Average Error: 0.0 → 0.0
Time: 14.1s
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 r6459773 = x;
        double r6459774 = y;
        double r6459775 = r6459773 * r6459774;
        double r6459776 = 1.0;
        double r6459777 = r6459773 - r6459776;
        double r6459778 = z;
        double r6459779 = r6459777 * r6459778;
        double r6459780 = r6459775 + r6459779;
        return r6459780;
}
↓
double f(double x, double y, double z) {
        double r6459781 = x;
        double r6459782 = 1.0;
        double r6459783 = r6459781 - r6459782;
        double r6459784 = z;
        double r6459785 = y;
        double r6459786 = r6459785 * r6459781;
        double r6459787 = fma(r6459783, r6459784, r6459786);
        return r6459787;
}

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 2019172 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  (+ (* x y) (* (- x 1.0) z)))