Average Error: 0.0 → 0.0
Time: 9.4s
Precision: 64
\[x \cdot y + \left(x - 1.0\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, y, \left(x - 1.0\right) \cdot z\right)\]
x \cdot y + \left(x - 1.0\right) \cdot z
↓
\mathsf{fma}\left(x, y, \left(x - 1.0\right) \cdot z\right)
double f(double x, double y, double z) {
        double r7852165 = x;
        double r7852166 = y;
        double r7852167 = r7852165 * r7852166;
        double r7852168 = 1.0;
        double r7852169 = r7852165 - r7852168;
        double r7852170 = z;
        double r7852171 = r7852169 * r7852170;
        double r7852172 = r7852167 + r7852171;
        return r7852172;
}
↓
double f(double x, double y, double z) {
        double r7852173 = x;
        double r7852174 = y;
        double r7852175 = 1.0;
        double r7852176 = r7852173 - r7852175;
        double r7852177 = z;
        double r7852178 = r7852176 * r7852177;
        double r7852179 = fma(r7852173, r7852174, r7852178);
        return r7852179;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x \cdot y + \left(x - 1.0\right) \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \left(x - 1.0\right) \cdot z\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, \left(x - 1.0\right) \cdot z\right)\]

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  (+ (* x y) (* (- x 1.0) z)))