Average Error: 0.0 → 0.0
Time: 7.4s
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 r8437 = x;
        double r8438 = y;
        double r8439 = z;
        double r8440 = r8439 - r8437;
        double r8441 = r8438 * r8440;
        double r8442 = r8437 + r8441;
        return r8442;
}
↓
double f(double x, double y, double z) {
        double r8443 = z;
        double r8444 = x;
        double r8445 = r8443 - r8444;
        double r8446 = y;
        double r8447 = fma(r8445, r8446, r8444);
        return r8447;
}

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 2019212 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))