Average Error: 0.0 → 0.0
Time: 15.3s
Precision: 64
\[x \cdot y + \left(x - 1\right) \cdot z\]
↓
\[\mathsf{fma}\left(x - 1, z, y \cdot x\right)\]
x \cdot y + \left(x - 1\right) \cdot z
↓
\mathsf{fma}\left(x - 1, z, y \cdot x\right)
double f(double x, double y, double z) {
        double r194888 = x;
        double r194889 = y;
        double r194890 = r194888 * r194889;
        double r194891 = 1.0;
        double r194892 = r194888 - r194891;
        double r194893 = z;
        double r194894 = r194892 * r194893;
        double r194895 = r194890 + r194894;
        return r194895;
}
↓
double f(double x, double y, double z) {
        double r194896 = x;
        double r194897 = 1.0;
        double r194898 = r194896 - r194897;
        double r194899 = z;
        double r194900 = y;
        double r194901 = r194900 * r194896;
        double r194902 = fma(r194898, r194899, r194901);
        return r194902;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x \cdot y + \left(x - 1\right) \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x - 1, z, x \cdot y\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x - 1, z, y \cdot x\right)\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  (+ (* x y) (* (- x 1.0) z)))