Average Error: 0.0 → 0.0
Time: 9.3s
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 r127044 = x;
        double r127045 = y;
        double r127046 = r127044 * r127045;
        double r127047 = 1.0;
        double r127048 = r127044 - r127047;
        double r127049 = z;
        double r127050 = r127048 * r127049;
        double r127051 = r127046 + r127050;
        return r127051;
}
↓
double f(double x, double y, double z) {
        double r127052 = x;
        double r127053 = y;
        double r127054 = 1.0;
        double r127055 = r127052 - r127054;
        double r127056 = z;
        double r127057 = r127055 * r127056;
        double r127058 = fma(r127052, r127053, r127057);
        return r127058;
}

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 2019323 +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)))