Average Error: 0.0 → 0.0
Time: 4.2s
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 r63127 = x;
        double r63128 = y;
        double r63129 = z;
        double r63130 = r63129 - r63127;
        double r63131 = r63128 * r63130;
        double r63132 = r63127 + r63131;
        return r63132;
}
↓
double f(double x, double y, double z) {
        double r63133 = y;
        double r63134 = z;
        double r63135 = x;
        double r63136 = r63134 - r63135;
        double r63137 = fma(r63133, r63136, r63135);
        return r63137;
}

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 2019156 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))