Average Error: 0.0 → 0.0
Time: 9.2s
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 r1284118 = x;
        double r1284119 = y;
        double r1284120 = z;
        double r1284121 = r1284120 - r1284118;
        double r1284122 = r1284119 * r1284121;
        double r1284123 = r1284118 + r1284122;
        return r1284123;
}
↓
double f(double x, double y, double z) {
        double r1284124 = y;
        double r1284125 = z;
        double r1284126 = x;
        double r1284127 = r1284125 - r1284126;
        double r1284128 = fma(r1284124, r1284127, r1284126);
        return r1284128;
}

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 2019173 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))