Average Error: 0.0 → 0.0
Time: 15.0s
Precision: 64
\[x + y \cdot \left(z - x\right)\]
↓
\[\left(z \cdot y + x\right) + \left(-x\right) \cdot y\]
x + y \cdot \left(z - x\right)
↓
\left(z \cdot y + x\right) + \left(-x\right) \cdot y
double f(double x, double y, double z) {
        double r23151 = x;
        double r23152 = y;
        double r23153 = z;
        double r23154 = r23153 - r23151;
        double r23155 = r23152 * r23154;
        double r23156 = r23151 + r23155;
        return r23156;
}
↓
double f(double x, double y, double z) {
        double r23157 = z;
        double r23158 = y;
        double r23159 = r23157 * r23158;
        double r23160 = x;
        double r23161 = r23159 + r23160;
        double r23162 = -r23160;
        double r23163 = r23162 * r23158;
        double r23164 = r23161 + r23163;
        return r23164;
}

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. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))