Average Error: 0.0 → 0.0
Time: 7.0s
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 r180778 = x;
        double r180779 = y;
        double r180780 = r180778 * r180779;
        double r180781 = 1.0;
        double r180782 = r180778 - r180781;
        double r180783 = z;
        double r180784 = r180782 * r180783;
        double r180785 = r180780 + r180784;
        return r180785;
}
↓
double f(double x, double y, double z) {
        double r180786 = x;
        double r180787 = 1.0;
        double r180788 = r180786 - r180787;
        double r180789 = z;
        double r180790 = y;
        double r180791 = r180790 * r180786;
        double r180792 = fma(r180788, r180789, r180791);
        return r180792;
}

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 2019179 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  (+ (* x y) (* (- x 1.0) z)))