Average Error: 0.0 → 0.0
Time: 10.4s
Precision: 64
\[x + y \cdot \left(z - x\right)\]
↓
\[\mathsf{fma}\left(y, z - x, x\right)\]
x + y \cdot \left(z - x\right)
↓
\mathsf{fma}\left(y, z - x, x\right)
double f(double x, double y, double z) {
        double r9976 = x;
        double r9977 = y;
        double r9978 = z;
        double r9979 = r9978 - r9976;
        double r9980 = r9977 * r9979;
        double r9981 = r9976 + r9980;
        return r9981;
}
↓
double f(double x, double y, double z) {
        double r9982 = y;
        double r9983 = z;
        double r9984 = x;
        double r9985 = r9983 - r9984;
        double r9986 = fma(r9982, r9985, r9984);
        return r9986;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))