Details

Time bar (total: 13.9s)

analyze0.0ms (0%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
100%0%0%1
Compiler

Compiled 14 to 13 computations (7.1% saved)

sample2.2s (15.9%)

Results
1.1s2133×body2048valid
611.0ms4574×body256valid
385.0ms1030×body1024valid
128.0ms519×body512valid

preprocess34.0ms (0.2%)

Algorithm
2×egg-herbie
Rules
8×sub-neg_binary64
8×fma-def_binary64
5×+-commutative_binary64
3×*-commutative_binary64
3×associate-+l-_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01018
12215
22915
33715
44415
55415
66515
77715
88015
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
Outputs
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (*.f64 (/.f64 1 (hypot.f64 1 x)) 1/2))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
Compiler

Compiled 14 to 13 computations (7.1% saved)

simplify17.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
8×sub-neg_binary64
8×fma-def_binary64
5×+-commutative_binary64
3×*-commutative_binary64
3×associate-+l-_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01018
12215
22915
33715
44415
55415
66515
77715
88015
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
Outputs
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (*.f64 (/.f64 1 (hypot.f64 1 x)) 1/2))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

eval2.0ms (0%)

Compiler

Compiled 23 to 21 computations (8.7% saved)

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
15.2b
Counts
3 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶15.2b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
Compiler

Compiled 11 to 10 computations (9.1% saved)

localize36.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
✓0.0b
(/.f64 1/2 (hypot.f64 1 x))
✓0.0b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓2.1b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
Compiler

Compiled 37 to 31 computations (16.2% saved)

series12.0ms (0.1%)

Counts
4 → 48
Calls

12 calls:

TimeVariablePointExpression
2.0ms
x
@0
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
2.0ms
x
@inf
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
1.0ms
x
@-inf
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
1.0ms
x
@inf
(/.f64 1/2 (hypot.f64 1 x))
1.0ms
x
@-inf
(/.f64 1/2 (hypot.f64 1 x))

rewrite175.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
595×unpow-prod-down_binary64
406×log-prod_binary64
387×prod-diff_binary64
249×pow2_binary64
228×pow-prod-down_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0944
120144
2260244
Stop Event
1×node limit
Counts
4 → 201
Calls
Call 1
Inputs
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
(/.f64 1/2 (hypot.f64 1 x))
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
Outputs
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#<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 1/8 (pow.f64 (hypot.f64 1 x) -3) 1/8)) (neg.f64 (+.f64 1/4 (-.f64 (/.f64 1/4 (fma.f64 x x 1)) (/.f64 1/4 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1)))) (neg.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (/.f64 1/4 (fma.f64 x x 1)) 1/4) (-.f64 (/.f64 1/2 (hypot.f64 1 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/6) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1/4 (-.f64 (/.f64 1/4 (fma.f64 x x 1)) (/.f64 1/4 (hypot.f64 1 x)))) (fma.f64 1/8 (pow.f64 (hypot.f64 1 x) -3) 1/8)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1/2 (hypot.f64 1 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (/.f64 1 (hypot.f64 1 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1/2 (hypot.f64 1 x)) 1 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/2 (/.f64 1 (neg.f64 (hypot.f64 1 x))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (hypot.f64 1 x)) 1/2 1/2)))))

simplify132.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
482×fma-def_binary64
325×+-commutative_binary64
323×*-commutative_binary64
310×times-frac_binary64
297×associate-*l/_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0130910
1388838
21154822
33526822
Stop Event
1×node limit
Counts
249 → 281
Calls
Call 1
Inputs
(*.f64 1/8 (pow.f64 x 2))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (+.f64 (*.f64 -1843/32768 (pow.f64 x 8)) (*.f64 -11/128 (pow.f64 x 4)))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 1 (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))) (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (*.f64 -1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))) (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))) (sqrt.f64 1/2))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 1 (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))) (sqrt.f64 1/2))
1
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 1 (*.f64 11/128 (pow.f64 x 4))))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 -69/1024 (pow.f64 x 6)) (+.f64 1 (*.f64 11/128 (pow.f64 x 4)))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(sqrt.f64 1/2)
(-.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(-.f64 (+.f64 (sqrt.f64 1/2) (*.f64 -1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
1/2
(+.f64 1/2 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 1/2 (+.f64 (*.f64 -1/4 (pow.f64 x 2)) (*.f64 3/16 (pow.f64 x 4))))
(+.f64 1/2 (+.f64 (*.f64 -1/4 (pow.f64 x 2)) (+.f64 (*.f64 -5/32 (pow.f64 x 6)) (*.f64 3/16 (pow.f64 x 4)))))
(/.f64 1/2 x)
(-.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 3/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 3/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))) (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 3))) (*.f64 5/32 (/.f64 1 (pow.f64 x 7)))))
(/.f64 -1/2 x)
(-.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 3/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 3))) (*.f64 5/32 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 3/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
1
(+.f64 1 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 1 (+.f64 (*.f64 -1/4 (pow.f64 x 2)) (*.f64 3/16 (pow.f64 x 4))))
(+.f64 1 (+.f64 (*.f64 -1/4 (pow.f64 x 2)) (+.f64 (*.f64 -5/32 (pow.f64 x 6)) (*.f64 3/16 (pow.f64 x 4)))))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) 1/2) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1/2 (*.f64 3/16 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
1/2
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 3/16 (/.f64 1 (pow.f64 x 5)))))
Outputs
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
(fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 -11/128 (pow.f64 x 4))))
(fma.f64 1/8 (*.f64 x x) (fma.f64 -11/128 (pow.f64 x 4) (*.f64 69/1024 (pow.f64 x 6))))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 1/8 (*.f64 x x))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (+.f64 (*.f64 -1843/32768 (pow.f64 x 8)) (*.f64 -11/128 (pow.f64 x 4)))))
(fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 -1843/32768 (pow.f64 x 8) (*.f64 -11/128 (pow.f64 x 4)))))
(fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 -11/128 (pow.f64 x 4) (*.f64 -1843/32768 (pow.f64 x 8)))))
(fma.f64 1/8 (*.f64 x x) (fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 -1843/32768 (pow.f64 x 8)))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(-.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))))
(-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1))
(-.f64 (+.f64 1 (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))) (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(+.f64 1 (-.f64 (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))))
(-.f64 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) 1) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))))
(+.f64 1 (+.f64 (-.f64 (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))) (sqrt.f64 1/2)) (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2)))))
(+.f64 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1)) (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (*.f64 -1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))) (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 (+.f64 1 (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)))) (*.f64 -1/2 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))))
(+.f64 1 (-.f64 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)))))
(+.f64 1 (+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (-.f64 (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))) (sqrt.f64 1/2)) (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2))))))
(+.f64 (+.f64 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1)) (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2)))) (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(+.f64 1 (-.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (sqrt.f64 1/2)))
(+.f64 1 (-.f64 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)) (sqrt.f64 1/2)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))) (sqrt.f64 1/2))
(+.f64 1 (-.f64 (+.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)))) (sqrt.f64 1/2)))
(+.f64 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))) (-.f64 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)) (sqrt.f64 1/2))))
(-.f64 1 (-.f64 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2))) (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2)))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 1 (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))) (sqrt.f64 1/2))
(-.f64 (fma.f64 1/2 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 1 (+.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)))))) (sqrt.f64 1/2))
(+.f64 (+.f64 1 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)))) (-.f64 (/.f64 -3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (+.f64 (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))) (-.f64 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)) (sqrt.f64 1/2))) (/.f64 -3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))
(+.f64 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)) (-.f64 (+.f64 (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))) (+.f64 1 (/.f64 -3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (sqrt.f64 1/2)))
1
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) 1)
(fma.f64 -1/8 (*.f64 x x) 1)
(fma.f64 (*.f64 x x) -1/8 1)
(fma.f64 x (*.f64 x -1/8) 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 1 (*.f64 11/128 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/8 (*.f64 x x) 1) (*.f64 (pow.f64 x 4) 11/128))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 (pow.f64 x 4) 11/128 1))
(fma.f64 x (*.f64 x -1/8) (fma.f64 (pow.f64 x 4) 11/128 1))
(fma.f64 (pow.f64 x 4) 11/128 (fma.f64 (*.f64 x x) -1/8 1))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 -69/1024 (pow.f64 x 6)) (+.f64 1 (*.f64 11/128 (pow.f64 x 4)))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 -69/1024 (pow.f64 x 6) (+.f64 1 (*.f64 (pow.f64 x 4) 11/128))))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 (pow.f64 x 6) -69/1024 (fma.f64 (pow.f64 x 4) 11/128 1)))
(fma.f64 x (*.f64 x -1/8) (fma.f64 (pow.f64 x 4) 11/128 (fma.f64 (pow.f64 x 6) -69/1024 1)))
(fma.f64 (pow.f64 x 6) -69/1024 (fma.f64 (pow.f64 x 4) 11/128 (fma.f64 (*.f64 x x) -1/8 1)))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))
(+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)))
(-.f64 (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(-.f64 (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))) (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))))
(-.f64 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))) (/.f64 (*.f64 (/.f64 2 (sqrt.f64 1/2)) 1/32) (*.f64 x x)))
(-.f64 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)) (-.f64 (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))) (sqrt.f64 1/2)))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (*.f64 x x))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(-.f64 (fma.f64 1/2 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))) (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))))
(+.f64 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))) (-.f64 (/.f64 -3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (/.f64 (*.f64 (/.f64 2 (sqrt.f64 1/2)) 1/32) (*.f64 x x))))
(+.f64 (/.f64 -3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (-.f64 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)) (-.f64 (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))) (sqrt.f64 1/2))))
(+.f64 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) (-.f64 (/.f64 -3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))))))
(sqrt.f64 1/2)
(-.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))
(-.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)))
(+.f64 (sqrt.f64 1/2) (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2))))
(+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)))
(-.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(-.f64 (sqrt.f64 1/2) (+.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)))))
(-.f64 (sqrt.f64 1/2) (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))))
(+.f64 (sqrt.f64 1/2) (-.f64 (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2))) (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2)))))
(-.f64 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2))) (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))))
(-.f64 (+.f64 (sqrt.f64 1/2) (*.f64 -1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(+.f64 (sqrt.f64 1/2) (-.f64 (*.f64 -1/2 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (-.f64 (sqrt.f64 1/2) (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (sqrt.f64 1/2) (-.f64 (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2))) (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (-.f64 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2))) (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2)))))
1/2
(+.f64 1/2 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 1/2 (*.f64 (*.f64 x x) -1/4))
(fma.f64 (*.f64 x x) -1/4 1/2)
(fma.f64 x (*.f64 x -1/4) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/4 (pow.f64 x 2)) (*.f64 3/16 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 -1/4 (*.f64 x x) (*.f64 (pow.f64 x 4) 3/16)))
(+.f64 1/2 (fma.f64 (*.f64 x x) -1/4 (*.f64 (pow.f64 x 4) 3/16)))
(fma.f64 x (*.f64 x -1/4) (fma.f64 (pow.f64 x 4) 3/16 1/2))
(fma.f64 (pow.f64 x 4) 3/16 (fma.f64 (*.f64 x x) -1/4 1/2))
(+.f64 1/2 (+.f64 (*.f64 -1/4 (pow.f64 x 2)) (+.f64 (*.f64 -5/32 (pow.f64 x 6)) (*.f64 3/16 (pow.f64 x 4)))))
(+.f64 1/2 (fma.f64 -1/4 (*.f64 x x) (fma.f64 -5/32 (pow.f64 x 6) (*.f64 (pow.f64 x 4) 3/16))))
(+.f64 1/2 (fma.f64 (*.f64 x x) -1/4 (fma.f64 (pow.f64 x 4) 3/16 (*.f64 (pow.f64 x 6) -5/32))))
(+.f64 1/2 (fma.f64 x (*.f64 x -1/4) (fma.f64 (pow.f64 x 4) 3/16 (*.f64 (pow.f64 x 6) -5/32))))
(+.f64 1/2 (fma.f64 (pow.f64 x 6) -5/32 (fma.f64 (pow.f64 x 4) 3/16 (*.f64 x (*.f64 x -1/4)))))
(/.f64 1/2 x)
(-.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (/.f64 1/2 x) (/.f64 1/4 (pow.f64 x 3)))
(+.f64 (/.f64 1/2 x) (/.f64 -1/4 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 3/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 3/16 (pow.f64 x 5)) (-.f64 (/.f64 1/2 x) (/.f64 1/4 (pow.f64 x 3))))
(+.f64 (+.f64 (/.f64 1/2 x) (/.f64 -1/4 (pow.f64 x 3))) (/.f64 3/16 (pow.f64 x 5)))
(-.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 -3/16 (pow.f64 x 5))))
(-.f64 (+.f64 (*.f64 3/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))) (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 3))) (*.f64 5/32 (/.f64 1 (pow.f64 x 7)))))
(-.f64 (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5))) (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 5/32 (pow.f64 x 7))))
(+.f64 (/.f64 3/16 (pow.f64 x 5)) (-.f64 (+.f64 (/.f64 1/2 x) (/.f64 -1/4 (pow.f64 x 3))) (/.f64 5/32 (pow.f64 x 7))))
(+.f64 (+.f64 (/.f64 1/2 x) (/.f64 -1/4 (pow.f64 x 3))) (-.f64 (/.f64 3/16 (pow.f64 x 5)) (/.f64 5/32 (pow.f64 x 7))))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 3/16 (pow.f64 x 5)) (+.f64 (/.f64 -1/4 (pow.f64 x 3)) (/.f64 -5/32 (pow.f64 x 7)))))
(/.f64 -1/2 x)
(-.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 -1/2 x))
(-.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 3/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
(-.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5))))
(+.f64 (-.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 3/16 (pow.f64 x 5))) (/.f64 -1/2 x))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -3/16 (pow.f64 x 5))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 3))) (*.f64 5/32 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 3/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (-.f64 (/.f64 5/32 (pow.f64 x 7)) (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5)))))
(+.f64 (+.f64 (/.f64 5/32 (pow.f64 x 7)) (-.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 3/16 (pow.f64 x 5)))) (/.f64 -1/2 x))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 5/32 (pow.f64 x 7)) (+.f64 (/.f64 -1/2 x) (/.f64 -3/16 (pow.f64 x 5)))))
1
(+.f64 1 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 1 (*.f64 (*.f64 x x) -1/4))
(fma.f64 (*.f64 x x) -1/4 1)
(fma.f64 x (*.f64 x -1/4) 1)
(+.f64 1 (+.f64 (*.f64 -1/4 (pow.f64 x 2)) (*.f64 3/16 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/4 (*.f64 x x) (*.f64 (pow.f64 x 4) 3/16)))
(+.f64 1 (fma.f64 (*.f64 x x) -1/4 (*.f64 (pow.f64 x 4) 3/16)))
(fma.f64 (pow.f64 x 4) 3/16 (fma.f64 x (*.f64 x -1/4) 1))
(fma.f64 x (*.f64 x -1/4) (fma.f64 (pow.f64 x 4) 3/16 1))
(+.f64 1 (+.f64 (*.f64 -1/4 (pow.f64 x 2)) (+.f64 (*.f64 -5/32 (pow.f64 x 6)) (*.f64 3/16 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/4 (*.f64 x x) (fma.f64 -5/32 (pow.f64 x 6) (*.f64 (pow.f64 x 4) 3/16))))
(+.f64 (fma.f64 (pow.f64 x 4) 3/16 (*.f64 (pow.f64 x 6) -5/32)) (fma.f64 (*.f64 x x) -1/4 1))
(+.f64 (*.f64 (pow.f64 x 6) -5/32) (fma.f64 (pow.f64 x 4) 3/16 (fma.f64 x (*.f64 x -1/4) 1)))
(+.f64 1 (fma.f64 (pow.f64 x 6) -5/32 (fma.f64 (pow.f64 x 4) 3/16 (*.f64 x (*.f64 x -1/4)))))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(+.f64 1/2 (/.f64 1/2 x))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) 1/2) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (-.f64 1/2 (/.f64 1/4 (pow.f64 x 3))))
(+.f64 1/2 (+.f64 (/.f64 1/2 x) (/.f64 -1/4 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1/2 (*.f64 3/16 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (-.f64 (+.f64 1/2 (/.f64 3/16 (pow.f64 x 5))) (/.f64 1/4 (pow.f64 x 3))))
(+.f64 (+.f64 (/.f64 3/16 (pow.f64 x 5)) (+.f64 1/2 (/.f64 1/2 x))) (/.f64 -1/4 (pow.f64 x 3)))
(+.f64 1/2 (+.f64 (+.f64 (/.f64 1/2 x) (/.f64 -1/4 (pow.f64 x 3))) (/.f64 3/16 (pow.f64 x 5))))
(+.f64 1/2 (-.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 -3/16 (pow.f64 x 5)))))
1/2
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/2 (/.f64 1/2 x))
(+.f64 1/2 (/.f64 -1/2 x))
(-.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (/.f64 1 x)))
(+.f64 1/2 (-.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 1/2 (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 -1/2 x)))
(-.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 3/16 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (+.f64 1/2 (-.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 1/2 x))) (/.f64 3/16 (pow.f64 x 5)))
(-.f64 (+.f64 1/2 (/.f64 1/4 (pow.f64 x 3))) (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5))))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 1/2 (+.f64 (/.f64 -1/2 x) (/.f64 -3/16 (pow.f64 x 5)))))
(+.f64 1/2 (+.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -3/16 (pow.f64 x 5)))))

eval316.0ms (2.3%)

Compiler

Compiled 5106 to 4567 computations (10.6% saved)

prune66.0ms (0.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New26615281
Fresh000
Picked011
Done000
Total26616282
Error
0.1b
Counts
282 → 16
Alt Table
Click to see full alt table
StatusErrorProgram
33.4b
(-.f64 1 (sqrt.f64 1/2))
14.7b
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
▶34.5b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
44.2b
(-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))
15.4b
(cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))
14.7b
(/.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
▶44.6b
(-.f64 1 1)
14.7b
(/.f64 1 (/.f64 (+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))
▶14.7b
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
29.9b
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
▶30.3b
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
29.8b
(*.f64 1/8 (*.f64 x x))
34.3b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
✓15.2b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
▶15.2b
(exp.f64 (log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
15.2b
(fma.f64 (neg.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/6) 1)
Compiler

Compiled 455 to 402 computations (11.6% saved)

localize111.0ms (0.8%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1/2 (hypot.f64 1 x))
✓0.0b
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓1.6b
(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
Compiler

Compiled 82 to 71 computations (13.4% saved)

series10.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
4.0ms
x
@inf
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
2.0ms
x
@-inf
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
1.0ms
x
@0
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
1.0ms
x
@0
(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
1.0ms
x
@inf
(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite119.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
630×log-prod_binary64
504×prod-diff_binary64
323×fma-def_binary64
243×log-div_binary64
236×expm1-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01240
127925
2397325
Stop Event
1×node limit
Counts
2 → 108
Calls
Call 1
Inputs
(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (*.f64 (/.f64 -1/2 (hypot.f64 1 x)) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 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x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (/.f64 -1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (pow.f64 (/.f64 1 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (/.f64 1 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 2) -1) (pow.f64 (/.f64 1 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 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(+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 2) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)) (/.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)) (/.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))) (/.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 2) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 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(hypot.f64 1 x))) (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1) (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 2)) (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))))) (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))) 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (*.f64 (/.f64 -1/2 (hypot.f64 1 x)) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1/2 (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 -1/2 (hypot.f64 1 x))))))))

simplify79.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
657×fma-def_binary64
626×times-frac_binary64
567×associate-*l*_binary64
420×associate-*r*_binary64
293×associate-+l+_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01641326
15301133
219091050
Stop Event
1×node limit
Counts
132 → 151
Calls
Call 1
Inputs
(*.f64 1/4 (pow.f64 x 2))
(+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 -3/16 (pow.f64 x 4)))
(+.f64 (*.f64 5/32 (pow.f64 x 6)) (+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 -3/16 (pow.f64 x 4))))
(+.f64 (*.f64 5/32 (pow.f64 x 6)) (+.f64 (*.f64 1/4 (pow.f64 x 2)) (+.f64 (*.f64 -3/16 (pow.f64 x 4)) (*.f64 -35/256 (pow.f64 x 8)))))
1/2
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 3/16 (/.f64 1 (pow.f64 x 5)))))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) 1/2) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1/2 (*.f64 3/16 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(*.f64 1/8 (pow.f64 x 2))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (+.f64 (*.f64 -1843/32768 (pow.f64 x 8)) (*.f64 -11/128 (pow.f64 x 4)))))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)))
(-.f64 (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)))) (*.f64 -1/4 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
(-.f64 (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)) (*.f64 1/4 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (pow.f64 x 3))))))) (+.f64 (*.f64 -1/4 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (+.f64 (*.f64 1/32 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 3))))) (+.f64 (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 3)))))) (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 -1/4 (/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))))))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(+.f64 (/.f64 1/8 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))) (+.f64 (/.f64 1/2 (*.f64 (+.f64 (sqrt.f64 1/2) 1) x)) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) x))) (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))))))) (*.f64 -1/4 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) x))) (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 1/4 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (+.f64 (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 -1/4 (/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (sqrt.f64 1/2)))) (+.f64 (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/32 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (pow.f64 (sqrt.f64 1/2) 3))))))) (pow.f64 x 3))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))))))) (*.f64 -1/4 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
Outputs
(*.f64 1/4 (pow.f64 x 2))
(*.f64 1/4 (*.f64 x x))
(+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 -3/16 (pow.f64 x 4)))
(fma.f64 1/4 (*.f64 x x) (*.f64 -3/16 (pow.f64 x 4)))
(fma.f64 (pow.f64 x 4) -3/16 (*.f64 1/4 (*.f64 x x)))
(+.f64 (*.f64 5/32 (pow.f64 x 6)) (+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 -3/16 (pow.f64 x 4))))
(fma.f64 5/32 (pow.f64 x 6) (fma.f64 1/4 (*.f64 x x) (*.f64 -3/16 (pow.f64 x 4))))
(fma.f64 5/32 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -3/16 (*.f64 1/4 (*.f64 x x))))
(fma.f64 (pow.f64 x 4) -3/16 (fma.f64 5/32 (pow.f64 x 6) (*.f64 1/4 (*.f64 x x))))
(+.f64 (*.f64 5/32 (pow.f64 x 6)) (+.f64 (*.f64 1/4 (pow.f64 x 2)) (+.f64 (*.f64 -3/16 (pow.f64 x 4)) (*.f64 -35/256 (pow.f64 x 8)))))
(fma.f64 5/32 (pow.f64 x 6) (fma.f64 1/4 (*.f64 x x) (fma.f64 -3/16 (pow.f64 x 4) (*.f64 -35/256 (pow.f64 x 8)))))
(fma.f64 5/32 (pow.f64 x 6) (fma.f64 1/4 (*.f64 x x) (fma.f64 -35/256 (pow.f64 x 8) (*.f64 (pow.f64 x 4) -3/16))))
(fma.f64 1/4 (*.f64 x x) (fma.f64 5/32 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -3/16 (*.f64 -35/256 (pow.f64 x 8)))))
1/2
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/2 (/.f64 1/2 x))
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(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) x))) (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 1/4 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (+.f64 (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 -1/4 (/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (sqrt.f64 1/2)))) (+.f64 (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/32 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (pow.f64 (sqrt.f64 1/2) 3))))))) (pow.f64 x 3))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))))))) (*.f64 -1/4 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))
(+.f64 (/.f64 1/2 (*.f64 x (+.f64 1 (sqrt.f64 1/2)))) (-.f64 (+.f64 (/.f64 1/64 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (*.f64 x x) (+.f64 1 (sqrt.f64 1/2)))))) (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (fma.f64 -1 (/.f64 (-.f64 (/.f64 1/4 (+.f64 1 (sqrt.f64 1/2))) (fma.f64 1/4 (/.f64 (+.f64 (/.f64 1/64 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 (sqrt.f64 1/2) 3)))) (*.f64 1/4 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))) (fma.f64 1/4 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))) (*.f64 1/32 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 (sqrt.f64 1/2) 3))))))) (pow.f64 x 3)) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (*.f64 x (+.f64 1 (sqrt.f64 1/2))))))))) (*.f64 -1/4 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (*.f64 x x) (sqrt.f64 1/2)))))))
(+.f64 (/.f64 (/.f64 1/2 x) (+.f64 1 (sqrt.f64 1/2))) (+.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (+.f64 (-.f64 (/.f64 1/8 (*.f64 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))) x)) (/.f64 (-.f64 (/.f64 1/4 (+.f64 1 (sqrt.f64 1/2))) (fma.f64 1/4 (/.f64 (+.f64 (/.f64 1/64 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/4 (*.f64 1/2 (sqrt.f64 1/2))))) (*.f64 1/4 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (+.f64 1/2 (sqrt.f64 1/2))))) (+.f64 1/2 (sqrt.f64 1/2))) (fma.f64 1/32 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (+.f64 1/4 (*.f64 1/2 (sqrt.f64 1/2)))) (/.f64 -3/64 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))))) (pow.f64 x 3))) (/.f64 1/64 (*.f64 (*.f64 x (*.f64 x (+.f64 1 (sqrt.f64 1/2)))) (+.f64 1/4 (*.f64 1/2 (sqrt.f64 1/2))))))) (*.f64 1/4 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 (*.f64 x x) (+.f64 1/2 (sqrt.f64 1/2)))))))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (+.f64 (+.f64 (/.f64 1/64 (*.f64 x (*.f64 (fma.f64 x (sqrt.f64 1/2) x) (fma.f64 1/2 (sqrt.f64 1/2) 1/4)))) (-.f64 (/.f64 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))) (fma.f64 x (sqrt.f64 1/2) x)) (/.f64 (-.f64 (-.f64 (/.f64 1/4 (+.f64 1 (sqrt.f64 1/2))) (*.f64 (/.f64 1/4 (+.f64 1 (sqrt.f64 1/2))) (+.f64 (-.f64 (/.f64 (/.f64 1/64 (fma.f64 1/2 (sqrt.f64 1/2) 1/4)) (+.f64 1/2 (sqrt.f64 1/2))) (/.f64 (+.f64 (/.f64 -1/8 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/32 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (+.f64 1/2 (*.f64 1/2 (sqrt.f64 1/2))))) (/.f64 -3/16 (+.f64 1/2 (sqrt.f64 1/2)))))) (/.f64 (+.f64 (/.f64 1/64 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/256 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (fma.f64 1/2 (sqrt.f64 1/2) 1/4))) (pow.f64 x 3)))) (-.f64 (/.f64 1/2 (fma.f64 x (sqrt.f64 1/2) x)) (/.f64 (+.f64 (/.f64 -1/8 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/32 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 (*.f64 x x) (+.f64 1/2 (sqrt.f64 1/2)))))))

localize5.0ms (0%)

Compiler

Compiled 5 to 5 computations (0% saved)

localize26.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 1/2 (/.f64 -1/2 x))
✓0.0b
(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
✓0.5b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
Compiler

Compiled 27 to 22 computations (18.5% saved)

series8.0ms (0.1%)

Counts
3 → 28
Calls

9 calls:

TimeVariablePointExpression
2.0ms
x
@0
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
1.0ms
x
@inf
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
1.0ms
x
@0
(+.f64 1/2 (/.f64 -1/2 x))
1.0ms
x
@-inf
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
1.0ms
x
@0
(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))

rewrite99.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
974×pow1_binary64
910×add-log-exp_binary64
910×log1p-expm1-u_binary64
910×expm1-log1p-u_binary64
98×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0928
119928
2249628
Stop Event
1×node limit
Counts
3 → 89
Calls
Call 1
Inputs
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))
(+.f64 1/2 (/.f64 -1/2 x))
Outputs
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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1/2 (/.f64 -1/2 x)) 1/4) (pow.f64 (+.f64 1/2 (/.f64 -1/2 x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1/4 (/.f64 1/4 (*.f64 x x)))) (sqrt.f64 (-.f64 1/2 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1/8 (/.f64 -1/8 (pow.f64 x 3)))) (sqrt.f64 (-.f64 (+.f64 1/4 (/.f64 1/4 (*.f64 x x))) (/.f64 -1/4 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1/2 (/.f64 -1/2 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/2 (/.f64 -1/2 x)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/2 (/.f64 -1/2 x)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 -1/2 x)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1/2 (/.f64 -1/2 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/4 (-.f64 1/2 (/.f64 -1/2 x))) (/.f64 (/.f64 1/4 (*.f64 x x)) (-.f64 1/2 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1/2 (/.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/2 (/.f64 -1/2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 2) (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1/2 (/.f64 -1/2 x)) 1/4) (*.f64 (pow.f64 (+.f64 1/2 (/.f64 -1/2 x)) 1/4) (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/8 (/.f64 -1/8 (pow.f64 x 3))) (/.f64 1 (-.f64 (+.f64 1/4 (/.f64 1/4 (*.f64 x x))) (/.f64 -1/4 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/4 (/.f64 1/4 (*.f64 x x))) (/.f64 1 (-.f64 1/2 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) (pow.f64 (+.f64 1/2 (/.f64 -1/2 x)) 1/4)) (pow.f64 (+.f64 1/2 (/.f64 -1/2 x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))) (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (+.f64 1/4 (/.f64 1/4 (*.f64 x x))) (/.f64 -1/4 x)) (+.f64 1/8 (/.f64 -1/8 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1/2 (/.f64 -1/2 x)) (-.f64 1/4 (/.f64 1/4 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/8 (/.f64 -1/8 (pow.f64 x 3))) (-.f64 (+.f64 1/4 (/.f64 1/4 (*.f64 x x))) (/.f64 -1/4 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/8 (/.f64 -1/8 (pow.f64 x 3))) (+.f64 (/.f64 1/4 (*.f64 x x)) (-.f64 1/4 (/.f64 -1/4 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (/.f64 1/4 (*.f64 x x))) (-.f64 1/2 (/.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1/8 (/.f64 -1/8 (pow.f64 x 3)))) (neg.f64 (-.f64 (+.f64 1/4 (/.f64 1/4 (*.f64 x x))) (/.f64 -1/4 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/4 (/.f64 1/4 (*.f64 x x)))) (neg.f64 (-.f64 1/2 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (/.f64 1/4 (*.f64 x x)) 1/4) (-.f64 (/.f64 -1/2 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1/2 (/.f64 -1/2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/2 (/.f64 -1/2 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/2 (/.f64 -1/2 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1/2 (/.f64 -1/2 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1/2 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1/2 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 -1/2 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1/2 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1/2 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 -1/2 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/2 (/.f64 1 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 1/4 (*.f64 x x))) (cbrt.f64 (/.f64 -1/2 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 -1/2 x)) (sqrt.f64 (/.f64 -1/2 x)) 1/2)))))

simplify99.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
835×distribute-neg-frac_binary64
830×fma-neg_binary64
741×cancel-sign-sub-inv_binary64
641×associate-/r*_binary64
388×fma-def_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
041477
1125461
2363453
31245453
45418453
Stop Event
1×node limit
Counts
117 → 107
Calls
Call 1
Inputs
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/128 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))) (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/128 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))) (sqrt.f64 1/2))
(sqrt.f64 1/2)
(-.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(-.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/128 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))))
(sqrt.f64 1/2)
(-.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(-.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/128 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))))
(/.f64 -1/2 x)
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
1/2
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
1/2
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
Outputs
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(+.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 1 (-.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2)))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (/.f64 1/32 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 x x))))) (sqrt.f64 1/2))
(+.f64 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)) (-.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2))))
(+.f64 1 (+.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)) (sqrt.f64 1/2))))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/128 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))) (sqrt.f64 1/2))
(+.f64 1 (-.f64 (+.f64 (+.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (/.f64 1/32 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 x x)))) (/.f64 1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (sqrt.f64 1/2)))
(+.f64 (+.f64 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))) (/.f64 1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (+.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (+.f64 1 (-.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2))))
(+.f64 1 (+.f64 (+.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))) (-.f64 (/.f64 1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3))) (sqrt.f64 1/2))))
(+.f64 (+.f64 1 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))) (-.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)) (+.f64 (sqrt.f64 1/2) (/.f64 -1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3))))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))) (sqrt.f64 1/2))
(+.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 1 (-.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2)))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (/.f64 1/32 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 x x))))) (sqrt.f64 1/2))
(+.f64 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)) (-.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2))))
(+.f64 1 (+.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)) (sqrt.f64 1/2))))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/128 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))) (sqrt.f64 1/2))
(+.f64 1 (-.f64 (+.f64 (+.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (/.f64 1/32 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 x x)))) (/.f64 1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (sqrt.f64 1/2)))
(+.f64 (+.f64 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))) (/.f64 1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (+.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (+.f64 1 (-.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2))))
(+.f64 1 (+.f64 (+.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))) (-.f64 (/.f64 1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3))) (sqrt.f64 1/2))))
(+.f64 (+.f64 1 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))) (-.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)) (+.f64 (sqrt.f64 1/2) (/.f64 -1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3))))))
(sqrt.f64 1/2)
(-.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (sqrt.f64 1/2) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
(-.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(-.f64 (sqrt.f64 1/2) (+.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (/.f64 1/32 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 x x)))))
(-.f64 (sqrt.f64 1/2) (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (sqrt.f64 1/2) (+.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (*.f64 x x))))
(-.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/128 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))))
(-.f64 (-.f64 (sqrt.f64 1/2) (/.f64 1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (+.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (/.f64 1/32 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 x x)))))
(-.f64 (-.f64 (sqrt.f64 1/2) (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))) (/.f64 1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3))))
(+.f64 (sqrt.f64 1/2) (-.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)) (+.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3))))))
(+.f64 (+.f64 (sqrt.f64 1/2) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))) (+.f64 (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 (/.f64 -1/128 (pow.f64 (sqrt.f64 1/2) 5)) (pow.f64 x 3))))
(+.f64 (+.f64 (sqrt.f64 1/2) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))) (+.f64 (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 -1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))))
(sqrt.f64 1/2)
(-.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (sqrt.f64 1/2) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
(-.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(-.f64 (sqrt.f64 1/2) (+.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (/.f64 1/32 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 x x)))))
(-.f64 (sqrt.f64 1/2) (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (sqrt.f64 1/2) (+.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (*.f64 x x))))
(-.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/128 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))))
(-.f64 (-.f64 (sqrt.f64 1/2) (/.f64 1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (+.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (/.f64 1/32 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 x x)))))
(-.f64 (-.f64 (sqrt.f64 1/2) (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))) (/.f64 1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3))))
(+.f64 (sqrt.f64 1/2) (-.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)) (+.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3))))))
(+.f64 (+.f64 (sqrt.f64 1/2) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))) (+.f64 (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 (/.f64 -1/128 (pow.f64 (sqrt.f64 1/2) 5)) (pow.f64 x 3))))
(+.f64 (+.f64 (sqrt.f64 1/2) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))) (+.f64 (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 -1/128 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))))
(/.f64 -1/2 x)
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/2 (/.f64 1/2 x))
(+.f64 1/2 (/.f64 -1/2 x))
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/2 (/.f64 1/2 x))
(+.f64 1/2 (/.f64 -1/2 x))
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/2 (/.f64 1/2 x))
(+.f64 1/2 (/.f64 -1/2 x))
1/2
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/2 (/.f64 1/2 x))
(+.f64 1/2 (/.f64 -1/2 x))
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/2 (/.f64 1/2 x))
(+.f64 1/2 (/.f64 -1/2 x))
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/2 (/.f64 1/2 x))
(+.f64 1/2 (/.f64 -1/2 x))
1/2
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/2 (/.f64 1/2 x))
(+.f64 1/2 (/.f64 -1/2 x))
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/2 (/.f64 1/2 x))
(+.f64 1/2 (/.f64 -1/2 x))
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/2 (/.f64 1/2 x))
(+.f64 1/2 (/.f64 -1/2 x))

localize26.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 1/8 (*.f64 x x))
✓14.3b
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
Compiler

Compiled 26 to 15 computations (42.3% saved)

series6.0ms (0%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
1.0ms
x
@-inf
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
1.0ms
x
@0
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
1.0ms
x
@inf
(*.f64 1/8 (*.f64 x x))
1.0ms
x
@0
(*.f64 1/8 (*.f64 x x))

rewrite109.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
746×pow1_binary64
698×add-log-exp_binary64
698×log1p-expm1-u_binary64
698×expm1-log1p-u_binary64
684×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0921
118821
2197721
Stop Event
1×node limit
Counts
2 → 32
Calls
Call 1
Inputs
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(*.f64 1/8 (*.f64 x x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 -11/128 (pow.f64 x 4)) (*.f64 x (*.f64 x 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 -11/128 (pow.f64 x 4)) 1) (*.f64 x (*.f64 x 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))) (pow.f64 (cbrt.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))) 2) (cbrt.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))) (sqrt.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 -11/128 (pow.f64 x 4)) 3) (pow.f64 (*.f64 x (*.f64 x 1/8)) 3)) (+.f64 (*.f64 (*.f64 -11/128 (pow.f64 x 4)) (*.f64 -11/128 (pow.f64 x 4))) (-.f64 (*.f64 (pow.f64 x 4) 1/64) (*.f64 (*.f64 -11/128 (pow.f64 x 4)) (*.f64 x (*.f64 x 1/8))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 -11/128 (pow.f64 x 4)) (*.f64 -11/128 (pow.f64 x 4))) (*.f64 (pow.f64 x 4) 1/64)) (-.f64 (*.f64 -11/128 (pow.f64 x 4)) (*.f64 x (*.f64 x 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (*.f64 x 1/8))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 x 1/8)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (*.f64 x 1/8)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (*.f64 x 1/8))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 1/8)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 4) 1/64))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/8) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (*.f64 x 1/8)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (*.f64 x 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (*.f64 x 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (*.f64 x 1/8))))))))

simplify218.0ms (1.6%)

Algorithm
1×egg-herbie
Rules
1057×sqr-pow_binary64
538×fma-def_binary64
506×pow-sqr_binary64
443×cube-prod_binary64
419×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
011231
122231
245231
3114231
4354231
51406231
62652231
73114231
83283231
93482231
103753231
114112231
124563231
135094231
145720231
156469231
166783231
177007231
187201231
197257231
207279231
Stop Event
1×node limit
Counts
56 → 37
Calls
Call 1
Inputs
(*.f64 1/8 (pow.f64 x 2))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(*.f64 -11/128 (pow.f64 x 4))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(*.f64 -11/128 (pow.f64 x 4))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
Outputs
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(*.f64 x (fma.f64 1/8 x (*.f64 -11/128 (pow.f64 x 3))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(*.f64 x (fma.f64 1/8 x (*.f64 -11/128 (pow.f64 x 3))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(*.f64 x (fma.f64 1/8 x (*.f64 -11/128 (pow.f64 x 3))))
(*.f64 -11/128 (pow.f64 x 4))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(*.f64 x (fma.f64 1/8 x (*.f64 -11/128 (pow.f64 x 3))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(*.f64 x (fma.f64 1/8 x (*.f64 -11/128 (pow.f64 x 3))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(*.f64 x (fma.f64 1/8 x (*.f64 -11/128 (pow.f64 x 3))))
(*.f64 -11/128 (pow.f64 x 4))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(*.f64 x (fma.f64 1/8 x (*.f64 -11/128 (pow.f64 x 3))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(*.f64 x (fma.f64 1/8 x (*.f64 -11/128 (pow.f64 x 3))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(*.f64 x (fma.f64 1/8 x (*.f64 -11/128 (pow.f64 x 3))))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))

localize72.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1/2 (hypot.f64 1 x))
0.0b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓0.1b
(exp.f64 (log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
✓2.0b
(log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
Compiler

Compiled 57 to 49 computations (14% saved)

series18.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
6.0ms
x
@-inf
(log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
3.0ms
x
@inf
(log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
3.0ms
x
@0
(log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
3.0ms
x
@inf
(exp.f64 (log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
2.0ms
x
@-inf
(exp.f64 (log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

rewrite86.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
990×pow1_binary64
917×add-log-exp_binary64
917×expm1-log1p-u_binary64
916×log1p-expm1-u_binary64
111×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01134
122729
2275329
Stop Event
1×node limit
Counts
2 → 42
Calls
Call 1
Inputs
(log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(exp.f64 (log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2))) (log.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (log.f64 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (pow.f64 (cbrt.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2) (cbrt.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2)) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (+.f64 1 (-.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (sqrt.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)) (cbrt.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))))

simplify115.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
539×fma-def_binary64
513×fma-neg_binary64
451×associate-/r*_binary64
355×associate-*r*_binary64
332×associate-*l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01331557
14051231
215081025
368111020
Stop Event
1×node limit
Counts
66 → 85
Calls
Call 1
Inputs
(+.f64 (log.f64 1/8) (*.f64 2 (log.f64 x)))
(+.f64 (*.f64 -11/16 (pow.f64 x 2)) (+.f64 (log.f64 1/8) (*.f64 2 (log.f64 x))))
(+.f64 (*.f64 -11/16 (pow.f64 x 2)) (+.f64 (*.f64 155/512 (pow.f64 x 4)) (+.f64 (log.f64 1/8) (*.f64 2 (log.f64 x)))))
(+.f64 (*.f64 -11/16 (pow.f64 x 2)) (+.f64 (*.f64 155/512 (pow.f64 x 4)) (+.f64 (*.f64 -1153/6144 (pow.f64 x 6)) (+.f64 (log.f64 1/8) (*.f64 2 (log.f64 x))))))
(log.f64 (-.f64 1 (sqrt.f64 1/2)))
(-.f64 (log.f64 (-.f64 1 (sqrt.f64 1/2))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (*.f64 x (-.f64 1 (sqrt.f64 1/2)))))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (-.f64 1 (sqrt.f64 1/2))))) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (pow.f64 x 2))) (log.f64 (-.f64 1 (sqrt.f64 1/2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (*.f64 x (-.f64 1 (sqrt.f64 1/2)))))))
(-.f64 (+.f64 (*.f64 1/6 (/.f64 (-.f64 (+.f64 (*.f64 -3 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (-.f64 1 (sqrt.f64 1/2))))) (*.f64 3/64 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 4) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 3))))) (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (-.f64 1 (sqrt.f64 1/2))))) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (pow.f64 x 2))) (log.f64 (-.f64 1 (sqrt.f64 1/2))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (*.f64 x (-.f64 1 (sqrt.f64 1/2)))))))
(log.f64 (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (*.f64 x (-.f64 1 (sqrt.f64 1/2)))))) (log.f64 (-.f64 1 (sqrt.f64 1/2))))
(+.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (-.f64 1 (sqrt.f64 1/2))))) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (pow.f64 x 2))) (+.f64 (log.f64 (-.f64 1 (sqrt.f64 1/2))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (*.f64 x (-.f64 1 (sqrt.f64 1/2))))))))
(+.f64 (*.f64 -1/6 (/.f64 (-.f64 (+.f64 (*.f64 -3 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (-.f64 1 (sqrt.f64 1/2))))) (*.f64 3/64 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 4) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 3))))) (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (-.f64 1 (sqrt.f64 1/2))))) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (pow.f64 x 2))) (+.f64 (log.f64 (-.f64 1 (sqrt.f64 1/2))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (*.f64 x (-.f64 1 (sqrt.f64 1/2)))))))))
(exp.f64 (+.f64 (log.f64 1/8) (*.f64 2 (log.f64 x))))
(+.f64 (*.f64 -11/16 (*.f64 (exp.f64 (+.f64 (log.f64 1/8) (*.f64 2 (log.f64 x)))) (pow.f64 x 2))) (exp.f64 (+.f64 (log.f64 1/8) (*.f64 2 (log.f64 x)))))
(+.f64 (*.f64 -11/16 (*.f64 (exp.f64 (+.f64 (log.f64 1/8) (*.f64 2 (log.f64 x)))) (pow.f64 x 2))) (+.f64 (*.f64 69/128 (*.f64 (exp.f64 (+.f64 (log.f64 1/8) (*.f64 2 (log.f64 x)))) (pow.f64 x 4))) (exp.f64 (+.f64 (log.f64 1/8) (*.f64 2 (log.f64 x))))))
(+.f64 (*.f64 -11/16 (*.f64 (exp.f64 (+.f64 (log.f64 1/8) (*.f64 2 (log.f64 x)))) (pow.f64 x 2))) (+.f64 (*.f64 -1843/4096 (*.f64 (exp.f64 (+.f64 (log.f64 1/8) (*.f64 2 (log.f64 x)))) (pow.f64 x 6))) (+.f64 (*.f64 69/128 (*.f64 (exp.f64 (+.f64 (log.f64 1/8) (*.f64 2 (log.f64 x)))) (pow.f64 x 4))) (exp.f64 (+.f64 (log.f64 1/8) (*.f64 2 (log.f64 x)))))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 1/2 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (-.f64 1 (sqrt.f64 1/2))))) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2)))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (-.f64 1 (sqrt.f64 1/2))) (pow.f64 x 2)) 1) (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 1/2 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (-.f64 1 (sqrt.f64 1/2))))) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2)))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (-.f64 1 (sqrt.f64 1/2))) (pow.f64 x 2)) (+.f64 1 (/.f64 (*.f64 (-.f64 (+.f64 (*.f64 1/6 (-.f64 (+.f64 (*.f64 -3 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (-.f64 1 (sqrt.f64 1/2))))) (*.f64 3/64 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 4) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 3)))))) (*.f64 -1/8 (/.f64 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (-.f64 1 (sqrt.f64 1/2))))) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (*.f64 (sqrt.f64 1/2) (-.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/384 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 3))))) (-.f64 1 (sqrt.f64 1/2))) (pow.f64 x 3)))) (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 1/2 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (-.f64 1 (sqrt.f64 1/2))))) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2)))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (-.f64 1 (sqrt.f64 1/2))) (pow.f64 x 2)) (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))) (sqrt.f64 1/2))
(-.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 1/2 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (-.f64 1 (sqrt.f64 1/2))))) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2)))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (-.f64 1 (sqrt.f64 1/2))) (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 -1 (/.f64 (*.f64 (-.f64 (+.f64 (*.f64 1/6 (-.f64 (+.f64 (*.f64 -3 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (-.f64 1 (sqrt.f64 1/2))))) (*.f64 3/64 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 4) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 3)))))) (*.f64 -1/8 (/.f64 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (-.f64 1 (sqrt.f64 1/2))))) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (*.f64 (sqrt.f64 1/2) (-.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/384 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 3))))) (-.f64 1 (sqrt.f64 1/2))) (pow.f64 x 3))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))) (sqrt.f64 1/2))
Outputs
(+.f64 (log.f64 1/8) (*.f64 2 (log.f64 x)))
(fma.f64 2 (log.f64 x) (log.f64 1/8))
(+.f64 (*.f64 -11/16 (pow.f64 x 2)) (+.f64 (log.f64 1/8) (*.f64 2 (log.f64 x))))
(fma.f64 -11/16 (*.f64 x x) (+.f64 (log.f64 1/8) (*.f64 2 (log.f64 x))))
(fma.f64 -11/16 (*.f64 x x) (fma.f64 2 (log.f64 x) (log.f64 1/8)))
(fma.f64 2 (log.f64 x) (fma.f64 x (*.f64 x -11/16) (log.f64 1/8)))
(+.f64 (*.f64 -11/16 (pow.f64 x 2)) (+.f64 (*.f64 155/512 (pow.f64 x 4)) (+.f64 (log.f64 1/8) (*.f64 2 (log.f64 x)))))
(fma.f64 -11/16 (*.f64 x x) (fma.f64 155/512 (pow.f64 x 4) (+.f64 (log.f64 1/8) (*.f64 2 (log.f64 x)))))
(fma.f64 -11/16 (*.f64 x x) (fma.f64 155/512 (pow.f64 x 4) (fma.f64 2 (log.f64 x) (log.f64 1/8))))
(fma.f64 x (*.f64 x -11/16) (fma.f64 2 (log.f64 x) (fma.f64 155/512 (pow.f64 x 4) (log.f64 1/8))))
(+.f64 (*.f64 -11/16 (pow.f64 x 2)) (+.f64 (*.f64 155/512 (pow.f64 x 4)) (+.f64 (*.f64 -1153/6144 (pow.f64 x 6)) (+.f64 (log.f64 1/8) (*.f64 2 (log.f64 x))))))
(fma.f64 -11/16 (*.f64 x x) (fma.f64 155/512 (pow.f64 x 4) (fma.f64 -1153/6144 (pow.f64 x 6) (+.f64 (log.f64 1/8) (*.f64 2 (log.f64 x))))))
(fma.f64 -11/16 (*.f64 x x) (fma.f64 155/512 (pow.f64 x 4) (fma.f64 -1153/6144 (pow.f64 x 6) (fma.f64 2 (log.f64 x) (log.f64 1/8)))))
(fma.f64 x (*.f64 x -11/16) (fma.f64 155/512 (pow.f64 x 4) (fma.f64 2 (log.f64 x) (fma.f64 -1153/6144 (pow.f64 x 6) (log.f64 1/8)))))
(log.f64 (-.f64 1 (sqrt.f64 1/2)))
(log1p.f64 (neg.f64 (sqrt.f64 1/2)))
(-.f64 (log.f64 (-.f64 1 (sqrt.f64 1/2))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (*.f64 x (-.f64 1 (sqrt.f64 1/2)))))))
(-.f64 (log.f64 (-.f64 1 (sqrt.f64 1/2))) (/.f64 1/4 (*.f64 (*.f64 x (sqrt.f64 1/2)) (-.f64 1 (sqrt.f64 1/2)))))
(+.f64 (log1p.f64 (neg.f64 (sqrt.f64 1/2))) (/.f64 -1/4 (*.f64 x (*.f64 (sqrt.f64 1/2) (-.f64 1 (sqrt.f64 1/2))))))
(+.f64 (log1p.f64 (neg.f64 (sqrt.f64 1/2))) (/.f64 -1/4 (*.f64 x (+.f64 (sqrt.f64 1/2) -1/2))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (-.f64 1 (sqrt.f64 1/2))))) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (pow.f64 x 2))) (log.f64 (-.f64 1 (sqrt.f64 1/2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (*.f64 x (-.f64 1 (sqrt.f64 1/2)))))))
(-.f64 (fma.f64 1/2 (/.f64 (-.f64 (/.f64 1/16 (*.f64 (-.f64 1 (sqrt.f64 1/2)) (pow.f64 (sqrt.f64 1/2) 3))) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2)))) (*.f64 x x)) (log.f64 (-.f64 1 (sqrt.f64 1/2)))) (/.f64 1/4 (*.f64 (*.f64 x (sqrt.f64 1/2)) (-.f64 1 (sqrt.f64 1/2)))))
(+.f64 (fma.f64 1/2 (/.f64 (fma.f64 1/16 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (-.f64 1 (sqrt.f64 1/2))) (/.f64 -1/8 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))) (*.f64 x x)) (log1p.f64 (neg.f64 (sqrt.f64 1/2)))) (/.f64 -1/4 (*.f64 x (*.f64 (sqrt.f64 1/2) (-.f64 1 (sqrt.f64 1/2))))))
(+.f64 (log1p.f64 (neg.f64 (sqrt.f64 1/2))) (+.f64 (/.f64 (fma.f64 1/2 (/.f64 1/8 (+.f64 (sqrt.f64 1/2) -1/2)) (/.f64 -1/16 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))) (*.f64 x x)) (/.f64 -1/4 (*.f64 x (+.f64 (sqrt.f64 1/2) -1/2)))))
(+.f64 (log1p.f64 (neg.f64 (sqrt.f64 1/2))) (fma.f64 (/.f64 1/2 (*.f64 x x)) (+.f64 (/.f64 1/8 (+.f64 (sqrt.f64 1/2) -1/2)) (/.f64 -1/8 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))) (/.f64 -1/4 (*.f64 x (+.f64 (sqrt.f64 1/2) -1/2)))))
(-.f64 (+.f64 (*.f64 1/6 (/.f64 (-.f64 (+.f64 (*.f64 -3 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (-.f64 1 (sqrt.f64 1/2))))) (*.f64 3/64 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 4) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 3))))) (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (-.f64 1 (sqrt.f64 1/2))))) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (pow.f64 x 2))) (log.f64 (-.f64 1 (sqrt.f64 1/2))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (*.f64 x (-.f64 1 (sqrt.f64 1/2)))))))
(-.f64 (fma.f64 1/6 (/.f64 (-.f64 (fma.f64 -3 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4) (*.f64 (sqrt.f64 1/2) (-.f64 1 (sqrt.f64 1/2)))) (/.f64 3/64 (*.f64 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2) (pow.f64 (sqrt.f64 1/2) 4)))) (/.f64 1/32 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 3)))) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 (-.f64 (/.f64 1/16 (*.f64 (-.f64 1 (sqrt.f64 1/2)) (pow.f64 (sqrt.f64 1/2) 3))) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2)))) (*.f64 x x)) (log.f64 (-.f64 1 (sqrt.f64 1/2))))) (/.f64 1/4 (*.f64 (*.f64 x (sqrt.f64 1/2)) (-.f64 1 (sqrt.f64 1/2)))))
(+.f64 (fma.f64 1/6 (/.f64 (+.f64 (/.f64 9/16 (*.f64 (sqrt.f64 1/2) (-.f64 1 (sqrt.f64 1/2)))) (+.f64 (/.f64 3/16 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2)) (*.f64 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 3)) -1/32))) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 (fma.f64 1/16 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (-.f64 1 (sqrt.f64 1/2))) (/.f64 -1/8 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))) (*.f64 x x)) (log1p.f64 (neg.f64 (sqrt.f64 1/2))))) (/.f64 -1/4 (*.f64 x (*.f64 (sqrt.f64 1/2) (-.f64 1 (sqrt.f64 1/2))))))
(+.f64 (log1p.f64 (neg.f64 (sqrt.f64 1/2))) (+.f64 (/.f64 (fma.f64 1/2 (/.f64 1/8 (+.f64 (sqrt.f64 1/2) -1/2)) (/.f64 -1/16 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))) (*.f64 x x)) (fma.f64 1/6 (/.f64 (+.f64 (/.f64 3/16 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2)) (+.f64 (/.f64 9/16 (+.f64 (sqrt.f64 1/2) -1/2)) (/.f64 -1/32 (pow.f64 (+.f64 (sqrt.f64 1/2) -1/2) 3)))) (pow.f64 x 3)) (/.f64 -1/4 (*.f64 x (+.f64 (sqrt.f64 1/2) -1/2))))))
(log.f64 (-.f64 1 (sqrt.f64 1/2)))
(log1p.f64 (neg.f64 (sqrt.f64 1/2)))
(+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (*.f64 x (-.f64 1 (sqrt.f64 1/2)))))) (log.f64 (-.f64 1 (sqrt.f64 1/2))))
(+.f64 (log.f64 (-.f64 1 (sqrt.f64 1/2))) (/.f64 1/4 (*.f64 (*.f64 x (sqrt.f64 1/2)) (-.f64 1 (sqrt.f64 1/2)))))
(+.f64 (log1p.f64 (neg.f64 (sqrt.f64 1/2))) (/.f64 1/4 (*.f64 x (*.f64 (sqrt.f64 1/2) (-.f64 1 (sqrt.f64 1/2))))))
(+.f64 (log1p.f64 (neg.f64 (sqrt.f64 1/2))) (/.f64 1/4 (*.f64 x (+.f64 (sqrt.f64 1/2) -1/2))))
(+.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (-.f64 1 (sqrt.f64 1/2))))) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (pow.f64 x 2))) (+.f64 (log.f64 (-.f64 1 (sqrt.f64 1/2))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (*.f64 x (-.f64 1 (sqrt.f64 1/2))))))))
(+.f64 (fma.f64 1/2 (/.f64 (-.f64 (/.f64 1/16 (*.f64 (-.f64 1 (sqrt.f64 1/2)) (pow.f64 (sqrt.f64 1/2) 3))) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2)))) (*.f64 x x)) (log.f64 (-.f64 1 (sqrt.f64 1/2)))) (/.f64 1/4 (*.f64 (*.f64 x (sqrt.f64 1/2)) (-.f64 1 (sqrt.f64 1/2)))))
(+.f64 (/.f64 1/4 (*.f64 x (*.f64 (sqrt.f64 1/2) (-.f64 1 (sqrt.f64 1/2))))) (fma.f64 1/2 (/.f64 (fma.f64 1/16 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (-.f64 1 (sqrt.f64 1/2))) (/.f64 -1/8 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))) (*.f64 x x)) (log1p.f64 (neg.f64 (sqrt.f64 1/2)))))
(fma.f64 1/2 (/.f64 (+.f64 (/.f64 1/8 (+.f64 (sqrt.f64 1/2) -1/2)) (/.f64 -1/8 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))) (*.f64 x x)) (+.f64 (log1p.f64 (neg.f64 (sqrt.f64 1/2))) (/.f64 1/4 (*.f64 x (+.f64 (sqrt.f64 1/2) -1/2)))))
(+.f64 (*.f64 -1/6 (/.f64 (-.f64 (+.f64 (*.f64 -3 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (-.f64 1 (sqrt.f64 1/2))))) (*.f64 3/64 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 4) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 3))))) (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (-.f64 1 (sqrt.f64 1/2))))) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (pow.f64 x 2))) (+.f64 (log.f64 (-.f64 1 (sqrt.f64 1/2))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (*.f64 x (-.f64 1 (sqrt.f64 1/2)))))))))
(fma.f64 -1/6 (/.f64 (-.f64 (fma.f64 -3 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4) (*.f64 (sqrt.f64 1/2) (-.f64 1 (sqrt.f64 1/2)))) (/.f64 3/64 (*.f64 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2) (pow.f64 (sqrt.f64 1/2) 4)))) (/.f64 1/32 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 3)))) (pow.f64 x 3)) (+.f64 (fma.f64 1/2 (/.f64 (-.f64 (/.f64 1/16 (*.f64 (-.f64 1 (sqrt.f64 1/2)) (pow.f64 (sqrt.f64 1/2) 3))) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2)))) (*.f64 x x)) (log.f64 (-.f64 1 (sqrt.f64 1/2)))) (/.f64 1/4 (*.f64 (*.f64 x (sqrt.f64 1/2)) (-.f64 1 (sqrt.f64 1/2))))))
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(+.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (*.f64 (+.f64 (/.f64 (fma.f64 1/2 (+.f64 (/.f64 1/8 (+.f64 (sqrt.f64 1/2) -1/2)) (/.f64 -1/8 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))) (/.f64 1/16 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))) (*.f64 x x)) 1) (-.f64 1 (sqrt.f64 1/2))))
(-.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 1/2 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (-.f64 1 (sqrt.f64 1/2))))) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2)))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (-.f64 1 (sqrt.f64 1/2))) (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 -1 (/.f64 (*.f64 (-.f64 (+.f64 (*.f64 1/6 (-.f64 (+.f64 (*.f64 -3 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (-.f64 1 (sqrt.f64 1/2))))) (*.f64 3/64 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 4) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 3)))))) (*.f64 -1/8 (/.f64 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (-.f64 1 (sqrt.f64 1/2))))) (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (*.f64 (sqrt.f64 1/2) (-.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/384 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 3))))) (-.f64 1 (sqrt.f64 1/2))) (pow.f64 x 3))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))) (sqrt.f64 1/2))
(-.f64 (+.f64 (+.f64 1 (/.f64 (fma.f64 1/2 (-.f64 (/.f64 1/16 (*.f64 (-.f64 1 (sqrt.f64 1/2)) (pow.f64 (sqrt.f64 1/2) 3))) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2)))) (/.f64 1/32 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2)))) (/.f64 (*.f64 x x) (-.f64 1 (sqrt.f64 1/2))))) (fma.f64 -1 (/.f64 (-.f64 (fma.f64 1/6 (-.f64 (fma.f64 -3 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4) (*.f64 (sqrt.f64 1/2) (-.f64 1 (sqrt.f64 1/2)))) (/.f64 3/64 (*.f64 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2) (pow.f64 (sqrt.f64 1/2) 4)))) (/.f64 1/32 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 3)))) (/.f64 (*.f64 -1/8 (-.f64 (/.f64 1/16 (*.f64 (-.f64 1 (sqrt.f64 1/2)) (pow.f64 (sqrt.f64 1/2) 3))) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (*.f64 (sqrt.f64 1/2) (-.f64 1 (sqrt.f64 1/2))))) (/.f64 1/384 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 3)))) (/.f64 (pow.f64 x 3) (-.f64 1 (sqrt.f64 1/2)))) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))) (sqrt.f64 1/2))
(+.f64 (/.f64 (fma.f64 1/2 (fma.f64 1/16 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (-.f64 1 (sqrt.f64 1/2))) (/.f64 -1/8 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))) (/.f64 1/16 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))) (/.f64 (*.f64 x x) (-.f64 1 (sqrt.f64 1/2)))) (+.f64 1 (-.f64 (-.f64 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)) (/.f64 (fma.f64 1/6 (+.f64 (/.f64 9/16 (*.f64 (sqrt.f64 1/2) (-.f64 1 (sqrt.f64 1/2)))) (+.f64 (/.f64 3/16 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2)) (*.f64 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 3)) -1/32))) (fma.f64 -1/8 (/.f64 (fma.f64 1/16 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (-.f64 1 (sqrt.f64 1/2))) (/.f64 -1/8 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))) (*.f64 (sqrt.f64 1/2) (-.f64 1 (sqrt.f64 1/2)))) (*.f64 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 3)) -1/384))) (/.f64 (pow.f64 x 3) (-.f64 1 (sqrt.f64 1/2))))) (sqrt.f64 1/2))))
(+.f64 (-.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (*.f64 (/.f64 (-.f64 1 (sqrt.f64 1/2)) (pow.f64 x 3)) (fma.f64 -1/8 (+.f64 (/.f64 1/16 (*.f64 1/4 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))) (/.f64 -1/16 (pow.f64 (+.f64 (sqrt.f64 1/2) -1/2) 3))) (fma.f64 1/6 (+.f64 (/.f64 3/16 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2)) (+.f64 (/.f64 9/16 (+.f64 (sqrt.f64 1/2) -1/2)) (/.f64 -1/32 (pow.f64 (+.f64 (sqrt.f64 1/2) -1/2) 3)))) (/.f64 -1/384 (pow.f64 (+.f64 (sqrt.f64 1/2) -1/2) 3)))))) (*.f64 (+.f64 (/.f64 (fma.f64 1/2 (+.f64 (/.f64 1/8 (+.f64 (sqrt.f64 1/2) -1/2)) (/.f64 -1/8 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))) (/.f64 1/16 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))) (*.f64 x x)) 1) (-.f64 1 (sqrt.f64 1/2))))

eval496.0ms (3.6%)

Compiler

Compiled 16964 to 15221 computations (10.3% saved)

prune159.0ms (1.1%)

Pruning

20 alts after pruning (16 fresh and 4 done)

PrunedKeptTotal
New68910699
Fresh4610
Picked101
Done145
Total69520715
Error
0.0b
Counts
715 → 20
Alt Table
Click to see full alt table
StatusErrorProgram
▶14.7b
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
▶29.8b
(*.f64 x (*.f64 x 1/8))
▶14.7b
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (/.f64 (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
15.4b
(cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))
29.9b
(+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6))))
✓34.5b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
▶44.2b
(-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))
14.7b
(/.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
✓44.6b
(-.f64 1 1)
14.7b
(/.f64 1 (/.f64 (+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))
34.3b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
33.0b
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
✓15.2b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
33.4b
(-.f64 1 (sqrt.f64 1/2))
34.0b
(/.f64 (-.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))
▶14.7b
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
✓14.7b
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
15.8b
(/.f64 1 (/.f64 (+.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
14.7b
(/.f64 (-.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
30.3b
(+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4)))
Compiler

Compiled 605 to 533 computations (11.9% saved)

localize55.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (/.f64 (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓0.0b
(/.f64 (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓0.3b
(/.f64 1/4 (fma.f64 x x 1))
✓1.6b
(-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1)))
Compiler

Compiled 128 to 105 computations (18% saved)

series9.0ms (0.1%)

Counts
4 → 48
Calls

12 calls:

TimeVariablePointExpression
3.0ms
x
@inf
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (/.f64 (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
1.0ms
x
@-inf
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (/.f64 (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
1.0ms
x
@0
(-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1)))
1.0ms
x
@inf
(-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1)))
0.0ms
x
@inf
(/.f64 1/4 (fma.f64 x x 1))

rewrite179.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
813×prod-diff_binary64
311×log1p-udef_binary64
192×add-sqr-sqrt_binary64
186×pow1_binary64
185×*-un-lft-identity_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01685
138244
2578544
Stop Event
1×node limit
Counts
4 → 259
Calls
Call 1
Inputs
(-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1)))
(/.f64 1/4 (fma.f64 x x 1))
(/.f64 (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (/.f64 (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
Outputs
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(hypot.f64 1 x)))))) 1) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (+.f64 1/4 (/.f64 -1/4 (fma.f64 x x 1)))) (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (cbrt.f64 (pow.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2))) (cbrt.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))))

simplify76.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
718×associate-*l*_binary64
461×times-frac_binary64
450×distribute-rgt-in_binary64
407×distribute-lft-in_binary64
264×associate-/l*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02212154
17941964
228161936
Stop Event
1×node limit
Counts
307 → 328
Calls
Call 1
Inputs
(*.f64 1/4 (pow.f64 x 2))
(+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 -1/4 (pow.f64 x 4)))
(+.f64 (*.f64 1/4 (pow.f64 x 6)) (+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 -1/4 (pow.f64 x 4))))
(+.f64 (*.f64 1/4 (pow.f64 x 6)) (+.f64 (*.f64 1/4 (pow.f64 x 2)) (+.f64 (*.f64 -1/4 (pow.f64 x 4)) (*.f64 -1/4 (pow.f64 x 8)))))
1/4
(-.f64 1/4 (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 1/4 (*.f64 1/4 (/.f64 1 (pow.f64 x 4)))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 1/4 (*.f64 1/4 (/.f64 1 (pow.f64 x 4)))) (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
1/4
(-.f64 1/4 (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 1/4 (*.f64 1/4 (/.f64 1 (pow.f64 x 4)))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 1/4 (*.f64 1/4 (/.f64 1 (pow.f64 x 4)))) (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
1/4
(+.f64 1/4 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 1/4 (+.f64 (*.f64 1/4 (pow.f64 x 4)) (*.f64 -1/4 (pow.f64 x 2))))
(+.f64 (*.f64 -1/4 (pow.f64 x 6)) (+.f64 1/4 (+.f64 (*.f64 1/4 (pow.f64 x 4)) (*.f64 -1/4 (pow.f64 x 2)))))
(/.f64 1/4 (pow.f64 x 2))
(-.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 2))) (*.f64 1/4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 2))) (*.f64 1/4 (/.f64 1 (pow.f64 x 6)))) (*.f64 1/4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 2))) (*.f64 1/4 (/.f64 1 (pow.f64 x 6)))) (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 4))) (*.f64 1/4 (/.f64 1 (pow.f64 x 8)))))
(/.f64 1/4 (pow.f64 x 2))
(-.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 2))) (*.f64 1/4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 2))) (*.f64 1/4 (/.f64 1 (pow.f64 x 6)))) (*.f64 1/4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 2))) (*.f64 1/4 (/.f64 1 (pow.f64 x 6)))) (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 4))) (*.f64 1/4 (/.f64 1 (pow.f64 x 8)))))
(*.f64 1/4 (pow.f64 x 2))
(+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 -3/16 (pow.f64 x 4)))
(+.f64 (*.f64 5/32 (pow.f64 x 6)) (+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 -3/16 (pow.f64 x 4))))
(+.f64 (*.f64 5/32 (pow.f64 x 6)) (+.f64 (*.f64 1/4 (pow.f64 x 2)) (+.f64 (*.f64 -3/16 (pow.f64 x 4)) (*.f64 -35/256 (pow.f64 x 8)))))
1/2
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 3/16 (/.f64 1 (pow.f64 x 5)))))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) 1/2) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1/2 (*.f64 3/16 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(*.f64 1/8 (pow.f64 x 2))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (+.f64 (*.f64 -1843/32768 (pow.f64 x 8)) (*.f64 -11/128 (pow.f64 x 4)))))
(/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)))
(-.f64 (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)))) (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))) (+.f64 (*.f64 -2 (/.f64 (*.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (+.f64 (*.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (*.f64 1/8 (/.f64 1 (sqrt.f64 1/2))))) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))))))
(-.f64 (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 3)))))) (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (pow.f64 x 3)))) (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))))))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 -2 (/.f64 (*.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (+.f64 (*.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (*.f64 1/8 (/.f64 1 (sqrt.f64 1/2))))) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))) (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))) (+.f64 (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 3)))))) (+.f64 (*.f64 2 (/.f64 (*.f64 (-.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2)))))) (+.f64 (*.f64 -2 (/.f64 (*.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) (+.f64 (*.f64 1/8 (/.f64 1 (sqrt.f64 1/2))) (*.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))) (+.f64 (sqrt.f64 1/2) 1))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))))) (+.f64 (*.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (*.f64 1/8 (/.f64 1 (sqrt.f64 1/2))))) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 3)))) (*.f64 -2 (/.f64 (*.f64 (-.f64 (*.f64 1/8 (/.f64 1 (sqrt.f64 1/2))) (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3)))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))))) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 3))))))))))
(/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))
(+.f64 (/.f64 1/8 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))) (+.f64 (/.f64 1/2 (*.f64 (+.f64 (sqrt.f64 1/2) 1) x)) (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) x))) (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))))))) (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))) (+.f64 (*.f64 -2 (/.f64 (*.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (+.f64 (*.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (*.f64 1/8 (/.f64 1 (sqrt.f64 1/2))))) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) x))) (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 -1 (/.f64 (-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2))))))) (+.f64 (*.f64 -2 (/.f64 (*.f64 (-.f64 (*.f64 1/8 (/.f64 1 (sqrt.f64 1/2))) (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3)))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))))) (+.f64 1 (sqrt.f64 1/2)))) (+.f64 (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 2 (/.f64 (*.f64 (-.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2)))))) (+.f64 (*.f64 -2 (/.f64 (*.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) (+.f64 (*.f64 1/8 (/.f64 1 (sqrt.f64 1/2))) (*.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))) (+.f64 (sqrt.f64 1/2) 1))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))))) (+.f64 (*.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (*.f64 1/8 (/.f64 1 (sqrt.f64 1/2))))) (+.f64 1 (sqrt.f64 1/2))))))) (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))))))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 -2 (/.f64 (*.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (+.f64 (*.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (*.f64 1/8 (/.f64 1 (sqrt.f64 1/2))))) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))))
Outputs
(*.f64 1/4 (pow.f64 x 2))
(*.f64 1/4 (*.f64 x x))
(+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 -1/4 (pow.f64 x 4)))
(fma.f64 1/4 (*.f64 x x) (*.f64 -1/4 (pow.f64 x 4)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -1/4 1/4))
(+.f64 (*.f64 1/4 (pow.f64 x 6)) (+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 -1/4 (pow.f64 x 4))))
(fma.f64 1/4 (pow.f64 x 6) (fma.f64 1/4 (*.f64 x x) (*.f64 -1/4 (pow.f64 x 4))))
(fma.f64 1/4 (pow.f64 x 6) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -1/4 1/4)))
(+.f64 (*.f64 1/4 (pow.f64 x 6)) (+.f64 (*.f64 1/4 (pow.f64 x 2)) (+.f64 (*.f64 -1/4 (pow.f64 x 4)) (*.f64 -1/4 (pow.f64 x 8)))))
(fma.f64 1/4 (pow.f64 x 6) (fma.f64 1/4 (*.f64 x x) (*.f64 -1/4 (+.f64 (pow.f64 x 4) (pow.f64 x 8)))))
(fma.f64 1/4 (pow.f64 x 6) (fma.f64 -1/4 (+.f64 (pow.f64 x 4) (pow.f64 x 8)) (*.f64 1/4 (*.f64 x x))))
1/4
(-.f64 1/4 (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 1/4 (/.f64 1/4 (*.f64 x x)))
(+.f64 1/4 (/.f64 -1/4 (*.f64 x x)))
(-.f64 (+.f64 1/4 (*.f64 1/4 (/.f64 1 (pow.f64 x 4)))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/4 (-.f64 (/.f64 1/4 (pow.f64 x 4)) (/.f64 1/4 (*.f64 x x))))
(+.f64 1/4 (+.f64 (/.f64 1/4 (pow.f64 x 4)) (/.f64 -1/4 (*.f64 x x))))
(+.f64 (/.f64 1/4 (pow.f64 x 4)) (+.f64 1/4 (/.f64 -1/4 (*.f64 x x))))
(-.f64 (+.f64 1/4 (*.f64 1/4 (/.f64 1 (pow.f64 x 4)))) (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 1/4 (/.f64 1/4 (pow.f64 x 4))) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 1/4 (pow.f64 x 6))))
(+.f64 1/4 (-.f64 (/.f64 1/4 (pow.f64 x 4)) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 1/4 (pow.f64 x 6)))))
(+.f64 1/4 (+.f64 (/.f64 1/4 (pow.f64 x 4)) (+.f64 (/.f64 -1/4 (*.f64 x x)) (/.f64 -1/4 (pow.f64 x 6)))))
1/4
(-.f64 1/4 (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 1/4 (/.f64 1/4 (*.f64 x x)))
(+.f64 1/4 (/.f64 -1/4 (*.f64 x x)))
(-.f64 (+.f64 1/4 (*.f64 1/4 (/.f64 1 (pow.f64 x 4)))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/4 (-.f64 (/.f64 1/4 (pow.f64 x 4)) (/.f64 1/4 (*.f64 x x))))
(+.f64 1/4 (+.f64 (/.f64 1/4 (pow.f64 x 4)) (/.f64 -1/4 (*.f64 x x))))
(+.f64 (/.f64 1/4 (pow.f64 x 4)) (+.f64 1/4 (/.f64 -1/4 (*.f64 x x))))
(-.f64 (+.f64 1/4 (*.f64 1/4 (/.f64 1 (pow.f64 x 4)))) (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 1/4 (/.f64 1/4 (pow.f64 x 4))) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 1/4 (pow.f64 x 6))))
(+.f64 1/4 (-.f64 (/.f64 1/4 (pow.f64 x 4)) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 1/4 (pow.f64 x 6)))))
(+.f64 1/4 (+.f64 (/.f64 1/4 (pow.f64 x 4)) (+.f64 (/.f64 -1/4 (*.f64 x x)) (/.f64 -1/4 (pow.f64 x 6)))))
1/4
(+.f64 1/4 (*.f64 -1/4 (pow.f64 x 2)))
(+.f64 1/4 (*.f64 (*.f64 x x) -1/4))
(fma.f64 (*.f64 x x) -1/4 1/4)
(+.f64 1/4 (+.f64 (*.f64 1/4 (pow.f64 x 4)) (*.f64 -1/4 (pow.f64 x 2))))
(+.f64 1/4 (fma.f64 1/4 (pow.f64 x 4) (*.f64 (*.f64 x x) -1/4)))
(+.f64 1/4 (fma.f64 1/4 (pow.f64 x 4) (*.f64 x (*.f64 x -1/4))))
(+.f64 (fma.f64 (*.f64 x x) -1/4 1/4) (*.f64 1/4 (pow.f64 x 4)))
(+.f64 (*.f64 -1/4 (pow.f64 x 6)) (+.f64 1/4 (+.f64 (*.f64 1/4 (pow.f64 x 4)) (*.f64 -1/4 (pow.f64 x 2)))))
(fma.f64 -1/4 (pow.f64 x 6) (+.f64 1/4 (fma.f64 1/4 (pow.f64 x 4) (*.f64 (*.f64 x x) -1/4))))
(+.f64 (fma.f64 1/4 (pow.f64 x 4) (*.f64 x (*.f64 x -1/4))) (fma.f64 -1/4 (pow.f64 x 6) 1/4))
(fma.f64 -1/4 (pow.f64 x 6) (+.f64 (fma.f64 (*.f64 x x) -1/4 1/4) (*.f64 1/4 (pow.f64 x 4))))
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (*.f64 x x))
(-.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 2))) (*.f64 1/4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 1/4 (pow.f64 x 4)))
(+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 -1/4 (pow.f64 x 4)))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 2))) (*.f64 1/4 (/.f64 1 (pow.f64 x 6)))) (*.f64 1/4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 1/4 (pow.f64 x 6))) (/.f64 1/4 (pow.f64 x 4)))
(+.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 (/.f64 1/4 (pow.f64 x 6)) (/.f64 -1/4 (pow.f64 x 4))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 2))) (*.f64 1/4 (/.f64 1 (pow.f64 x 6)))) (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 4))) (*.f64 1/4 (/.f64 1 (pow.f64 x 8)))))
(+.f64 (/.f64 1/4 (*.f64 x x)) (-.f64 (/.f64 1/4 (pow.f64 x 6)) (+.f64 (/.f64 1/4 (pow.f64 x 4)) (/.f64 1/4 (pow.f64 x 8)))))
(+.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 (+.f64 (/.f64 1/4 (pow.f64 x 6)) (/.f64 -1/4 (pow.f64 x 4))) (/.f64 -1/4 (pow.f64 x 8))))
(/.f64 1/4 (pow.f64 x 2))
(/.f64 1/4 (*.f64 x x))
(-.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 2))) (*.f64 1/4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 1/4 (pow.f64 x 4)))
(+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 -1/4 (pow.f64 x 4)))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 2))) (*.f64 1/4 (/.f64 1 (pow.f64 x 6)))) (*.f64 1/4 (/.f64 1 (pow.f64 x 4))))
(-.f64 (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 1/4 (pow.f64 x 6))) (/.f64 1/4 (pow.f64 x 4)))
(+.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 (/.f64 1/4 (pow.f64 x 6)) (/.f64 -1/4 (pow.f64 x 4))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 2))) (*.f64 1/4 (/.f64 1 (pow.f64 x 6)))) (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 4))) (*.f64 1/4 (/.f64 1 (pow.f64 x 8)))))
(+.f64 (/.f64 1/4 (*.f64 x x)) (-.f64 (/.f64 1/4 (pow.f64 x 6)) (+.f64 (/.f64 1/4 (pow.f64 x 4)) (/.f64 1/4 (pow.f64 x 8)))))
(+.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 (+.f64 (/.f64 1/4 (pow.f64 x 6)) (/.f64 -1/4 (pow.f64 x 4))) (/.f64 -1/4 (pow.f64 x 8))))
(*.f64 1/4 (pow.f64 x 2))
(*.f64 1/4 (*.f64 x x))
(+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 -3/16 (pow.f64 x 4)))
(fma.f64 1/4 (*.f64 x x) (*.f64 (pow.f64 x 4) -3/16))
(+.f64 (*.f64 5/32 (pow.f64 x 6)) (+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 -3/16 (pow.f64 x 4))))
(fma.f64 5/32 (pow.f64 x 6) (fma.f64 1/4 (*.f64 x x) (*.f64 (pow.f64 x 4) -3/16)))
(fma.f64 (pow.f64 x 6) 5/32 (fma.f64 1/4 (*.f64 x x) (*.f64 (pow.f64 x 4) -3/16)))
(+.f64 (*.f64 5/32 (pow.f64 x 6)) (+.f64 (*.f64 1/4 (pow.f64 x 2)) (+.f64 (*.f64 -3/16 (pow.f64 x 4)) (*.f64 -35/256 (pow.f64 x 8)))))
(fma.f64 5/32 (pow.f64 x 6) (fma.f64 1/4 (*.f64 x x) (fma.f64 -3/16 (pow.f64 x 4) (*.f64 (pow.f64 x 8) -35/256))))
(fma.f64 (pow.f64 x 6) 5/32 (fma.f64 1/4 (*.f64 x x) (fma.f64 (pow.f64 x 4) -3/16 (*.f64 (pow.f64 x 8) -35/256))))
(fma.f64 (pow.f64 x 6) 5/32 (fma.f64 1/4 (*.f64 x x) (fma.f64 (pow.f64 x 8) -35/256 (*.f64 (pow.f64 x 4) -3/16))))
1/2
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/2 (/.f64 1/2 x))
(-.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (/.f64 1/4 (pow.f64 x 3))) (/.f64 1/2 x))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (-.f64 1/2 (/.f64 1/2 x)))
(-.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 3/16 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (+.f64 1/2 (/.f64 1/4 (pow.f64 x 3))) (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5))))
(+.f64 1/2 (-.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5)))))
(+.f64 1/2 (+.f64 (/.f64 1/4 (pow.f64 x 3)) (-.f64 (/.f64 -1/2 x) (/.f64 3/16 (pow.f64 x 5)))))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(+.f64 1/2 (/.f64 1/2 x))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) 1/2) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 1/2 (/.f64 1/2 x)) (/.f64 1/4 (pow.f64 x 3)))
(+.f64 1/2 (-.f64 (/.f64 1/2 x) (/.f64 1/4 (pow.f64 x 3))))
(+.f64 1/2 (+.f64 (/.f64 1/2 x) (/.f64 -1/4 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1/2 (*.f64 3/16 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (-.f64 (+.f64 1/2 (/.f64 3/16 (pow.f64 x 5))) (/.f64 1/4 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 3/16 (pow.f64 x 5)) (+.f64 1/2 (/.f64 -1/4 (pow.f64 x 3)))))
(+.f64 (/.f64 1/2 x) (+.f64 1/2 (+.f64 (/.f64 3/16 (pow.f64 x 5)) (/.f64 -1/4 (pow.f64 x 3)))))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 (*.f64 x x) 1/8)
(*.f64 x (*.f64 x 1/8))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (*.f64 x x) (*.f64 (pow.f64 x 4) -11/128))
(fma.f64 (*.f64 x x) 1/8 (*.f64 (pow.f64 x 4) -11/128))
(fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
(fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))
(fma.f64 (*.f64 x x) 1/8 (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (pow.f64 x 6) 69/1024)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (+.f64 (*.f64 -1843/32768 (pow.f64 x 8)) (*.f64 -11/128 (pow.f64 x 4)))))
(fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 -1843/32768 (pow.f64 x 8) (*.f64 (pow.f64 x 4) -11/128))))
(fma.f64 (*.f64 x x) 1/8 (fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (pow.f64 x 8) -1843/32768))))
(/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (neg.f64 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) x)))
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) x))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (+.f64 (/.f64 -1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) x))
(-.f64 (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)))) (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))) (+.f64 (*.f64 -2 (/.f64 (*.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (+.f64 (*.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (*.f64 1/8 (/.f64 1 (sqrt.f64 1/2))))) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))))))
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(+.f64 (/.f64 (/.f64 1/2 x) (+.f64 1 (sqrt.f64 1/2))) (-.f64 (-.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (+.f64 (/.f64 (/.f64 1/8 (+.f64 1 (sqrt.f64 1/2))) (*.f64 x (+.f64 1/2 (sqrt.f64 1/2)))) (/.f64 1/64 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (*.f64 x x) (+.f64 1/4 (*.f64 1/2 (sqrt.f64 1/2)))))))) (/.f64 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))) (*.f64 x (*.f64 x (+.f64 1 (sqrt.f64 1/2)))))) (fma.f64 -2 (*.f64 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (+.f64 1 (sqrt.f64 1/2))) (/.f64 (+.f64 (fma.f64 1/2 (sqrt.f64 1/2) 1/2) (/.f64 1/8 (sqrt.f64 1/2))) (*.f64 x x))) (/.f64 1/2 (*.f64 x (*.f64 x (+.f64 1 (sqrt.f64 1/2))))))))
(+.f64 (/.f64 1/2 (+.f64 x (*.f64 (sqrt.f64 1/2) x))) (+.f64 (/.f64 (/.f64 (/.f64 1/32 (+.f64 1/2 (sqrt.f64 1/2))) (+.f64 1 (sqrt.f64 1/2))) (*.f64 x x)) (+.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (/.f64 1/8 (+.f64 1 (sqrt.f64 1/2))) (*.f64 x (+.f64 1/2 (sqrt.f64 1/2))))) (-.f64 (/.f64 -1/8 (*.f64 (+.f64 1/2 (sqrt.f64 1/2)) (*.f64 x (+.f64 x (*.f64 (sqrt.f64 1/2) x))))) (fma.f64 -2 (*.f64 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) x) (/.f64 (+.f64 (fma.f64 1/2 (sqrt.f64 1/2) 1/2) (/.f64 1/8 (sqrt.f64 1/2))) (+.f64 x (*.f64 (sqrt.f64 1/2) x)))) (/.f64 1/2 (*.f64 x (+.f64 x (*.f64 (sqrt.f64 1/2) x)))))))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) x))) (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 -1 (/.f64 (-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2))))))) (+.f64 (*.f64 -2 (/.f64 (*.f64 (-.f64 (*.f64 1/8 (/.f64 1 (sqrt.f64 1/2))) (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3)))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))))) (+.f64 1 (sqrt.f64 1/2)))) (+.f64 (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 2 (/.f64 (*.f64 (-.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2)))))) (+.f64 (*.f64 -2 (/.f64 (*.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) (+.f64 (*.f64 1/8 (/.f64 1 (sqrt.f64 1/2))) (*.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))) (+.f64 (sqrt.f64 1/2) 1))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))))) (+.f64 (*.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (*.f64 1/8 (/.f64 1 (sqrt.f64 1/2))))) (+.f64 1 (sqrt.f64 1/2))))))) (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))))))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 -2 (/.f64 (*.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) (+.f64 (*.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (*.f64 1/8 (/.f64 1 (sqrt.f64 1/2))))) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))))
(+.f64 (/.f64 1/2 (*.f64 x (+.f64 1 (sqrt.f64 1/2)))) (-.f64 (+.f64 (/.f64 1/64 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (*.f64 x x) (+.f64 1 (sqrt.f64 1/2)))))) (fma.f64 -1 (/.f64 (-.f64 (+.f64 (/.f64 1/64 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 (sqrt.f64 1/2) 3)))) (/.f64 1/4 (+.f64 1 (sqrt.f64 1/2)))) (fma.f64 -2 (/.f64 (-.f64 (/.f64 1/8 (sqrt.f64 1/2)) (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 3))) (/.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))))) (fma.f64 1/4 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))) (*.f64 2 (/.f64 (-.f64 (/.f64 1/64 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 (sqrt.f64 1/2) 3)))) (fma.f64 -2 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (/.f64 (+.f64 1 (sqrt.f64 1/2)) (fma.f64 1/2 (+.f64 1 (sqrt.f64 1/2)) (/.f64 1/8 (sqrt.f64 1/2))))) (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))))) (/.f64 (+.f64 1 (sqrt.f64 1/2)) (fma.f64 1/2 (+.f64 1 (sqrt.f64 1/2)) (/.f64 1/8 (sqrt.f64 1/2))))))))) (pow.f64 x 3)) (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (*.f64 x (+.f64 1 (sqrt.f64 1/2))))))))) (+.f64 (/.f64 1/2 (*.f64 (*.f64 x x) (+.f64 1 (sqrt.f64 1/2)))) (fma.f64 -2 (*.f64 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (+.f64 1 (sqrt.f64 1/2))) (/.f64 (fma.f64 1/2 (+.f64 1 (sqrt.f64 1/2)) (/.f64 1/8 (sqrt.f64 1/2))) (*.f64 x x))) (/.f64 1/8 (*.f64 (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))) (*.f64 (*.f64 x x) (+.f64 1 (sqrt.f64 1/2)))))))))
(+.f64 (+.f64 (/.f64 1/64 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (*.f64 x x) (+.f64 1/4 (*.f64 1/2 (sqrt.f64 1/2)))))) (-.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (/.f64 1/8 (+.f64 1 (sqrt.f64 1/2))) (*.f64 x (+.f64 1/2 (sqrt.f64 1/2))))) (/.f64 (-.f64 (+.f64 (/.f64 1/64 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/4 (*.f64 1/2 (sqrt.f64 1/2))))) (/.f64 1/4 (+.f64 1 (sqrt.f64 1/2)))) (fma.f64 -2 (*.f64 (/.f64 (-.f64 (/.f64 1/8 (sqrt.f64 1/2)) (/.f64 1/32 (sqrt.f64 1/2))) (+.f64 1 (sqrt.f64 1/2))) (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2)))))) (fma.f64 2 (*.f64 (/.f64 (-.f64 (/.f64 1/64 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/4 (*.f64 1/2 (sqrt.f64 1/2))))) (fma.f64 -2 (*.f64 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (+.f64 1 (sqrt.f64 1/2))) (+.f64 (fma.f64 1/2 (sqrt.f64 1/2) 1/2) (/.f64 1/8 (sqrt.f64 1/2)))) (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))))) (+.f64 1 (sqrt.f64 1/2))) (+.f64 (fma.f64 1/2 (sqrt.f64 1/2) 1/2) (/.f64 1/8 (sqrt.f64 1/2)))) (/.f64 -3/64 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))))) (pow.f64 x 3)))) (-.f64 (/.f64 (/.f64 1/2 x) (+.f64 1 (sqrt.f64 1/2))) (+.f64 (/.f64 1/2 (*.f64 x (*.f64 x (+.f64 1 (sqrt.f64 1/2))))) (fma.f64 -2 (*.f64 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (+.f64 1 (sqrt.f64 1/2))) (/.f64 (+.f64 (fma.f64 1/2 (sqrt.f64 1/2) 1/2) (/.f64 1/8 (sqrt.f64 1/2))) (*.f64 x x))) (/.f64 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))) (*.f64 x (*.f64 x (+.f64 1 (sqrt.f64 1/2)))))))))
(+.f64 (/.f64 1/2 (+.f64 x (*.f64 (sqrt.f64 1/2) x))) (+.f64 (/.f64 (/.f64 (/.f64 1/32 (+.f64 1/2 (sqrt.f64 1/2))) (+.f64 1 (sqrt.f64 1/2))) (*.f64 x x)) (+.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (-.f64 (/.f64 (/.f64 1/8 (+.f64 1 (sqrt.f64 1/2))) (*.f64 x (+.f64 1/2 (sqrt.f64 1/2)))) (/.f64 (+.f64 (/.f64 (/.f64 1/32 (+.f64 1/2 (sqrt.f64 1/2))) (+.f64 1 (sqrt.f64 1/2))) (-.f64 (/.f64 1/4 (+.f64 1 (sqrt.f64 1/2))) (fma.f64 -2 (*.f64 (-.f64 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))) (/.f64 1/32 (+.f64 1/2 (sqrt.f64 1/2)))) (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2)))))) (fma.f64 2 (*.f64 (/.f64 (-.f64 (/.f64 (/.f64 1/32 (+.f64 1/2 (sqrt.f64 1/2))) (+.f64 1 (sqrt.f64 1/2))) (fma.f64 -2 (*.f64 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (+.f64 1 (sqrt.f64 1/2))) (+.f64 (fma.f64 1/2 (sqrt.f64 1/2) 1/2) (/.f64 1/8 (sqrt.f64 1/2)))) (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))))) (+.f64 1 (sqrt.f64 1/2))) (+.f64 (fma.f64 1/2 (sqrt.f64 1/2) 1/2) (/.f64 1/8 (sqrt.f64 1/2)))) (/.f64 -3/64 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2)))))))) (pow.f64 x 3)))) (-.f64 (/.f64 -1/8 (*.f64 (+.f64 1/2 (sqrt.f64 1/2)) (*.f64 x (+.f64 x (*.f64 (sqrt.f64 1/2) x))))) (fma.f64 -2 (*.f64 (/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) x) (/.f64 (+.f64 (fma.f64 1/2 (sqrt.f64 1/2) 1/2) (/.f64 1/8 (sqrt.f64 1/2))) (+.f64 x (*.f64 (sqrt.f64 1/2) x)))) (/.f64 1/2 (*.f64 x (+.f64 x (*.f64 (sqrt.f64 1/2) x)))))))))

localize5.0ms (0%)

Compiler

Compiled 11 to 7 computations (36.4% saved)

localize10.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓1.6b
(-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))
Compiler

Compiled 21 to 15 computations (28.6% saved)

series54.0ms (0.4%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
53.0ms
x
@0
(-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))
1.0ms
x
@inf
(-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))
1.0ms
x
@-inf
(-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))

rewrite54.0ms (0.4%)

Algorithm
1×batch-egg-rewrite
Rules
705×pow1_binary64
658×add-log-exp_binary64
658×log1p-expm1-u_binary64
658×expm1-log1p-u_binary64
646×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
114511
2172711
Stop Event
1×node limit
Counts
1 → 28
Calls
Call 1
Inputs
(-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (fma.f64 x (*.f64 x -1/8) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (fma.f64 x (*.f64 x -1/8) 1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (fma.f64 x (*.f64 x -1/8) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (fma.f64 x (*.f64 x -1/8) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (fma.f64 x (*.f64 x -1/8) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))) (pow.f64 (cbrt.f64 (-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))) 2) (cbrt.f64 (-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))) (sqrt.f64 (-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (fma.f64 x (*.f64 x -1/8) 1) 3)) (/.f64 1 (+.f64 1 (*.f64 (fma.f64 x (*.f64 x -1/8) 1) (+.f64 1 (fma.f64 x (*.f64 x -1/8) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (fma.f64 x (*.f64 x -1/8) 1) 2)) (/.f64 1 (+.f64 1 (fma.f64 x (*.f64 x -1/8) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (*.f64 (fma.f64 x (*.f64 x -1/8) 1) (+.f64 1 (fma.f64 x (*.f64 x -1/8) 1)))) (-.f64 1 (pow.f64 (fma.f64 x (*.f64 x -1/8) 1) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (fma.f64 x (*.f64 x -1/8) 1)) (-.f64 1 (pow.f64 (fma.f64 x (*.f64 x -1/8) 1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (fma.f64 x (*.f64 x -1/8) 1) 3)) (+.f64 1 (*.f64 (fma.f64 x (*.f64 x -1/8) 1) (+.f64 1 (fma.f64 x (*.f64 x -1/8) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (fma.f64 x (*.f64 x -1/8) 1) 2)) (+.f64 1 (fma.f64 x (*.f64 x -1/8) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (fma.f64 x (*.f64 x -1/8) 1) 3))) (neg.f64 (+.f64 1 (*.f64 (fma.f64 x (*.f64 x -1/8) 1) (+.f64 1 (fma.f64 x (*.f64 x -1/8) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (fma.f64 x (*.f64 x -1/8) 1) 2))) (neg.f64 (+.f64 1 (fma.f64 x (*.f64 x -1/8) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (neg.f64 (fma.f64 x (*.f64 x -1/8) 1)) 3)) (+.f64 1 (-.f64 (*.f64 (neg.f64 (fma.f64 x (*.f64 x -1/8) 1)) (neg.f64 (fma.f64 x (*.f64 x -1/8) 1))) (neg.f64 (fma.f64 x (*.f64 x -1/8) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (neg.f64 (fma.f64 x (*.f64 x -1/8) 1)) (neg.f64 (fma.f64 x (*.f64 x -1/8) 1)))) (-.f64 1 (neg.f64 (fma.f64 x (*.f64 x -1/8) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (fma.f64 x (*.f64 x -1/8) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (fma.f64 x (*.f64 x -1/8) 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1 (fma.f64 x (*.f64 x -1/8) 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (fma.f64 x (*.f64 x -1/8) 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (neg.f64 (fma.f64 x (*.f64 x -1/8) 1))))))))

simplify228.0ms (1.6%)

Algorithm
1×egg-herbie
Rules
1082×sqr-pow_binary64
617×cube-prod_binary64
559×fabs-mul_binary64
523×pow-sqr_binary64
446×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0684
11284
22384
34484
410484
531884
6126884
7214084
8230484
9248884
10269684
11299184
12338284
13386584
14443184
15511984
16595084
17634684
18664084
19692084
20699484
21703084
22797184
Stop Event
1×node limit
Counts
40 → 30
Calls
Call 1
Inputs
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (pow.f64 x 2))
Outputs
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(*.f64 x (*.f64 1/8 x))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(*.f64 x (*.f64 1/8 x))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(*.f64 x (*.f64 1/8 x))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(*.f64 x (*.f64 1/8 x))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(*.f64 x (*.f64 1/8 x))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(*.f64 x (*.f64 1/8 x))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(*.f64 x (*.f64 1/8 x))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(*.f64 x (*.f64 1/8 x))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(*.f64 x (*.f64 1/8 x))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(*.f64 x (*.f64 1/8 x))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(*.f64 x (*.f64 1/8 x))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(*.f64 x (*.f64 1/8 x))

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0b
(/.f64 1/2 (hypot.f64 1 x))
0.0b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
1.6b
(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
Compiler

Compiled 62 to 53 computations (14.5% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite65.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
585×unpow-prod-down_binary64
441×prod-diff_binary64
395×log-prod_binary64
265×fma-def_binary64
243×pow2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0915
120015
2262015
Stop Event
1×node limit
Counts
1 → 48
Calls
Call 1
Inputs
(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (/.f64 1 (+.f64 1 (-.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (pow.f64 (/.f64 1 (+.f64 1 (-.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (pow.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 2) 1/3) (cbrt.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 5/2) 1/3) (cbrt.f64 (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 2) 3) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (-.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (+.f64 1 (-.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1) (-.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))) (neg.f64 (+.f64 1 (-.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (neg.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1 (-.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/6) (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4) 1)))))

simplify72.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
856×fma-def_binary64
559×associate-*l*_binary64
410×associate-*r*_binary64
390×distribute-neg-frac_binary64
251×associate-+l+_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
056286
1167252
2550244
31846244
47107244
Stop Event
1×node limit
Counts
60 → 68
Calls
Call 1
Inputs
2
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) 2)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 2 (*.f64 11/128 (pow.f64 x 4))))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 -69/1024 (pow.f64 x 6)) (+.f64 2 (*.f64 11/128 (pow.f64 x 4)))))
(+.f64 1 (sqrt.f64 1/2))
(+.f64 (sqrt.f64 1/2) (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (sqrt.f64 1/2) (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(+.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (+.f64 (sqrt.f64 1/2) 1) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 1 (*.f64 -1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
Outputs
2
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) 2)
(fma.f64 -1/8 (*.f64 x x) 2)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 2 (*.f64 11/128 (pow.f64 x 4))))
(+.f64 (fma.f64 -1/8 (*.f64 x x) 2) (*.f64 11/128 (pow.f64 x 4)))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 11/128 (pow.f64 x 4) 2))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x 11/128) -1/8) 2)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 -69/1024 (pow.f64 x 6)) (+.f64 2 (*.f64 11/128 (pow.f64 x 4)))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 -69/1024 (pow.f64 x 6) (+.f64 2 (*.f64 11/128 (pow.f64 x 4)))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 -69/1024 (pow.f64 x 6) (fma.f64 11/128 (pow.f64 x 4) 2)))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 11/128 (pow.f64 x 4) (fma.f64 -69/1024 (pow.f64 x 6) 2)))
(+.f64 1 (sqrt.f64 1/2))
(+.f64 (sqrt.f64 1/2) (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(+.f64 (sqrt.f64 1/2) (+.f64 1 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))))
(+.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (+.f64 1 (sqrt.f64 1/2)))
(+.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))))
(+.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x)))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(+.f64 (sqrt.f64 1/2) (-.f64 (+.f64 1 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))) (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)))))
(+.f64 (+.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/32 (*.f64 (*.f64 (*.f64 x x) (sqrt.f64 1/2)) 1/2)))
(+.f64 1 (+.f64 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)) (-.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)))))
(+.f64 1 (+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (*.f64 x x)))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (sqrt.f64 1/2) (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(-.f64 (fma.f64 1/2 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (sqrt.f64 1/2) (+.f64 1 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))))) (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))))
(+.f64 (+.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (+.f64 1 (sqrt.f64 1/2))) (-.f64 (/.f64 -3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (/.f64 1/32 (*.f64 (*.f64 (*.f64 x x) (sqrt.f64 1/2)) 1/2))))
(+.f64 (sqrt.f64 1/2) (+.f64 (+.f64 1 (-.f64 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)))) (/.f64 -3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))
(+.f64 (+.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))) (+.f64 (/.f64 -3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (*.f64 x x))))
(+.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (sqrt.f64 1/2) (-.f64 1 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))))
(+.f64 1 (-.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))))
(+.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2))))
(+.f64 (sqrt.f64 1/2) (-.f64 1 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x)))
(-.f64 (+.f64 (sqrt.f64 1/2) 1) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(-.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)))))
(+.f64 (sqrt.f64 1/2) (-.f64 1 (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))))
(+.f64 (sqrt.f64 1/2) (+.f64 (-.f64 1 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))) (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2))))
(+.f64 1 (+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2))) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (*.f64 x x)))))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 1 (*.f64 -1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))) (+.f64 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 1 (*.f64 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) -1/2))) (+.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)))))
(+.f64 (+.f64 1 (sqrt.f64 1/2)) (-.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))))
(+.f64 1 (-.f64 (+.f64 (sqrt.f64 1/2) (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (+.f64 1 (/.f64 (/.f64 3/32 (sqrt.f64 1/2)) (pow.f64 x 3))) (+.f64 (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2))) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (*.f64 x x)))))

localize40.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓0.0b
(/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓0.1b
(/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓1.6b
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
Compiler

Compiled 94 to 82 computations (12.8% saved)

series14.0ms (0.1%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
3.0ms
x
@inf
(/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
3.0ms
x
@0
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
3.0ms
x
@inf
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
1.0ms
x
@inf
(/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
1.0ms
x
@-inf
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

rewrite135.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
690×log-prod_binary64
587×fma-def_binary64
365×log-div_binary64
300×fma-neg_binary64
251×expm1-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01269
128757
2451757
Stop Event
1×node limit
Counts
3 → 231
Calls
Call 1
Inputs
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 -1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (*.f64 (/.f64 (/.f64 -1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (fma.f64 (/.f64 (/.f64 -1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1 (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (fma.f64 (neg.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (/.f64 1/2 (hypot.f64 1 x)) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (cbrt.f64 (pow.f64 (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 (/.f64 (/.f64 -1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (/.f64 -1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (cbrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) 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simplify92.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
502×associate-/l*_binary64
407×distribute-rgt-in_binary64
406×associate-*l/_binary64
387×associate-*r/_binary64
360×distribute-lft-in_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02533047
19232482
234442257
Stop Event
1×node limit
Counts
267 → 293
Calls
Call 1
Inputs
(*.f64 1/8 (pow.f64 x 2))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (+.f64 (*.f64 -1843/32768 (pow.f64 x 8)) (*.f64 -11/128 (pow.f64 x 4)))))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)))
(+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/32 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2))))))) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)))))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/32 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2))))))) (pow.f64 x 2))) (+.f64 (*.f64 -1/2 (/.f64 (+.f64 (*.f64 1/4 (/.f64 (+.f64 (*.f64 1/32 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/16 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (+.f64 1 (sqrt.f64 1/2)) 2)))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (sqrt.f64 1/2)))) (+.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/128 (/.f64 1 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 4) (+.f64 1 (sqrt.f64 1/2)))))))) (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 -1 (/.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))))) x)))))) (*.f64 1/2 (/.f64 (-.f64 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/32 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))))) (pow.f64 x 3))))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(+.f64 (/.f64 1/8 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))) (+.f64 (/.f64 1/2 (*.f64 (+.f64 (sqrt.f64 1/2) 1) x)) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))))
(+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) x))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/32 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2))))))) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))))))))
(+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) x))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1/2 (+.f64 (*.f64 1/4 (/.f64 (+.f64 (*.f64 1/32 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/16 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (+.f64 1 (sqrt.f64 1/2)) 2)))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (sqrt.f64 1/2)))) (+.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/128 (/.f64 1 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 4) (+.f64 1 (sqrt.f64 1/2))))))))) (*.f64 1/2 (-.f64 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/32 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2))))))) (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))))))) (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/32 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2))))))) (pow.f64 x 2))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))))))))
1/4
(+.f64 1/4 (*.f64 -7/64 (pow.f64 x 2)))
(+.f64 1/4 (+.f64 (*.f64 -7/64 (pow.f64 x 2)) (*.f64 39/512 (pow.f64 x 4))))
(+.f64 1/4 (+.f64 (*.f64 -987/16384 (pow.f64 x 6)) (+.f64 (*.f64 -7/64 (pow.f64 x 2)) (*.f64 39/512 (pow.f64 x 4)))))
(/.f64 1/2 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))
(-.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))))
(-.f64 (+.f64 (*.f64 1/32 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (*.f64 (pow.f64 (+.f64 1 (sqrt.f64 1/2)) 2) (pow.f64 x 3)))))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (*.f64 1/32 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3)))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 3)))))))
(-.f64 (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (*.f64 1/32 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3)))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))) (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (sqrt.f64 1/2))) (*.f64 1/8 (/.f64 1 (sqrt.f64 1/2)))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (+.f64 1 (sqrt.f64 1/2))))) (*.f64 -1/8 (/.f64 (-.f64 (*.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (*.f64 1/32 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3)))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 (+.f64 1 (sqrt.f64 1/2)) 2))))))) (pow.f64 x 4))) (+.f64 (*.f64 1/32 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (*.f64 (pow.f64 (+.f64 1 (sqrt.f64 1/2)) 2) (pow.f64 x 3)))))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (*.f64 1/32 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3)))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 3)))))))
(/.f64 -1/2 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))
(neg.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))))
(-.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 1/32 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (+.f64 1 (sqrt.f64 1/2)) 2))))) (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (*.f64 1/32 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3)))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (+.f64 1 (sqrt.f64 1/2)))))) (pow.f64 x 3))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))))
(-.f64 (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (*.f64 1/32 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3)))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))) (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (sqrt.f64 1/2))) (*.f64 1/8 (/.f64 1 (sqrt.f64 1/2)))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (+.f64 1 (sqrt.f64 1/2))))) (*.f64 -1/8 (/.f64 (-.f64 (*.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (*.f64 1/32 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3)))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 (+.f64 1 (sqrt.f64 1/2)) 2))))))) (pow.f64 x 4))) (*.f64 -1 (/.f64 (-.f64 (*.f64 1/32 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (+.f64 1 (sqrt.f64 1/2)) 2))))) (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (*.f64 1/32 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 3)))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (+.f64 1 (sqrt.f64 1/2)))))) (pow.f64 x 3)))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x)))))
1/4
(+.f64 1/4 (*.f64 1/64 (pow.f64 x 2)))
(+.f64 (*.f64 -5/512 (pow.f64 x 4)) (+.f64 1/4 (*.f64 1/64 (pow.f64 x 2))))
(+.f64 (*.f64 -5/512 (pow.f64 x 4)) (+.f64 (*.f64 117/16384 (pow.f64 x 6)) (+.f64 1/4 (*.f64 1/64 (pow.f64 x 2)))))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))))
(-.f64 (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))))
(-.f64 (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2)))))) (+.f64 (*.f64 1/4 (/.f64 (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/32 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (+.f64 1 (sqrt.f64 1/2)) 2)))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (sqrt.f64 1/2)))) (*.f64 1/256 (/.f64 1 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 4) (+.f64 1 (sqrt.f64 1/2)))))))) (pow.f64 x 3))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2))))))))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))))
(+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))))))
(+.f64 (*.f64 1/4 (/.f64 (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/32 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (+.f64 1 (sqrt.f64 1/2)) 2)))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))) (+.f64 (*.f64 1/256 (/.f64 1 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 4) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 3)))))) (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 3)))))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2))))))))))))
Outputs
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
(fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 -11/128 (pow.f64 x 4))))
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1/4
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1/4
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(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/8 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 x (+.f64 (sqrt.f64 1/2) 1))))))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (/.f64 1/8 (+.f64 (sqrt.f64 1/2) 1)) (*.f64 x (+.f64 1/2 (sqrt.f64 1/2)))))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))) (+.f64 x (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))))))
(+.f64 (/.f64 1/64 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (*.f64 (*.f64 x x) (+.f64 (sqrt.f64 1/2) 1)) (pow.f64 (sqrt.f64 1/2) 3)))) (+.f64 (+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/8 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 x (+.f64 (sqrt.f64 1/2) 1)))))) (/.f64 1/32 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (*.f64 (*.f64 x x) (+.f64 (sqrt.f64 1/2) 1)) (pow.f64 (sqrt.f64 1/2) 2))))))
(+.f64 (+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (/.f64 1/8 (+.f64 (sqrt.f64 1/2) 1)) (*.f64 x (+.f64 1/2 (sqrt.f64 1/2))))) (+.f64 (/.f64 1/64 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (*.f64 x x) (+.f64 (*.f64 1/2 (sqrt.f64 1/2)) 1/4)))) (/.f64 1/32 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (*.f64 x x) (fma.f64 1/2 (sqrt.f64 1/2) 1/2))))))
(+.f64 (+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))) (+.f64 x (*.f64 (sqrt.f64 1/2) x)))) (+.f64 (/.f64 1/64 (*.f64 (*.f64 (+.f64 1/2 (sqrt.f64 1/2)) (fma.f64 1/2 (sqrt.f64 1/2) 1/2)) (*.f64 x x))) (/.f64 1/32 (*.f64 (*.f64 x x) (*.f64 1/2 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 3))))))
(+.f64 (*.f64 1/4 (/.f64 (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 1 (sqrt.f64 1/2)))))) (*.f64 1/32 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (pow.f64 (+.f64 1 (sqrt.f64 1/2)) 2)))))) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) x))))) (+.f64 (*.f64 1/256 (/.f64 1 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 4) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 3)))))) (+.f64 (*.f64 1/64 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 1/4 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 3)))))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (*.f64 (+.f64 1 (sqrt.f64 1/2)) (pow.f64 x 2))))))))))))
(fma.f64 1/4 (/.f64 (+.f64 (/.f64 1/32 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (pow.f64 (sqrt.f64 1/2) 2)))) (/.f64 1/64 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (pow.f64 (sqrt.f64 1/2) 3))))) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (pow.f64 x 3)))) (+.f64 (/.f64 1/8 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 x (+.f64 (sqrt.f64 1/2) 1))))) (+.f64 (/.f64 1/256 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (pow.f64 (sqrt.f64 1/2) 4) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (pow.f64 x 3))))) (+.f64 (/.f64 1/64 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (*.f64 (*.f64 x x) (+.f64 (sqrt.f64 1/2) 1)) (pow.f64 (sqrt.f64 1/2) 3)))) (fma.f64 1/4 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (pow.f64 x 3))))) (+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/32 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (*.f64 (*.f64 x x) (+.f64 (sqrt.f64 1/2) 1)) (pow.f64 (sqrt.f64 1/2) 2))))))))))
(+.f64 (+.f64 (/.f64 1/64 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (*.f64 x x) (+.f64 (*.f64 1/2 (sqrt.f64 1/2)) 1/4)))) (+.f64 (+.f64 (/.f64 1/32 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (*.f64 x x) (fma.f64 1/2 (sqrt.f64 1/2) 1/2)))) (+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 -3/64 (*.f64 (+.f64 1/2 (sqrt.f64 1/2)) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (pow.f64 x 3)))))) (/.f64 1/256 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (*.f64 (+.f64 (sqrt.f64 1/2) 1) (*.f64 1/4 (pow.f64 x 3))))))) (fma.f64 1/4 (/.f64 (+.f64 (/.f64 1/32 (*.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 2) (fma.f64 1/2 (sqrt.f64 1/2) 1/2))) (/.f64 1/64 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (+.f64 (*.f64 1/2 (sqrt.f64 1/2)) 1/4)))) (*.f64 (+.f64 1/2 (sqrt.f64 1/2)) (pow.f64 x 3))) (/.f64 (/.f64 1/8 (+.f64 (sqrt.f64 1/2) 1)) (*.f64 x (+.f64 1/2 (sqrt.f64 1/2))))))
(+.f64 (/.f64 (/.f64 (+.f64 (/.f64 1/128 (*.f64 1/2 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 3))) (/.f64 1/256 (*.f64 (+.f64 1/2 (sqrt.f64 1/2)) (fma.f64 1/2 (sqrt.f64 1/2) 1/2)))) (+.f64 1/2 (sqrt.f64 1/2))) (pow.f64 x 3)) (+.f64 (+.f64 (+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/32 (*.f64 (*.f64 x x) (*.f64 1/2 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 3))))) (+.f64 (/.f64 1/64 (*.f64 (*.f64 (+.f64 1/2 (sqrt.f64 1/2)) (fma.f64 1/2 (sqrt.f64 1/2) 1/2)) (*.f64 x x))) (/.f64 (/.f64 (/.f64 -3/64 (+.f64 1/2 (sqrt.f64 1/2))) (+.f64 (sqrt.f64 1/2) 1)) (pow.f64 x 3)))) (+.f64 (/.f64 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))) (+.f64 x (*.f64 (sqrt.f64 1/2) x))) (/.f64 1/256 (*.f64 (*.f64 1/4 (pow.f64 (+.f64 (sqrt.f64 1/2) 1) 3)) (pow.f64 x 3))))))

eval1.7s (12.2%)

Compiler

Compiled 48799 to 43254 computations (11.4% saved)

prune255.0ms (1.8%)

Pruning

26 alts after pruning (18 fresh and 8 done)

PrunedKeptTotal
New1105101115
Fresh3811
Picked011
Done178
Total1109261135
Error
0.0b
Counts
1135 → 26
Alt Table
Click to see full alt table
StatusErrorProgram
✓14.7b
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓29.8b
(*.f64 x (*.f64 x 1/8))
15.1b
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 (fma.f64 (sqrt.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (neg.f64 (*.f64 (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (/.f64 1/4 (fma.f64 x x 1))))) (fma.f64 (neg.f64 (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (/.f64 1/4 (fma.f64 x x 1)) (*.f64 (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (/.f64 1/4 (fma.f64 x x 1)))))))
✓44.2b
(-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))
✓34.5b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
38.2b
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)
29.9b
(+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6))))
14.7b
(/.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
14.7b
(*.f64 (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (+.f64 1/4 (/.f64 -1/4 (fma.f64 x x 1)))) (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓14.7b
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
15.2b
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 (fma.f64 (sqrt.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (neg.f64 (*.f64 (+.f64 1/4 (-.f64 (/.f64 1/4 (fma.f64 x x 1)) (/.f64 1/4 (hypot.f64 1 x)))) (/.f64 (/.f64 1/4 (fma.f64 x x 1)) (+.f64 1/8 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3))))))) (fma.f64 (neg.f64 (+.f64 1/4 (-.f64 (/.f64 1/4 (fma.f64 x x 1)) (/.f64 1/4 (hypot.f64 1 x))))) (/.f64 (/.f64 1/4 (fma.f64 x x 1)) (+.f64 1/8 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3)))) (*.f64 (+.f64 1/4 (-.f64 (/.f64 1/4 (fma.f64 x x 1)) (/.f64 1/4 (hypot.f64 1 x)))) (/.f64 (/.f64 1/4 (fma.f64 x x 1)) (+.f64 1/8 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3)))))))))
▶14.7b
(/.f64 1 (/.f64 (+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))
✓44.6b
(-.f64 1 1)
33.0b
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
34.3b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
15.8b
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))))
▶14.7b
(/.f64 (/.f64 (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
32.7b
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 (fma.f64 (sqrt.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (neg.f64 (*.f64 (/.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (/.f64 (cbrt.f64 (/.f64 1/16 (pow.f64 (fma.f64 x x 1) 2))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (cbrt.f64 (/.f64 1/16 (pow.f64 (fma.f64 x x 1) 2))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (*.f64 (/.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (/.f64 (cbrt.f64 (/.f64 1/16 (pow.f64 (fma.f64 x x 1) 2))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))
✓15.2b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
▶33.4b
(-.f64 1 (sqrt.f64 1/2))
34.0b
(/.f64 (-.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))
✓14.7b
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
14.7b
(/.f64 (-.f64 (/.f64 1/4 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2)) (*.f64 (/.f64 (/.f64 -1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 -1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 -1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
▶14.7b
(/.f64 (-.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
15.4b
(cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))
▶30.3b
(+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4)))
Compiler

Compiled 1495 to 1298 computations (13.2% saved)

localize58.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b
(/.f64 (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.3b
(/.f64 1/4 (fma.f64 x x 1))
1.6b
(-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1)))
Compiler

Compiled 99 to 80 computations (19.2% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

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

Compiled 9 to 9 computations (0% saved)

series0.0ms (0%)

Counts
1 → 0

rewrite59.0ms (0.4%)

Algorithm
1×batch-egg-rewrite
Rules
443×pow1_binary64
438×add-sqr-sqrt_binary64
426×*-un-lft-identity_binary64
418×add-log-exp_binary64
418×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
11046
211246
Stop Event
1×node limit
Counts
1 → 28
Calls
Call 1
Inputs
(-.f64 1 (sqrt.f64 1/2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (sqrt.f64 1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (sqrt.f64 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (sqrt.f64 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 1/2))) (pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 1/2))) 2) (cbrt.f64 (-.f64 1 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 1/2))) (sqrt.f64 (-.f64 1 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 1/2 3/2)) (/.f64 1 (+.f64 3/2 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (sqrt.f64 1/2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 3/2 (sqrt.f64 1/2)) (-.f64 1 (pow.f64 1/2 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 3/2 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1/2 (neg.f64 (+.f64 1 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 1/2 3/2))) (neg.f64 (+.f64 3/2 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (neg.f64 (sqrt.f64 1/2)) 3)) (+.f64 1 (-.f64 (*.f64 (neg.f64 (sqrt.f64 1/2)) (neg.f64 (sqrt.f64 1/2))) (neg.f64 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (neg.f64 (sqrt.f64 1/2)) (neg.f64 (sqrt.f64 1/2)))) (-.f64 1 (neg.f64 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (sqrt.f64 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (neg.f64 (sqrt.f64 1/2))))))))

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
28 → 28
Calls
Call 1
Inputs
Outputs

localize15.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 -11/128 (pow.f64 x 4))
✓14.3b
(+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4)))
Compiler

Compiled 32 to 23 computations (28.1% saved)

series3.0ms (0%)

Counts
2 → 12
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4)))
0.0ms
x
@0
(+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4)))
0.0ms
x
@inf
(*.f64 -11/128 (pow.f64 x 4))
0.0ms
x
@0
(*.f64 -11/128 (pow.f64 x 4))
0.0ms
x
@-inf
(+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4)))

rewrite69.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
476×log-prod_binary64
353×exp-prod_binary64
343×fma-def_binary64
340×prod-exp_binary64
292×pow-prod-down_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01021
122021
2269421
Stop Event
1×node limit
Counts
2 → 98
Calls
Call 1
Inputs
(+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4)))
(*.f64 -11/128 (pow.f64 x 4))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (pow.f64 x 4) 1/64) (fma.f64 x (*.f64 x 1/8) (*.f64 11/128 (pow.f64 x 4)))) (/.f64 (*.f64 (pow.f64 x 8) 121/16384) (fma.f64 x (*.f64 x 1/8) (*.f64 11/128 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))) (pow.f64 (cbrt.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))) 2) (cbrt.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))) (sqrt.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (pow.f64 x 12) -1331/2097152 (*.f64 (pow.f64 x 6) 1/512)) (/.f64 1 (fma.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 -11/128 (pow.f64 x 4) (neg.f64 (*.f64 x (*.f64 x 1/8)))) (*.f64 (pow.f64 x 4) 1/64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (pow.f64 x 4) 1/64) (*.f64 (pow.f64 x 8) 121/16384)) (/.f64 1 (fma.f64 x (*.f64 x 1/8) (*.f64 11/128 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 -11/128 (pow.f64 x 4) (neg.f64 (*.f64 x (*.f64 x 1/8)))) (*.f64 (pow.f64 x 4) 1/64)) (fma.f64 (pow.f64 x 12) -1331/2097152 (*.f64 (pow.f64 x 6) 1/512))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x (*.f64 x 1/8) (*.f64 11/128 (pow.f64 x 4))) (-.f64 (*.f64 (pow.f64 x 4) 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pow.f64 (exp.f64 1) (log.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 -11/128 (pow.f64 x 4) (neg.f64 (*.f64 x (*.f64 x 1/8)))) (*.f64 (pow.f64 x 4) 1/64)) (fma.f64 (pow.f64 x 12) -1331/2097152 (*.f64 (pow.f64 x 6) 1/512))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 x (*.f64 x 1/8) (*.f64 11/128 (pow.f64 x 4))) (-.f64 (*.f64 (pow.f64 x 4) 1/64) (*.f64 (pow.f64 x 8) 121/16384))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8))))) 2)) (cbrt.f64 (log.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))))) (sqrt.f64 (log.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 -11/128 (pow.f64 x 4) (*.f64 x (*.f64 x 1/8))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 x (*.f64 x 1/8)))) (pow.f64 (exp.f64 -11/128) (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 x) (*.f64 x 1/8)) (+.f64 1 (expm1.f64 (*.f64 -11/128 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 x (*.f64 x 1/8)))) (+.f64 1 (expm1.f64 (*.f64 -11/128 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 -11/128 (pow.f64 x 4)))) (pow.f64 (exp.f64 x) (*.f64 x 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x 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(*.f64 x x) (sqrt.f64 -11/128)) (*.f64 x (*.f64 x 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 1/8)) (*.f64 (sqrt.f64 (*.f64 x 1/8)) x) (*.f64 -11/128 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (*.f64 x 1/8)) 2)) (cbrt.f64 (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 (*.f64 x 1/8))) (sqrt.f64 (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x 1/8) (cbrt.f64 (*.f64 x x))) (cbrt.f64 x) (*.f64 -11/128 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x 1/8) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 -11/128 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -11/128 (cbrt.f64 (pow.f64 x 8))) (*.f64 (cbrt.f64 x) x) (*.f64 x (*.f64 x 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -11/128 (*.f64 x x)) (*.f64 x x) (*.f64 x (*.f64 x 1/8)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 -11/128 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 -11/128) (pow.f64 x 4))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -11/128) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -11/128) (pow.f64 x 4)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -11/128) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 -11/128 (pow.f64 x 4)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -11/128 (pow.f64 x 4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 8) 121/16384) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 -11/128 (pow.f64 x 4))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) (sqrt.f64 -11/128)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 12) -1331/2097152) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (fma.f64 4 (log.f64 x) (log.f64 -11/128)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 4 (log.f64 x) (log.f64 -11/128))) 2)) (cbrt.f64 (fma.f64 4 (log.f64 x) (log.f64 -11/128))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (fma.f64 4 (log.f64 x) (log.f64 -11/128)))) (sqrt.f64 (fma.f64 4 (log.f64 x) (log.f64 -11/128))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 8) 121/16384))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -11/128) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 -11/128 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 12) -1331/2097152))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -11/128 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -11/128 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 4 (log.f64 x) (log.f64 -11/128)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 4 (log.f64 x) (log.f64 -11/128)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 -11/128 (pow.f64 x 4)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 x x) (sqrt.f64 -11/128))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 12) -1331/2097152)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 4 (log.f64 x) (log.f64 -11/128)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 4 (log.f64 x) (log.f64 -11/128)) 3) 1/3))))))

simplify240.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
1057×sqr-pow_binary64
538×fma-def_binary64
506×pow-sqr_binary64
443×cube-prod_binary64
419×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
011147
122147
245147
3114147
4354147
51406147
62652147
73114147
83283147
93482147
103753147
114112147
124563147
135094147
145720147
156469147
166783147
177007147
187201147
197257147
207279147
Stop Event
1×node limit
Counts
110 → 103
Calls
Call 1
Inputs
(*.f64 1/8 (pow.f64 x 2))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(*.f64 -11/128 (pow.f64 x 4))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(*.f64 -11/128 (pow.f64 x 4))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
Outputs
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(*.f64 x (fma.f64 1/8 x (*.f64 -11/128 (pow.f64 x 3))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(*.f64 x (fma.f64 1/8 x (*.f64 -11/128 (pow.f64 x 3))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(*.f64 x (fma.f64 1/8 x (*.f64 -11/128 (pow.f64 x 3))))
(*.f64 -11/128 (pow.f64 x 4))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(*.f64 x (fma.f64 1/8 x (*.f64 -11/128 (pow.f64 x 3))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(*.f64 x (fma.f64 1/8 x (*.f64 -11/128 (pow.f64 x 3))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(*.f64 x (fma.f64 1/8 x (*.f64 -11/128 (pow.f64 x 3))))
(*.f64 -11/128 (pow.f64 x 4))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(*.f64 x (fma.f64 1/8 x (*.f64 -11/128 (pow.f64 x 3))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(*.f64 x (fma.f64 1/8 x (*.f64 -11/128 (pow.f64 x 3))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(*.f64 x (*.f64 x (fma.f64 (*.f64 x x) -11/128 1/8)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -11/128 1/8))
(*.f64 x (fma.f64 1/8 x (*.f64 -11/128 (pow.f64 x 3))))

localize38.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0b
(/.f64 1/2 (hypot.f64 1 x))
0.0b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓1.6b
(-.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
Compiler

Compiled 66 to 57 computations (13.6% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite63.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
966×pow1_binary64
902×add-log-exp_binary64
902×log1p-expm1-u_binary64
902×expm1-log1p-u_binary64
92×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
118410
2237410
Stop Event
1×node limit
Counts
1 → 36
Calls
Call 1
Inputs
(-.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 -1/2 (neg.f64 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (+.f64 -1/2 (neg.f64 (/.f64 1/2 (hypot.f64 1 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (neg.f64 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (*.f64 -1 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (*.f64 -1/2 (/.f64 1 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (*.f64 (neg.f64 (pow.f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 2)) (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (*.f64 (neg.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 -1/2 (neg.f64 (/.f64 1/2 (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (pow.f64 (cbrt.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2) (cbrt.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3)) (/.f64 1 (+.f64 1 (*.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 3/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)) (/.f64 1 (+.f64 3/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (*.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 3/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 3/2 (/.f64 1/2 (hypot.f64 1 x))) (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3)) (+.f64 1 (*.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 3/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)) (+.f64 3/2 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (/.f64 1/4 (+.f64 1 (*.f64 x x)))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3))) (neg.f64 (+.f64 1 (*.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 3/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2))) (neg.f64 (+.f64 3/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/8 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3))) (+.f64 1/4 (+.f64 (/.f64 1/4 (+.f64 1 (*.f64 x x))) (/.f64 1/4 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 -1/2 (neg.f64 (/.f64 1/2 (hypot.f64 1 x)))) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 -1/2 (neg.f64 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 -1/2 (neg.f64 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 -1/2 (neg.f64 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (+.f64 -1/2 (neg.f64 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 -1/2 (neg.f64 (/.f64 1/2 (hypot.f64 1 x)))))) (-.f64 1 (+.f64 -1/2 (neg.f64 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))

simplify148.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
772×unswap-sqr_binary64
582×distribute-rgt-out_binary64
554×fma-def_binary64
553×associate-*l*_binary64
534×times-frac_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
047168
1132168
2332168
3965168
44253168
Stop Event
1×node limit
Counts
48 → 57
Calls
Call 1
Inputs
(*.f64 1/4 (pow.f64 x 2))
(+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 -3/16 (pow.f64 x 4)))
(+.f64 (*.f64 5/32 (pow.f64 x 6)) (+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 -3/16 (pow.f64 x 4))))
(+.f64 (*.f64 5/32 (pow.f64 x 6)) (+.f64 (*.f64 1/4 (pow.f64 x 2)) (+.f64 (*.f64 -3/16 (pow.f64 x 4)) (*.f64 -35/256 (pow.f64 x 8)))))
1/2
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 3/16 (/.f64 1 (pow.f64 x 5)))))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) 1/2) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1/2 (*.f64 3/16 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
Outputs
(*.f64 1/4 (pow.f64 x 2))
(*.f64 1/4 (*.f64 x x))
(+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 -3/16 (pow.f64 x 4)))
(fma.f64 1/4 (*.f64 x x) (*.f64 -3/16 (pow.f64 x 4)))
(*.f64 x (*.f64 x (fma.f64 x (*.f64 x -3/16) 1/4)))
(fma.f64 -3/16 (pow.f64 x 4) (*.f64 1/4 (*.f64 x x)))
(+.f64 (*.f64 5/32 (pow.f64 x 6)) (+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 -3/16 (pow.f64 x 4))))
(fma.f64 5/32 (pow.f64 x 6) (fma.f64 1/4 (*.f64 x x) (*.f64 -3/16 (pow.f64 x 4))))
(fma.f64 1/4 (*.f64 x x) (fma.f64 -3/16 (pow.f64 x 4) (*.f64 5/32 (pow.f64 x 6))))
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x -3/16) 1/4) (*.f64 5/32 (pow.f64 x 6)))
(fma.f64 5/32 (pow.f64 x 6) (fma.f64 -3/16 (pow.f64 x 4) (*.f64 1/4 (*.f64 x x))))
(+.f64 (*.f64 5/32 (pow.f64 x 6)) (+.f64 (*.f64 1/4 (pow.f64 x 2)) (+.f64 (*.f64 -3/16 (pow.f64 x 4)) (*.f64 -35/256 (pow.f64 x 8)))))
(fma.f64 5/32 (pow.f64 x 6) (fma.f64 1/4 (*.f64 x x) (fma.f64 -3/16 (pow.f64 x 4) (*.f64 -35/256 (pow.f64 x 8)))))
(fma.f64 5/32 (pow.f64 x 6) (fma.f64 1/4 (*.f64 x x) (fma.f64 -35/256 (pow.f64 x 8) (*.f64 -3/16 (pow.f64 x 4)))))
(fma.f64 1/4 (*.f64 x x) (fma.f64 -3/16 (pow.f64 x 4) (fma.f64 5/32 (pow.f64 x 6) (*.f64 -35/256 (pow.f64 x 8)))))
1/2
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/2 (/.f64 1/2 x))
(+.f64 1/2 (/.f64 -1/2 x))
(-.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (/.f64 1 x)))
(+.f64 1/2 (-.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 1/2 (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 -1/2 x)))
(+.f64 (+.f64 1/2 (/.f64 -1/2 x)) (/.f64 1/4 (pow.f64 x 3)))
(-.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) -1/2))
(-.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 3/16 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (+.f64 1/2 (/.f64 1/4 (pow.f64 x 3))) (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5))))
(+.f64 1/2 (-.f64 (-.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 3/16 (pow.f64 x 5))) (/.f64 1/2 x)))
(+.f64 1/2 (+.f64 (-.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 3/16 (pow.f64 x 5))) (/.f64 -1/2 x)))
(+.f64 1/2 (+.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -3/16 (pow.f64 x 5)))))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(+.f64 1/2 (/.f64 1/2 x))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) 1/2) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (-.f64 1/2 (/.f64 1/4 (pow.f64 x 3))))
(+.f64 1/2 (-.f64 (/.f64 1/2 x) (/.f64 1/4 (pow.f64 x 3))))
(+.f64 1/2 (+.f64 (/.f64 1/2 x) (/.f64 -1/4 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 1/2 (*.f64 3/16 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 1/2 x) (+.f64 1/2 (/.f64 3/16 (pow.f64 x 5)))) (/.f64 1/4 (pow.f64 x 3)))
(+.f64 (+.f64 1/2 (/.f64 1/2 x)) (-.f64 (/.f64 3/16 (pow.f64 x 5)) (/.f64 1/4 (pow.f64 x 3))))
(+.f64 (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5))) (+.f64 1/2 (/.f64 -1/4 (pow.f64 x 3))))
(+.f64 (+.f64 (/.f64 3/16 (pow.f64 x 5)) (+.f64 1/2 (/.f64 1/2 x))) (/.f64 -1/4 (pow.f64 x 3)))
(-.f64 1/2 (+.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -3/16 (pow.f64 x 5)))))

localize71.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 1 (/.f64 (+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))
✓0.0b
(+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
✓0.0b
(pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)
✓1.6b
(-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))
Compiler

Compiled 154 to 136 computations (11.7% saved)

series12.0ms (0.1%)

Counts
4 → 48
Calls

12 calls:

TimeVariablePointExpression
3.0ms
x
@inf
(/.f64 1 (/.f64 (+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))
2.0ms
x
@-inf
(/.f64 1 (/.f64 (+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))
1.0ms
x
@0
(-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))
1.0ms
x
@inf
(-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))
1.0ms
x
@inf
(+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

rewrite127.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
732×fma-def_binary64
414×fma-neg_binary64
332×expm1-udef_binary64
331×log1p-udef_binary64
201×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
016104
1392101
25828101
Stop Event
1×node limit
Counts
4 → 191
Calls
Call 1
Inputs
(-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))
(pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)
(+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(/.f64 1 (/.f64 (+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))) (pow.f64 (cbrt.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))) 2) (cbrt.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))) (sqrt.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 9/2)) (/.f64 1 (+.f64 (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3)) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3)) (/.f64 1 (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3)) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 9/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 9/2)) (+.f64 (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3)) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3)) (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 9/2))) (neg.f64 (+.f64 (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3)) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3))) (neg.f64 (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (neg.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) 3)) (+.f64 1 (-.f64 (*.f64 (neg.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (neg.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))) (neg.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (neg.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (neg.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)))) (-.f64 1 (neg.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (neg.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 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(hypot.f64 1 x)) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1) 1) (*.f64 (neg.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (/.f64 1 (+.f64 1 (+.f64 1/2 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (+.f64 1 (pow.f64 (+.f64 1/2 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 3))) (fma.f64 (+.f64 1/2 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (-.f64 (+.f64 1/2 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1) 1) (neg.f64 (/.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2) (+.f64 1 (+.f64 1/2 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (-.f64 1 (pow.f64 (+.f64 1/2 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2))) (-.f64 (-.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (*.f64 (neg.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (/.f64 1 (+.f64 1 (+.f64 1/2 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (-.f64 1 (pow.f64 (+.f64 1/2 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2))) (-.f64 (-.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (neg.f64 (/.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2) (+.f64 1 (+.f64 1/2 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))))))

simplify115.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
610×associate-/l*_binary64
565×associate-*l*_binary64
334×distribute-rgt-in_binary64
306×distribute-lft-in_binary64
278×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02502501
18512354
231362217
Stop Event
1×node limit
Counts
239 → 274
Calls
Call 1
Inputs
(*.f64 3/8 (pow.f64 x 2))
(+.f64 (*.f64 3/8 (pow.f64 x 2)) (*.f64 -39/128 (pow.f64 x 4)))
(+.f64 (*.f64 275/1024 (pow.f64 x 6)) (+.f64 (*.f64 3/8 (pow.f64 x 2)) (*.f64 -39/128 (pow.f64 x 4))))
(+.f64 (*.f64 275/1024 (pow.f64 x 6)) (+.f64 (*.f64 3/8 (pow.f64 x 2)) (+.f64 (*.f64 -39/128 (pow.f64 x 4)) (*.f64 -8043/32768 (pow.f64 x 8)))))
(-.f64 1 (pow.f64 1/2 3/2))
(-.f64 (+.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) x)) 1) (pow.f64 1/2 3/2))
(-.f64 (+.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) x)) (+.f64 (*.f64 -3/8 (/.f64 (sqrt.f64 1/8) (pow.f64 x 2))) 1)) (pow.f64 1/2 3/2))
(-.f64 (+.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) x)) (+.f64 (*.f64 13/16 (/.f64 (sqrt.f64 1/8) (pow.f64 x 3))) (+.f64 (*.f64 -3/8 (/.f64 (sqrt.f64 1/8) (pow.f64 x 2))) 1))) (pow.f64 1/2 3/2))
(-.f64 1 (pow.f64 1/2 3/2))
(-.f64 (+.f64 (*.f64 3/2 (/.f64 (sqrt.f64 1/8) x)) 1) (pow.f64 1/2 3/2))
(-.f64 (+.f64 (*.f64 3/2 (/.f64 (sqrt.f64 1/8) x)) (+.f64 (*.f64 -3/8 (/.f64 (sqrt.f64 1/8) (pow.f64 x 2))) 1)) (pow.f64 1/2 3/2))
(-.f64 (+.f64 (*.f64 3/2 (/.f64 (sqrt.f64 1/8) x)) (+.f64 (*.f64 -3/8 (/.f64 (sqrt.f64 1/8) (pow.f64 x 2))) (+.f64 (*.f64 -13/16 (/.f64 (sqrt.f64 1/8) (pow.f64 x 3))) 1))) (pow.f64 1/2 3/2))
1
(+.f64 1 (*.f64 -3/8 (pow.f64 x 2)))
(+.f64 1 (+.f64 (*.f64 -3/8 (pow.f64 x 2)) (*.f64 39/128 (pow.f64 x 4))))
(+.f64 1 (+.f64 (*.f64 -275/1024 (pow.f64 x 6)) (+.f64 (*.f64 -3/8 (pow.f64 x 2)) (*.f64 39/128 (pow.f64 x 4)))))
(sqrt.f64 1/8)
(+.f64 (*.f64 3/2 (/.f64 (sqrt.f64 1/8) x)) (sqrt.f64 1/8))
(+.f64 (*.f64 3/2 (/.f64 (sqrt.f64 1/8) x)) (+.f64 (*.f64 3/8 (/.f64 (sqrt.f64 1/8) (pow.f64 x 2))) (sqrt.f64 1/8)))
(+.f64 (*.f64 3/2 (/.f64 (sqrt.f64 1/8) x)) (+.f64 (*.f64 -13/16 (/.f64 (sqrt.f64 1/8) (pow.f64 x 3))) (+.f64 (*.f64 3/8 (/.f64 (sqrt.f64 1/8) (pow.f64 x 2))) (sqrt.f64 1/8))))
(sqrt.f64 1/8)
(+.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) x)) (sqrt.f64 1/8))
(+.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) x)) (+.f64 (*.f64 3/8 (/.f64 (sqrt.f64 1/8) (pow.f64 x 2))) (sqrt.f64 1/8)))
(+.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) x)) (+.f64 (*.f64 13/16 (/.f64 (sqrt.f64 1/8) (pow.f64 x 3))) (+.f64 (*.f64 3/8 (/.f64 (sqrt.f64 1/8) (pow.f64 x 2))) (sqrt.f64 1/8))))
3
(+.f64 3 (*.f64 -3/8 (pow.f64 x 2)))
(+.f64 3 (+.f64 (*.f64 -3/8 (pow.f64 x 2)) (*.f64 35/128 (pow.f64 x 4))))
(+.f64 3 (+.f64 (*.f64 -3/8 (pow.f64 x 2)) (+.f64 (*.f64 -229/1024 (pow.f64 x 6)) (*.f64 35/128 (pow.f64 x 4)))))
(+.f64 3/2 (sqrt.f64 1/2))
(+.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (+.f64 (sqrt.f64 1/2) (+.f64 3/2 (*.f64 1/2 (/.f64 1 x)))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (sqrt.f64 1/2) (+.f64 3/2 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (sqrt.f64 1/2) (+.f64 3/2 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))))) (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 3))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(+.f64 3/2 (sqrt.f64 1/2))
(+.f64 (sqrt.f64 1/2) (+.f64 3/2 (*.f64 -1 (/.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2)))) x))))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 3/2 (*.f64 -1 (/.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2)))) x)))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (sqrt.f64 1/2))) 1/4) (pow.f64 x 3))) (+.f64 (sqrt.f64 1/2) (+.f64 3/2 (*.f64 -1 (/.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2)))) x))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(*.f64 1/8 (pow.f64 x 2))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 -11/128 (pow.f64 x 4)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (+.f64 (*.f64 -1843/32768 (pow.f64 x 8)) (*.f64 -11/128 (pow.f64 x 4)))))
(/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 (sqrt.f64 1/2) 3/2))
(-.f64 (+.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) x))) (/.f64 1 (+.f64 (sqrt.f64 1/2) 3/2))) (+.f64 (*.f64 (/.f64 1 (+.f64 (sqrt.f64 1/2) 3/2)) (sqrt.f64 (pow.f64 1/2 3))) (/.f64 (*.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2))))) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (*.f64 (+.f64 3/2 (sqrt.f64 1/2)) x)))))
(-.f64 (+.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) x))) (+.f64 (/.f64 1 (+.f64 (sqrt.f64 1/2) 3/2)) (*.f64 -3/8 (/.f64 (sqrt.f64 1/8) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (pow.f64 x 2)))))) (+.f64 (*.f64 -1/32 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (*.f64 (+.f64 3/2 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 (/.f64 1 (+.f64 (sqrt.f64 1/2) 3/2)) (sqrt.f64 (pow.f64 1/2 3))) (+.f64 (/.f64 (*.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2)))) (-.f64 1 (pow.f64 1/2 3/2))) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (*.f64 (+.f64 3/2 (sqrt.f64 1/2)) x))) (/.f64 (*.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2)))) (-.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) (+.f64 3/2 (sqrt.f64 1/2)))) (/.f64 (*.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2)))) (-.f64 1 (pow.f64 1/2 3/2))) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (+.f64 3/2 (sqrt.f64 1/2)))))) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (pow.f64 x 2)))))))
(-.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 1/2) 3/2)) (+.f64 (*.f64 -3/8 (/.f64 (sqrt.f64 1/8) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (pow.f64 x 2)))) (+.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) x))) (*.f64 13/16 (/.f64 (sqrt.f64 1/8) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (pow.f64 x 3))))))) (+.f64 (*.f64 (/.f64 1 (+.f64 (sqrt.f64 1/2) 3/2)) (sqrt.f64 (pow.f64 1/2 3))) (+.f64 (*.f64 -1/32 (/.f64 (-.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) (+.f64 3/2 (sqrt.f64 1/2)))) (/.f64 (*.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2)))) (-.f64 1 (pow.f64 1/2 3/2))) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (+.f64 3/2 (sqrt.f64 1/2))))) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (pow.f64 x 3))))) (+.f64 (/.f64 (*.f64 (-.f64 1 (pow.f64 1/2 3/2)) (-.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (sqrt.f64 1/2))) 1/4)) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (*.f64 (+.f64 3/2 (sqrt.f64 1/2)) (pow.f64 x 3)))) (+.f64 (/.f64 (*.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2)))) (-.f64 (*.f64 -3/8 (/.f64 (sqrt.f64 1/8) (+.f64 3/2 (sqrt.f64 1/2)))) (+.f64 (/.f64 (*.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2)))) (-.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) (+.f64 (sqrt.f64 1/2) 3/2))) (/.f64 (*.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2))))) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (+.f64 3/2 (sqrt.f64 1/2)))))) (+.f64 3/2 (sqrt.f64 1/2))) (*.f64 -1/32 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (+.f64 3/2 (sqrt.f64 1/2))))))))) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (pow.f64 x 3))) (+.f64 (/.f64 (*.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2)))) (-.f64 1 (pow.f64 1/2 3/2))) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (*.f64 (+.f64 3/2 (sqrt.f64 1/2)) x))) (+.f64 (/.f64 (*.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2)))) (-.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) (+.f64 3/2 (sqrt.f64 1/2)))) (/.f64 (*.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2)))) (-.f64 1 (pow.f64 1/2 3/2))) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (+.f64 3/2 (sqrt.f64 1/2)))))) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (pow.f64 x 2))) (*.f64 -1/32 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (*.f64 (+.f64 3/2 (sqrt.f64 1/2)) (pow.f64 x 2)))))))))))))
(/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 (sqrt.f64 1/2) 3/2))
(-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) (+.f64 (sqrt.f64 1/2) 3/2))) (/.f64 (*.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2))))) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (+.f64 3/2 (sqrt.f64 1/2))))) x)) (/.f64 1 (+.f64 (sqrt.f64 1/2) 3/2))) (*.f64 (/.f64 1 (+.f64 (sqrt.f64 1/2) 3/2)) (sqrt.f64 (pow.f64 1/2 3))))
(-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) (+.f64 (sqrt.f64 1/2) 3/2))) (/.f64 (*.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2))))) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (+.f64 3/2 (sqrt.f64 1/2))))) x)) (+.f64 (/.f64 1 (+.f64 (sqrt.f64 1/2) 3/2)) (*.f64 -3/8 (/.f64 (sqrt.f64 1/8) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (pow.f64 x 2)))))) (+.f64 (*.f64 -1/32 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (*.f64 (+.f64 3/2 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 (/.f64 1 (+.f64 (sqrt.f64 1/2) 3/2)) (sqrt.f64 (pow.f64 1/2 3))) (/.f64 (*.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2)))) (-.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) (+.f64 3/2 (sqrt.f64 1/2)))) (/.f64 (*.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2)))) (-.f64 1 (pow.f64 1/2 3/2))) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (+.f64 3/2 (sqrt.f64 1/2)))))) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (pow.f64 x 2))))))
(-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) (+.f64 (sqrt.f64 1/2) 3/2))) (/.f64 (*.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2))))) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (+.f64 3/2 (sqrt.f64 1/2))))) x)) (+.f64 (/.f64 1 (+.f64 (sqrt.f64 1/2) 3/2)) (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 13/16 (/.f64 (sqrt.f64 1/8) (+.f64 (sqrt.f64 1/2) 3/2))) (+.f64 (/.f64 (*.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2)))) (-.f64 (*.f64 -3/8 (/.f64 (sqrt.f64 1/8) (+.f64 3/2 (sqrt.f64 1/2)))) (+.f64 (/.f64 (*.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2)))) (-.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) (+.f64 (sqrt.f64 1/2) 3/2))) (/.f64 (*.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2))))) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (+.f64 3/2 (sqrt.f64 1/2)))))) (+.f64 3/2 (sqrt.f64 1/2))) (*.f64 -1/32 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (+.f64 3/2 (sqrt.f64 1/2))))))))) (+.f64 (sqrt.f64 1/2) 3/2)) (+.f64 (/.f64 (*.f64 (-.f64 1 (pow.f64 1/2 3/2)) (-.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (sqrt.f64 1/2))) 1/4)) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (+.f64 3/2 (sqrt.f64 1/2)))) (*.f64 -1/32 (/.f64 (-.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) (+.f64 3/2 (sqrt.f64 1/2)))) (/.f64 (*.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2)))) (-.f64 1 (pow.f64 1/2 3/2))) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (+.f64 3/2 (sqrt.f64 1/2))))) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (pow.f64 (sqrt.f64 1/2) 3))))))) (pow.f64 x 3))) (*.f64 -3/8 (/.f64 (sqrt.f64 1/8) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (pow.f64 x 2))))))) (+.f64 (*.f64 -1/32 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (*.f64 (+.f64 3/2 (sqrt.f64 1/2)) (pow.f64 x 2)))))) (+.f64 (*.f64 (/.f64 1 (+.f64 (sqrt.f64 1/2) 3/2)) (sqrt.f64 (pow.f64 1/2 3))) (/.f64 (*.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2)))) (-.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) (+.f64 3/2 (sqrt.f64 1/2)))) (/.f64 (*.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2)))) (-.f64 1 (pow.f64 1/2 3/2))) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (+.f64 3/2 (sqrt.f64 1/2)))))) (*.f64 (+.f64 (sqrt.f64 1/2) 3/2) (pow.f64 x 2))))))
Outputs
(*.f64 3/8 (pow.f64 x 2))
(*.f64 3/8 (*.f64 x x))
(+.f64 (*.f64 3/8 (pow.f64 x 2)) (*.f64 -39/128 (pow.f64 x 4)))
(fma.f64 3/8 (*.f64 x x) (*.f64 -39/128 (pow.f64 x 4)))
(fma.f64 -39/128 (pow.f64 x 4) (*.f64 3/8 (*.f64 x x)))
(+.f64 (*.f64 275/1024 (pow.f64 x 6)) (+.f64 (*.f64 3/8 (pow.f64 x 2)) (*.f64 -39/128 (pow.f64 x 4))))
(fma.f64 275/1024 (pow.f64 x 6) (fma.f64 3/8 (*.f64 x x) (*.f64 -39/128 (pow.f64 x 4))))
(fma.f64 275/1024 (pow.f64 x 6) (fma.f64 -39/128 (pow.f64 x 4) (*.f64 3/8 (*.f64 x x))))
(+.f64 (*.f64 275/1024 (pow.f64 x 6)) (+.f64 (*.f64 3/8 (pow.f64 x 2)) (+.f64 (*.f64 -39/128 (pow.f64 x 4)) (*.f64 -8043/32768 (pow.f64 x 8)))))
(fma.f64 275/1024 (pow.f64 x 6) (fma.f64 3/8 (*.f64 x x) (fma.f64 -39/128 (pow.f64 x 4) (*.f64 -8043/32768 (pow.f64 x 8)))))
(-.f64 1 (pow.f64 1/2 3/2))
(-.f64 (+.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) x)) 1) (pow.f64 1/2 3/2))
(-.f64 (fma.f64 -3/2 (/.f64 (sqrt.f64 1/8) x) 1) (pow.f64 1/2 3/2))
(-.f64 (+.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) x)) (+.f64 (*.f64 -3/8 (/.f64 (sqrt.f64 1/8) (pow.f64 x 2))) 1)) (pow.f64 1/2 3/2))
(-.f64 (fma.f64 -3/2 (/.f64 (sqrt.f64 1/8) x) (fma.f64 -3/8 (/.f64 (sqrt.f64 1/8) (*.f64 x x)) 1)) (pow.f64 1/2 3/2))
(+.f64 (*.f64 (/.f64 (sqrt.f64 1/8) x) (+.f64 -3/2 (/.f64 -3/8 x))) (-.f64 1 (pow.f64 1/2 3/2)))
(-.f64 (+.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) x)) (+.f64 (*.f64 13/16 (/.f64 (sqrt.f64 1/8) (pow.f64 x 3))) (+.f64 (*.f64 -3/8 (/.f64 (sqrt.f64 1/8) (pow.f64 x 2))) 1))) (pow.f64 1/2 3/2))
(-.f64 (fma.f64 -3/2 (/.f64 (sqrt.f64 1/8) x) (fma.f64 13/16 (/.f64 (sqrt.f64 1/8) (pow.f64 x 3)) (fma.f64 -3/8 (/.f64 (sqrt.f64 1/8) (*.f64 x x)) 1))) (pow.f64 1/2 3/2))
(-.f64 (+.f64 (*.f64 (/.f64 (sqrt.f64 1/8) (*.f64 x x)) (+.f64 -3/8 (/.f64 13/16 x))) (fma.f64 -3/2 (/.f64 (sqrt.f64 1/8) x) 1)) (pow.f64 1/2 3/2))
(-.f64 1 (pow.f64 1/2 3/2))
(-.f64 (+.f64 (*.f64 3/2 (/.f64 (sqrt.f64 1/8) x)) 1) (pow.f64 1/2 3/2))
(-.f64 (fma.f64 3/2 (/.f64 (sqrt.f64 1/8) x) 1) (pow.f64 1/2 3/2))
(-.f64 (+.f64 (*.f64 3/2 (/.f64 (sqrt.f64 1/8) x)) (+.f64 (*.f64 -3/8 (/.f64 (sqrt.f64 1/8) (pow.f64 x 2))) 1)) (pow.f64 1/2 3/2))
(-.f64 (fma.f64 3/2 (/.f64 (sqrt.f64 1/8) x) (fma.f64 -3/8 (/.f64 (sqrt.f64 1/8) (*.f64 x x)) 1)) (pow.f64 1/2 3/2))
(+.f64 (*.f64 (/.f64 (sqrt.f64 1/8) x) (+.f64 (/.f64 -3/8 x) 3/2)) (-.f64 1 (pow.f64 1/2 3/2)))
(-.f64 (+.f64 (*.f64 3/2 (/.f64 (sqrt.f64 1/8) x)) (+.f64 (*.f64 -3/8 (/.f64 (sqrt.f64 1/8) (pow.f64 x 2))) (+.f64 (*.f64 -13/16 (/.f64 (sqrt.f64 1/8) (pow.f64 x 3))) 1))) (pow.f64 1/2 3/2))
(-.f64 (fma.f64 3/2 (/.f64 (sqrt.f64 1/8) x) (fma.f64 -3/8 (/.f64 (sqrt.f64 1/8) (*.f64 x x)) (fma.f64 -13/16 (/.f64 (sqrt.f64 1/8) (pow.f64 x 3)) 1))) (pow.f64 1/2 3/2))
(-.f64 (fma.f64 3/2 (/.f64 (sqrt.f64 1/8) x) (fma.f64 -3/8 (/.f64 (sqrt.f64 1/8) (*.f64 x x)) (fma.f64 (/.f64 (sqrt.f64 1/8) (pow.f64 x 3)) -13/16 1))) (pow.f64 1/2 3/2))
(+.f64 (*.f64 (/.f64 (sqrt.f64 1/8) x) (+.f64 (/.f64 -3/8 x) 3/2)) (-.f64 (fma.f64 (/.f64 (sqrt.f64 1/8) (pow.f64 x 3)) -13/16 1) (pow.f64 1/2 3/2)))
1
(+.f64 1 (*.f64 -3/8 (pow.f64 x 2)))
(+.f64 1 (*.f64 (*.f64 x x) -3/8))
(fma.f64 (*.f64 x x) -3/8 1)
(+.f64 1 (+.f64 (*.f64 -3/8 (pow.f64 x 2)) (*.f64 39/128 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -3/8 (*.f64 x x) (*.f64 (pow.f64 x 4) 39/128)))
(+.f64 1 (fma.f64 (pow.f64 x 4) 39/128 (*.f64 x (*.f64 x -3/8))))
(+.f64 1 (+.f64 (*.f64 -275/1024 (pow.f64 x 6)) (+.f64 (*.f64 -3/8 (pow.f64 x 2)) (*.f64 39/128 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -275/1024 (pow.f64 x 6) (fma.f64 -3/8 (*.f64 x x) (*.f64 (pow.f64 x 4) 39/128))))
(+.f64 1 (fma.f64 (pow.f64 x 6) -275/1024 (fma.f64 (pow.f64 x 4) 39/128 (*.f64 x (*.f64 x -3/8)))))
(sqrt.f64 1/8)
(+.f64 (*.f64 3/2 (/.f64 (sqrt.f64 1/8) x)) (sqrt.f64 1/8))
(fma.f64 3/2 (/.f64 (sqrt.f64 1/8) x) (sqrt.f64 1/8))
(+.f64 (*.f64 3/2 (/.f64 (sqrt.f64 1/8) x)) (+.f64 (*.f64 3/8 (/.f64 (sqrt.f64 1/8) (pow.f64 x 2))) (sqrt.f64 1/8)))
(fma.f64 3/2 (/.f64 (sqrt.f64 1/8) x) (fma.f64 3/8 (/.f64 (sqrt.f64 1/8) (*.f64 x x)) (sqrt.f64 1/8)))
(+.f64 (sqrt.f64 1/8) (*.f64 (/.f64 (sqrt.f64 1/8) x) (+.f64 3/2 (/.f64 3/8 x))))
(+.f64 (*.f64 3/2 (/.f64 (sqrt.f64 1/8) x)) (+.f64 (*.f64 -13/16 (/.f64 (sqrt.f64 1/8) (pow.f64 x 3))) (+.f64 (*.f64 3/8 (/.f64 (sqrt.f64 1/8) (pow.f64 x 2))) (sqrt.f64 1/8))))
(fma.f64 3/2 (/.f64 (sqrt.f64 1/8) x) (fma.f64 -13/16 (/.f64 (sqrt.f64 1/8) (pow.f64 x 3)) (fma.f64 3/8 (/.f64 (sqrt.f64 1/8) (*.f64 x x)) (sqrt.f64 1/8))))
(fma.f64 3/2 (/.f64 (sqrt.f64 1/8) x) (fma.f64 (/.f64 (sqrt.f64 1/8) (pow.f64 x 3)) -13/16 (fma.f64 3/8 (/.f64 (sqrt.f64 1/8) (*.f64 x x)) (sqrt.f64 1/8))))
(+.f64 (*.f64 (/.f64 (sqrt.f64 1/8) (*.f64 x x)) (+.f64 (/.f64 -13/16 x) 3/8)) (fma.f64 3/2 (/.f64 (sqrt.f64 1/8) x) (sqrt.f64 1/8)))
(sqrt.f64 1/8)
(+.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) x)) (sqrt.f64 1/8))
(fma.f64 -3/2 (/.f64 (sqrt.f64 1/8) x) (sqrt.f64 1/8))
(+.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) x)) (+.f64 (*.f64 3/8 (/.f64 (sqrt.f64 1/8) (pow.f64 x 2))) (sqrt.f64 1/8)))
(fma.f64 -3/2 (/.f64 (sqrt.f64 1/8) x) (fma.f64 3/8 (/.f64 (sqrt.f64 1/8) (*.f64 x x)) (sqrt.f64 1/8)))
(+.f64 (sqrt.f64 1/8) (*.f64 (/.f64 (sqrt.f64 1/8) x) (+.f64 -3/2 (/.f64 3/8 x))))
(+.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) x)) (+.f64 (*.f64 13/16 (/.f64 (sqrt.f64 1/8) (pow.f64 x 3))) (+.f64 (*.f64 3/8 (/.f64 (sqrt.f64 1/8) (pow.f64 x 2))) (sqrt.f64 1/8))))
(fma.f64 -3/2 (/.f64 (sqrt.f64 1/8) x) (fma.f64 13/16 (/.f64 (sqrt.f64 1/8) (pow.f64 x 3)) (fma.f64 3/8 (/.f64 (sqrt.f64 1/8) (*.f64 x x)) (sqrt.f64 1/8))))
(+.f64 (*.f64 (/.f64 (sqrt.f64 1/8) (*.f64 x x)) (+.f64 (/.f64 13/16 x) 3/8)) (fma.f64 -3/2 (/.f64 (sqrt.f64 1/8) x) (sqrt.f64 1/8)))
3
(+.f64 3 (*.f64 -3/8 (pow.f64 x 2)))
(+.f64 3 (*.f64 (*.f64 x x) -3/8))
(fma.f64 (*.f64 x x) -3/8 3)
(+.f64 3 (+.f64 (*.f64 -3/8 (pow.f64 x 2)) (*.f64 35/128 (pow.f64 x 4))))
(+.f64 3 (fma.f64 -3/8 (*.f64 x x) (*.f64 (pow.f64 x 4) 35/128)))
(+.f64 3 (fma.f64 (pow.f64 x 4) 35/128 (*.f64 x (*.f64 x -3/8))))
(+.f64 3 (+.f64 (*.f64 -3/8 (pow.f64 x 2)) (+.f64 (*.f64 -229/1024 (pow.f64 x 6)) (*.f64 35/128 (pow.f64 x 4)))))
(+.f64 3 (fma.f64 -3/8 (*.f64 x x) (fma.f64 -229/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) 35/128))))
(+.f64 3 (fma.f64 (*.f64 x x) -3/8 (fma.f64 (pow.f64 x 4) 35/128 (*.f64 (pow.f64 x 6) -229/1024))))
(+.f64 (fma.f64 (*.f64 x x) -3/8 3) (fma.f64 (pow.f64 x 4) 35/128 (*.f64 (pow.f64 x 6) -229/1024)))
(+.f64 3/2 (sqrt.f64 1/2))
(+.f64 (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)) (+.f64 (sqrt.f64 1/2) (+.f64 3/2 (*.f64 1/2 (/.f64 1 x)))))
(+.f64 (+.f64 (sqrt.f64 1/2) (+.f64 3/2 (/.f64 1/2 x))) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))
(+.f64 (sqrt.f64 1/2) (+.f64 (+.f64 3/2 (/.f64 1/2 x)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (sqrt.f64 1/2) (+.f64 3/2 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(+.f64 (/.f64 1/2 x) (-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 3/2 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))) (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)))))
(+.f64 (+.f64 (sqrt.f64 1/2) (+.f64 3/2 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)))) (+.f64 (/.f64 1/2 x) (*.f64 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) -1/32)))
(+.f64 (/.f64 1/2 x) (+.f64 (+.f64 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)) (+.f64 3/2 (sqrt.f64 1/2))) (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (*.f64 x x))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (sqrt.f64 1/2) (+.f64 3/2 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))))) (+.f64 (*.f64 1/4 (/.f64 1 (pow.f64 x 3))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2))))))
(-.f64 (+.f64 (/.f64 1/2 x) (fma.f64 1/2 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4) (*.f64 (pow.f64 x 3) (sqrt.f64 1/2))) (+.f64 (sqrt.f64 1/2) (+.f64 3/2 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))))) (+.f64 (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))) (/.f64 1/4 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 1/2 x) (+.f64 (+.f64 3/2 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 -3/32 (sqrt.f64 1/2)) (pow.f64 x 3))))) (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 1/4 (pow.f64 x 3))))
(+.f64 (+.f64 (sqrt.f64 1/2) (+.f64 (+.f64 3/2 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))) (/.f64 -3/32 (*.f64 (pow.f64 x 3) (sqrt.f64 1/2))))) (+.f64 (/.f64 1/2 x) (+.f64 (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 -1/4 (pow.f64 x 3)))))
(+.f64 3/2 (sqrt.f64 1/2))
(+.f64 (sqrt.f64 1/2) (+.f64 3/2 (*.f64 -1 (/.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2)))) x))))
(+.f64 (sqrt.f64 1/2) (+.f64 3/2 (neg.f64 (/.f64 (+.f64 1/2 (/.f64 1/4 (sqrt.f64 1/2))) x))))
(+.f64 (sqrt.f64 1/2) (-.f64 3/2 (/.f64 (+.f64 1/2 (/.f64 1/4 (sqrt.f64 1/2))) x)))
(+.f64 (/.f64 (+.f64 -1/2 (/.f64 -1/4 (sqrt.f64 1/2))) x) (+.f64 3/2 (sqrt.f64 1/2)))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 3/2 (*.f64 -1 (/.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2)))) x)))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 3/2 (neg.f64 (/.f64 (+.f64 1/2 (/.f64 1/4 (sqrt.f64 1/2))) x)))) (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))))
(+.f64 (sqrt.f64 1/2) (+.f64 (-.f64 3/2 (/.f64 (+.f64 1/2 (/.f64 1/4 (sqrt.f64 1/2))) x)) (*.f64 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) -1/32)))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 (+.f64 -1/2 (/.f64 -1/4 (sqrt.f64 1/2))) x) (+.f64 3/2 (/.f64 (/.f64 -1/16 (sqrt.f64 1/2)) (*.f64 x x)))))
(-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 1/2 (/.f64 (-.f64 (*.f64 1/64 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4))) 1/4) (sqrt.f64 1/2))) 1/4) (pow.f64 x 3))) (+.f64 (sqrt.f64 1/2) (+.f64 3/2 (*.f64 -1 (/.f64 (+.f64 1/2 (*.f64 1/4 (/.f64 1 (sqrt.f64 1/2)))) x))))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(-.f64 (fma.f64 -1 (/.f64 (fma.f64 1/2 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4) (sqrt.f64 1/2)) -1/4) (pow.f64 x 3)) (+.f64 (sqrt.f64 1/2) (+.f64 3/2 (neg.f64 (/.f64 (+.f64 1/2 (/.f64 1/4 (sqrt.f64 1/2))) x))))) (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))))
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(-.f64 (+.f64 (fma.f64 -1 (/.f64 (-.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) (+.f64 3/2 (sqrt.f64 1/2)))) (*.f64 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 3/2 (sqrt.f64 1/2))) (/.f64 (+.f64 1/2 (/.f64 1/4 (sqrt.f64 1/2))) (+.f64 3/2 (sqrt.f64 1/2))))) x) (/.f64 1 (+.f64 3/2 (sqrt.f64 1/2)))) (fma.f64 -1 (/.f64 (-.f64 (*.f64 13/16 (/.f64 (sqrt.f64 1/8) (+.f64 3/2 (sqrt.f64 1/2)))) (+.f64 (/.f64 (*.f64 (+.f64 1/2 (/.f64 1/4 (sqrt.f64 1/2))) (-.f64 (/.f64 (*.f64 -3/8 (sqrt.f64 1/8)) (+.f64 3/2 (sqrt.f64 1/2))) (+.f64 (/.f64 (*.f64 (+.f64 1/2 (/.f64 1/4 (sqrt.f64 1/2))) (-.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) (+.f64 3/2 (sqrt.f64 1/2)))) (*.f64 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 3/2 (sqrt.f64 1/2))) (/.f64 (+.f64 1/2 (/.f64 1/4 (sqrt.f64 1/2))) (+.f64 3/2 (sqrt.f64 1/2)))))) (+.f64 3/2 (sqrt.f64 1/2))) (*.f64 -1/32 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 3/2 (sqrt.f64 1/2)) (+.f64 3/2 (sqrt.f64 1/2))))))))) (+.f64 3/2 (sqrt.f64 1/2))) (+.f64 (*.f64 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 3/2 (sqrt.f64 1/2))) (/.f64 (fma.f64 1/2 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 (sqrt.f64 1/2) 4)) -1/4) (sqrt.f64 1/2)) -1/4) (+.f64 3/2 (sqrt.f64 1/2)))) (*.f64 -1/32 (/.f64 (-.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) (+.f64 3/2 (sqrt.f64 1/2)))) (*.f64 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 3/2 (sqrt.f64 1/2))) (/.f64 (+.f64 1/2 (/.f64 1/4 (sqrt.f64 1/2))) (+.f64 3/2 (sqrt.f64 1/2))))) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (+.f64 3/2 (sqrt.f64 1/2)))))))) (pow.f64 x 3)) (*.f64 -3/8 (/.f64 (sqrt.f64 1/8) (*.f64 (*.f64 x x) (+.f64 3/2 (sqrt.f64 1/2))))))) (fma.f64 -1/32 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (*.f64 (+.f64 3/2 (sqrt.f64 1/2)) (*.f64 (*.f64 x x) (+.f64 3/2 (sqrt.f64 1/2)))))) (fma.f64 (/.f64 1 (+.f64 3/2 (sqrt.f64 1/2))) (sqrt.f64 1/8) (*.f64 (/.f64 (+.f64 1/2 (/.f64 1/4 (sqrt.f64 1/2))) (+.f64 3/2 (sqrt.f64 1/2))) (/.f64 (-.f64 (*.f64 -3/2 (/.f64 (sqrt.f64 1/8) (+.f64 3/2 (sqrt.f64 1/2)))) (*.f64 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 3/2 (sqrt.f64 1/2))) (/.f64 (+.f64 1/2 (/.f64 1/4 (sqrt.f64 1/2))) (+.f64 3/2 (sqrt.f64 1/2))))) (*.f64 x x))))))
(+.f64 (-.f64 (/.f64 1 (+.f64 3/2 (sqrt.f64 1/2))) (/.f64 (-.f64 (/.f64 -3/2 (/.f64 (+.f64 3/2 (sqrt.f64 1/2)) (sqrt.f64 1/8))) (*.f64 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 3/2 (sqrt.f64 1/2))) (/.f64 (+.f64 1/2 (/.f64 1/4 (sqrt.f64 1/2))) (+.f64 3/2 (sqrt.f64 1/2))))) x)) (-.f64 (-.f64 (*.f64 -3/8 (/.f64 (sqrt.f64 1/8) (*.f64 (*.f64 x x) (+.f64 3/2 (sqrt.f64 1/2))))) (/.f64 (-.f64 (/.f64 (*.f64 (sqrt.f64 1/8) 13/16) (+.f64 3/2 (sqrt.f64 1/2))) (+.f64 (*.f64 (/.f64 (+.f64 1/2 (/.f64 1/4 (sqrt.f64 1/2))) (+.f64 3/2 (sqrt.f64 1/2))) (-.f64 (/.f64 (*.f64 (sqrt.f64 1/8) -3/8) (+.f64 3/2 (sqrt.f64 1/2))) (fma.f64 -1/32 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (*.f64 (+.f64 3/2 (sqrt.f64 1/2)) (*.f64 1/2 (+.f64 1/2 (*.f64 3/2 (sqrt.f64 1/2)))))) (*.f64 (/.f64 (+.f64 1/2 (/.f64 1/4 (sqrt.f64 1/2))) (+.f64 3/2 (sqrt.f64 1/2))) (-.f64 (/.f64 -3/2 (/.f64 (+.f64 3/2 (sqrt.f64 1/2)) (sqrt.f64 1/8))) (*.f64 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 3/2 (sqrt.f64 1/2))) (/.f64 (+.f64 1/2 (/.f64 1/4 (sqrt.f64 1/2))) (+.f64 3/2 (sqrt.f64 1/2))))))))) (fma.f64 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 3/2 (sqrt.f64 1/2))) (/.f64 (+.f64 (/.f64 -3/32 (sqrt.f64 1/2)) -1/4) (+.f64 3/2 (sqrt.f64 1/2))) (*.f64 -1/32 (/.f64 (-.f64 (/.f64 -3/2 (/.f64 (+.f64 3/2 (sqrt.f64 1/2)) (sqrt.f64 1/8))) (*.f64 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 3/2 (sqrt.f64 1/2))) (/.f64 (+.f64 1/2 (/.f64 1/4 (sqrt.f64 1/2))) (+.f64 3/2 (sqrt.f64 1/2))))) (*.f64 1/2 (+.f64 1/2 (*.f64 3/2 (sqrt.f64 1/2))))))))) (pow.f64 x 3))) (fma.f64 -1/32 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (*.f64 (*.f64 (*.f64 x x) (+.f64 3/2 (sqrt.f64 1/2))) (*.f64 1/2 (+.f64 1/2 (*.f64 3/2 (sqrt.f64 1/2)))))) (fma.f64 (/.f64 (+.f64 1/2 (/.f64 1/4 (sqrt.f64 1/2))) (+.f64 3/2 (sqrt.f64 1/2))) (/.f64 (-.f64 (/.f64 -3/2 (/.f64 (+.f64 3/2 (sqrt.f64 1/2)) (sqrt.f64 1/8))) (*.f64 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 3/2 (sqrt.f64 1/2))) (/.f64 (+.f64 1/2 (/.f64 1/4 (sqrt.f64 1/2))) (+.f64 3/2 (sqrt.f64 1/2))))) (*.f64 x x)) (/.f64 (sqrt.f64 1/8) (+.f64 3/2 (sqrt.f64 1/2)))))))
(-.f64 (-.f64 (-.f64 (fma.f64 -3/8 (/.f64 (/.f64 (sqrt.f64 1/8) (*.f64 x x)) (+.f64 3/2 (sqrt.f64 1/2))) (/.f64 1 (+.f64 3/2 (sqrt.f64 1/2)))) (/.f64 (fma.f64 -3/2 (/.f64 (sqrt.f64 1/8) (+.f64 3/2 (sqrt.f64 1/2))) (*.f64 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 3/2 (sqrt.f64 1/2))) (/.f64 (+.f64 -1/2 (/.f64 -1/4 (sqrt.f64 1/2))) (+.f64 3/2 (sqrt.f64 1/2))))) x)) (/.f64 (-.f64 (fma.f64 13/16 (/.f64 (sqrt.f64 1/8) (+.f64 3/2 (sqrt.f64 1/2))) (*.f64 (/.f64 (+.f64 -1/2 (/.f64 -1/4 (sqrt.f64 1/2))) (+.f64 3/2 (sqrt.f64 1/2))) (+.f64 (fma.f64 -3/8 (/.f64 (sqrt.f64 1/8) (+.f64 3/2 (sqrt.f64 1/2))) (/.f64 1/32 (*.f64 (/.f64 (+.f64 1/4 (*.f64 (sqrt.f64 1/2) 3/4)) (-.f64 1 (pow.f64 1/2 3/2))) (+.f64 3/2 (sqrt.f64 1/2))))) (*.f64 (/.f64 (+.f64 -1/2 (/.f64 -1/4 (sqrt.f64 1/2))) (+.f64 3/2 (sqrt.f64 1/2))) (fma.f64 -3/2 (/.f64 (sqrt.f64 1/8) (+.f64 3/2 (sqrt.f64 1/2))) (*.f64 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 3/2 (sqrt.f64 1/2))) (/.f64 (+.f64 -1/2 (/.f64 -1/4 (sqrt.f64 1/2))) (+.f64 3/2 (sqrt.f64 1/2))))))))) (fma.f64 -1/32 (/.f64 (fma.f64 -3/2 (/.f64 (sqrt.f64 1/8) (+.f64 3/2 (sqrt.f64 1/2))) (*.f64 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 3/2 (sqrt.f64 1/2))) (/.f64 (+.f64 -1/2 (/.f64 -1/4 (sqrt.f64 1/2))) (+.f64 3/2 (sqrt.f64 1/2))))) (+.f64 1/4 (*.f64 (sqrt.f64 1/2) 3/4))) (*.f64 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 3/2 (sqrt.f64 1/2))) (/.f64 (+.f64 (/.f64 -3/32 (sqrt.f64 1/2)) -1/4) (+.f64 3/2 (sqrt.f64 1/2)))))) (pow.f64 x 3))) (fma.f64 -1/32 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (*.f64 (*.f64 x x) (*.f64 (+.f64 3/2 (sqrt.f64 1/2)) (+.f64 1/4 (*.f64 (sqrt.f64 1/2) 3/4))))) (fma.f64 (/.f64 (+.f64 1/2 (/.f64 1/4 (sqrt.f64 1/2))) (+.f64 3/2 (sqrt.f64 1/2))) (/.f64 (fma.f64 -3/2 (/.f64 (sqrt.f64 1/8) (+.f64 3/2 (sqrt.f64 1/2))) (*.f64 (/.f64 (-.f64 1 (pow.f64 1/2 3/2)) (+.f64 3/2 (sqrt.f64 1/2))) (/.f64 (+.f64 -1/2 (/.f64 -1/4 (sqrt.f64 1/2))) (+.f64 3/2 (sqrt.f64 1/2))))) (*.f64 x x)) (/.f64 (sqrt.f64 1/8) (+.f64 3/2 (sqrt.f64 1/2))))))

eval1.9s (13.3%)

Compiler

Compiled 42204 to 37010 computations (12.3% saved)

prune167.0ms (1.2%)

Pruning

26 alts after pruning (14 fresh and 12 done)

PrunedKeptTotal
New103651041
Fresh4913
Picked011
Done11112
Total1041261067
Error
0.0b
Counts
1067 → 26
Alt Table
Click to see full alt table
StatusErrorProgram
✓14.7b
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓29.8b
(*.f64 x (*.f64 x 1/8))
15.1b
(/.f64 (+.f64 (fma.f64 (sqrt.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (neg.f64 (*.f64 (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (/.f64 1/4 (fma.f64 x x 1))))) (fma.f64 (neg.f64 (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (/.f64 1/4 (fma.f64 x x 1)) (*.f64 (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (/.f64 1/4 (fma.f64 x x 1))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓34.5b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
✓44.2b
(-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))
38.2b
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)
29.9b
(+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6))))
14.7b
(/.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
14.7b
(*.f64 (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (+.f64 1/4 (/.f64 -1/4 (fma.f64 x x 1)))) (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓14.7b
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓44.6b
(-.f64 1 1)
✓14.7b
(/.f64 1 (/.f64 (+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))
33.0b
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
34.3b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
15.8b
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))))
✓15.2b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓33.4b
(-.f64 1 (sqrt.f64 1/2))
44.6b
(/.f64 1 (/.f64 (+.f64 3 (+.f64 (*.f64 -3/8 (pow.f64 x 2)) (+.f64 (*.f64 -229/1024 (pow.f64 x 6)) (*.f64 35/128 (pow.f64 x 4))))) (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))
34.0b
(/.f64 (-.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))
✓14.7b
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
✓14.7b
(/.f64 (-.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
32.7b
(/.f64 (+.f64 (fma.f64 (sqrt.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (neg.f64 (*.f64 (/.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (/.f64 (cbrt.f64 (/.f64 1/16 (pow.f64 (fma.f64 x x 1) 2))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (cbrt.f64 (/.f64 1/16 (pow.f64 (fma.f64 x x 1) 2))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (*.f64 (/.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (/.f64 (cbrt.f64 (/.f64 1/16 (pow.f64 (fma.f64 x x 1) 2))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
15.4b
(cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))
14.7b
(/.f64 (/.f64 (-.f64 1/4 (/.f64 1/4 (+.f64 1 (*.f64 x x)))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓30.3b
(+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4)))
15.2b
(/.f64 (+.f64 (fma.f64 (sqrt.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (neg.f64 (*.f64 (+.f64 1/4 (-.f64 (/.f64 1/4 (fma.f64 x x 1)) (/.f64 1/4 (hypot.f64 1 x)))) (/.f64 (/.f64 1/4 (fma.f64 x x 1)) (+.f64 1/8 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3))))))) (fma.f64 (neg.f64 (+.f64 1/4 (-.f64 (/.f64 1/4 (fma.f64 x x 1)) (/.f64 1/4 (hypot.f64 1 x))))) (/.f64 (/.f64 1/4 (fma.f64 x x 1)) (+.f64 1/8 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3)))) (*.f64 (+.f64 1/4 (-.f64 (/.f64 1/4 (fma.f64 x x 1)) (/.f64 1/4 (hypot.f64 1 x)))) (/.f64 (/.f64 1/4 (fma.f64 x x 1)) (+.f64 1/8 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3))))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
Compiler

Compiled 752 to 651 computations (13.4% saved)

regimes271.0ms (1.9%)

Counts
42 → 3
Calls
Call 1
Inputs
(-.f64 1 1)
(*.f64 x (*.f64 x 1/8))
(*.f64 1/8 (*.f64 x x))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)
(+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4)))
(/.f64 (-.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))))
(/.f64 (-.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(/.f64 1 (/.f64 (+.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(/.f64 (/.f64 (-.f64 1/4 (/.f64 1/4 (+.f64 1 (*.f64 x x)))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(exp.f64 (log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))
(cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))
(/.f64 (/.f64 (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (/.f64 (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(*.f64 (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (+.f64 1/4 (/.f64 -1/4 (fma.f64 x x 1)))) (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(fma.f64 (neg.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/6) 1)
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(/.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
(/.f64 1 (/.f64 (+.f64 1 (+.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1/2 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))
(/.f64 1 (/.f64 (+.f64 3 (+.f64 (*.f64 -3/8 (pow.f64 x 2)) (+.f64 (*.f64 -229/1024 (pow.f64 x 6)) (*.f64 35/128 (pow.f64 x 4))))) (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))
(/.f64 (-.f64 (/.f64 1/4 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2)) (*.f64 (/.f64 (/.f64 -1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 -1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 -1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
(/.f64 (+.f64 (fma.f64 (sqrt.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (neg.f64 (*.f64 (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (/.f64 1/4 (fma.f64 x x 1))))) (fma.f64 (neg.f64 (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (/.f64 1/4 (fma.f64 x x 1)) (*.f64 (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (/.f64 1/4 (fma.f64 x x 1))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 (fma.f64 (sqrt.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (neg.f64 (*.f64 (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (/.f64 1/4 (fma.f64 x x 1))))) (fma.f64 (neg.f64 (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (/.f64 1/4 (fma.f64 x x 1)) (*.f64 (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (/.f64 1/4 (fma.f64 x x 1)))))))
(/.f64 (+.f64 (fma.f64 (sqrt.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (neg.f64 (*.f64 (+.f64 1/4 (-.f64 (/.f64 1/4 (fma.f64 x x 1)) (/.f64 1/4 (hypot.f64 1 x)))) (/.f64 (/.f64 1/4 (fma.f64 x x 1)) (+.f64 1/8 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3))))))) (fma.f64 (neg.f64 (+.f64 1/4 (-.f64 (/.f64 1/4 (fma.f64 x x 1)) (/.f64 1/4 (hypot.f64 1 x))))) (/.f64 (/.f64 1/4 (fma.f64 x x 1)) (+.f64 1/8 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3)))) (*.f64 (+.f64 1/4 (-.f64 (/.f64 1/4 (fma.f64 x x 1)) (/.f64 1/4 (hypot.f64 1 x)))) (/.f64 (/.f64 1/4 (fma.f64 x x 1)) (+.f64 1/8 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3))))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 (fma.f64 (sqrt.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (neg.f64 (*.f64 (+.f64 1/4 (-.f64 (/.f64 1/4 (fma.f64 x x 1)) (/.f64 1/4 (hypot.f64 1 x)))) (/.f64 (/.f64 1/4 (fma.f64 x x 1)) (+.f64 1/8 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3))))))) (fma.f64 (neg.f64 (+.f64 1/4 (-.f64 (/.f64 1/4 (fma.f64 x x 1)) (/.f64 1/4 (hypot.f64 1 x))))) (/.f64 (/.f64 1/4 (fma.f64 x x 1)) (+.f64 1/8 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3)))) (*.f64 (+.f64 1/4 (-.f64 (/.f64 1/4 (fma.f64 x x 1)) (/.f64 1/4 (hypot.f64 1 x)))) (/.f64 (/.f64 1/4 (fma.f64 x x 1)) (+.f64 1/8 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3)))))))))
(/.f64 (+.f64 (fma.f64 (sqrt.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (neg.f64 (*.f64 (/.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (/.f64 (cbrt.f64 (/.f64 1/16 (pow.f64 (fma.f64 x x 1) 2))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (cbrt.f64 (/.f64 1/16 (pow.f64 (fma.f64 x x 1) 2))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (*.f64 (/.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (/.f64 (cbrt.f64 (/.f64 1/16 (pow.f64 (fma.f64 x x 1) 2))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 (fma.f64 (sqrt.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (sqrt.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (neg.f64 (*.f64 (/.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (/.f64 (cbrt.f64 (/.f64 1/16 (pow.f64 (fma.f64 x x 1) 2))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (cbrt.f64 (/.f64 1/16 (pow.f64 (fma.f64 x x 1) 2))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (*.f64 (/.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (/.f64 (cbrt.f64 (/.f64 1/16 (pow.f64 (fma.f64 x x 1) 2))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))
Outputs
(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6))))
(/.f64 (-.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
Calls

13 calls:

80.0ms
x
29.0ms
(/.f64 1 (hypot.f64 1 x))
29.0ms
(/.f64 1 (hypot.f64 1 x))
17.0ms
(hypot.f64 1 x)
14.0ms
(hypot.f64 1 x)
Results
ErrorSegmentsBranch
0.0b3x
0.1b2(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.1b2(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.1b2(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.1b2(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.1b2(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
0.1b2(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
0.1b2(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
0.1b2(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
0.1b2(/.f64 1 (hypot.f64 1 x))
0.1b2(/.f64 1 (hypot.f64 1 x))
0.1b2(hypot.f64 1 x)
0.1b2(hypot.f64 1 x)
Compiler

Compiled 1443 to 1241 computations (14% saved)

bsearch55.0ms (0.4%)

Algorithm
2×binary-search
Steps
TimeLeftRight
29.0ms
0.00033959049661280835
2.414315746490169
25.0ms
-0.026370478954838624
-0.00043140720506958433
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes173.0ms (1.2%)

Counts
31 → 2
Calls
Call 1
Inputs
(-.f64 1 1)
(*.f64 x (*.f64 x 1/8))
(*.f64 1/8 (*.f64 x x))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)
(+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4)))
(/.f64 (-.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))))
(/.f64 (-.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(/.f64 1 (/.f64 (+.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(/.f64 (/.f64 (-.f64 1/4 (/.f64 1/4 (+.f64 1 (*.f64 x x)))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(exp.f64 (log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))
(cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))
(/.f64 (/.f64 (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (/.f64 (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(*.f64 (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (+.f64 1/4 (/.f64 -1/4 (fma.f64 x x 1)))) (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(fma.f64 (neg.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/6) 1)
Outputs
(+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6))))
(/.f64 (/.f64 (-.f64 1/4 (/.f64 1/4 (+.f64 1 (*.f64 x x)))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
Calls

13 calls:

42.0ms
x
21.0ms
(/.f64 1 (hypot.f64 1 x))
21.0ms
(/.f64 1 (hypot.f64 1 x))
11.0ms
(hypot.f64 1 x)
10.0ms
(hypot.f64 1 x)
Results
ErrorSegmentsBranch
0.1b3x
0.1b2(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.1b2(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.1b2(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.1b2(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.1b2(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
0.1b2(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
0.1b2(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
0.1b2(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
0.1b2(/.f64 1 (hypot.f64 1 x))
0.1b2(/.f64 1 (hypot.f64 1 x))
0.1b2(hypot.f64 1 x)
0.1b2(hypot.f64 1 x)
Compiler

Compiled 533 to 460 computations (13.7% saved)

bsearch1.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.000000093056084
1.000347640653142
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes183.0ms (1.3%)

Counts
23 → 3
Calls
Call 1
Inputs
(-.f64 1 1)
(*.f64 x (*.f64 x 1/8))
(*.f64 1/8 (*.f64 x x))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)
(+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4)))
(/.f64 (-.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))))
(/.f64 (-.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(/.f64 1 (/.f64 (+.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
Outputs
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6))))
(/.f64 (-.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
Calls

13 calls:

78.0ms
x
19.0ms
(/.f64 1 (hypot.f64 1 x))
17.0ms
(/.f64 1 (hypot.f64 1 x))
9.0ms
(hypot.f64 1 x)
9.0ms
(hypot.f64 1 x)
Results
ErrorSegmentsBranch
0.1b3x
0.1b2(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.1b2(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.1b2(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.1b2(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.1b2(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
0.1b2(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
0.1b2(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
0.1b2(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
0.1b2(/.f64 1 (hypot.f64 1 x))
0.1b2(/.f64 1 (hypot.f64 1 x))
0.1b2(hypot.f64 1 x)
0.1b2(hypot.f64 1 x)
Compiler

Compiled 361 to 310 computations (14.1% saved)

bsearch164.0ms (1.2%)

Algorithm
2×binary-search
Steps
TimeLeftRight
137.0ms
0.00033959049661280835
2.414315746490169
26.0ms
-0.026370478954838624
-0.00043140720506958433
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes128.0ms (0.9%)

Counts
21 → 3
Calls
Call 1
Inputs
(-.f64 1 1)
(*.f64 x (*.f64 x 1/8))
(*.f64 1/8 (*.f64 x x))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)
(+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4)))
(/.f64 (-.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))))
(/.f64 (-.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
Outputs
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6))))
(/.f64 (-.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
Calls

13 calls:

29.0ms
x
16.0ms
(/.f64 1 (hypot.f64 1 x))
15.0ms
(/.f64 1 (hypot.f64 1 x))
9.0ms
(hypot.f64 1 x)
8.0ms
(hypot.f64 1 x)
Results
ErrorSegmentsBranch
0.1b3x
0.1b2(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.1b2(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.1b2(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.1b2(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.1b2(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
0.1b2(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
0.1b2(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
0.1b2(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
0.1b2(/.f64 1 (hypot.f64 1 x))
0.1b2(/.f64 1 (hypot.f64 1 x))
0.1b2(hypot.f64 1 x)
0.1b2(hypot.f64 1 x)
Compiler

Compiled 320 to 273 computations (14.7% saved)

bsearch69.0ms (0.5%)

Algorithm
2×binary-search
Steps
TimeLeftRight
43.0ms
0.00033959049661280835
2.414315746490169
26.0ms
-0.026370478954838624
-0.00043140720506958433
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes228.0ms (1.6%)

Counts
20 → 2
Calls
Call 1
Inputs
(-.f64 1 1)
(*.f64 x (*.f64 x 1/8))
(*.f64 1/8 (*.f64 x x))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)
(+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4)))
(/.f64 (-.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))))
Outputs
(+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6))))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
Calls

13 calls:

117.0ms
(/.f64 1 (hypot.f64 1 x))
28.0ms
x
15.0ms
(/.f64 1 (hypot.f64 1 x))
9.0ms
(hypot.f64 1 x)
9.0ms
(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
Results
ErrorSegmentsBranch
0.1b3x
0.1b2(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.1b2(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.1b2(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.1b2(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.1b2(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
0.1b2(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
0.1b2(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
0.1b2(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
0.1b2(/.f64 1 (hypot.f64 1 x))
0.1b2(/.f64 1 (hypot.f64 1 x))
0.1b2(hypot.f64 1 x)
0.1b2(hypot.f64 1 x)
Compiler

Compiled 300 to 255 computations (15% saved)

bsearch0.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.000000093056084
1.000347640653142
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes166.0ms (1.2%)

Counts
18 → 3
Calls
Call 1
Inputs
(-.f64 1 1)
(*.f64 x (*.f64 x 1/8))
(*.f64 1/8 (*.f64 x x))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)
(+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4)))
(/.f64 (-.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
Outputs
(/.f64 (-.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))
(+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6))))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
Calls

13 calls:

53.0ms
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
27.0ms
x
14.0ms
(/.f64 1 (hypot.f64 1 x))
14.0ms
(/.f64 1 (hypot.f64 1 x))
8.0ms
(hypot.f64 1 x)
Results
ErrorSegmentsBranch
0.4b3x
0.5b2(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.5b2(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.5b2(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.5b2(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.5b2(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
0.5b2(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
0.5b2(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
0.5b2(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
0.5b2(/.f64 1 (hypot.f64 1 x))
0.5b2(/.f64 1 (hypot.f64 1 x))
0.5b2(hypot.f64 1 x)
0.5b2(hypot.f64 1 x)
Compiler

Compiled 263 to 222 computations (15.6% saved)

bsearch49.0ms (0.4%)

Algorithm
2×binary-search
Steps
TimeLeftRight
23.0ms
0.00033959049661280835
2.414315746490169
26.0ms
-464108242255813.94
-0.17554372930257645
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes113.0ms (0.8%)

Counts
16 → 3
Calls
Call 1
Inputs
(-.f64 1 1)
(*.f64 x (*.f64 x 1/8))
(*.f64 1/8 (*.f64 x x))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)
(+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4)))
(/.f64 (-.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
Outputs
(/.f64 (-.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))
(+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4)))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
Calls

13 calls:

27.0ms
x
14.0ms
(/.f64 1 (hypot.f64 1 x))
14.0ms
(/.f64 1 (hypot.f64 1 x))
8.0ms
(hypot.f64 1 x)
7.0ms
(hypot.f64 1 x)
Results
ErrorSegmentsBranch
0.5b3x
0.6b2(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.6b2(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.6b2(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.6b2(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.6b2(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
0.6b2(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
0.6b2(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
0.6b2(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
0.6b2(/.f64 1 (hypot.f64 1 x))
0.6b2(/.f64 1 (hypot.f64 1 x))
0.6b2(hypot.f64 1 x)
0.6b2(hypot.f64 1 x)
Compiler

Compiled 230 to 197 computations (14.3% saved)

bsearch50.0ms (0.4%)

Algorithm
2×binary-search
Steps
TimeLeftRight
23.0ms
0.00033959049661280835
2.414315746490169
26.0ms
-464108242255813.94
-0.17554372930257645
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes73.0ms (0.5%)

Counts
14 → 3
Calls
Call 1
Inputs
(-.f64 1 1)
(*.f64 x (*.f64 x 1/8))
(*.f64 1/8 (*.f64 x x))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)
(+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4)))
(/.f64 (-.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
Outputs
(/.f64 (-.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x)))))
(+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4)))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
Calls

3 calls:

40.0ms
(hypot.f64 1 x)
22.0ms
x
6.0ms
(hypot.f64 1 x)
Results
ErrorSegmentsBranch
0.7b3x
0.8b2(hypot.f64 1 x)
0.8b2(hypot.f64 1 x)
Compiler

Compiled 112 to 91 computations (18.8% saved)

bsearch51.0ms (0.4%)

Algorithm
2×binary-search
Steps
TimeLeftRight
23.0ms
0.00033959049661280835
2.414315746490169
27.0ms
-464108242255813.94
-0.17554372930257645
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes132.0ms (0.9%)

Counts
12 → 2
Calls
Call 1
Inputs
(-.f64 1 1)
(*.f64 x (*.f64 x 1/8))
(*.f64 1/8 (*.f64 x x))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)
(+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4)))
Outputs
(+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4)))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
Calls

3 calls:

78.0ms
(hypot.f64 1 x)
44.0ms
x
6.0ms
(hypot.f64 1 x)
Results
ErrorSegmentsBranch
0.8b3x
0.8b2(hypot.f64 1 x)
0.8b2(hypot.f64 1 x)
Compiler

Compiled 88 to 73 computations (17% saved)

bsearch0.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.0152908947180883
2.6132203358596424
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes33.0ms (0.2%)

Counts
11 → 2
Calls
Call 1
Inputs
(-.f64 1 1)
(*.f64 x (*.f64 x 1/8))
(*.f64 1/8 (*.f64 x x))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))
(-.f64 1 (fma.f64 x (*.f64 x -1/8) 1))
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)
Outputs
(*.f64 x (*.f64 x 1/8))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
Calls

3 calls:

18.0ms
x
6.0ms
(hypot.f64 1 x)
5.0ms
(hypot.f64 1 x)
Results
ErrorSegmentsBranch
1.0b3x
1.0b2(hypot.f64 1 x)
1.0b2(hypot.f64 1 x)
Compiler

Compiled 77 to 65 computations (15.6% saved)

bsearch0.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.0152908947180883
2.6132203358596424
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes13.0ms (0.1%)

Counts
5 → 3
Calls
Call 1
Inputs
(-.f64 1 1)
(*.f64 x (*.f64 x 1/8))
(*.f64 1/8 (*.f64 x x))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1/2))
Outputs
(-.f64 1 (sqrt.f64 1/2))
(*.f64 x (*.f64 x 1/8))
(-.f64 1 (sqrt.f64 1/2))
Calls

1 calls:

12.0ms
x
Results
ErrorSegmentsBranch
1.5b3x
Compiler

Compiled 24 to 19 computations (20.8% saved)

bsearch48.0ms (0.3%)

Algorithm
2×binary-search
Steps
TimeLeftRight
24.0ms
0.00033959049661280835
2.414315746490169
24.0ms
-464108242255813.94
-0.17554372930257645
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes5.0ms (0%)

Accuracy

Total -15.3b remaining (-51.2%)

Threshold costs -15.3b (-51.2%)

Counts
3 → 1
Calls
Call 1
Inputs
(-.f64 1 1)
(*.f64 x (*.f64 x 1/8))
(*.f64 1/8 (*.f64 x x))
Outputs
(*.f64 x (*.f64 x 1/8))
Calls

1 calls:

3.0ms
x
Results
ErrorSegmentsBranch
29.8b1x
Compiler

Compiled 16 to 11 computations (31.3% saved)

simplify31.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
22×+-commutative_binary64
14×sub-neg_binary64
11×*-commutative_binary64
7×neg-sub0_binary64
7×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
080720
1107720
2139720
3154720
4161720
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(if (<=.f64 x -7600773068453935/288230376151711744) (-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (if (<=.f64 x 3132169490440203/9223372036854775808) (+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6)))) (/.f64 (-.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
(if (<=.f64 (hypot.f64 1 x) 2252250173647985/2251799813685248) (+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6)))) (/.f64 (/.f64 (-.f64 1/4 (/.f64 1/4 (+.f64 1 (*.f64 x x)))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(if (<=.f64 x -7600773068453935/288230376151711744) (/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (if (<=.f64 x 3132169490440203/9223372036854775808) (+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6)))) (/.f64 (-.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
(if (<=.f64 x -7600773068453935/288230376151711744) (/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (if (<=.f64 x 3132169490440203/9223372036854775808) (+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6)))) (/.f64 (-.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
(if (<=.f64 (hypot.f64 1 x) 2252250173647985/2251799813685248) (+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6)))) (/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(if (<=.f64 x -7425731876093023/16) (/.f64 (-.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))) (if (<=.f64 x 3132169490440203/9223372036854775808) (+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6)))) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(if (<=.f64 x -7425731876093023/16) (/.f64 (-.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))) (if (<=.f64 x 3132169490440203/9223372036854775808) (+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4))) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(if (<=.f64 x -7425731876093023/16) (/.f64 (-.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))) (if (<=.f64 x 3132169490440203/9223372036854775808) (+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))))
(if (<=.f64 (hypot.f64 1 x) 2) (+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
(if (<=.f64 (hypot.f64 1 x) 2) (*.f64 x (*.f64 x 1/8)) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
(if (<=.f64 x -7425731876093023/16) (-.f64 1 (sqrt.f64 1/2)) (if (<=.f64 x 3132169490440203/9223372036854775808) (*.f64 x (*.f64 x 1/8)) (-.f64 1 (sqrt.f64 1/2))))
(*.f64 x (*.f64 x 1/8))
(-.f64 1 1)
Outputs
(if (<=.f64 x -7600773068453935/288230376151711744) (-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (if (<=.f64 x 3132169490440203/9223372036854775808) (+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6)))) (/.f64 (-.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
(if (<=.f64 x -7600773068453935/288230376151711744) (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 -1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (if (<=.f64 x 3132169490440203/9223372036854775808) (+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6)))) (/.f64 (-.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
(if (<=.f64 (hypot.f64 1 x) 2252250173647985/2251799813685248) (+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6)))) (/.f64 (/.f64 (-.f64 1/4 (/.f64 1/4 (+.f64 1 (*.f64 x x)))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(if (<=.f64 (hypot.f64 1 x) 2252250173647985/2251799813685248) (+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6)))) (/.f64 (/.f64 (+.f64 1/4 (/.f64 -1/4 (+.f64 1 (*.f64 x x)))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(if (<=.f64 x -7600773068453935/288230376151711744) (/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (if (<=.f64 x 3132169490440203/9223372036854775808) (+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6)))) (/.f64 (-.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
(if (<=.f64 x -7600773068453935/288230376151711744) (/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))))) (if (<=.f64 x 3132169490440203/9223372036854775808) (+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6)))) (/.f64 (-.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
(if (<=.f64 x -7600773068453935/288230376151711744) (/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (if (<=.f64 x 3132169490440203/9223372036854775808) (+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6)))) (/.f64 (-.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
(if (<=.f64 x -7600773068453935/288230376151711744) (/.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (if (<=.f64 x 3132169490440203/9223372036854775808) (+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6)))) (/.f64 (-.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
(if (<=.f64 (hypot.f64 1 x) 2252250173647985/2251799813685248) (+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6)))) (/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(if (<=.f64 (hypot.f64 1 x) 2252250173647985/2251799813685248) (+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6)))) (/.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(if (<=.f64 x -7425731876093023/16) (/.f64 (-.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))) (if (<=.f64 x 3132169490440203/9223372036854775808) (+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6)))) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(if (<=.f64 x -7425731876093023/16) (/.f64 (+.f64 1/2 (/.f64 1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))) (if (<=.f64 x 3132169490440203/9223372036854775808) (+.f64 (*.f64 -11/128 (pow.f64 x 4)) (fma.f64 (*.f64 x x) 1/8 (*.f64 69/1024 (pow.f64 x 6)))) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(if (<=.f64 x -7425731876093023/16) (/.f64 (-.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))) (if (<=.f64 x 3132169490440203/9223372036854775808) (+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4))) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(if (<=.f64 x -7425731876093023/16) (/.f64 (-.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))) (if (<=.f64 x 3132169490440203/9223372036854775808) (+.f64 (*.f64 -11/128 (pow.f64 x 4)) (*.f64 x (*.f64 x 1/8))) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(if (<=.f64 x -7425731876093023/16) (/.f64 (+.f64 1/2 (/.f64 1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))) (if (<=.f64 x 3132169490440203/9223372036854775808) (+.f64 (*.f64 -11/128 (pow.f64 x 4)) (*.f64 x (*.f64 x 1/8))) (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
(if (<=.f64 x -7425731876093023/16) (/.f64 (-.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))) (if (<=.f64 x 3132169490440203/9223372036854775808) (+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))))
(if (<=.f64 x -7425731876093023/16) (/.f64 (-.f64 1/2 (/.f64 -1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))) (if (<=.f64 x 3132169490440203/9223372036854775808) (+.f64 (*.f64 -11/128 (pow.f64 x 4)) (*.f64 x (*.f64 x 1/8))) (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))))
(if (<=.f64 x -7425731876093023/16) (/.f64 (+.f64 1/2 (/.f64 1/2 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 x))))) (if (<=.f64 x 3132169490440203/9223372036854775808) (+.f64 (*.f64 -11/128 (pow.f64 x 4)) (*.f64 x (*.f64 x 1/8))) (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))))
(if (<=.f64 (hypot.f64 1 x) 2) (+.f64 (*.f64 x (*.f64 x 1/8)) (*.f64 -11/128 (pow.f64 x 4))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
(if (<=.f64 (hypot.f64 1 x) 2) (+.f64 (*.f64 -11/128 (pow.f64 x 4)) (*.f64 x (*.f64 x 1/8))) (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))))
(if (<=.f64 (hypot.f64 1 x) 2) (*.f64 x (*.f64 x 1/8)) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
(if (<=.f64 (hypot.f64 1 x) 2) (*.f64 x (*.f64 x 1/8)) (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))))
(if (<=.f64 x -7425731876093023/16) (-.f64 1 (sqrt.f64 1/2)) (if (<=.f64 x 3132169490440203/9223372036854775808) (*.f64 x (*.f64 x 1/8)) (-.f64 1 (sqrt.f64 1/2))))
(*.f64 x (*.f64 x 1/8))
(-.f64 1 1)
0
Compiler

Compiled 499 to 414 computations (17% saved)

soundness199.0ms (1.4%)

Algorithm
4×egg-herbie
Rules
539×fma-def_binary64
513×fma-neg_binary64
451×associate-/r*_binary64
355×associate-*r*_binary64
332×associate-*l*_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01018
12215
22915
33715
44415
55415
66515
77715
88015
01018
12215
22915
33715
44415
55415
66515
77715
88015
01331557
14051231
215081025
368111020
01018
12215
22915
33715
44415
55415
66515
77715
88015
Stop Event
1×saturated
1×node limit
1×saturated
1×saturated
Compiler

Compiled 1216 to 1038 computations (14.6% saved)

end719.0ms (5.2%)

Compiler

Compiled 487 to 397 computations (18.5% saved)

Profiling

Loading profile data...