Average Error: 0.0 → 0.0
Time: 32.0s
Precision: 64
\[x \cdot y + \left(x - 1\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, y, \left(x - 1\right) \cdot z\right)\]
x \cdot y + \left(x - 1\right) \cdot z
↓
\mathsf{fma}\left(x, y, \left(x - 1\right) \cdot z\right)
double f(double x, double y, double z) {
        double r9967333 = x;
        double r9967334 = y;
        double r9967335 = r9967333 * r9967334;
        double r9967336 = 1.0;
        double r9967337 = r9967333 - r9967336;
        double r9967338 = z;
        double r9967339 = r9967337 * r9967338;
        double r9967340 = r9967335 + r9967339;
        return r9967340;
}
↓
double f(double x, double y, double z) {
        double r9967341 = x;
        double r9967342 = y;
        double r9967343 = 1.0;
        double r9967344 = r9967341 - r9967343;
        double r9967345 = z;
        double r9967346 = r9967344 * r9967345;
        double r9967347 = fma(r9967341, r9967342, r9967346);
        return r9967347;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \left(x - 1\right) \cdot z\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, \left(x - 1\right) \cdot z\right)\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  (+ (* x y) (* (- x 1.0) z)))