Average Error: 0.0 → 0.0
Time: 2.5s
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 r7120 = x;
        double r7121 = y;
        double r7122 = z;
        double r7123 = r7122 - r7120;
        double r7124 = r7121 * r7123;
        double r7125 = r7120 + r7124;
        return r7125;
}
↓
double f(double x, double y, double z) {
        double r7126 = x;
        double r7127 = z;
        double r7128 = y;
        double r7129 = r7127 * r7128;
        double r7130 = r7126 + r7129;
        double r7131 = -r7126;
        double r7132 = r7131 * r7128;
        double r7133 = r7130 + r7132;
        return r7133;
}

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 2019352 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))