Average Error: 0.0 → 0.0
Time: 6.6s
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 r134491 = x;
        double r134492 = y;
        double r134493 = r134491 * r134492;
        double r134494 = 1.0;
        double r134495 = r134491 - r134494;
        double r134496 = z;
        double r134497 = r134495 * r134496;
        double r134498 = r134493 + r134497;
        return r134498;
}
↓
double f(double x, double y, double z) {
        double r134499 = x;
        double r134500 = 1.0;
        double r134501 = r134499 - r134500;
        double r134502 = z;
        double r134503 = y;
        double r134504 = r134503 * r134499;
        double r134505 = fma(r134501, r134502, r134504);
        return r134505;
}

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 2019196 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  (+ (* x y) (* (- x 1.0) z)))