Average Error: 0.0 → 0.0
Time: 3.5s
Precision: 64
\[x + y \cdot \left(z - x\right)\]
↓
\[\left(x + z \cdot y\right) + \left(-x\right) \cdot y\]
x + y \cdot \left(z - x\right)
↓
\left(x + z \cdot y\right) + \left(-x\right) \cdot y
double f(double x, double y, double z) {
        double r14605 = x;
        double r14606 = y;
        double r14607 = z;
        double r14608 = r14607 - r14605;
        double r14609 = r14606 * r14608;
        double r14610 = r14605 + r14609;
        return r14610;
}
↓
double f(double x, double y, double z) {
        double r14611 = x;
        double r14612 = z;
        double r14613 = y;
        double r14614 = r14612 * r14613;
        double r14615 = r14611 + r14614;
        double r14616 = -r14611;
        double r14617 = r14616 * r14613;
        double r14618 = r14615 + r14617;
        return r14618;
}

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-neg0.0

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

  4. Applied distribute-rgt-in0.0

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

  5. Applied associate-+r+0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020001 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))