Average Error: 0.0 → 0.0
Time: 3.9s
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 r164749 = x;
        double r164750 = y;
        double r164751 = r164749 * r164750;
        double r164752 = 1.0;
        double r164753 = r164749 - r164752;
        double r164754 = z;
        double r164755 = r164753 * r164754;
        double r164756 = r164751 + r164755;
        return r164756;
}
↓
double f(double x, double y, double z) {
        double r164757 = x;
        double r164758 = y;
        double r164759 = 1.0;
        double r164760 = r164757 - r164759;
        double r164761 = z;
        double r164762 = r164760 * r164761;
        double r164763 = fma(r164757, r164758, r164762);
        return r164763;
}

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 2020033 +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)))