Average Error: 0.0 → 0.0
Time: 1.9s
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 r125295 = x;
        double r125296 = y;
        double r125297 = r125295 * r125296;
        double r125298 = 1.0;
        double r125299 = r125295 - r125298;
        double r125300 = z;
        double r125301 = r125299 * r125300;
        double r125302 = r125297 + r125301;
        return r125302;
}
↓
double f(double x, double y, double z) {
        double r125303 = x;
        double r125304 = y;
        double r125305 = 1.0;
        double r125306 = r125303 - r125305;
        double r125307 = z;
        double r125308 = r125306 * r125307;
        double r125309 = fma(r125303, r125304, r125308);
        return r125309;
}

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 2020024 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1) z)))