 2)
(fma.f64 1 (+.f64 (sqrt.f64 2) 1) -1)
(sqrt.f64 2)
(fma.f64 (pow.f64 2 1/4) (pow.f64 2 1/4) 0)
(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 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2)) 0)
(*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 2))
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 2) 1)) 2) (cbrt.f64 (+.f64 (sqrt.f64 2) 1)) -1)
(sqrt.f64 2)

eval18.0ms (0.4%)

Compiler

Compiled 493 to 493 computations (0% saved)

prune7.0ms (0.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New50151
Fresh000
Picked101
Done044
Total51556
Error
0%
Counts
56 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
29.36%
(/.f64 2 (sqrt.f64 2))
✓35.71%
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
✓34.77%
(sqrt.f64 (+.f64 2 x))
✓0.02%
(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓28.43%
(sqrt.f64 2)
Compiler

Compiled 28 to 25 computations (10.7% saved)

regimes18.0ms (0.4%)

Counts
10 → 1
Calls
Call 1
Inputs
(sqrt.f64 2)
(sqrt.f64 (+.f64 2 x))
(/.f64 2 (sqrt.f64 2))
(-.f64 (+.f64 (sqrt.f64 2) 1) 1)
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (/.f64 (*.f64 2 (+.f64 (*.f64 x x) x)) (expm1.f64 x)))
(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 1 (exp.f64 x)))
Calls

3 calls:

10.0ms
x
3.0ms
(/.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
0.02%1x
0.02%1(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
0.02%1(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
Compiler

Compiled 94 to 73 computations (22.3% saved)

regimes5.0ms (0.1%)

Accuracy

Total -5.1b remaining (-27.9%)

Threshold costs -5.1b (-27.9%)

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

1 calls:

4.0ms
x
Results
ErrorSegmentsBranch
28.43%1x
Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify4.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

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

Compiled 9 to 8 computations (11.1% saved)

soundness75.0ms (1.6%)

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

Useful iterations: 5 (0.0ms)

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

Compiled 85 to 56 computations (34.1% saved)

end26.0ms (0.5%)

Compiler

Compiled 8 to 7 computations (12.5% saved)

Profiling

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