Average Error: 0.0 → 0.0
Time: 2.2s
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 r7103 = x;
        double r7104 = y;
        double r7105 = z;
        double r7106 = r7105 - r7103;
        double r7107 = r7104 * r7106;
        double r7108 = r7103 + r7107;
        return r7108;
}
↓
double f(double x, double y, double z) {
        double r7109 = z;
        double r7110 = x;
        double r7111 = r7109 - r7110;
        double r7112 = y;
        double r7113 = fma(r7111, r7112, r7110);
        return r7113;
}

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 2019354 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))