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 r36143 = x;
        double r36144 = y;
        double r36145 = z;
        double r36146 = r36145 - r36143;
        double r36147 = r36144 * r36146;
        double r36148 = r36143 + r36147;
        return r36148;
}
↓
double f(double x, double y, double z) {
        double r36149 = y;
        double r36150 = z;
        double r36151 = x;
        double r36152 = r36150 - r36151;
        double r36153 = fma(r36149, r36152, r36151);
        return r36153;
}

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 2019163 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))