Average Error: 0.0 → 0.0
Time: 9.9s
Precision: 64
\[x \cdot y + \left(x - 1.0\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, y, \left(x - 1.0\right) \cdot z\right)\]
x \cdot y + \left(x - 1.0\right) \cdot z
↓
\mathsf{fma}\left(x, y, \left(x - 1.0\right) \cdot z\right)
double f(double x, double y, double z) {
        double r6054324 = x;
        double r6054325 = y;
        double r6054326 = r6054324 * r6054325;
        double r6054327 = 1.0;
        double r6054328 = r6054324 - r6054327;
        double r6054329 = z;
        double r6054330 = r6054328 * r6054329;
        double r6054331 = r6054326 + r6054330;
        return r6054331;
}
↓
double f(double x, double y, double z) {
        double r6054332 = x;
        double r6054333 = y;
        double r6054334 = 1.0;
        double r6054335 = r6054332 - r6054334;
        double r6054336 = z;
        double r6054337 = r6054335 * r6054336;
        double r6054338 = fma(r6054332, r6054333, r6054337);
        return r6054338;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x \cdot y + \left(x - 1.0\right) \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \left(x - 1.0\right) \cdot z\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, \left(x - 1.0\right) \cdot z\right)\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  (+ (* x y) (* (- x 1.0) z)))