Details

Time bar (total: 12.9s)

analyze1.0ms (0%)

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

Compiled 14 to 13 computations (7.1% saved)

sample2.3s (17.6%)

Results
1.1s2102×body2048valid
617.0ms4516×body256valid
432.0ms1085×body1024valid
127.0ms553×body512valid

preprocess35.0ms (0.3%)

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)

simplify16.0ms (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)

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
16.2b
Counts
3 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶16.2b
(-.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 3 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 1/2 (hypot.f64 1 x))
✓0.0b
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
✓2.7b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
Compiler

Compiled 37 to 31 computations (16.2% saved)

series10.0ms (0.1%)

Counts
3 → 36
Calls

9 calls:

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

rewrite126.0ms (1%)

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
0932
120132
2260232
Stop Event
1×node limit
Counts
3 → 156
Calls
Call 1
Inputs
(-.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 1/2 (hypot.f64 1 x))
Outputs
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simplify104.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
627×unswap-sqr_binary64
529×sub-neg_binary64
357×fma-def_binary64
339×associate-+l+_binary64
275×times-frac_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0112648
1325610
2963602
32904602
47125602
Stop Event
1×node limit
Counts
192 → 217
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 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)))))
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))))
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 1/8 (*.f64 x x) (*.f64 69/1024 (pow.f64 x 6))))
(+.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 (sqrt.f64 1/2)) x)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 -1/4 (*.f64 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 (sqrt.f64 1/2)) x)))
(+.f64 1 (-.f64 (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)))))
(+.f64 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1)) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x 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 (-.f64 (+.f64 (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))) (/.f64 (*.f64 -1/2 (+.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 (sqrt.f64 1/2)) x))))
(+.f64 1 (+.f64 (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))) (+.f64 (-.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (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 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))) (/.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 (sqrt.f64 1/2)) x) (sqrt.f64 1/2)))
(-.f64 (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)) (-.f64 (sqrt.f64 1/2) 1))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))
(-.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 (sqrt.f64 1/2)) x)) (-.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 (-.f64 1 (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 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 (sqrt.f64 1/2)) x))) (-.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 1 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (+.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 -3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))
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)
(+.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 (*.f64 x 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 1 (fma.f64 (*.f64 x x) -1/4 (fma.f64 (pow.f64 x 4) 3/16 (*.f64 (pow.f64 x 6) -5/32))))
(+.f64 (fma.f64 (*.f64 x x) -1/4 1) (fma.f64 (pow.f64 x 6) -5/32 (*.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 (*.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 (/.f64 1/2 x) (-.f64 (/.f64 1/4 (pow.f64 x 3)) 1/2))
(-.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/4 (pow.f64 x 3)) -1/2))
(-.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 1/2 (-.f64 (/.f64 3/16 (pow.f64 x 5)) (/.f64 1/4 (pow.f64 x 3)))))
(+.f64 1/2 (+.f64 (/.f64 1/2 x) (+.f64 (/.f64 3/16 (pow.f64 x 5)) (/.f64 -1/4 (pow.f64 x 3)))))
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 (/.f64 1/4 (pow.f64 x 3)) (+.f64 1/2 (/.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 1/2 (-.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 1/2 (/.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 (/.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)))
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 (*.f64 (pow.f64 x 4) 3/16) (fma.f64 (*.f64 x x) -1/4 1/2))
(fma.f64 (pow.f64 x 4) 3/16 (fma.f64 (*.f64 x x) -1/4 1/2))
(fma.f64 (pow.f64 x 4) 3/16 (fma.f64 x (*.f64 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 (*.f64 (pow.f64 x 6) -5/32) (fma.f64 (pow.f64 x 4) 3/16 (fma.f64 (*.f64 x x) -1/4 1/2)))
(+.f64 1/2 (fma.f64 x (*.f64 x -1/4) (fma.f64 (pow.f64 x 6) -5/32 (*.f64 (pow.f64 x 4) 3/16))))
(/.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 1/2 x) (+.f64 (/.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 1/4 (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 (+.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 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 (+.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 -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 (pow.f64 x 3)) (/.f64 -3/16 (pow.f64 x 5))) (/.f64 1/2 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))))
(+.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 1/4 (pow.f64 x 3)) (+.f64 (-.f64 (/.f64 5/32 (pow.f64 x 7)) (/.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 (/.f64 5/32 (pow.f64 x 7)) (/.f64 -3/16 (pow.f64 x 5)))))

eval145.0ms (1.1%)

Compiler

Compiled 3925 to 3504 computations (10.7% saved)

prune46.0ms (0.4%)

Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New20215217
Fresh000
Picked011
Done000
Total20216218
Error
0.0b
Counts
218 → 16
Alt Table
Click to see full alt table
StatusErrorProgram
✓16.2b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
▶34.0b
(-.f64 1 (sqrt.f64 1/2))
▶15.7b
(/.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))))))
45.3b
(-.f64 1 (sqrt.f64 1))
34.9b
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (+.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 -3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))
29.7b
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
34.8b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
▶34.8b
(+.f64 (+.f64 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1)) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))) (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
34.4b
(-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1))
30.0b
(+.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)))))
30.1b
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x)))
▶34.6b
(+.f64 (-.f64 1 (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))))
29.4b
(*.f64 1/8 (*.f64 x x))
▶34.5b
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))
34.5b
(-.f64 (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
34.5b
(+.f64 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1)) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)))
Compiler

Compiled 485 to 420 computations (13.4% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
✓0.0b
(/.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))))))
✓0.0b
(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓2.2b
(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
Compiler

Compiled 62 to 53 computations (14.5% saved)

series6.0ms (0%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
2.0ms
x
@inf
(/.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))))))
1.0ms
x
@-inf
(/.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))))))
1.0ms
x
@-inf
(+.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)))))
0.0ms
x
@0
(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite160.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
614×prod-diff_binary64
581×log-prod_binary64
325×fma-def_binary64
228×log-div_binary64
219×expm1-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01152
125440
2366240
Stop Event
1×node limit
Counts
3 → 253
Calls
Call 1
Inputs
(-.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 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
Outputs
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((#(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 (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 1/2 (/.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 (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 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simplify63.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
824×fma-def_binary64
650×times-frac_binary64
605×associate-*l*_binary64
442×associate-*r*_binary64
320×associate-/l*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01961612
16371385
223211294
Stop Event
1×node limit
Counts
289 → 316
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))))
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))))))
(*.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))))
(+.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 5/32 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -3/16 (fma.f64 1/4 (*.f64 x x) (*.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 (+.f64 1/2 (/.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 1/4 (pow.f64 x 3))) (+.f64 (/.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 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 (+.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 1/2 (-.f64 (/.f64 3/16 (pow.f64 x 5)) (/.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)))))
2
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) 2)
(fma.f64 -1/8 (*.f64 x x) 2)
(fma.f64 (*.f64 x x) -1/8 2)
(fma.f64 x (*.f64 x -1/8) 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 (pow.f64 x 4) 11/128))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 (pow.f64 x 4) 11/128 2))
(fma.f64 x (*.f64 x -1/8) (fma.f64 (pow.f64 x 4) 11/128 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 (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 2)))
(fma.f64 x (*.f64 x -1/8) (fma.f64 (pow.f64 x 4) 11/128 (fma.f64 (pow.f64 x 6) -69/1024 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 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (sqrt.f64 1/2)))
(-.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 x x) (*.f64 1/2 (sqrt.f64 1/2)))))
(+.f64 (+.f64 1 (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 (*.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 (pow.f64 x 3) (sqrt.f64 1/2))) (+.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 (pow.f64 x 3) (sqrt.f64 1/2))) (/.f64 1/32 (*.f64 (*.f64 x x) (*.f64 1/2 (sqrt.f64 1/2))))))
(+.f64 (sqrt.f64 1/2) (-.f64 (+.f64 (+.f64 1 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))) (/.f64 -3/32 (*.f64 (pow.f64 x 3) (sqrt.f64 1/2)))) (/.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 -1/4 (*.f64 x (sqrt.f64 1/2)))))
(-.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 (sqrt.f64 1/2) (-.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))))))
(+.f64 1 (-.f64 (sqrt.f64 1/2) (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 (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 (pow.f64 x 3) (sqrt.f64 1/2))) -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 (+.f64 1 (/.f64 (/.f64 3/32 (pow.f64 x 3)) (sqrt.f64 1/2))) (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 (pow.f64 x 3) (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 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 (pow.f64 x 4) -11/128 (*.f64 x (*.f64 x 1/8)))
(fma.f64 x (*.f64 x 1/8) (*.f64 (pow.f64 x 4) -11/128))
(+.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)))
(fma.f64 x (*.f64 x 1/8) (fma.f64 (pow.f64 x 6) 69/1024 (*.f64 (pow.f64 x 4) -11/128)))
(+.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 8) -1843/32768 (*.f64 (pow.f64 x 4) -11/128))))
(fma.f64 x (*.f64 x 1/8) (fma.f64 (pow.f64 x 4) -11/128 (fma.f64 (pow.f64 x 6) 69/1024 (*.f64 (pow.f64 x 8) -1843/32768))))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))
(+.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 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 (*.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 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 (/.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 -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)))))))
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(+.f64 (/.f64 1/2 (fma.f64 x (sqrt.f64 1/2) x)) (+.f64 (/.f64 1/64 (*.f64 (*.f64 x (fma.f64 x (sqrt.f64 1/2) x)) (fma.f64 1/2 (sqrt.f64 1/2) 1/4))) (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (-.f64 (-.f64 (/.f64 1/8 (*.f64 (fma.f64 x (sqrt.f64 1/2) x) (+.f64 1/2 (sqrt.f64 1/2)))) (/.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 (/.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))))))))

localize8.0ms (0.1%)

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

rewrite51.0ms (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

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))
✓0.5b
(/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x)
1.0b
(-.f64 1 (sqrt.f64 1/2))
✓1.0b
(/.f64 1/4 (sqrt.f64 1/2))
Compiler

Compiled 32 to 29 computations (9.4% saved)

series4.0ms (0%)

Counts
3 → 24
Calls

6 calls:

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

rewrite137.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
473×log-prod_binary64
368×fma-def_binary64
332×pow-prod-down_binary64
280×pow2_binary64
211×log-div_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01032
122823
2327823
Stop Event
1×node limit
Counts
3 → 167
Calls
Call 1
Inputs
(/.f64 1/4 (sqrt.f64 1/2))
(/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x)
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))
Outputs
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(#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/8) x))) (-.f64 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2) (/.f64 1/8 (*.f64 x x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (/.f64 (sqrt.f64 1/8) x) (-.f64 1 (sqrt.f64 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (/.f64 (sqrt.f64 1/8) x) (-.f64 1 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (/.f64 (sqrt.f64 1/8) x) (-.f64 1 (sqrt.f64 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 1/8) x))) (exp.f64 (-.f64 1 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (/.f64 (sqrt.f64 1/8) x)) (+.f64 1 (expm1.f64 (-.f64 1 (sqrt.f64 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 1/8) x))) (+.f64 1 (expm1.f64 (-.f64 1 (sqrt.f64 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (-.f64 1 (sqrt.f64 1/2)))) (exp.f64 (/.f64 (sqrt.f64 1/8) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (-.f64 1 (sqrt.f64 1/2))) (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 1/8) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (-.f64 1 (sqrt.f64 1/2)))) (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 1/8) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (/.f64 (sqrt.f64 1/8) x) (-.f64 1 (sqrt.f64 1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (/.f64 (sqrt.f64 1/8) x) (-.f64 1 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (/.f64 (sqrt.f64 1/8) x) (-.f64 1 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (fma.f64 -1 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/8) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (fma.f64 -1 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/8) x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log1p.f64 (fma.f64 -1 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/8) x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (log1p.f64 (fma.f64 -1 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/8) x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 (fma.f64 -1 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/8) x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/4 (/.f64 (pow.f64 1/2 -1/2) x) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (/.f64 (cbrt.f64 (sqrt.f64 1/8)) x) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (sqrt.f64 1/8) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (*.f64 (cbrt.f64 (sqrt.f64 1/8)) (/.f64 1 x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 1/8) (/.f64 1 x) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 1/8) x) 1 (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 (sqrt.f64 1/8) x) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/8) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (sqrt.f64 1/2)) 1 (/.f64 (sqrt.f64 1/8) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 1/2))) (cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2)) (/.f64 (sqrt.f64 1/8) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2)) (cbrt.f64 (-.f64 1 (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/8) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 (sqrt.f64 1/8) x)) (cbrt.f64 (/.f64 1/8 (*.f64 x x))) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 1/8 (*.f64 x x))) (cbrt.f64 (/.f64 (sqrt.f64 1/8) x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (sqrt.f64 1/8)) (*.f64 (sqrt.f64 (sqrt.f64 1/8)) (/.f64 1 x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 1/2))) (sqrt.f64 (-.f64 1 (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/8) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (sqrt.f64 1/8) x)) (sqrt.f64 (/.f64 (sqrt.f64 1/8) x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (sqrt.f64 1/8)) (/.f64 1 (neg.f64 x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (pow.f64 1/2 3/2)) (/.f64 1 (+.f64 3/2 (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/8) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) (sqrt.f64 1/8) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (sqrt.f64 1/8)) 1) (/.f64 (sqrt.f64 (sqrt.f64 1/8)) x) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1/4 (cbrt.f64 (*.f64 x x))) (/.f64 (pow.f64 1/2 -1/2) (cbrt.f64 x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) -2) (/.f64 (sqrt.f64 1/8) (cbrt.f64 x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1/2 (cbrt.f64 (*.f64 x x))) (cbrt.f64 (/.f64 (sqrt.f64 1/8) x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (sqrt.f64 1/8)) (cbrt.f64 (*.f64 x x))) (/.f64 (sqrt.f64 (sqrt.f64 1/8)) (cbrt.f64 x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1/4 (sqrt.f64 x)) (/.f64 (pow.f64 1/2 -1/2) (sqrt.f64 x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (/.f64 (sqrt.f64 1/8) (sqrt.f64 x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1/2 (sqrt.f64 x)) (/.f64 (cbrt.f64 (sqrt.f64 1/8)) (sqrt.f64 x)) (-.f64 1 (sqrt.f64 1/2)))))))

simplify136.0ms (1%)

Algorithm
1×egg-herbie
Rules
1067×fma-neg_binary64
415×cancel-sign-sub-inv_binary64
290×fma-def_binary64
274×div-sub_binary64
271×distribute-rgt-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
013282
128282
249282
376282
4115282
5189282
6384282
7718282
81199282
91602282
102834282
115096282
125249282
135343282
145371282
155387282
165507282
175663282
185667282
Stop Event
1×saturated
Counts
191 → 171
Calls
Call 1
Inputs
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(-.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 1 (*.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (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 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (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 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
Outputs
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(-.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 (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 (-.f64 1 (sqrt.f64 1/2)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
(-.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 (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 (-.f64 1 (sqrt.f64 1/2)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
(-.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 (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 (-.f64 1 (sqrt.f64 1/2)) (/.f64 -1/4 (*.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 1 (-.f64 (/.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 (-.f64 1 (sqrt.f64 1/2)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
(-.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 (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 (-.f64 1 (sqrt.f64 1/2)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
(-.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 (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 (-.f64 1 (sqrt.f64 1/2)) (/.f64 -1/4 (*.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 1 (-.f64 (/.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 (-.f64 1 (sqrt.f64 1/2)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
(-.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 (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 (-.f64 1 (sqrt.f64 1/2)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
(-.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 (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 (-.f64 1 (sqrt.f64 1/2)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))

localize37.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.6b
(/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))
1.0b
(-.f64 1 (sqrt.f64 1/2))
✓1.0b
(/.f64 1/16 (sqrt.f64 1/2))
1.0b
(/.f64 1/4 (sqrt.f64 1/2))
Compiler

Compiled 72 to 57 computations (20.8% saved)

series2.0ms (0%)

Counts
2 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
(/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))
1.0ms
x
@inf
(/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))
0.0ms
x
@-inf
(/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))

rewrite60.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
879×pow1_binary64
833×add-log-exp_binary64
833×log1p-expm1-u_binary64
833×expm1-log1p-u_binary64
815×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0818
117712
2227112
Stop Event
1×node limit
Counts
2 → 57
Calls
Call 1
Inputs
(/.f64 1/16 (sqrt.f64 1/2))
(/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 1/128)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/16 (pow.f64 1/2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 1/128) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 1/128))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 1/128)) (cbrt.f64 1/128))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 1/128) (cbrt.f64 (sqrt.f64 1/128)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sqrt.f64 1/128)) (sqrt.f64 (sqrt.f64 1/128)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/16 (/.f64 1 (neg.f64 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1/2 -1/2) 1/16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 1/128) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/2048 (sqrt.f64 1/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 1/128)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 1/128)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/2) 16) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 1/128)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 1/128)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 1/2048 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 1/128)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 1/128)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 1/128)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (sqrt.f64 1/128) (pow.f64 x -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/16 (/.f64 (pow.f64 1/2 -1/2) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/16 (*.f64 (pow.f64 1/2 -1/2) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 1/128) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 1/128) (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (sqrt.f64 1/128) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/128) (pow.f64 x -2))) (cbrt.f64 (/.f64 1/128 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1/128 (pow.f64 x 4))) (cbrt.f64 (*.f64 (sqrt.f64 1/128) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 1/128) (*.f64 (cbrt.f64 (sqrt.f64 1/128)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (sqrt.f64 1/128)) x) (/.f64 (sqrt.f64 (sqrt.f64 1/128)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sqrt.f64 1/128)) (*.f64 (sqrt.f64 (sqrt.f64 1/128)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 1/128)) (/.f64 1 (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -2) (sqrt.f64 1/128))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 1/128) x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/16 x) (/.f64 (pow.f64 1/2 -1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 (sqrt.f64 1/128) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 1/128) x) (/.f64 (cbrt.f64 (sqrt.f64 1/128)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 1/128) 1) (/.f64 (cbrt.f64 (sqrt.f64 1/128)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (sqrt.f64 1/128)) 1) (/.f64 (sqrt.f64 (sqrt.f64 1/128)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/16 (cbrt.f64 (pow.f64 x 4))) (/.f64 (pow.f64 1/2 -1/2) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (pow.f64 x 4))) (/.f64 (sqrt.f64 1/128) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 1/128) (cbrt.f64 (pow.f64 x 4))) (cbrt.f64 (*.f64 (sqrt.f64 1/128) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (sqrt.f64 1/128)) (cbrt.f64 (pow.f64 x 4))) (/.f64 (sqrt.f64 (sqrt.f64 1/128)) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/128) (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/128) (pow.f64 x -2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/128) (pow.f64 x -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (sqrt.f64 1/128)) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (/.f64 (sqrt.f64 1/128) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 1/128) (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/128 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 1/128)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/128) (pow.f64 x -2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (/.f64 1/2048 (sqrt.f64 1/2)) (pow.f64 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/128) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/128) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 1/128) (pow.f64 x -2))))))))

simplify197.0ms (1.5%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
09144
117144
231144
362144
4160144
5511144
61947144
72823144
82987144
93171144
103379144
113678144
124073144
134552144
145120144
155810144
166649144
177045144
187333144
197609144
207683144
217717144
Stop Event
1×node limit
Counts
69 → 59
Calls
Call 1
Inputs
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
Outputs
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x)))
(/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x)))
(/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x)))
(/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x)))
(/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x)))
(/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x)))
(/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x)))
(/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x)))
(/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x)))
(/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x)))
(/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x)))
(/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))
(/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x)))
(/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))

localize69.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))
1.0b
(/.f64 1/16 (sqrt.f64 1/2))
✓1.0b
(+.f64 (sqrt.f64 1/2) -1)
✓7.0b
(+.f64 (+.f64 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1)) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))) (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
Compiler

Compiled 115 to 94 computations (18.3% saved)

series3.0ms (0%)

Counts
2 → 12
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@inf
(+.f64 (+.f64 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1)) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))) (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
1.0ms
x
@0
(+.f64 (+.f64 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1)) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))) (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
1.0ms
x
@-inf
(+.f64 (+.f64 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1)) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))) (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))

rewrite121.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
424×log1p-udef_binary64
251×add-sqr-sqrt_binary64
238×add-cbrt-cube_binary64
238×add-log-exp_binary64
238×pow1_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02151
151045
2791345
Stop Event
1×node limit
Counts
2 → 93
Calls
Call 1
Inputs
(+.f64 (+.f64 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1)) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))) (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(+.f64 (sqrt.f64 1/2) -1)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2))) (-.f64 (+.f64 (sqrt.f64 1/2) -1) (fma.f64 (sqrt.f64 1/128) (pow.f64 x -2) (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2))) (-.f64 (+.f64 (sqrt.f64 1/2) (-.f64 -1 (*.f64 (sqrt.f64 1/128) (pow.f64 x -2)))) (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2))) (sqrt.f64 1/2)) (-.f64 -1 (fma.f64 (sqrt.f64 1/128) (pow.f64 x -2) (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 3/32 (/.f64 (pow.f64 1/2 -1/2) (pow.f64 x 3)) (fma.f64 (sqrt.f64 1/128) (pow.f64 x -2) (+.f64 (-.f64 (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2))) (sqrt.f64 1/2)) 1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (fma.f64 (sqrt.f64 1/128) (pow.f64 x -2) (+.f64 (-.f64 (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2))) (sqrt.f64 1/2)) 1)) 2) (-.f64 (fma.f64 (sqrt.f64 1/128) (pow.f64 x -2) (+.f64 (-.f64 (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2))) (sqrt.f64 1/2)) 1)) (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (/.f64 (/.f64 9/1024 (*.f64 1/2 (pow.f64 x 6))) (-.f64 (fma.f64 (sqrt.f64 1/128) (pow.f64 x -2) (+.f64 (-.f64 (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2))) (sqrt.f64 1/2)) 1)) (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2)))) (+.f64 (sqrt.f64 1/2) (-.f64 -1 (*.f64 (sqrt.f64 1/128) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 3/32 (/.f64 (pow.f64 1/2 -1/2) (pow.f64 x 3)) (fma.f64 (sqrt.f64 1/128) (pow.f64 x -2) (+.f64 (-.f64 (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2))) (sqrt.f64 1/2)) 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 3/32 (/.f64 (pow.f64 1/2 -1/2) 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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (sqrt.f64 1/2) -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 1/2) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (sqrt.f64 1/2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (sqrt.f64 1/2) -1)) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 1/2) -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 1/2) -1)) 2) (cbrt.f64 (+.f64 (sqrt.f64 1/2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (sqrt.f64 1/2) -1)) (sqrt.f64 (+.f64 (sqrt.f64 1/2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 -1 (pow.f64 1/2 3/2)) (/.f64 1 (-.f64 3/2 (neg.f64 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/2 (/.f64 1 (-.f64 (sqrt.f64 1/2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 1/2 1/4) 1) (-.f64 (pow.f64 1/2 1/4) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1/2 (neg.f64 (-.f64 (sqrt.f64 1/2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1/2 (-.f64 -1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 3/2 (neg.f64 (sqrt.f64 1/2))) (+.f64 -1 (pow.f64 1/2 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (sqrt.f64 1/2) -1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1 (pow.f64 1/2 3/2)) (-.f64 3/2 (neg.f64 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1 (pow.f64 1/2 3/2)) (+.f64 1 (-.f64 1/2 (neg.f64 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1/2 (-.f64 (sqrt.f64 1/2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 -1 (pow.f64 1/2 3/2))) (neg.f64 (-.f64 3/2 (neg.f64 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (sqrt.f64 1/2) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 1/2) -1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 1/2) -1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) -1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) -1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (sqrt.f64 1/2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (sqrt.f64 1/2) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 1/2) -1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 1/2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (sqrt.f64 1/2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (sqrt.f64 1/2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 1/2) -1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 1/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 1/2) (cbrt.f64 (sqrt.f64 1/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1/2 1/4) (pow.f64 1/2 1/4) -1)))))

simplify49.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
790×fma-def_binary64
609×times-frac_binary64
518×fma-neg_binary64
421×associate-/l/_binary64
402×associate-*l*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
033318
1101318
2269318
3688283
42413259
Stop Event
1×node limit
Counts
105 → 107
Calls
Call 1
Inputs
(/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))
(+.f64 (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (+.f64 (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 1 (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))) (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) 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 1 (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (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 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))) (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) 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 1 (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (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 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))) (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
Outputs
(/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))
(/.f64 (/.f64 3/32 (sqrt.f64 1/2)) (pow.f64 x 3))
(+.f64 (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))))
(*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (+.f64 (/.f64 3/32 x) 1/16))
(/.f64 (*.f64 (/.f64 1 x) (+.f64 (/.f64 3/32 x) 1/16)) (*.f64 (sqrt.f64 1/2) x))
(-.f64 (+.f64 (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (-.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 (/.f64 3/32 (sqrt.f64 1/2)) (pow.f64 x 3)) (*.f64 (/.f64 (/.f64 1 x) (sqrt.f64 1/2)) (-.f64 (/.f64 1/16 x) 1/4)))
(*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/16 x) (-.f64 1/4 (/.f64 (/.f64 3/32 x) x))))
(-.f64 (+.f64 (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 1 (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))) (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 1 (-.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (-.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 1 (-.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x)))))
(+.f64 (+.f64 (/.f64 (/.f64 3/32 (sqrt.f64 1/2)) (pow.f64 x 3)) (*.f64 (/.f64 (/.f64 1 x) (sqrt.f64 1/2)) (-.f64 (/.f64 1/16 x) 1/4))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/16 x) (-.f64 1/4 (/.f64 (/.f64 3/32 x) x)))) (-.f64 1 (sqrt.f64 1/2)))
(-.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 (sqrt.f64 1/2) x)))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x)))
(-.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)))
(-.f64 (+.f64 1 (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(+.f64 1 (-.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))))
(+.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (-.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 1 (-.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))))
(+.f64 1 (-.f64 (*.f64 (/.f64 (/.f64 1 x) (sqrt.f64 1/2)) (-.f64 (/.f64 1/16 x) 1/4)) (sqrt.f64 1/2)))
(-.f64 (fma.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (+.f64 (/.f64 1/16 x) -1/4) 1) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))) (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 1 (-.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (-.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 1 (-.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x)))))
(+.f64 (+.f64 (/.f64 (/.f64 3/32 (sqrt.f64 1/2)) (pow.f64 x 3)) (*.f64 (/.f64 (/.f64 1 x) (sqrt.f64 1/2)) (-.f64 (/.f64 1/16 x) 1/4))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/16 x) (-.f64 1/4 (/.f64 (/.f64 3/32 x) x)))) (-.f64 1 (sqrt.f64 1/2)))
(-.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 (sqrt.f64 1/2) x)))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x)))
(-.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)))
(-.f64 (+.f64 1 (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(+.f64 1 (-.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))))
(+.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (-.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 1 (-.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))))
(+.f64 1 (-.f64 (*.f64 (/.f64 (/.f64 1 x) (sqrt.f64 1/2)) (-.f64 (/.f64 1/16 x) 1/4)) (sqrt.f64 1/2)))
(-.f64 (fma.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (+.f64 (/.f64 1/16 x) -1/4) 1) (sqrt.f64 1/2))
(-.f64 (+.f64 1 (+.f64 (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))) (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 1 (-.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (-.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 1 (-.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x)))))
(+.f64 (+.f64 (/.f64 (/.f64 3/32 (sqrt.f64 1/2)) (pow.f64 x 3)) (*.f64 (/.f64 (/.f64 1 x) (sqrt.f64 1/2)) (-.f64 (/.f64 1/16 x) 1/4))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/16 x) (-.f64 1/4 (/.f64 (/.f64 3/32 x) x)))) (-.f64 1 (sqrt.f64 1/2)))

eval1.4s (10.6%)

Compiler

Compiled 32706 to 29057 computations (11.2% saved)

prune158.0ms (1.2%)

Pruning

25 alts after pruning (22 fresh and 3 done)

PrunedKeptTotal
New88818906
Fresh6410
Picked101
Done235
Total89725922
Error
0.0b
Counts
922 → 25
Alt Table
Click to see full alt table
StatusErrorProgram
34.8b
(+.f64 (*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/16 x) (-.f64 1/4 (/.f64 (/.f64 3/32 x) x)))) (-.f64 1 (sqrt.f64 1/2)))
30.0b
(+.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)))))
34.4b
(-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1))
✓34.0b
(-.f64 1 (sqrt.f64 1/2))
39.1b
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)
▶15.7b
(/.f64 (exp.f64 (log.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))))))
32.5b
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (cbrt.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (cbrt.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (neg.f64 (*.f64 (/.f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))) (/.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)))) (/.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))) (*.f64 (/.f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))) (/.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))))))
✓16.2b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
29.7b
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
▶34.1b
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))
✓15.7b
(/.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))))))
34.8b
(+.f64 (+.f64 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1)) (/.f64 (sqrt.f64 1/128) (*.f64 x x))) (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
▶45.3b
(-.f64 1 (sqrt.f64 1))
34.6b
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (-.f64 (+.f64 1 (*.f64 (sqrt.f64 1/128) (pow.f64 x -2))) 1)))
34.9b
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (+.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 -3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))
34.5b
(-.f64 (+.f64 (/.f64 (sqrt.f64 1/8) x) 1) (sqrt.f64 1/2))
29.4b
(*.f64 x (*.f64 x 1/8))
34.2b
(+.f64 (/.f64 1/2 (+.f64 1 (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))))
▶34.0b
(-.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))
34.6b
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (/.f64 (sqrt.f64 1/128) (*.f64 x x))))
33.6b
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
34.5b
(+.f64 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1)) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)))
30.1b
(fma.f64 x (*.f64 x 1/8) (*.f64 (pow.f64 x 4) -11/128))
▶34.3b
(+.f64 (+.f64 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (/.f64 1/2 (-.f64 -1 (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))))
45.0b
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (fma.f64 x (*.f64 x -1/8) 2))
Compiler

Compiled 1115 to 978 computations (12.3% saved)

localize42.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 (exp.f64 (log.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))))))
0.0b
(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓0.1b
(exp.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))
✓2.2b
(+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))
Compiler

Compiled 87 to 75 computations (13.8% saved)

series3.0ms (0%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(/.f64 (exp.f64 (log.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))))))
1.0ms
x
@-inf
(/.f64 (exp.f64 (log.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))))))
0.0ms
x
@0
(+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))
0.0ms
x
@0
(exp.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))
0.0ms
x
@inf
(+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))

rewrite82.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
646×prod-diff_binary64
556×log-prod_binary64
300×fma-def_binary64
216×log1p-udef_binary64
215×expm1-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01547
132235
2453735
Stop Event
1×node limit
Counts
3 → 158
Calls
Call 1
Inputs
(+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))
(exp.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))
(/.f64 (exp.f64 (log.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))))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (#(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 (exp.f64 (log1p.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/4 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (/.f64 (/.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 (-.f64 1 (/.f64 1/2 (hypot.f64 1 x))) 1/2)))) (#(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 (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 (cbrt.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)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (*.f64 (cbrt.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 (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 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4) (*.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4) (sqrt.f64 (+.f64 1/2 (/.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 (-.f64 (+.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) (/.f64 1/4 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) 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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 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 (E.f64) (log.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(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 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 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(#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (hypot.f64 1 x)) 1/2 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (hypot.f64 1 x)) -1/2 1/2)))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (#(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 (neg.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1)))) (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 1 (+.f64 -1/2 (neg.f64 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1/2 (hypot.f64 1 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.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 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (cbrt.f64 (exp.f64 (+.f64 1/2 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simplify53.0ms (0.4%)

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
01641494
15301301
219091218
Stop Event
1×node limit
Counts
194 → 149
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 1/4 (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))
(+.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 1/2 (*.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 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 x) (+.f64 (/.f64 3/16 (pow.f64 x 5)) (-.f64 1/2 (/.f64 1/4 (pow.f64 x 3)))))
(+.f64 1/2 (-.f64 (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5))) (/.f64 1/4 (pow.f64 x 3))))
(*.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))
(+.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 1/2 (*.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 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 x) (+.f64 (/.f64 3/16 (pow.f64 x 5)) (-.f64 1/2 (/.f64 1/4 (pow.f64 x 3)))))
(+.f64 1/2 (-.f64 (+.f64 (/.f64 1/2 x) (/.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 6) 69/1024 (*.f64 (pow.f64 x 4) -11/128)))
(fma.f64 (pow.f64 x 4) -11/128 (fma.f64 (pow.f64 x 6) 69/1024 (*.f64 (*.f64 x x) 1/8)))
(+.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))))
(fma.f64 x (*.f64 x 1/8) (fma.f64 (pow.f64 x 4) -11/128 (fma.f64 (pow.f64 x 6) 69/1024 (*.f64 (pow.f64 x 8) -1843/32768))))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))
(+.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 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)))
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(+.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 8 to 8 computations (0% saved)

localize19.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))
0.5b
(/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x)
1.0b
(/.f64 1/4 (sqrt.f64 1/2))
Compiler

Compiled 40 to 37 computations (7.5% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite103.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
566×log-prod_binary64
400×fma-def_binary64
321×pow2_binary64
297×log-div_binary64
231×fma-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01120
125814
2386214
Stop Event
1×node limit
Counts
1 → 97
Calls
Call 1
Inputs
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))
Outputs
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(#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (/.f64 1/8 (*.f64 x x)) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2)) (-.f64 (/.f64 (sqrt.f64 1/8) x) (-.f64 1 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (fma.f64 (+.f64 1 (sqrt.f64 1/2)) (sqrt.f64 1/8) (*.f64 1/2 x)) (+.f64 1 (sqrt.f64 1/2))) x)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/8) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/8) x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/8) x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/8) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/8) x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (+.f64 1 (sqrt.f64 1/2)) x) (fma.f64 (+.f64 1 (sqrt.f64 1/2)) (sqrt.f64 1/8) (*.f64 1/2 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (/.f64 (sqrt.f64 1/8) x) (-.f64 (/.f64 (sqrt.f64 1/8) x) (-.f64 1 (sqrt.f64 1/2))) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2)) (+.f64 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 3) (pow.f64 (/.f64 (sqrt.f64 1/8) x) 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/8) x)) (-.f64 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2) (/.f64 1/8 (*.f64 x x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/8) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/8) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/8) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (-.f64 1 (sqrt.f64 1/2)))) (exp.f64 (/.f64 (sqrt.f64 1/8) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (-.f64 1 (sqrt.f64 1/2))) (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 1/8) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (-.f64 1 (sqrt.f64 1/2)))) (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 1/8) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 1/8) x))) (exp.f64 (-.f64 1 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (/.f64 (sqrt.f64 1/8) x)) (+.f64 1 (expm1.f64 (-.f64 1 (sqrt.f64 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 1/8) x))) (+.f64 1 (expm1.f64 (-.f64 1 (sqrt.f64 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/8) x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/8) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/8) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/8) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/8) x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (*.f64 2 (-.f64 1 (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/8) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (/.f64 (cbrt.f64 (sqrt.f64 1/8)) x) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (*.f64 (cbrt.f64 (sqrt.f64 1/8)) (/.f64 1 x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/8) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 (sqrt.f64 1/8) x) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (sqrt.f64 1/2)) 1 (/.f64 (sqrt.f64 1/8) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/4 (/.f64 (pow.f64 1/2 -1/2) x) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/4 (*.f64 (pow.f64 1/2 -1/2) (/.f64 1 x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 1/8) (/.f64 1 x) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 1/8) x) 1 (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 1/2))) (cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2)) (/.f64 (sqrt.f64 1/8) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2)) (cbrt.f64 (-.f64 1 (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/8) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 (sqrt.f64 1/8) x)) (cbrt.f64 (/.f64 1/8 (*.f64 x x))) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 1/8 (*.f64 x x))) (cbrt.f64 (/.f64 (sqrt.f64 1/8) x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (sqrt.f64 1/8)) (*.f64 (sqrt.f64 (sqrt.f64 1/8)) (/.f64 1 x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 1/2))) (sqrt.f64 (-.f64 1 (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/8) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (sqrt.f64 1/8) x)) (sqrt.f64 (/.f64 (sqrt.f64 1/8) x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/2 (/.f64 1 (fma.f64 -1 (sqrt.f64 1/2) -1)) (/.f64 (sqrt.f64 1/8) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (sqrt.f64 1/8)) (/.f64 1 (neg.f64 x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 2 (-.f64 1 (sqrt.f64 1/2))) 1/2 (/.f64 (sqrt.f64 1/8) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) (sqrt.f64 1/8) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (sqrt.f64 1/8)) 1) (/.f64 (sqrt.f64 (sqrt.f64 1/8)) x) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 (*.f64 x x))) (/.f64 (sqrt.f64 1/8) (cbrt.f64 x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1/4 (cbrt.f64 (*.f64 x x))) (/.f64 (pow.f64 1/2 -1/2) (cbrt.f64 x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1/2 (cbrt.f64 (*.f64 x x))) (cbrt.f64 (/.f64 (sqrt.f64 1/8) x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (sqrt.f64 1/8)) (cbrt.f64 (*.f64 x x))) (/.f64 (sqrt.f64 (sqrt.f64 1/8)) (cbrt.f64 x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 1/8) (sqrt.f64 x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1/4 (sqrt.f64 x)) (/.f64 (pow.f64 1/2 -1/2) (sqrt.f64 x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1/2 (sqrt.f64 x)) (/.f64 (cbrt.f64 (sqrt.f64 1/8)) (sqrt.f64 x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1/2 (fma.f64 1/2 (sqrt.f64 1/2) 1)) (-.f64 3/2 (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/8) x))))))

simplify19.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
11×associate-*l/_binary64
11×associate-/r/_binary64
11×fma-def_binary64
10×*-commutative_binary64
10×associate-/l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
015207
129207
242207
350207
459207
576207
6104207
7115207
8120207
9120207
Stop Event
1×saturated
Counts
109 → 102
Calls
Call 1
Inputs
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
Outputs
(/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))

localize70.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(-.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))
✓0.5b
(/.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)
✓1.0b
(*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2)))
✓1.0b
(/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))
Compiler

Compiled 106 to 103 computations (2.8% saved)

series6.0ms (0%)

Counts
4 → 24
Calls

6 calls:

TimeVariablePointExpression
2.0ms
x
@0
(/.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)
2.0ms
x
@0
(-.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))
1.0ms
x
@inf
(/.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)
1.0ms
x
@-inf
(/.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)
0.0ms
x
@-inf
(-.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))

rewrite234.0ms (1.8%)

Algorithm
1×batch-egg-rewrite
Rules
791×fma-def_binary64
389×fma-neg_binary64
303×expm1-udef_binary64
303×log1p-udef_binary64
178×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
014104
134695
2563795
Stop Event
1×node limit
Counts
4 → 278
Calls
Call 1
Inputs
(/.f64 1/8 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))
(*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (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))
Outputs
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simplify159.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
669×fma-neg_binary64
539×associate-+r+_binary64
445×distribute-rgt-out_binary64
418×cancel-sign-sub-inv_binary64
394×fma-def_binary64
Iterations

Useful iterations: 7 (0.0ms)

IterNodesCost
037810
1101801
2159799
3268755
4501689
51193627
63673596
75751587
Stop Event
1×node limit
Counts
302 → 288
Calls
Call 1
Inputs
(/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)
(/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)
(/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)
(/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)
(/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)
(/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)
(/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)
(/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)
(/.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) 1/2))))) x)
(/.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) 1/2))))) x)
(/.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) 1/2))))) x)
(/.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) 1/2))))) x)
(*.f64 -1 (/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) 1/2)))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x))
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) 1/2)))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)) (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))))
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) 1/2)))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)) (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))))
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) 1/2)))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)) (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))))
(/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)) (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))))
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)) (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))))
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)) (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))))
(/.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 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (+.f64 (sqrt.f64 1/2) 1/2))))) x)))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 -1 (/.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) 1/2))))) x)))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 -1 (/.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) 1/2))))) x)))
Outputs
(/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)
(/.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 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (fma.f64 1/2 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))) x)
(/.f64 (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))))) x)
(/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1))) x)
(/.f64 (/.f64 (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2)))) (+.f64 1 (sqrt.f64 1/2))) x)
(/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)
(/.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 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (fma.f64 1/2 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))) x)
(/.f64 (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))))) x)
(/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1))) x)
(/.f64 (/.f64 (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2)))) (+.f64 1 (sqrt.f64 1/2))) x)
(/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)
(/.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 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (fma.f64 1/2 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))) x)
(/.f64 (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))))) x)
(/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1))) x)
(/.f64 (/.f64 (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2)))) (+.f64 1 (sqrt.f64 1/2))) x)
(/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)
(/.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 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (fma.f64 1/2 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))) x)
(/.f64 (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))))) x)
(/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1))) x)
(/.f64 (/.f64 (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2)))) (+.f64 1 (sqrt.f64 1/2))) x)
(/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)
(/.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 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (fma.f64 1/2 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))) x)
(/.f64 (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))))) x)
(/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1))) x)
(/.f64 (/.f64 (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2)))) (+.f64 1 (sqrt.f64 1/2))) x)
(/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)
(/.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 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (fma.f64 1/2 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))) x)
(/.f64 (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))))) x)
(/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1))) x)
(/.f64 (/.f64 (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2)))) (+.f64 1 (sqrt.f64 1/2))) x)
(/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)
(/.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 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (fma.f64 1/2 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))) x)
(/.f64 (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))))) x)
(/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1))) x)
(/.f64 (/.f64 (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2)))) (+.f64 1 (sqrt.f64 1/2))) x)
(/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)
(/.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 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (fma.f64 1/2 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))) x)
(/.f64 (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))))) x)
(/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1))) x)
(/.f64 (/.f64 (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2)))) (+.f64 1 (sqrt.f64 1/2))) x)
(/.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) 1/2))))) x)
(/.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 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (fma.f64 1/2 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))) x)
(/.f64 (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))))) x)
(/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1))) x)
(/.f64 (/.f64 (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2)))) (+.f64 1 (sqrt.f64 1/2))) x)
(/.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) 1/2))))) x)
(/.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 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (fma.f64 1/2 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))) x)
(/.f64 (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))))) x)
(/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1))) x)
(/.f64 (/.f64 (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2)))) (+.f64 1 (sqrt.f64 1/2))) x)
(/.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) 1/2))))) x)
(/.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 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (fma.f64 1/2 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))) x)
(/.f64 (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))))) x)
(/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1))) x)
(/.f64 (/.f64 (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2)))) (+.f64 1 (sqrt.f64 1/2))) x)
(/.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) 1/2))))) x)
(/.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 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (fma.f64 1/2 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))) x)
(/.f64 (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))))) x)
(/.f64 (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1))) x)
(/.f64 (/.f64 (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2)))) (+.f64 1 (sqrt.f64 1/2))) x)
(*.f64 -1 (/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) 1/2)))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x))
(neg.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 (/.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 -1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/8 (fma.f64 1/2 (sqrt.f64 1/2) (+.f64 1 (sqrt.f64 1/2))))) x)
(/.f64 (+.f64 (/.f64 -1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/8 (+.f64 1 (*.f64 (sqrt.f64 1/2) 3/2)))) x)
(/.f64 (+.f64 (/.f64 -1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1))) x)
(/.f64 (/.f64 (-.f64 -1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2)))) (+.f64 1 (sqrt.f64 1/2))) x)
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) 1/2)))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)) (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))))
(fma.f64 -1 (/.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 1/2 (+.f64 1 (sqrt.f64 1/2))))
(-.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 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (+.f64 (/.f64 -1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/8 (fma.f64 1/2 (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 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))))) x))
(+.f64 (/.f64 (/.f64 -1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1)) x) (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 (/.f64 -1/2 x) 1/2)))
(fma.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 -1/2 x)) (/.f64 (/.f64 -1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1)) x))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (fma.f64 (/.f64 -1 x) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2)))) 1/2))
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) 1/2)))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)) (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))))
(fma.f64 -1 (/.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 1/2 (+.f64 1 (sqrt.f64 1/2))))
(-.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 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (+.f64 (/.f64 -1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/8 (fma.f64 1/2 (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 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))))) x))
(+.f64 (/.f64 (/.f64 -1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1)) x) (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 (/.f64 -1/2 x) 1/2)))
(fma.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 -1/2 x)) (/.f64 (/.f64 -1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1)) x))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (fma.f64 (/.f64 -1 x) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2)))) 1/2))
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) 1/2)))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)) (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))))
(fma.f64 -1 (/.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 1/2 (+.f64 1 (sqrt.f64 1/2))))
(-.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 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (+.f64 (/.f64 -1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/8 (fma.f64 1/2 (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 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))))) x))
(+.f64 (/.f64 (/.f64 -1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1)) x) (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 (/.f64 -1/2 x) 1/2)))
(fma.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 -1/2 x)) (/.f64 (/.f64 -1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1)) x))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (fma.f64 (/.f64 -1 x) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2)))) 1/2))
(/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)) (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))))
(fma.f64 -1 (/.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 1/2 (+.f64 1 (sqrt.f64 1/2))))
(-.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 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (+.f64 (/.f64 -1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/8 (fma.f64 1/2 (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 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))))) x))
(+.f64 (/.f64 (/.f64 -1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1)) x) (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 (/.f64 -1/2 x) 1/2)))
(fma.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 -1/2 x)) (/.f64 (/.f64 -1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1)) x))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (fma.f64 (/.f64 -1 x) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2)))) 1/2))
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)) (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))))
(fma.f64 -1 (/.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 1/2 (+.f64 1 (sqrt.f64 1/2))))
(-.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 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (+.f64 (/.f64 -1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/8 (fma.f64 1/2 (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 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))))) x))
(+.f64 (/.f64 (/.f64 -1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1)) x) (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 (/.f64 -1/2 x) 1/2)))
(fma.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 -1/2 x)) (/.f64 (/.f64 -1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1)) x))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (fma.f64 (/.f64 -1 x) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2)))) 1/2))
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 1 (sqrt.f64 1/2)) (+.f64 1/2 (sqrt.f64 1/2))))) (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1)))) x)) (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))))
(fma.f64 -1 (/.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 1/2 (+.f64 1 (sqrt.f64 1/2))))
(-.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 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (+.f64 (/.f64 -1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/8 (fma.f64 1/2 (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 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))))) x))
(+.f64 (/.f64 (/.f64 -1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1)) x) (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 (/.f64 -1/2 x) 1/2)))
(fma.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 -1/2 x)) (/.f64 (/.f64 -1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1)) x))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (fma.f64 (/.f64 -1 x) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2)))) 1/2))
(/.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 1 (sqrt.f64 1/2)))) (*.f64 1/8 (/.f64 1 (*.f64 (+.f64 (sqrt.f64 1/2) 1) (+.f64 (sqrt.f64 1/2) 1/2))))) x)))
(fma.f64 -1 (/.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 1/2 (+.f64 1 (sqrt.f64 1/2))))
(-.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 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (+.f64 (/.f64 -1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/8 (fma.f64 1/2 (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 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))))) x))
(+.f64 (/.f64 (/.f64 -1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1)) x) (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 (/.f64 -1/2 x) 1/2)))
(fma.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 -1/2 x)) (/.f64 (/.f64 -1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1)) x))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (fma.f64 (/.f64 -1 x) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2)))) 1/2))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 -1 (/.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) 1/2))))) x)))
(fma.f64 -1 (/.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 1/2 (+.f64 1 (sqrt.f64 1/2))))
(-.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 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (+.f64 (/.f64 -1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/8 (fma.f64 1/2 (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 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))))) x))
(+.f64 (/.f64 (/.f64 -1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1)) x) (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 (/.f64 -1/2 x) 1/2)))
(fma.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 -1/2 x)) (/.f64 (/.f64 -1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1)) x))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (fma.f64 (/.f64 -1 x) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2)))) 1/2))
(+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 -1 (/.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) 1/2))))) x)))
(fma.f64 -1 (/.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 1/2 (+.f64 1 (sqrt.f64 1/2))))
(-.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 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (+.f64 (/.f64 -1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 -1/8 (fma.f64 1/2 (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 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2))))) x))
(+.f64 (/.f64 (/.f64 -1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1)) x) (*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 (/.f64 -1/2 x) 1/2)))
(fma.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (+.f64 1/2 (/.f64 -1/2 x)) (/.f64 (/.f64 -1/8 (fma.f64 (sqrt.f64 1/2) 3/2 1)) x))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 1/2))) (fma.f64 (/.f64 -1 x) (+.f64 1/2 (/.f64 1/8 (+.f64 1/2 (sqrt.f64 1/2)))) 1/2))

localize145.0ms (1.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.4b
(/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2))
0.6b
(/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x))
1.0b
(/.f64 1/16 (sqrt.f64 1/2))
✓7.0b
(+.f64 (+.f64 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (/.f64 1/2 (-.f64 -1 (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))))
Compiler

Compiled 127 to 106 computations (16.5% saved)

series6.0ms (0%)

Counts
2 → 24
Calls

6 calls:

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

rewrite142.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
267×add-sqr-sqrt_binary64
254×pow1_binary64
253×*-un-lft-identity_binary64
253×add-cbrt-cube_binary64
253×add-log-exp_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02257
153948
Stop Event
1×node limit
Counts
2 → 92
Calls
Call 1
Inputs
(+.f64 (+.f64 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (/.f64 1/2 (-.f64 -1 (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 -1/4 x) (sqrt.f64 1/2))
Outputs
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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/4 (/.f64 (/.f64 1 x) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/4 (*.f64 (/.f64 1 x) (pow.f64 1/2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1/4 x) (pow.f64 1/2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))) (cbrt.f64 (/.f64 (/.f64 1/16 (*.f64 x x)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (/.f64 1/16 (*.f64 x x)) 1/2)) (cbrt.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 -1/4 x)) 2) (*.f64 (cbrt.f64 (/.f64 -1/4 x)) (pow.f64 1/2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))) (sqrt.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 -1/4 x)) (*.f64 (sqrt.f64 (/.f64 -1/4 x)) (pow.f64 1/2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/4 x) (/.f64 1 (neg.f64 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1/2 -1/2) (/.f64 -1/4 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 -1/4 x)) 2) 1) (/.f64 (cbrt.f64 (/.f64 -1/4 x)) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (/.f64 -1/4 x)) 1) (/.f64 (sqrt.f64 (/.f64 -1/4 x)) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1/4 (cbrt.f64 1/2)) (/.f64 (/.f64 1 x) (cbrt.f64 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 1/2)) (/.f64 (/.f64 -1/4 x) (cbrt.f64 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 -1/4 x)) 2) (cbrt.f64 1/2)) (cbrt.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (/.f64 -1/4 x)) (cbrt.f64 1/2)) (/.f64 (sqrt.f64 (/.f64 -1/4 x)) (cbrt.f64 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1/4 (pow.f64 1/2 1/4)) (/.f64 (/.f64 1 x) (pow.f64 1/2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 1/2 1/4)) (/.f64 (/.f64 -1/4 x) (pow.f64 1/2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 -1/4 x)) 2) (pow.f64 1/2 1/4)) (/.f64 (cbrt.f64 (/.f64 -1/4 x)) (pow.f64 1/2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 -1/64 (pow.f64 (*.f64 (sqrt.f64 1/2) x) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 x -4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (/.f64 -1/4 x) (neg.f64 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (/.f64 1/16 (*.f64 x x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 -1/64 (pow.f64 (*.f64 (sqrt.f64 1/2) x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))) 1))))))

simplify64.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
884×distribute-neg-frac_binary64
609×times-frac_binary64
536×unswap-sqr_binary64
425×fma-def_binary64
424×associate-/l/_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
037453
1103453
2231453
3529418
41703394
56503389
Stop Event
1×node limit
Counts
116 → 108
Calls
Call 1
Inputs
(/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))
(+.f64 (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (+.f64 (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (+.f64 (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (+.f64 (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
Outputs
(/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))
(+.f64 (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))))
(*.f64 (/.f64 (/.f64 1 (sqrt.f64 1/2)) (*.f64 x x)) (+.f64 (/.f64 3/32 x) 1/16))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 1/2)) (+.f64 1/16 (/.f64 3/32 x))) (*.f64 x x))
(/.f64 (+.f64 1/16 (/.f64 3/32 x)) (*.f64 (sqrt.f64 1/2) (*.f64 x x)))
(-.f64 (+.f64 (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (-.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (/.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 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2))))
(-.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 1/2)) (*.f64 x x)) (+.f64 (/.f64 3/32 x) 1/16)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2)))
(*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (+.f64 (+.f64 -1/4 (/.f64 1/16 x)) (/.f64 (/.f64 3/32 x) x)))
(*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/16 x) (+.f64 1/4 (/.f64 -3/32 (*.f64 x x)))))
(-.f64 (+.f64 (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (-.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.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 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)))))
(+.f64 (-.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 1/2)) (*.f64 x x)) (+.f64 (/.f64 3/32 x) 1/16)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
(+.f64 (*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (+.f64 (+.f64 -1/4 (/.f64 1/16 x)) (/.f64 (/.f64 3/32 x) x))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
(+.f64 (*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/16 x) (+.f64 1/4 (/.f64 -3/32 (*.f64 x x))))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
(/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (-.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x)))
(+.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2))))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x) (-.f64 (/.f64 1/16 x) 1/4)))
(fma.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (+.f64 -1/4 (/.f64 1/16 x)) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (+.f64 -1/4 (/.f64 1/16 x)) (*.f64 (sqrt.f64 1/2) x)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (+.f64 (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (-.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.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 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)))))
(+.f64 (-.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 1/2)) (*.f64 x x)) (+.f64 (/.f64 3/32 x) 1/16)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
(+.f64 (*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (+.f64 (+.f64 -1/4 (/.f64 1/16 x)) (/.f64 (/.f64 3/32 x) x))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
(+.f64 (*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/16 x) (+.f64 1/4 (/.f64 -3/32 (*.f64 x x))))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
(/.f64 1/2 (+.f64 1 (sqrt.f64 1/2)))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (-.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x)))
(+.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2))))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 1/2)) x) (-.f64 (/.f64 1/16 x) 1/4)))
(fma.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (+.f64 -1/4 (/.f64 1/16 x)) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (+.f64 -1/4 (/.f64 1/16 x)) (*.f64 (sqrt.f64 1/2) x)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (+.f64 1 (sqrt.f64 1/2)))) (+.f64 (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (-.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (/.f64 1/16 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.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 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)))))
(+.f64 (-.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 1/2)) (*.f64 x x)) (+.f64 (/.f64 3/32 x) 1/16)) (/.f64 (/.f64 1/4 x) (sqrt.f64 1/2))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
(+.f64 (*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (+.f64 (+.f64 -1/4 (/.f64 1/16 x)) (/.f64 (/.f64 3/32 x) x))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
(+.f64 (*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/16 x) (+.f64 1/4 (/.f64 -3/32 (*.f64 x x))))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x)
(/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x)
(/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x)
(/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x)
(/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x)
(/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x)
(/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x)
(/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x)
(/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x)
(/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x)
(/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x)
(/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x)
(/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2))

eval1.2s (9.5%)

Compiler

Compiled 29292 to 26952 computations (8% saved)

prune389.0ms (3%)

Pruning

27 alts after pruning (22 fresh and 5 done)

PrunedKeptTotal
New8499858
Fresh41317
Picked101
Done257
Total85627883
Error
0.0b
Counts
883 → 27
Alt Table
Click to see full alt table
StatusErrorProgram
34.8b
(+.f64 (*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/16 x) (-.f64 1/4 (/.f64 (/.f64 3/32 x) x)))) (-.f64 1 (sqrt.f64 1/2)))
30.0b
(+.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)))))
34.4b
(-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1))
16.2b
(/.f64 (exp.f64 (log.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)))))))))
✓34.0b
(-.f64 1 (sqrt.f64 1/2))
39.1b
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)
33.6b
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
✓15.7b
(/.f64 (exp.f64 (log.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))))))
32.5b
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (cbrt.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (cbrt.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (neg.f64 (*.f64 (/.f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))) (/.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)))) (/.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))) (*.f64 (/.f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))) (/.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))))))
✓16.2b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓15.7b
(/.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))))))
34.8b
(+.f64 (+.f64 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1)) (/.f64 (sqrt.f64 1/128) (*.f64 x x))) (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
✓45.3b
(-.f64 1 (sqrt.f64 1))
34.6b
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (-.f64 (+.f64 1 (*.f64 (sqrt.f64 1/128) (pow.f64 x -2))) 1)))
34.9b
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (+.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 -3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))
▶34.3b
(+.f64 (*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/16 x) (+.f64 1/4 (/.f64 -3/32 (*.f64 x x))))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
34.5b
(-.f64 (+.f64 (/.f64 (sqrt.f64 1/8) x) 1) (sqrt.f64 1/2))
▶29.4b
(*.f64 x (*.f64 x 1/8))
▶30.1b
(fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8))
34.1b
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/8) x))
▶15.7b
(/.f64 (exp.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 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))
45.0b
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (fma.f64 x (*.f64 x -1/8) 2))
34.1b
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (+.f64 -1/4 (/.f64 1/16 x)) (*.f64 (sqrt.f64 1/2) x)))
▶34.0b
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
34.2b
(+.f64 (/.f64 1/2 (+.f64 1 (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))))
29.7b
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
34.6b
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (/.f64 (sqrt.f64 1/128) (*.f64 x x))))
Compiler

Compiled 1183 to 1036 computations (12.4% saved)

localize114.0ms (0.9%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(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)
✓0.0b
(pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)
0.1b
(exp.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))
2.2b
(+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))
Compiler

Compiled 109 to 95 computations (12.8% saved)

series4.0ms (0%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@0
(pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)
1.0ms
x
@inf
(pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)
1.0ms
x
@inf
(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)
1.0ms
x
@-inf
(pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)
1.0ms
x
@-inf
(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)

rewrite162.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
600×unpow-prod-down_binary64
407×log-prod_binary64
321×exp-prod_binary64
258×pow2_binary64
218×pow-prod-down_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01042
121628
2255028
Stop Event
1×node limit
Counts
2 → 77
Calls
Call 1
Inputs
(pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)
(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)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.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 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/12) (sqrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/12) (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 4) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.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))) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (pow.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/24) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/8) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/16) (pow.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 1/8 (pow.f64 (hypot.f64 1 x) -3) 1/8) 1/4) (pow.f64 (/.f64 1 (-.f64 (+.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) (/.f64 1/4 (hypot.f64 1 x)))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) 1/4) (pow.f64 (/.f64 1 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/4)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/4)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1/3) (cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 5/8) 1/3) (cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 4) 1/8) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2) 1/8) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/16))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 5) 1/8) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/24))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/12)) 2) 3) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/12)) 3) (pow.f64 (sqrt.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/12)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/4 (log.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/4 (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 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/4)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/12)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/8 (log.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 1/4 (log.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1/8) 2))))))
((#(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 0 (+.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 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) 2)) (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 (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)))))) (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 (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 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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 (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 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 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 exp.f64 (*.f64 (*.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1) 1))))))

simplify79.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
693×associate-*l/_binary64
635×associate-/l*_binary64
619×associate-/r*_binary64
552×fma-def_binary64
430×associate-+l+_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0102557
1282495
2928454
33811416
Stop Event
1×node limit
Counts
101 → 118
Calls
Call 1
Inputs
1
(+.f64 (*.f64 -1/16 (pow.f64 x 2)) 1)
(+.f64 (*.f64 21/512 (pow.f64 x 4)) (+.f64 (*.f64 -1/16 (pow.f64 x 2)) 1))
(+.f64 (*.f64 -255/8192 (pow.f64 x 6)) (+.f64 (*.f64 21/512 (pow.f64 x 4)) (+.f64 (*.f64 -1/16 (pow.f64 x 2)) 1)))
(pow.f64 1/2 1/4)
(+.f64 (*.f64 1/4 (*.f64 (/.f64 1 x) (pow.f64 1/2 1/4))) (pow.f64 1/2 1/4))
(+.f64 (*.f64 1/4 (*.f64 (/.f64 1 x) (pow.f64 1/2 1/4))) (+.f64 (*.f64 -3/32 (*.f64 (/.f64 1 (pow.f64 x 2)) (pow.f64 1/2 1/4))) (pow.f64 1/2 1/4)))
(+.f64 (*.f64 1/4 (*.f64 (/.f64 1 x) (pow.f64 1/2 1/4))) (+.f64 (*.f64 -3/32 (*.f64 (/.f64 1 (pow.f64 x 2)) (pow.f64 1/2 1/4))) (+.f64 (*.f64 -9/128 (*.f64 (/.f64 1 (pow.f64 x 3)) (pow.f64 1/2 1/4))) (pow.f64 1/2 1/4))))
(pow.f64 1/2 1/4)
(+.f64 (pow.f64 1/2 1/4) (*.f64 -1/4 (*.f64 (/.f64 1 x) (pow.f64 1/2 1/4))))
(+.f64 (*.f64 -3/32 (*.f64 (/.f64 1 (pow.f64 x 2)) (pow.f64 1/2 1/4))) (+.f64 (pow.f64 1/2 1/4) (*.f64 -1/4 (*.f64 (/.f64 1 x) (pow.f64 1/2 1/4)))))
(+.f64 (*.f64 9/128 (*.f64 (/.f64 1 (pow.f64 x 3)) (pow.f64 1/2 1/4))) (+.f64 (*.f64 -3/32 (*.f64 (/.f64 1 (pow.f64 x 2)) (pow.f64 1/2 1/4))) (+.f64 (pow.f64 1/2 1/4) (*.f64 -1/4 (*.f64 (/.f64 1 x) (pow.f64 1/2 1/4))))))
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 (sqrt.f64 1/2) 1)
(+.f64 1 (+.f64 (sqrt.f64 1/2) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))))
(+.f64 (*.f64 -3/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 1 (+.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))))))
(+.f64 (*.f64 -3/64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (*.f64 -3/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 1 (+.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (*.f64 -9/64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))))))))
(+.f64 (sqrt.f64 1/2) 1)
(+.f64 1 (+.f64 (sqrt.f64 1/2) (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x))))
(+.f64 (*.f64 -3/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 1 (+.f64 (sqrt.f64 1/2) (+.f64 (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (*.f64 1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))))
(+.f64 (*.f64 -3/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 1 (+.f64 (sqrt.f64 1/2) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -9/64 (sqrt.f64 1/2)) (*.f64 -3/64 (sqrt.f64 1/2))) (pow.f64 x 3))) (+.f64 (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (*.f64 1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))))
Outputs
1
(+.f64 (*.f64 -1/16 (pow.f64 x 2)) 1)
(fma.f64 -1/16 (*.f64 x x) 1)
(+.f64 (*.f64 21/512 (pow.f64 x 4)) (+.f64 (*.f64 -1/16 (pow.f64 x 2)) 1))
(fma.f64 21/512 (pow.f64 x 4) (fma.f64 -1/16 (*.f64 x x) 1))
(fma.f64 -1/16 (*.f64 x x) (fma.f64 21/512 (pow.f64 x 4) 1))
(+.f64 (*.f64 -255/8192 (pow.f64 x 6)) (+.f64 (*.f64 21/512 (pow.f64 x 4)) (+.f64 (*.f64 -1/16 (pow.f64 x 2)) 1)))
(fma.f64 -255/8192 (pow.f64 x 6) (fma.f64 21/512 (pow.f64 x 4) (fma.f64 -1/16 (*.f64 x x) 1)))
(fma.f64 21/512 (pow.f64 x 4) (fma.f64 -255/8192 (pow.f64 x 6) (fma.f64 -1/16 (*.f64 x x) 1)))
(pow.f64 1/2 1/4)
(+.f64 (*.f64 1/4 (*.f64 (/.f64 1 x) (pow.f64 1/2 1/4))) (pow.f64 1/2 1/4))
(fma.f64 1/4 (*.f64 (pow.f64 1/2 1/4) (/.f64 1 x)) (pow.f64 1/2 1/4))
(*.f64 (+.f64 (/.f64 1/4 x) 1) (pow.f64 1/2 1/4))
(*.f64 (pow.f64 1/2 1/4) (+.f64 1 (/.f64 1/4 x)))
(+.f64 (*.f64 1/4 (*.f64 (/.f64 1 x) (pow.f64 1/2 1/4))) (+.f64 (*.f64 -3/32 (*.f64 (/.f64 1 (pow.f64 x 2)) (pow.f64 1/2 1/4))) (pow.f64 1/2 1/4)))
(fma.f64 1/4 (*.f64 (pow.f64 1/2 1/4) (/.f64 1 x)) (fma.f64 -3/32 (*.f64 (pow.f64 1/2 1/4) (/.f64 1 (*.f64 x x))) (pow.f64 1/2 1/4)))
(+.f64 (pow.f64 1/2 1/4) (*.f64 (pow.f64 1/2 1/4) (+.f64 (/.f64 1/4 x) (/.f64 -3/32 (*.f64 x x)))))
(*.f64 (pow.f64 1/2 1/4) (+.f64 (/.f64 1/4 x) (+.f64 1 (/.f64 -3/32 (*.f64 x x)))))
(+.f64 (*.f64 1/4 (*.f64 (/.f64 1 x) (pow.f64 1/2 1/4))) (+.f64 (*.f64 -3/32 (*.f64 (/.f64 1 (pow.f64 x 2)) (pow.f64 1/2 1/4))) (+.f64 (*.f64 -9/128 (*.f64 (/.f64 1 (pow.f64 x 3)) (pow.f64 1/2 1/4))) (pow.f64 1/2 1/4))))
(fma.f64 1/4 (*.f64 (pow.f64 1/2 1/4) (/.f64 1 x)) (fma.f64 -3/32 (*.f64 (pow.f64 1/2 1/4) (/.f64 1 (*.f64 x x))) (fma.f64 -9/128 (/.f64 (*.f64 1 (pow.f64 1/2 1/4)) (pow.f64 x 3)) (pow.f64 1/2 1/4))))
(+.f64 (*.f64 (+.f64 (/.f64 -9/128 (pow.f64 x 3)) 1) (pow.f64 1/2 1/4)) (*.f64 (pow.f64 1/2 1/4) (+.f64 (/.f64 1/4 x) (/.f64 -3/32 (*.f64 x x)))))
(+.f64 (pow.f64 1/2 1/4) (*.f64 (pow.f64 1/2 1/4) (+.f64 (/.f64 1/4 x) (+.f64 (/.f64 -3/32 (*.f64 x x)) (/.f64 -9/128 (pow.f64 x 3))))))
(*.f64 (pow.f64 1/2 1/4) (+.f64 (/.f64 -9/128 (pow.f64 x 3)) (+.f64 (+.f64 1 (/.f64 1/4 x)) (/.f64 -3/32 (*.f64 x x)))))
(pow.f64 1/2 1/4)
(+.f64 (pow.f64 1/2 1/4) (*.f64 -1/4 (*.f64 (/.f64 1 x) (pow.f64 1/2 1/4))))
(+.f64 (pow.f64 1/2 1/4) (*.f64 (*.f64 (pow.f64 1/2 1/4) (/.f64 1 x)) -1/4))
(*.f64 (+.f64 (/.f64 -1/4 x) 1) (pow.f64 1/2 1/4))
(*.f64 (pow.f64 1/2 1/4) (+.f64 1 (/.f64 -1/4 x)))
(+.f64 (*.f64 -3/32 (*.f64 (/.f64 1 (pow.f64 x 2)) (pow.f64 1/2 1/4))) (+.f64 (pow.f64 1/2 1/4) (*.f64 -1/4 (*.f64 (/.f64 1 x) (pow.f64 1/2 1/4)))))
(+.f64 (fma.f64 -3/32 (*.f64 (pow.f64 1/2 1/4) (/.f64 1 (*.f64 x x))) (pow.f64 1/2 1/4)) (*.f64 (*.f64 (pow.f64 1/2 1/4) (/.f64 1 x)) -1/4))
(fma.f64 -3/32 (/.f64 (pow.f64 1/2 1/4) (*.f64 x x)) (*.f64 (+.f64 (/.f64 -1/4 x) 1) (pow.f64 1/2 1/4)))
(*.f64 (pow.f64 1/2 1/4) (+.f64 (/.f64 -3/32 (*.f64 x x)) (+.f64 1 (/.f64 -1/4 x))))
(+.f64 (pow.f64 1/2 1/4) (*.f64 (/.f64 (pow.f64 1/2 1/4) x) (+.f64 (/.f64 -3/32 x) -1/4)))
(+.f64 (*.f64 9/128 (*.f64 (/.f64 1 (pow.f64 x 3)) (pow.f64 1/2 1/4))) (+.f64 (*.f64 -3/32 (*.f64 (/.f64 1 (pow.f64 x 2)) (pow.f64 1/2 1/4))) (+.f64 (pow.f64 1/2 1/4) (*.f64 -1/4 (*.f64 (/.f64 1 x) (pow.f64 1/2 1/4))))))
(fma.f64 9/128 (/.f64 (*.f64 1 (pow.f64 1/2 1/4)) (pow.f64 x 3)) (+.f64 (fma.f64 -3/32 (*.f64 (pow.f64 1/2 1/4) (/.f64 1 (*.f64 x x))) (pow.f64 1/2 1/4)) (*.f64 (*.f64 (pow.f64 1/2 1/4) (/.f64 1 x)) -1/4)))
(+.f64 (*.f64 (+.f64 (/.f64 -1/4 x) 1) (pow.f64 1/2 1/4)) (*.f64 (pow.f64 1/2 1/4) (+.f64 (/.f64 9/128 (pow.f64 x 3)) (/.f64 -3/32 (*.f64 x x)))))
(+.f64 (pow.f64 1/2 1/4) (*.f64 (pow.f64 1/2 1/4) (+.f64 (+.f64 (/.f64 -3/32 (*.f64 x x)) (/.f64 9/128 (pow.f64 x 3))) (/.f64 -1/4 x))))
(*.f64 (pow.f64 1/2 1/4) (+.f64 (/.f64 -1/4 x) (+.f64 (/.f64 9/128 (pow.f64 x 3)) (+.f64 1 (/.f64 -3/32 (*.f64 x x))))))
2
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) 2)
(fma.f64 -1/8 (*.f64 x x) 2)
(fma.f64 (*.f64 x x) -1/8 2)
(fma.f64 x (*.f64 x -1/8) 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 (pow.f64 x 4) 11/128))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 (pow.f64 x 4) 11/128 2))
(fma.f64 x (*.f64 x -1/8) (fma.f64 (pow.f64 x 4) 11/128 2))
(fma.f64 (pow.f64 x 4) 11/128 (fma.f64 x (*.f64 x -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 (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 2)))
(fma.f64 x (*.f64 x -1/8) (fma.f64 (pow.f64 x 6) -69/1024 (fma.f64 (pow.f64 x 4) 11/128 2)))
(fma.f64 (pow.f64 x 6) -69/1024 (fma.f64 (pow.f64 x 4) 11/128 (fma.f64 x (*.f64 x -1/8) 2)))
(+.f64 (sqrt.f64 1/2) 1)
(+.f64 1 (sqrt.f64 1/2))
(+.f64 1 (+.f64 (sqrt.f64 1/2) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))))
(+.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))
(+.f64 1 (fma.f64 1/2 (/.f64 (sqrt.f64 1/2) x) (sqrt.f64 1/2)))
(+.f64 1 (*.f64 (+.f64 (/.f64 1/2 x) 1) (sqrt.f64 1/2)))
(+.f64 (*.f64 -3/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 1 (+.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))))))
(fma.f64 -3/16 (/.f64 (sqrt.f64 1/2) (*.f64 x x)) (+.f64 (+.f64 1 (sqrt.f64 1/2)) (fma.f64 1/16 (/.f64 (sqrt.f64 1/2) (*.f64 x x)) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))))
(+.f64 (+.f64 (sqrt.f64 1/2) (fma.f64 1/2 (/.f64 (sqrt.f64 1/2) x) (*.f64 (/.f64 1/16 x) (/.f64 (sqrt.f64 1/2) x)))) (fma.f64 -3/16 (/.f64 (sqrt.f64 1/2) (*.f64 x x)) 1))
(+.f64 (sqrt.f64 1/2) (+.f64 (*.f64 (/.f64 (sqrt.f64 1/2) x) (+.f64 1/2 (/.f64 1/16 x))) (fma.f64 -3/16 (/.f64 (sqrt.f64 1/2) (*.f64 x x)) 1)))
(+.f64 (sqrt.f64 1/2) (+.f64 1 (*.f64 (/.f64 (sqrt.f64 1/2) x) (+.f64 (/.f64 -3/16 x) (+.f64 1/2 (/.f64 1/16 x))))))
(+.f64 (*.f64 -3/64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (*.f64 -3/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 1 (+.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 (*.f64 -9/64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x))))))))
(fma.f64 -3/64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (fma.f64 -3/16 (/.f64 (sqrt.f64 1/2) (*.f64 x x)) (+.f64 (+.f64 1 (sqrt.f64 1/2)) (fma.f64 1/16 (/.f64 (sqrt.f64 1/2) (*.f64 x x)) (fma.f64 -9/64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (*.f64 1/2 (/.f64 (sqrt.f64 1/2) x)))))))
(fma.f64 -3/64 (/.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (+.f64 (+.f64 (sqrt.f64 1/2) (fma.f64 (/.f64 (sqrt.f64 1/2) (*.f64 x x)) 1/16 (fma.f64 1/2 (/.f64 (sqrt.f64 1/2) x) (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 x 3) -9/64))))) (fma.f64 -3/16 (/.f64 (sqrt.f64 1/2) (*.f64 x x)) 1)))
(+.f64 (+.f64 (*.f64 (/.f64 (sqrt.f64 1/2) (*.f64 x x)) (+.f64 -3/16 (/.f64 -3/64 x))) (sqrt.f64 1/2)) (+.f64 1 (fma.f64 1/2 (/.f64 (sqrt.f64 1/2) x) (*.f64 (/.f64 (sqrt.f64 1/2) (*.f64 x x)) (+.f64 (/.f64 -9/64 x) 1/16)))))
(+.f64 1 (+.f64 (*.f64 (/.f64 (sqrt.f64 1/2) (*.f64 x x)) (+.f64 (+.f64 -3/16 (/.f64 -3/64 x)) (+.f64 (/.f64 -9/64 x) 1/16))) (*.f64 (+.f64 (/.f64 1/2 x) 1) (sqrt.f64 1/2))))
(+.f64 (sqrt.f64 1/2) 1)
(+.f64 1 (sqrt.f64 1/2))
(+.f64 1 (+.f64 (sqrt.f64 1/2) (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x))))
(+.f64 (+.f64 1 (sqrt.f64 1/2)) (*.f64 (/.f64 (sqrt.f64 1/2) x) -1/2))
(+.f64 1 (fma.f64 (/.f64 (sqrt.f64 1/2) x) -1/2 (sqrt.f64 1/2)))
(+.f64 1 (*.f64 (+.f64 (/.f64 -1/2 x) 1) (sqrt.f64 1/2)))
(+.f64 (*.f64 -3/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 1 (+.f64 (sqrt.f64 1/2) (+.f64 (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (*.f64 1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))))
(fma.f64 -3/16 (/.f64 (sqrt.f64 1/2) (*.f64 x x)) (+.f64 (+.f64 1 (sqrt.f64 1/2)) (fma.f64 -1/2 (/.f64 (sqrt.f64 1/2) x) (*.f64 (/.f64 (sqrt.f64 1/2) (*.f64 x x)) 1/16))))
(+.f64 (+.f64 (sqrt.f64 1/2) (fma.f64 (/.f64 (sqrt.f64 1/2) x) -1/2 (*.f64 (/.f64 1/16 x) (/.f64 (sqrt.f64 1/2) x)))) (fma.f64 -3/16 (/.f64 (sqrt.f64 1/2) (*.f64 x x)) 1))
(+.f64 1 (fma.f64 -3/16 (/.f64 (sqrt.f64 1/2) (*.f64 x x)) (+.f64 (sqrt.f64 1/2) (*.f64 (/.f64 (sqrt.f64 1/2) x) (+.f64 (/.f64 1/16 x) -1/2)))))
(+.f64 (+.f64 1 (*.f64 (+.f64 (/.f64 -1/2 x) 1) (sqrt.f64 1/2))) (*.f64 (/.f64 (sqrt.f64 1/2) (*.f64 x x)) -1/8))
(+.f64 (*.f64 -3/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))) (+.f64 1 (+.f64 (sqrt.f64 1/2) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -9/64 (sqrt.f64 1/2)) (*.f64 -3/64 (sqrt.f64 1/2))) (pow.f64 x 3))) (+.f64 (*.f64 -1/2 (/.f64 (sqrt.f64 1/2) x)) (*.f64 1/16 (/.f64 (sqrt.f64 1/2) (pow.f64 x 2))))))))
(fma.f64 -3/16 (/.f64 (sqrt.f64 1/2) (*.f64 x x)) (+.f64 (+.f64 1 (sqrt.f64 1/2)) (fma.f64 -1 (/.f64 (*.f64 (sqrt.f64 1/2) -3/16) (pow.f64 x 3)) (fma.f64 -1/2 (/.f64 (sqrt.f64 1/2) x) (*.f64 (/.f64 (sqrt.f64 1/2) (*.f64 x x)) 1/16)))))
(+.f64 (+.f64 (fma.f64 (/.f64 (sqrt.f64 1/2) x) -1/2 (*.f64 (/.f64 1/16 x) (/.f64 (sqrt.f64 1/2) x))) (-.f64 (sqrt.f64 1/2) (/.f64 (*.f64 (sqrt.f64 1/2) -3/16) (pow.f64 x 3)))) (fma.f64 -3/16 (/.f64 (sqrt.f64 1/2) (*.f64 x x)) 1))
(+.f64 1 (+.f64 (/.f64 (*.f64 (sqrt.f64 1/2) 3/16) (pow.f64 x 3)) (fma.f64 -3/16 (/.f64 (sqrt.f64 1/2) (*.f64 x x)) (+.f64 (sqrt.f64 1/2) (*.f64 (/.f64 (sqrt.f64 1/2) x) (+.f64 (/.f64 1/16 x) -1/2))))))
(+.f64 1 (+.f64 (sqrt.f64 1/2) (+.f64 (*.f64 (/.f64 (sqrt.f64 1/2) x) (-.f64 -1/2 (/.f64 (/.f64 -3/16 x) x))) (*.f64 (/.f64 (sqrt.f64 1/2) (*.f64 x x)) -1/8))))

localize12.0ms (0.1%)

Compiler

Compiled 11 to 7 computations (36.4% saved)

localize44.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
✓0.3b
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
✓0.5b
(*.f64 (sqrt.f64 1/2) x)
Compiler

Compiled 40 to 36 computations (10% saved)

series14.0ms (0.1%)

Counts
3 → 12
Calls

9 calls:

TimeVariablePointExpression
6.0ms
x
@inf
(*.f64 (sqrt.f64 1/2) x)
3.0ms
x
@inf
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
1.0ms
x
@0
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
1.0ms
x
@-inf
(*.f64 (sqrt.f64 1/2) x)
1.0ms
x
@inf
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))

rewrite100.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
551×log-prod_binary64
386×fma-def_binary64
314×pow2_binary64
256×log-div_binary64
228×fma-neg_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01135
125432
2361931
Stop Event
1×node limit
Counts
3 → 134
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 1/2) x)
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
Outputs
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(+.f64 (sqrt.f64 1/2) 1)) (fma.f64 -1/4 (+.f64 (sqrt.f64 1/2) 1) (*.f64 (pow.f64 1/2 3/2) x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2))) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2)) (fma.f64 -1/64 (pow.f64 (*.f64 (sqrt.f64 1/2) x) -3) (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))) (-.f64 (pow.f64 (-.f64 1 (sqrt.f64 1/2)) 2) (/.f64 1/16 (*.f64 1/2 (*.f64 x x))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 -1/4 (/.f64 (pow.f64 1/2 -1/2) x) (-.f64 1 (sqrt.f64 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 -1/4 (/.f64 (pow.f64 1/2 -1/2) x) (-.f64 1 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 -1/4 (/.f64 (pow.f64 1/2 -1/2) x) (-.f64 1 (sqrt.f64 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))) (exp.f64 (-.f64 1 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))) (+.f64 1 (expm1.f64 (-.f64 1 (sqrt.f64 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))) (+.f64 1 (expm1.f64 (-.f64 1 (sqrt.f64 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (-.f64 1 (sqrt.f64 1/2)))) (exp.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (-.f64 1 (sqrt.f64 1/2))) (+.f64 1 (expm1.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (-.f64 1 (sqrt.f64 1/2)))) (+.f64 1 (expm1.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 -1/4 (/.f64 (pow.f64 1/2 -1/2) x) (-.f64 1 (sqrt.f64 1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 -1/4 (/.f64 (pow.f64 1/2 -1/2) x) (-.f64 1 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 -1/4 (/.f64 (pow.f64 1/2 -1/2) x) (-.f64 1 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 -1/4 (/.f64 (pow.f64 1/2 -1/2) x) (-.f64 1 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 -1/4 (/.f64 (pow.f64 1/2 -1/2) x) (-.f64 1 (sqrt.f64 1/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (*.f64 -2 (+.f64 (sqrt.f64 1/2) -1)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/4 (/.f64 (pow.f64 1/2 -1/2) x) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)) 1 (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (-.f64 1 (sqrt.f64 1/2)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (sqrt.f64 1/2)) 1 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (neg.f64 x))) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 1/2))) (pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 1/2))) 2) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 1/2))) 2) (cbrt.f64 (-.f64 1 (sqrt.f64 1/2))) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))) (cbrt.f64 (/.f64 1/16 (*.f64 1/2 (*.f64 x x)))) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 1/16 (*.f64 1/2 (*.f64 x x)))) (cbrt.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 1/2))) (sqrt.f64 (-.f64 1 (sqrt.f64 1/2))) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))) (sqrt.f64 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/2 (/.f64 1 (+.f64 -1 (neg.f64 (sqrt.f64 1/2)))) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -2 (+.f64 (sqrt.f64 1/2) -1)) 1/2 (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 1/2 -1/2) x) -1/4 (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 -1/4 (sqrt.f64 1/2)) (/.f64 1 x) (-.f64 1 (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (+.f64 (sqrt.f64 1/2) -1) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1/2 (+.f64 1 (pow.f64 1/2 3/2))) (-.f64 3/2 (sqrt.f64 1/2)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))))))

simplify73.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
560×fma-def_binary64
229×fma-neg_binary64
74×associate-/l/_binary64
73×associate-/r/_binary64
69×div-sub_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
016207
135207
264207
3114207
4189207
5302207
6514207
7723207
8928207
91191207
101718207
111789207
Stop Event
1×saturated
Counts
146 → 139
Calls
Call 1
Inputs
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/4 (/.f64 1 (*.f64 (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 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/4 (/.f64 1 (*.f64 (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 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
Outputs
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 -1/4 (*.f64 (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 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 -1/4 (*.f64 (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 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
(-.f64 (*.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 1/2) 1))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))

localize187.0ms (1.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/16 x) (+.f64 1/4 (/.f64 -3/32 (*.f64 x x)))))
✓0.3b
(/.f64 1 (*.f64 (sqrt.f64 1/2) x))
0.5b
(*.f64 (sqrt.f64 1/2) x)
✓0.5b
(/.f64 -3/32 (*.f64 x x))
Compiler

Compiled 101 to 75 computations (25.7% saved)

series5.0ms (0%)

Counts
3 → 24
Calls

9 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/16 x) (+.f64 1/4 (/.f64 -3/32 (*.f64 x x)))))
1.0ms
x
@0
(*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/16 x) (+.f64 1/4 (/.f64 -3/32 (*.f64 x x)))))
1.0ms
x
@0
(/.f64 -3/32 (*.f64 x x))
1.0ms
x
@inf
(*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/16 x) (+.f64 1/4 (/.f64 -3/32 (*.f64 x x)))))
0.0ms
x
@-inf
(/.f64 1 (*.f64 (sqrt.f64 1/2) x))

rewrite92.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
713×prod-diff_binary64
367×fma-def_binary64
293×expm1-udef_binary64
293×log1p-udef_binary64
236×log-pow_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01640
136036
2478936
Stop Event
1×node limit
Counts
3 → 100
Calls
Call 1
Inputs
(/.f64 -3/32 (*.f64 x x))
(/.f64 1 (*.f64 (sqrt.f64 1/2) x))
(*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/16 x) (+.f64 1/4 (/.f64 -3/32 (*.f64 x x)))))
Outputs
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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 1/2 -1/2) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 1/2 -1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 1/2 -1/2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 1/2 -1/2) x)) (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) -2)) (cbrt.f64 (/.f64 (pow.f64 1/2 -1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 1/2 -1/2) x)) (sqrt.f64 (/.f64 (pow.f64 1/2 -1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (*.f64 (sqrt.f64 1/2) (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (pow.f64 1/2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1/2 -1/2) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 x x) 1/2)) -1) (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 1/2))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 1/2))) -1) (pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 1/2))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 1/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 1/2 -1/2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 1/2 -1/2) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 1/2 -1/2) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 1/2 -1/2) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (sqrt.f64 1/2)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 1/2 -1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 1/2 -1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 1/2 -1/2) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 1/2 -1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 1/2 -1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 1/2 -1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (sqrt.f64 1/2))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 1/2 -1/2) x)) 1))))))
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simplify56.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
983×distribute-neg-frac_binary64
695×fma-neg_binary64
609×times-frac_binary64
536×unswap-sqr_binary64
450×associate-/l/_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
031408
178408
2174408
3422363
41462333
56062324
Stop Event
1×node limit
Counts
124 → 113
Calls
Call 1
Inputs
(/.f64 -3/32 (pow.f64 x 2))
(/.f64 -3/32 (pow.f64 x 2))
(/.f64 -3/32 (pow.f64 x 2))
(/.f64 -3/32 (pow.f64 x 2))
(/.f64 -3/32 (pow.f64 x 2))
(/.f64 -3/32 (pow.f64 x 2))
(/.f64 -3/32 (pow.f64 x 2))
(/.f64 -3/32 (pow.f64 x 2))
(/.f64 -3/32 (pow.f64 x 2))
(/.f64 -3/32 (pow.f64 x 2))
(/.f64 -3/32 (pow.f64 x 2))
(/.f64 -3/32 (pow.f64 x 2))
(/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))
(+.f64 (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (+.f64 (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
Outputs
(/.f64 -3/32 (pow.f64 x 2))
(/.f64 -3/32 (*.f64 x x))
(/.f64 -3/32 (pow.f64 x 2))
(/.f64 -3/32 (*.f64 x x))
(/.f64 -3/32 (pow.f64 x 2))
(/.f64 -3/32 (*.f64 x x))
(/.f64 -3/32 (pow.f64 x 2))
(/.f64 -3/32 (*.f64 x x))
(/.f64 -3/32 (pow.f64 x 2))
(/.f64 -3/32 (*.f64 x x))
(/.f64 -3/32 (pow.f64 x 2))
(/.f64 -3/32 (*.f64 x x))
(/.f64 -3/32 (pow.f64 x 2))
(/.f64 -3/32 (*.f64 x x))
(/.f64 -3/32 (pow.f64 x 2))
(/.f64 -3/32 (*.f64 x x))
(/.f64 -3/32 (pow.f64 x 2))
(/.f64 -3/32 (*.f64 x x))
(/.f64 -3/32 (pow.f64 x 2))
(/.f64 -3/32 (*.f64 x x))
(/.f64 -3/32 (pow.f64 x 2))
(/.f64 -3/32 (*.f64 x x))
(/.f64 -3/32 (pow.f64 x 2))
(/.f64 -3/32 (*.f64 x x))
(/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))
(/.f64 (/.f64 3/32 (sqrt.f64 1/2)) (pow.f64 x 3))
(+.f64 (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 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))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (/.f64 1/16 (*.f64 x (*.f64 x (sqrt.f64 1/2)))))
(*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) (*.f64 x x))) (+.f64 (/.f64 3/32 x) 1/16))
(*.f64 (/.f64 1 (*.f64 x (*.f64 x (sqrt.f64 1/2)))) (+.f64 1/16 (/.f64 3/32 x)))
(/.f64 (+.f64 1/16 (/.f64 3/32 x)) (*.f64 x (*.f64 x (sqrt.f64 1/2))))
(-.f64 (+.f64 (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (-.f64 (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (/.f64 1/16 (*.f64 x (*.f64 x (sqrt.f64 1/2)))) (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2)))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 (/.f64 1 (*.f64 x (sqrt.f64 1/2))) (-.f64 (/.f64 1/16 x) 1/4)))
(*.f64 (/.f64 1 (*.f64 x (sqrt.f64 1/2))) (-.f64 (/.f64 3/32 (*.f64 x x)) (+.f64 1/4 (/.f64 -1/16 x))))
(-.f64 (+.f64 (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (-.f64 (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (/.f64 1/16 (*.f64 x (*.f64 x (sqrt.f64 1/2)))) (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2)))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 (/.f64 1 (*.f64 x (sqrt.f64 1/2))) (-.f64 (/.f64 1/16 x) 1/4)))
(*.f64 (/.f64 1 (*.f64 x (sqrt.f64 1/2))) (-.f64 (/.f64 3/32 (*.f64 x x)) (+.f64 1/4 (/.f64 -1/16 x))))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 -1/4 (*.f64 x (sqrt.f64 1/2)))
(/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2))
(-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))
(+.f64 (/.f64 1/16 (*.f64 x (*.f64 x (sqrt.f64 1/2)))) (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2))))
(*.f64 (/.f64 1 (*.f64 x (sqrt.f64 1/2))) (-.f64 (/.f64 1/16 x) 1/4))
(*.f64 (/.f64 -1 (*.f64 x (sqrt.f64 1/2))) (+.f64 1/4 (/.f64 -1/16 x)))
(/.f64 (+.f64 -1/4 (/.f64 1/16 x)) (*.f64 x (sqrt.f64 1/2)))
(-.f64 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (-.f64 (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (/.f64 1/16 (*.f64 x (*.f64 x (sqrt.f64 1/2)))) (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2)))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 (/.f64 1 (*.f64 x (sqrt.f64 1/2))) (-.f64 (/.f64 1/16 x) 1/4)))
(*.f64 (/.f64 1 (*.f64 x (sqrt.f64 1/2))) (-.f64 (/.f64 3/32 (*.f64 x x)) (+.f64 1/4 (/.f64 -1/16 x))))
(-.f64 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (-.f64 (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (/.f64 1/16 (*.f64 x (*.f64 x (sqrt.f64 1/2)))) (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2)))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 (/.f64 1 (*.f64 x (sqrt.f64 1/2))) (-.f64 (/.f64 1/16 x) 1/4)))
(*.f64 (/.f64 1 (*.f64 x (sqrt.f64 1/2))) (-.f64 (/.f64 3/32 (*.f64 x x)) (+.f64 1/4 (/.f64 -1/16 x))))
(/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x))
(/.f64 -1/4 (*.f64 x (sqrt.f64 1/2)))
(/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2))
(-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))
(+.f64 (/.f64 1/16 (*.f64 x (*.f64 x (sqrt.f64 1/2)))) (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2))))
(*.f64 (/.f64 1 (*.f64 x (sqrt.f64 1/2))) (-.f64 (/.f64 1/16 x) 1/4))
(*.f64 (/.f64 -1 (*.f64 x (sqrt.f64 1/2))) (+.f64 1/4 (/.f64 -1/16 x)))
(/.f64 (+.f64 -1/4 (/.f64 1/16 x)) (*.f64 x (sqrt.f64 1/2)))
(-.f64 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (-.f64 (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (/.f64 1/16 (*.f64 x (*.f64 x (sqrt.f64 1/2)))) (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2)))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 (/.f64 1 (*.f64 x (sqrt.f64 1/2))) (-.f64 (/.f64 1/16 x) 1/4)))
(*.f64 (/.f64 1 (*.f64 x (sqrt.f64 1/2))) (-.f64 (/.f64 3/32 (*.f64 x x)) (+.f64 1/4 (/.f64 -1/16 x))))
(-.f64 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 2)))) (*.f64 3/32 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (-.f64 (/.f64 1/16 (*.f64 (*.f64 x x) (sqrt.f64 1/2))) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (+.f64 (/.f64 1/16 (*.f64 x (*.f64 x (sqrt.f64 1/2)))) (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2)))))
(+.f64 (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (*.f64 (/.f64 1 (*.f64 x (sqrt.f64 1/2))) (-.f64 (/.f64 1/16 x) 1/4)))
(*.f64 (/.f64 1 (*.f64 x (sqrt.f64 1/2))) (-.f64 (/.f64 3/32 (*.f64 x x)) (+.f64 1/4 (/.f64 -1/16 x))))

localize12.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓13.5b
(fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8))
Compiler

Compiled 26 to 15 computations (42.3% saved)

series2.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite55.0ms (0.4%)

Algorithm
1×batch-egg-rewrite
Rules
745×pow1_binary64
697×add-log-exp_binary64
697×log1p-expm1-u_binary64
697×expm1-log1p-u_binary64
683×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
118814
2197314
Stop Event
1×node limit
Counts
1 → 21
Calls
Call 1
Inputs
(fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) 1/8) (*.f64 (pow.f64 x 4) -11/128))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x 4) -11/128) (*.f64 (*.f64 x x) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (pow.f64 x 4) -11/128) 1) (*.f64 (*.f64 x x) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8))) (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8)) 2)) (cbrt.f64 (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8))) (sqrt.f64 (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 (pow.f64 x 4) -11/128) 3) (pow.f64 (*.f64 (*.f64 x x) 1/8) 3)) (+.f64 (*.f64 (*.f64 (pow.f64 x 4) -11/128) (*.f64 (pow.f64 x 4) -11/128)) (-.f64 (*.f64 (pow.f64 x 4) 1/64) (*.f64 (*.f64 (pow.f64 x 4) -11/128) (*.f64 (*.f64 x x) 1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 (pow.f64 x 4) -11/128) (*.f64 (pow.f64 x 4) -11/128)) (*.f64 (pow.f64 x 4) 1/64)) (-.f64 (*.f64 (pow.f64 x 4) -11/128) (*.f64 (*.f64 x x) 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8))))))))

simplify181.0ms (1.4%)

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
33 → 26
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))))

eval1.1s (8.4%)

Compiler

Compiled 16128 to 14202 computations (11.9% saved)

prune166.0ms (1.3%)

Pruning

28 alts after pruning (19 fresh and 9 done)

PrunedKeptTotal
New5554559
Fresh21517
Picked101
Done099
Total55828586
Error
0.0b
Counts
586 → 28
Alt Table
Click to see full alt table
StatusErrorProgram
34.8b
(+.f64 (*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/16 x) (-.f64 1/4 (/.f64 (/.f64 3/32 x) x)))) (-.f64 1 (sqrt.f64 1/2)))
30.0b
(+.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)))))
34.4b
(-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1))
16.2b
(/.f64 (exp.f64 (log.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)))))))))
✓34.0b
(-.f64 1 (sqrt.f64 1/2))
39.1b
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)
✓15.7b
(/.f64 (exp.f64 (log.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))))))
32.5b
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (cbrt.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (cbrt.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (neg.f64 (*.f64 (/.f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))) (/.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)))) (/.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))) (*.f64 (/.f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))) (/.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))))))
✓16.2b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓15.7b
(/.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))))))
34.8b
(+.f64 (+.f64 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1)) (/.f64 (sqrt.f64 1/128) (*.f64 x x))) (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
✓45.3b
(-.f64 1 (sqrt.f64 1))
34.6b
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (-.f64 (+.f64 1 (*.f64 (sqrt.f64 1/128) (pow.f64 x -2))) 1)))
34.9b
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (+.f64 (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 -3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))
33.6b
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
34.5b
(-.f64 (+.f64 (/.f64 (sqrt.f64 1/8) x) 1) (sqrt.f64 1/2))
✓34.3b
(+.f64 (*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/16 x) (+.f64 1/4 (/.f64 -3/32 (*.f64 x x))))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
✓29.4b
(*.f64 x (*.f64 x 1/8))
30.1b
(+.f64 (*.f64 (pow.f64 x 4) -11/128) (*.f64 (*.f64 x x) 1/8))
34.6b
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (/.f64 (sqrt.f64 1/128) (*.f64 x x))))
✓15.7b
(/.f64 (exp.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 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))
34.1b
(+.f64 (/.f64 (+.f64 -1/4 (/.f64 1/16 x)) (*.f64 x (sqrt.f64 1/2))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
45.0b
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (fma.f64 x (*.f64 x -1/8) 2))
✓34.0b
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
16.2b
(/.f64 (exp.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))))) (fma.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4) (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/12)) 2) 3) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/12)) 1))
34.2b
(+.f64 (/.f64 1/2 (+.f64 1 (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))))
29.7b
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4))))
34.1b
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/8) x))
Compiler

Compiled 669 to 589 computations (12% saved)

regimes505.0ms (3.9%)

Counts
48 → 2
Calls
Call 1
Inputs
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (cbrt.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (cbrt.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (neg.f64 (*.f64 (/.f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))) (/.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)))) (/.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))) (*.f64 (/.f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))) (/.f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))))))
(/.f64 (exp.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))))) (fma.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4) (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/12)) 2) 3) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/12)) 1))
(/.f64 (exp.f64 (log.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 (exp.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 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))
(/.f64 (exp.f64 (log.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 1/8 (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 1/8 (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 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
(+.f64 (*.f64 1/8 (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 -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 1/2 (/.f64 1/2 (hypot.f64 1 x))) (fma.f64 x (*.f64 x -1/8) 2))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8))
(fma.f64 x (*.f64 x 1/8) (*.f64 (pow.f64 x 4) -11/128))
(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 (+.f64 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (/.f64 1/2 (-.f64 -1 (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 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (+.f64 (/.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 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1)) (/.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 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1)) (/.f64 (sqrt.f64 1/128) (*.f64 x x))) (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (-.f64 (+.f64 1 (*.f64 (sqrt.f64 1/128) (pow.f64 x -2))) 1)))
(+.f64 (*.f64 (pow.f64 x 4) -11/128) (*.f64 (*.f64 x x) 1/8))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(+.f64 (*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/16 x) (+.f64 1/4 (/.f64 -3/32 (*.f64 x x))))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
(-.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 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/16 x) (-.f64 1/4 (/.f64 (/.f64 3/32 x) x)))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (/.f64 1/2 (+.f64 1 (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 1 (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 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1)) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)))
(+.f64 (/.f64 (+.f64 -1/4 (/.f64 1/16 x)) (*.f64 x (sqrt.f64 1/2))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (+.f64 -1/4 (/.f64 1/16 x)) (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (/.f64 (sqrt.f64 1/128) (*.f64 x x))))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))
(-.f64 (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/8) x))
(-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))
(-.f64 (+.f64 (/.f64 (sqrt.f64 1/8) x) 1) (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(*.f64 x (*.f64 x 1/8))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(*.f64 1/8 (*.f64 x x))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1))
Outputs
(+.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 (exp.f64 (log.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
x
108.0ms
(/.f64 1 (hypot.f64 1 x))
43.0ms
(hypot.f64 1 x)
38.0ms
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
34.0ms
(/.f64 1 (hypot.f64 1 x))
Results
ErrorSegmentsBranch
0.0b3x
0.0b2(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.0b2(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.0b2(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.0b2(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.0b2(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
0.0b2(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
0.0b2(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
0.0b2(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
0.0b2(/.f64 1 (hypot.f64 1 x))
0.0b2(/.f64 1 (hypot.f64 1 x))
0.0b2(hypot.f64 1 x)
0.0b2(hypot.f64 1 x)
Compiler

Compiled 1053 to 905 computations (14.1% saved)

bsearch1.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.000004088123177
1.004681364745584
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes312.0ms (2.4%)

Counts
41 → 2
Calls
Call 1
Inputs
(/.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 1/8 (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 -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 1/2 (/.f64 1/2 (hypot.f64 1 x))) (fma.f64 x (*.f64 x -1/8) 2))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8))
(fma.f64 x (*.f64 x 1/8) (*.f64 (pow.f64 x 4) -11/128))
(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 (+.f64 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (/.f64 1/2 (-.f64 -1 (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 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (+.f64 (/.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 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1)) (/.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 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1)) (/.f64 (sqrt.f64 1/128) (*.f64 x x))) (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (-.f64 (+.f64 1 (*.f64 (sqrt.f64 1/128) (pow.f64 x -2))) 1)))
(+.f64 (*.f64 (pow.f64 x 4) -11/128) (*.f64 (*.f64 x x) 1/8))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(+.f64 (*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/16 x) (+.f64 1/4 (/.f64 -3/32 (*.f64 x x))))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
(-.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 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/16 x) (-.f64 1/4 (/.f64 (/.f64 3/32 x) x)))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (/.f64 1/2 (+.f64 1 (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 1 (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 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1)) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)))
(+.f64 (/.f64 (+.f64 -1/4 (/.f64 1/16 x)) (*.f64 x (sqrt.f64 1/2))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (+.f64 -1/4 (/.f64 1/16 x)) (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (/.f64 (sqrt.f64 1/128) (*.f64 x x))))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))
(-.f64 (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/8) x))
(-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))
(-.f64 (+.f64 (/.f64 (sqrt.f64 1/8) x) 1) (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(*.f64 x (*.f64 x 1/8))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(*.f64 1/8 (*.f64 x x))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1))
Outputs
(+.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))))))
Calls

13 calls:

89.0ms
x
82.0ms
(/.f64 1 (hypot.f64 1 x))
29.0ms
(/.f64 1 (hypot.f64 1 x))
14.0ms
(hypot.f64 1 x)
12.0ms
(hypot.f64 1 x)
Results
ErrorSegmentsBranch
0.0b3x
0.0b2(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.0b2(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
0.0b2(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.0b2(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x)))))
0.0b2(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
0.0b2(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
0.0b2(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
0.0b2(+.f64 1 (/.f64 1 (hypot.f64 1 x)))
0.0b2(/.f64 1 (hypot.f64 1 x))
0.0b2(/.f64 1 (hypot.f64 1 x))
0.0b2(hypot.f64 1 x)
0.0b2(hypot.f64 1 x)
Compiler

Compiled 714 to 605 computations (15.3% saved)

bsearch1.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.000004088123177
1.004681364745584
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes517.0ms (4%)

Counts
37 → 3
Calls
Call 1
Inputs
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (fma.f64 x (*.f64 x -1/8) 2))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
(fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8))
(fma.f64 x (*.f64 x 1/8) (*.f64 (pow.f64 x 4) -11/128))
(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 (+.f64 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (/.f64 1/2 (-.f64 -1 (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 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (+.f64 (/.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 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1)) (/.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 (-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1)) (/.f64 (sqrt.f64 1/128) (*.f64 x x))) (/.f64 3/32 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (-.f64 (+.f64 1 (*.f64 (sqrt.f64 1/128) (pow.f64 x -2))) 1)))
(+.f64 (*.f64 (pow.f64 x 4) -11/128) (*.f64 (*.f64 x x) 1/8))
(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 2)
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 x))))
(+.f64 (*.f64 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/16 x) (+.f64 1/4 (/.f64 -3/32 (*.f64 x x))))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
(-.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 (*.f64 (sqrt.f64 1/2) x)) (-.f64 (/.f64 1/16 x) (-.f64 1/4 (/.f64 (/.f64 3/32 x) x)))) (-.f64 1 (sqrt.f64 1/2)))
(+.f64 (/.f64 1/2 (+.f64 1 (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 1 (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 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1)) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)))
(+.f64 (/.f64 (+.f64 -1/4 (/.f64 1/16 x)) (*.f64 x (sqrt.f64 1/2))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (+.f64 -1/4 (/.f64 1/16 x)) (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (/.f64 (sqrt.f64 1/128) (*.f64 x x))))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))
(-.f64 (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/8) x))
(-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))
(-.f64 (+.f64 (/.f64 (sqrt.f64 1/8) x) 1) (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(*.f64 x (*.f64 x 1/8))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(*.f64 1/8 (*.f64 x x))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1))
Outputs
(+.f64 (/.f64 1/2 (+.f64 1 (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))))
(fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8))
(-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))
Calls

13 calls:

177.0ms
x
66.0ms
(/.f64 1 (hypot.f64 1 x))
53.0ms
(*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))
50.0ms
(/.f64 1 (hypot.f64 1 x))
22.0ms
(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 645 to 547 computations (15.2% saved)

bsearch85.0ms (0.7%)

Algorithm
2×binary-search
Steps
TimeLeftRight
39.0ms
1.110504878131793e-7
0.002859416560612119
45.0ms
-484.483050810706
-2.95809535884691e-11
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes112.0ms (0.9%)

Counts
19 → 3
Calls
Call 1
Inputs
(+.f64 (-.f64 1 (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 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1)) (/.f64 (/.f64 1/16 (sqrt.f64 1/2)) (*.f64 x x)))
(+.f64 (/.f64 (+.f64 -1/4 (/.f64 1/16 x)) (*.f64 x (sqrt.f64 1/2))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 (+.f64 -1/4 (/.f64 1/16 x)) (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (+.f64 (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x) (/.f64 (sqrt.f64 1/128) (*.f64 x x))))
(+.f64 (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)) (/.f64 -1/4 (*.f64 (sqrt.f64 1/2) x)))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))
(-.f64 (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/8) x))
(-.f64 (/.f64 (/.f64 -1/4 x) (sqrt.f64 1/2)) (+.f64 (sqrt.f64 1/2) -1))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))
(-.f64 (+.f64 (/.f64 (sqrt.f64 1/8) x) 1) (sqrt.f64 1/2))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(*.f64 x (*.f64 x 1/8))
(/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1))
(*.f64 1/8 (*.f64 x x))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (sqrt.f64 1))
Outputs
(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x))
(*.f64 x (*.f64 x 1/8))
(+.f64 (/.f64 (+.f64 -1/4 (/.f64 1/16 x)) (*.f64 x (sqrt.f64 1/2))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))
Calls

1 calls:

99.0ms
x
Results
ErrorSegmentsBranch
0.9b3x
Compiler

Compiled 212 to 184 computations (13.2% saved)

bsearch186.0ms (1.4%)

Algorithm
2×binary-search
Steps
TimeLeftRight
58.0ms
0.571042581190123
224.2927834902696
127.0ms
-484.483050810706
-2.95809535884691e-11
Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes11.0ms (0.1%)

Accuracy

Total -44.5b remaining (-256.5%)

Threshold costs -44.5b (-256.5%)

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

1 calls:

9.0ms
x
Results
ErrorSegmentsBranch
17.4b3x
Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch206.0ms (1.6%)

Algorithm
2×binary-search
Steps
TimeLeftRight
75.0ms
3.6609140921918206e-82
5.5561953788452465e-59
131.0ms
-9.923401470510721e-64
-2.4191277101645197e-78
Compiler

Compiled 17 to 15 computations (11.8% saved)

simplify52.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
20×+-commutative_binary64
12×*-commutative_binary64
6×sub-neg_binary64
3×neg-sub0_binary64
3×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
093303
1125303
2136303
3142303
4145303
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(if (<=.f64 (hypot.f64 1 x) 4512606826625237/4503599627370496) (+.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 (exp.f64 (log.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) 4512606826625237/4503599627370496) (+.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)))))))
(if (<=.f64 x -4261557982614095/8796093022208) (+.f64 (/.f64 1/2 (+.f64 1 (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)))) (if (<=.f64 x 8390737624884511/75557863725914323419136) (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8)) (-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))))
(if (<=.f64 x -4261557982614095/8796093022208) (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x)) (if (<=.f64 x 10533876350404706304/18446744073709551616) (*.f64 x (*.f64 x 1/8)) (+.f64 (/.f64 (+.f64 -1/4 (/.f64 1/16 x)) (*.f64 x (sqrt.f64 1/2))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))))
(if (<=.f64 x -3676964443555495/3705346855594118253554271520278013051304639509300498049262642688253220148477952) (-.f64 1 (sqrt.f64 1/2)) (if (<=.f64 x 6255732032433517/17087896287367280659160173649356416916821636178853222159576332862577757806245124400183696695492608) (-.f64 1 (sqrt.f64 1)) (-.f64 1 (sqrt.f64 1/2))))
Outputs
(if (<=.f64 (hypot.f64 1 x) 4512606826625237/4503599627370496) (+.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 (exp.f64 (log.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) 4512606826625237/4503599627370496) (+.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)))))))
(if (<=.f64 (hypot.f64 1 x) 4512606826625237/4503599627370496) (+.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)))))))
(if (<=.f64 x -4261557982614095/8796093022208) (+.f64 (/.f64 1/2 (+.f64 1 (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)))) (if (<=.f64 x 8390737624884511/75557863725914323419136) (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (*.f64 x x) 1/8)) (-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))))
(if (<=.f64 x -4261557982614095/8796093022208) (+.f64 (/.f64 1/2 (+.f64 1 (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)))) (if (<=.f64 x 8390737624884511/75557863725914323419136) (fma.f64 (pow.f64 x 4) -11/128 (*.f64 1/8 (*.f64 x x))) (-.f64 1 (sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 1 (hypot.f64 1 x))))))))
(if (<=.f64 x -4261557982614095/8796093022208) (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x)) (if (<=.f64 x 10533876350404706304/18446744073709551616) (*.f64 x (*.f64 x 1/8)) (+.f64 (/.f64 (+.f64 -1/4 (/.f64 1/16 x)) (*.f64 x (sqrt.f64 1/2))) (/.f64 1/2 (+.f64 (sqrt.f64 1/2) 1)))))
(if (<=.f64 x -4261557982614095/8796093022208) (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (/.f64 1/4 (sqrt.f64 1/2)) x)) (if (<=.f64 x 642936788965131/1125899906842624) (*.f64 x (*.f64 x 1/8)) (+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 1/2))) (/.f64 (+.f64 -1/4 (/.f64 1/16 x)) (*.f64 x (sqrt.f64 1/2))))))
(if (<=.f64 x -3676964443555495/3705346855594118253554271520278013051304639509300498049262642688253220148477952) (-.f64 1 (sqrt.f64 1/2)) (if (<=.f64 x 6255732032433517/17087896287367280659160173649356416916821636178853222159576332862577757806245124400183696695492608) (-.f64 1 (sqrt.f64 1)) (-.f64 1 (sqrt.f64 1/2))))
(if (<=.f64 x -3676964443555495/3705346855594118253554271520278013051304639509300498049262642688253220148477952) (-.f64 1 (sqrt.f64 1/2)) (if (<=.f64 x 6255732032433517/17087896287367280659160173649356416916821636178853222159576332862577757806245124400183696695492608) 0 (-.f64 1 (sqrt.f64 1/2))))
Compiler

Compiled 207 to 175 computations (15.5% saved)

soundness25.0ms (0.2%)

Algorithm
2×egg-herbie
Rules
8×sub-neg_binary64
8×fma-def_binary64
8×sub-neg_binary64
8×fma-def_binary64
5×+-commutative_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
Stop Event
1×saturated
1×saturated
Compiler

Compiled 134 to 124 computations (7.5% saved)

end226.0ms (1.8%)

Compiler

Compiled 203 to 171 computations (15.8% saved)

Profiling

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