Average Error: 0.0 → 0.0
Time: 2.0s
Precision: 64
\[x + y \cdot \left(z - x\right)\]
↓
\[\mathsf{fma}\left(z - x, y, x\right)\]
x + y \cdot \left(z - x\right)
↓
\mathsf{fma}\left(z - x, y, x\right)
double f(double x, double y, double z) {
        double r7092 = x;
        double r7093 = y;
        double r7094 = z;
        double r7095 = r7094 - r7092;
        double r7096 = r7093 * r7095;
        double r7097 = r7092 + r7096;
        return r7097;
}
↓
double f(double x, double y, double z) {
        double r7098 = z;
        double r7099 = x;
        double r7100 = r7098 - r7099;
        double r7101 = y;
        double r7102 = fma(r7100, r7101, r7099);
        return r7102;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(z - x, y, x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(z - x, y, x\right)\]

Reproduce

herbie shell --seed 2020056 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))