Average Error: 0.0 → 0.0
Time: 1.1s
Precision: binary64
\[x + y \cdot \left(z - x\right)\]
↓
\[x + \left(y \cdot z - x \cdot y\right)\]
x + y \cdot \left(z - x\right)
↓
x + \left(y \cdot z - x \cdot y\right)
(FPCore (x y z) :precision binary64 (+ x (* y (- z x))))
↓
(FPCore (x y z) :precision binary64 (+ x (- (* y z) (* x y))))
double code(double x, double y, double z) {
	return x + (y * (z - x));
}
↓
double code(double x, double y, double z) {
	return x + ((y * z) - (x * y));
}

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_binary640.0

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

  4. Applied distribute-rgt-in_binary640.0

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

  5. Simplified0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020233 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))