Average Error: 0.0 → 0.0
Time: 10.5s
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 r6263869 = x;
        double r6263870 = y;
        double r6263871 = r6263869 * r6263870;
        double r6263872 = 1.0;
        double r6263873 = r6263869 - r6263872;
        double r6263874 = z;
        double r6263875 = r6263873 * r6263874;
        double r6263876 = r6263871 + r6263875;
        return r6263876;
}
↓
double f(double x, double y, double z) {
        double r6263877 = x;
        double r6263878 = 1.0;
        double r6263879 = r6263877 - r6263878;
        double r6263880 = z;
        double r6263881 = y;
        double r6263882 = r6263881 * r6263877;
        double r6263883 = fma(r6263879, r6263880, r6263882);
        return r6263883;
}

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 2019192 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  (+ (* x y) (* (- x 1.0) z)))