Details

Time bar (total: 3.8s)

analyze0.0ms (0%)

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

Compiled 14 to 13 computations (7.1% saved)

sample2.1s (54.5%)

Results
1.0s2167×body2048valid
426.0ms4256×body128valid
397.0ms1038×body1024valid
146.0ms515×body512valid
52.0ms280×body256valid
Compiler

Compiled 28 to 26 computations (7.1% saved)

preprocess14.0ms (0.4%)

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 13 to 12 computations (7.7% saved)

simplify7.0ms (0.2%)

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)))))

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
17.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶17.1b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
Compiler

Compiled 45 to 41 computations (8.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 1/2 (hypot.f64 1 x))
✓0.0b
(hypot.f64 1 x)
✓0.0b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓3.0b
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series12.0ms (0.3%)

Counts
4 → 48
Calls

12 calls:

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

rewrite57.0ms (1.5%)

Algorithm
1×batch-egg-rewrite
Rules
406×log-prod_binary64
387×prod-diff_binary64
205×fma-def_binary64
170×expm1-udef_binary64
169×log1p-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0938
120138
2259138
Stop Event
1×node limit
Counts
4 → 119
Calls
Call 1
Inputs
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
(hypot.f64 1 x)
(/.f64 1/2 (hypot.f64 1 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1))))) (#(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 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (cbrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (/.f64 1 (+.f64 (+.f64 1 (+.f64 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(/.f64 1/2 (hypot.f64 1 x)))))) (cbrt.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (cbrt.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4) 1)))) (#(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 +.f64 0 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (log.f64 (cbrt.f64 (exp.f64 (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 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (log.f64 (sqrt.f64 (exp.f64 (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 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 (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (cbrt.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 (sqrt.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) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1)))) (sqrt.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3)))) (sqrt.f64 (-.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 pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (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 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.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))))))) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.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)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (hypot.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (hypot.f64 1 x))) (cbrt.f64 (exp.f64 (hypot.f64 1 x))))) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 1 x)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (hypot.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (hypot.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (hypot.f64 1 x)) (cbrt.f64 (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x x 1)) (cbrt.f64 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (hypot.f64 1 x)) (sqrt.f64 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 1 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 1 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 1 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (fma.f64 x x 1))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 1 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (hypot.f64 1 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 1 x)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.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 (hypot.f64 1 x)))) (cbrt.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1/2 (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1/2 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (/.f64 1 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (hypot.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.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 (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 -1/2 (/.f64 1 (neg.f64 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (hypot.f64 1 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (hypot.f64 1 x) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/4 (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 1/2 (hypot.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/2 (hypot.f64 1 x))))))))

simplify47.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
891×fma-neg_binary64
444×fma-def_binary64
232×associate--l+_binary64
220×cancel-sign-sub-inv_binary64
195×associate-/r*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0128942
1428918
21343892
34753892
Stop Event
1×node limit
Counts
167 → 202
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 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 1/8 (pow.f64 x 2))) (*.f64 11/128 (pow.f64 x 4)))
(-.f64 (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 1/8 (pow.f64 x 2))) (+.f64 (*.f64 11/128 (pow.f64 x 4)) (*.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 (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) 1) (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (+.f64 1 (*.f64 1/8 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))) (+.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/128 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 (+.f64 (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (+.f64 1 (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))) (sqrt.f64 1/2))
(-.f64 (+.f64 (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (+.f64 1 (+.f64 (*.f64 1/128 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))) (+.f64 (sqrt.f64 1/2) (*.f64 1/8 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))
1
(-.f64 1 (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 11/128 (pow.f64 x 4)) 1) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 11/128 (pow.f64 x 4)) 1) (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 1/8 (pow.f64 x 2))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))) (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/128 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))) (+.f64 (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (*.f64 1/8 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))
(sqrt.f64 1/2)
(-.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))
(-.f64 (sqrt.f64 1/2) (+.f64 (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 (sqrt.f64 1/2) (*.f64 1/8 (/.f64 1 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (+.f64 (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (+.f64 (*.f64 1/128 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (*.f64 1/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) x))))))
1
(+.f64 1 (*.f64 1/2 (pow.f64 x 2)))
(-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) (*.f64 1/8 (pow.f64 x 4)))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/16 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2)))) (*.f64 1/8 (pow.f64 x 4)))
x
(+.f64 (*.f64 1/2 (/.f64 1 x)) x)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) x) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (*.f64 1/2 (/.f64 1 x)) x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(*.f64 -1 x)
(neg.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) x))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/2 (/.f64 1 x)) x))
(-.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (*.f64 1/2 (/.f64 1 x)) x)))
1/2
(-.f64 1/2 (*.f64 1/4 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 3/16 (pow.f64 x 4)) 1/2) (*.f64 1/4 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 3/16 (pow.f64 x 4)) 1/2) (+.f64 (*.f64 5/32 (pow.f64 x 6)) (*.f64 1/4 (pow.f64 x 2))))
(/.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 5/32 (/.f64 1 (pow.f64 x 7))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3)))))
(/.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 5/32 (/.f64 1 (pow.f64 x 7))) (*.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))))
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)))
(+.f64 (*.f64 1/8 (*.f64 x x)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (*.f64 x x) (*.f64 (pow.f64 x 4) -11/128))
(-.f64 (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 1/8 (pow.f64 x 2))) (*.f64 11/128 (pow.f64 x 4)))
(+.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 1/8 (*.f64 x x))) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 69/1024 (pow.f64 x 6) (fma.f64 1/8 (*.f64 x x) (*.f64 (pow.f64 x 4) -11/128)))
(fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))
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1
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(sqrt.f64 1/2)
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(sqrt.f64 1/2)
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1
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(fma.f64 (*.f64 x x) 1/2 1)
(fma.f64 x (*.f64 x 1/2) 1)
(-.f64 (+.f64 1 (*.f64 1/2 (pow.f64 x 2))) (*.f64 1/8 (pow.f64 x 4)))
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(fma.f64 (pow.f64 x 4) -1/8 (fma.f64 x (*.f64 x 1/2) 1))
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(fma.f64 (pow.f64 x 4) -1/8 (fma.f64 x (*.f64 x 1/2) (fma.f64 (pow.f64 x 6) 1/16 1)))
x
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(*.f64 -1 x)
(neg.f64 x)
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1/2
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(fma.f64 (*.f64 x x) -1/4 1/2)
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(fma.f64 (*.f64 x x) -1/4 (fma.f64 (pow.f64 x 4) 3/16 1/2))
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(/.f64 1/2 x)
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(/.f64 -1/2 x)
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(-.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 5/32 (/.f64 1 (pow.f64 x 7))) (*.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 (pow.f64 x 3)) (/.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 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 3/16 (pow.f64 x 5)) (+.f64 (/.f64 1/2 x) (/.f64 -5/32 (pow.f64 x 7)))))

prune167.0ms (4.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New2002202
Fresh000
Picked101
Done000
Total2012203
Error
0b
Counts
203 → 2
Alt Table
StatusErrorProgram
▶16.6b
(/.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
(fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))
Compiler

Compiled 3708 to 3285 computations (11.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1/2 (hypot.f64 1 x))
0.0b
(hypot.f64 1 x)
0.0b
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓2.4b
(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series2.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

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

rewrite35.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
769×pow1_binary64
717×log1p-expm1-u_binary64
717×expm1-log1p-u_binary64
77×add-sqr-sqrt_binary64
72×add-cbrt-cube_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
115310
2189310
Stop Event
1×node limit
Counts
1 → 30
Calls
Call 1
Inputs
(-.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 1/2 (*.f64 (/.f64 -1/2 (hypot.f64 1 x)) 1))))) (#(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 1 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 2) (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/8 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3))) (/.f64 1 (+.f64 1/4 (+.f64 (/.f64 1/4 (+.f64 1 (*.f64 x x))) (/.f64 1/4 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/4 (/.f64 1/4 (+.f64 1 (*.f64 x x)))) (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1/4 (+.f64 (/.f64 1/4 (+.f64 1 (*.f64 x x))) (/.f64 1/4 (hypot.f64 1 x)))) (-.f64 1/8 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (-.f64 1/4 (/.f64 1/4 (+.f64 1 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/8 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3))) (+.f64 1/4 (+.f64 (/.f64 1/4 (+.f64 1 (*.f64 x x))) (/.f64 1/4 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (/.f64 1/4 (+.f64 1 (*.f64 x x)))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/8 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3)))) (neg.f64 (+.f64 1/4 (+.f64 (/.f64 1/4 (+.f64 1 (*.f64 x x))) (/.f64 1/4 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/4 (/.f64 1/4 (+.f64 1 (*.f64 x x))))) (neg.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/8 (pow.f64 (/.f64 -1/2 (hypot.f64 1 x)) 3)) (+.f64 1/4 (-.f64 (*.f64 (/.f64 -1/2 (hypot.f64 1 x)) (/.f64 -1/2 (hypot.f64 1 x))) (*.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (*.f64 (/.f64 -1/2 (hypot.f64 1 x)) (/.f64 -1/2 (hypot.f64 1 x)))) (-.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x)))))))))

simplify20.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
658×associate-*l*_binary64
524×fma-def_binary64
514×associate-*r*_binary64
323×cancel-sign-sub-inv_binary64
234×fma-neg_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
044174
1134170
2357168
31111168
Stop Event
1×node limit
Counts
42 → 51
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 (*.f64 5/32 (pow.f64 x 6)) (*.f64 1/4 (pow.f64 x 2))) (*.f64 3/16 (pow.f64 x 4)))
(-.f64 (+.f64 (*.f64 5/32 (pow.f64 x 6)) (*.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 3/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (*.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 1/2 (/.f64 1 x)))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
Outputs
(*.f64 1/4 (pow.f64 x 2))
(*.f64 1/4 (*.f64 x x))
(-.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 3/16 (pow.f64 x 4)))
(+.f64 (*.f64 1/4 (*.f64 x x)) (*.f64 -3/16 (pow.f64 x 4)))
(fma.f64 1/4 (*.f64 x x) (*.f64 (pow.f64 x 4) -3/16))
(fma.f64 (pow.f64 x 4) -3/16 (*.f64 1/4 (*.f64 x x)))
(*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -3/16 1/4))
(-.f64 (+.f64 (*.f64 5/32 (pow.f64 x 6)) (*.f64 1/4 (pow.f64 x 2))) (*.f64 3/16 (pow.f64 x 4)))
(+.f64 (fma.f64 5/32 (pow.f64 x 6) (*.f64 1/4 (*.f64 x x))) (*.f64 -3/16 (pow.f64 x 4)))
(fma.f64 5/32 (pow.f64 x 6) (fma.f64 1/4 (*.f64 x x) (*.f64 (pow.f64 x 4) -3/16)))
(fma.f64 (pow.f64 x 4) -3/16 (fma.f64 1/4 (*.f64 x x) (*.f64 5/32 (pow.f64 x 6))))
(-.f64 (+.f64 (*.f64 5/32 (pow.f64 x 6)) (*.f64 1/4 (pow.f64 x 2))) (+.f64 (*.f64 3/16 (pow.f64 x 4)) (*.f64 35/256 (pow.f64 x 8))))
(-.f64 (fma.f64 5/32 (pow.f64 x 6) (*.f64 1/4 (*.f64 x x))) (fma.f64 3/16 (pow.f64 x 4) (*.f64 35/256 (pow.f64 x 8))))
(fma.f64 1/4 (*.f64 x x) (fma.f64 5/32 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -3/16 (*.f64 (pow.f64 x 8) -35/256))))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) -3/16 1/4) (fma.f64 5/32 (pow.f64 x 6) (*.f64 (pow.f64 x 8) -35/256)))
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 1/2 x) (/.f64 -1/4 (pow.f64 x 3))))
(-.f64 (+.f64 1/2 (*.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 1/2 (/.f64 1/4 (pow.f64 x 3))) (/.f64 3/16 (pow.f64 x 5))) (/.f64 1/2 x))
(+.f64 (+.f64 1/2 (-.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 3/16 (pow.f64 x 5)))) (/.f64 -1/2 x))
(+.f64 (/.f64 -1/2 x) (+.f64 (+.f64 1/2 (/.f64 1/4 (pow.f64 x 3))) (/.f64 -3/16 (pow.f64 x 5))))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (-.f64 (+.f64 1/2 (/.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 1/2 (*.f64 1/2 (/.f64 1 x))) (*.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 (*.f64 3/16 (/.f64 1 (pow.f64 x 5))) (+.f64 1/2 (*.f64 1/2 (/.f64 1 x)))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 3/16 (pow.f64 x 5)) (+.f64 1/2 (/.f64 1/2 x))) (/.f64 1/4 (pow.f64 x 3)))
(+.f64 (/.f64 3/16 (pow.f64 x 5)) (+.f64 1/2 (+.f64 (/.f64 1/2 x) (/.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 1/2 (+.f64 (/.f64 3/16 (pow.f64 x 5)) (+.f64 (/.f64 1/2 x) (/.f64 -1/4 (pow.f64 x 3)))))

prune225.0ms (5.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New2800280
Fresh011
Picked011
Done000
Total2802282
Error
0b
Counts
282 → 2
Alt Table
StatusErrorProgram
✓16.6b
(/.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
(fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))
Compiler

Compiled 7011 to 6147 computations (12.3% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))
✓0.1b
(*.f64 (pow.f64 x 4) -11/128)
✓20.1b
(fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))

series10.0ms (0.3%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))
1.0ms
x
@-inf
(fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))
1.0ms
x
@-inf
(fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))
1.0ms
x
@0
(fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))
1.0ms
x
@inf
(fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))

rewrite46.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
448×log-prod_binary64
202×expm1-udef_binary64
202×log1p-udef_binary64
181×pow3_binary64
163×log-pow_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01342
127442
2284542
Stop Event
1×node limit
Counts
3 → 75
Calls
Call 1
Inputs
(fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))
(*.f64 (pow.f64 x 4) -11/128)
(fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x 4) -11/128) (*.f64 69/1024 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 (pow.f64 x 4) -11/128))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 69/1024 (pow.f64 x 6)) 1) (*.f64 (pow.f64 x 4) -11/128))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))) (cbrt.f64 (exp.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))))) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))) (pow.f64 (cbrt.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))) 2) (cbrt.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))) (sqrt.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 69/1024 (pow.f64 x 6)) 3) (pow.f64 (*.f64 (pow.f64 x 4) -11/128) 3)) (fma.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 69/1024 (pow.f64 x 6)) (-.f64 (*.f64 121/16384 (pow.f64 x 8)) (*.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 (pow.f64 x 4) -11/128)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 69/1024 (pow.f64 x 6))) (*.f64 121/16384 (pow.f64 x 8))) (-.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 (pow.f64 x 4) -11/128)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 -11/128) (pow.f64 x 4)) (exp.f64 (*.f64 69/1024 (pow.f64 x 6)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 x 4) -11/128))) (exp.f64 (*.f64 69/1024 (pow.f64 x 6)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (*.f64 69/1024 (pow.f64 x 6))) (+.f64 1 (expm1.f64 (*.f64 (pow.f64 x 4) -11/128)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (pow.f64 x 4) -11/128))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 -11/128) (pow.f64 x 4))) (cbrt.f64 (pow.f64 (exp.f64 -11/128) (pow.f64 x 4))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -11/128) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -11/128) (pow.f64 x 4)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -11/128) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 x 4) -11/128))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 4) -11/128) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 x 4) -11/128) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) -11/128)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) (sqrt.f64 -11/128)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 121/16384 (pow.f64 x 8)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -11/128) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 x 4) -11/128))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 x 4) -11/128) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 x 4) -11/128)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 x 4) -11/128)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 4) -11/128)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 x 4) -11/128)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)) (*.f64 1/8 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/8 (*.f64 x x)) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 1/8 (*.f64 x x)) 1) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1/8 (*.f64 x x) (*.f64 69/1024 (pow.f64 x 6))) (*.f64 (pow.f64 x 4) -11/128))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))))) (cbrt.f64 (exp.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))))))) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))) (pow.f64 (cbrt.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))) 2) (cbrt.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))) (sqrt.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 1/8 (*.f64 x x)) 3) (pow.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)) 3)) (fma.f64 (*.f64 1/8 (*.f64 x x)) (*.f64 1/8 (*.f64 x x)) (-.f64 (pow.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)) 2) (*.f64 (*.f64 1/8 (*.f64 x x)) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 1/8 (*.f64 x x)) (*.f64 1/8 (*.f64 x x))) (pow.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)) 2)) (-.f64 (*.f64 1/8 (*.f64 x x)) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))) (exp.f64 (*.f64 1/8 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))) (exp.f64 (*.f64 1/8 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (*.f64 1/8 (*.f64 x x))) (+.f64 1 (expm1.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))))))))

simplify35.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
678×distribute-rgt-neg-in_binary64
340×cancel-sign-sub-inv_binary64
285×unswap-sqr_binary64
275×fma-neg_binary64
255×*-commutative_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
020456
148420
2106420
3331420
41467420
54391420
Stop Event
1×node limit
Counts
111 → 85
Calls
Call 1
Inputs
(*.f64 -11/128 (pow.f64 x 4))
(-.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 11/128 (pow.f64 x 4)))
(-.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 11/128 (pow.f64 x 4)))
(-.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 11/128 (pow.f64 x 4)))
(*.f64 69/1024 (pow.f64 x 6))
(-.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 11/128 (pow.f64 x 4)))
(-.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 11/128 (pow.f64 x 4)))
(-.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 11/128 (pow.f64 x 4)))
(*.f64 69/1024 (pow.f64 x 6))
(-.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 11/128 (pow.f64 x 4)))
(-.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 11/128 (pow.f64 x 4)))
(-.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 11/128 (pow.f64 x 4)))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 1/8 (pow.f64 x 2))
(-.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 11/128 (pow.f64 x 4)))
(-.f64 (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 1/8 (pow.f64 x 2))) (*.f64 11/128 (pow.f64 x 4)))
(-.f64 (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 1/8 (pow.f64 x 2))) (*.f64 11/128 (pow.f64 x 4)))
(*.f64 69/1024 (pow.f64 x 6))
(-.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 11/128 (pow.f64 x 4)))
(-.f64 (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 1/8 (pow.f64 x 2))) (*.f64 11/128 (pow.f64 x 4)))
(-.f64 (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 1/8 (pow.f64 x 2))) (*.f64 11/128 (pow.f64 x 4)))
(*.f64 69/1024 (pow.f64 x 6))
(-.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 11/128 (pow.f64 x 4)))
(-.f64 (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 1/8 (pow.f64 x 2))) (*.f64 11/128 (pow.f64 x 4)))
(-.f64 (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 1/8 (pow.f64 x 2))) (*.f64 11/128 (pow.f64 x 4)))
Outputs
(*.f64 -11/128 (pow.f64 x 4))
(-.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 11/128 (pow.f64 x 4)))
(+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 69/1024 (pow.f64 x 6) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 69/1024 (pow.f64 x 6)))
(-.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 11/128 (pow.f64 x 4)))
(+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 69/1024 (pow.f64 x 6) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 69/1024 (pow.f64 x 6)))
(-.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 11/128 (pow.f64 x 4)))
(+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 69/1024 (pow.f64 x 6) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 69/1024 (pow.f64 x 6)))
(*.f64 69/1024 (pow.f64 x 6))
(-.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 11/128 (pow.f64 x 4)))
(+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 69/1024 (pow.f64 x 6) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 69/1024 (pow.f64 x 6)))
(-.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 11/128 (pow.f64 x 4)))
(+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 69/1024 (pow.f64 x 6) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 69/1024 (pow.f64 x 6)))
(-.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 11/128 (pow.f64 x 4)))
(+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 69/1024 (pow.f64 x 6) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 69/1024 (pow.f64 x 6)))
(*.f64 69/1024 (pow.f64 x 6))
(-.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 11/128 (pow.f64 x 4)))
(+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 69/1024 (pow.f64 x 6) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 69/1024 (pow.f64 x 6)))
(-.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 11/128 (pow.f64 x 4)))
(+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 69/1024 (pow.f64 x 6) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 69/1024 (pow.f64 x 6)))
(-.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 11/128 (pow.f64 x 4)))
(+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 69/1024 (pow.f64 x 6) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 69/1024 (pow.f64 x 6)))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 -11/128 (pow.f64 x 4))
(*.f64 1/8 (pow.f64 x 2))
(*.f64 1/8 (*.f64 x x))
(*.f64 x (*.f64 x 1/8))
(-.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 11/128 (pow.f64 x 4)))
(+.f64 (*.f64 1/8 (*.f64 x x)) (*.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 -11/128 (*.f64 x x) 1/8)))
(-.f64 (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 1/8 (pow.f64 x 2))) (*.f64 11/128 (pow.f64 x 4)))
(+.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 1/8 (*.f64 x x))) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 69/1024 (pow.f64 x 6) (fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4))))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 x (*.f64 x 1/8) (*.f64 69/1024 (pow.f64 x 6))))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 1/8 (*.f64 x x))))
(-.f64 (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 1/8 (pow.f64 x 2))) (*.f64 11/128 (pow.f64 x 4)))
(+.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 1/8 (*.f64 x x))) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 69/1024 (pow.f64 x 6) (fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4))))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 x (*.f64 x 1/8) (*.f64 69/1024 (pow.f64 x 6))))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 1/8 (*.f64 x x))))
(*.f64 69/1024 (pow.f64 x 6))
(-.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 11/128 (pow.f64 x 4)))
(+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 69/1024 (pow.f64 x 6) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 69/1024 (pow.f64 x 6)))
(-.f64 (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 1/8 (pow.f64 x 2))) (*.f64 11/128 (pow.f64 x 4)))
(+.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 1/8 (*.f64 x x))) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 69/1024 (pow.f64 x 6) (fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4))))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 x (*.f64 x 1/8) (*.f64 69/1024 (pow.f64 x 6))))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 1/8 (*.f64 x x))))
(-.f64 (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 1/8 (pow.f64 x 2))) (*.f64 11/128 (pow.f64 x 4)))
(+.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 1/8 (*.f64 x x))) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 69/1024 (pow.f64 x 6) (fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4))))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 x (*.f64 x 1/8) (*.f64 69/1024 (pow.f64 x 6))))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 1/8 (*.f64 x x))))
(*.f64 69/1024 (pow.f64 x 6))
(-.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 11/128 (pow.f64 x 4)))
(+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 69/1024 (pow.f64 x 6) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 69/1024 (pow.f64 x 6)))
(-.f64 (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 1/8 (pow.f64 x 2))) (*.f64 11/128 (pow.f64 x 4)))
(+.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 1/8 (*.f64 x x))) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 69/1024 (pow.f64 x 6) (fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4))))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 x (*.f64 x 1/8) (*.f64 69/1024 (pow.f64 x 6))))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 1/8 (*.f64 x x))))
(-.f64 (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 1/8 (pow.f64 x 2))) (*.f64 11/128 (pow.f64 x 4)))
(+.f64 (fma.f64 69/1024 (pow.f64 x 6) (*.f64 1/8 (*.f64 x x))) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 69/1024 (pow.f64 x 6) (fma.f64 1/8 (*.f64 x x) (*.f64 -11/128 (pow.f64 x 4))))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 x (*.f64 x 1/8) (*.f64 69/1024 (pow.f64 x 6))))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 1/8 (*.f64 x x))))

prune66.0ms (1.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New85085
Fresh000
Picked011
Done011
Total85287
Error
0b
Counts
87 → 2
Alt Table
StatusErrorProgram
✓16.6b
(/.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
(fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128)))
Compiler

Compiled 1811 to 1319 computations (27.2% saved)

regimes886.0ms (23.2%)

Accuracy

Total 0.1b remaining (78.5%)

Threshold costs 0.1b (78.5%)

Counts
110 → 2
Compiler

Compiled 12294 to 11157 computations (9.2% saved)

bsearch1.0ms (0%)

Algorithm
1×left-value
Calls

1 calls:

0.0ms
(hypot.f64 1 x)
Steps
ItersPointRange
2.0
∈ [
1.0000000052560345
, 
2.2354134437142807
]
Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
4×+-commutative_binary64
2×*-commutative_binary64
2×sub-neg_binary64
1×distribute-neg-frac_binary64
1×neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02657
13357
24057
34257
44357
Stop Event
1×saturated
Calls
Call 1
Inputs
(if (<=.f64 (hypot.f64 1 x) 2) (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))) (/.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
(if (<=.f64 (hypot.f64 1 x) 2) (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))) (/.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) 2) (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 4) -11/128))) (/.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)))))))

end71.0ms (1.9%)

Stop Event
1×done
Compiler

Compiled 115 to 95 computations (17.4% saved)

Profiling

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