Average Error: 0.0 → 0.0
Time: 9.9s
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 r9086 = x;
        double r9087 = y;
        double r9088 = z;
        double r9089 = r9088 - r9086;
        double r9090 = r9087 * r9089;
        double r9091 = r9086 + r9090;
        return r9091;
}
↓
double f(double x, double y, double z) {
        double r9092 = y;
        double r9093 = z;
        double r9094 = x;
        double r9095 = r9093 - r9094;
        double r9096 = fma(r9092, r9095, r9094);
        return r9096;
}

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 2019174 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))