Average Error: 0.0 → 0.0
Time: 3.1s
Precision: binary64
\[x + y \cdot \left(z - x\right)\]
↓
\[z \cdot y + \left(x - y \cdot x\right)\]
x + y \cdot \left(z - x\right)
↓
z \cdot y + \left(x - y \cdot x\right)
(FPCore (x y z) :precision binary64 (+ x (* y (- z x))))
↓
(FPCore (x y z) :precision binary64 (+ (* z y) (- x (* y x))))
double code(double x, double y, double z) {
	return x + (y * (z - x));
}
↓
double code(double x, double y, double z) {
	return (z * y) + (x - (y * x));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x + y \cdot \left(z - x\right)\]
  2. Using strategy rm

  3. Applied sub-neg_binary64_710.0

    \[\leadsto x + y \cdot \color{blue}{\left(z + \left(-x\right)\right)}\]

  4. Applied distribute-rgt-in_binary64_280.0

    \[\leadsto x + \color{blue}{\left(z \cdot y + \left(-x\right) \cdot y\right)}\]

  5. Applied associate-+r+_binary64_100.0

    \[\leadsto \color{blue}{\left(x + z \cdot y\right) + \left(-x\right) \cdot y}\]

  6. Simplified0.0

    \[\leadsto \color{blue}{\left(z \cdot y + x\right)} + \left(-x\right) \cdot y\]
  7. Using strategy rm

  8. Applied associate-+l+_binary64_110.0

    \[\leadsto \color{blue}{z \cdot y + \left(x + \left(-x\right) \cdot y\right)}\]

  9. Simplified0.0

    \[\leadsto z \cdot y + \color{blue}{\left(x - x \cdot y\right)}\]

  10. Final simplification0.0

    \[\leadsto z \cdot y + \left(x - y \cdot x\right)\]

Reproduce

herbie shell --seed 2021098 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))