Average Error: 0.0 → 0.0
Time: 5.4s
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 r2305022 = x;
        double r2305023 = y;
        double r2305024 = r2305022 * r2305023;
        double r2305025 = 1.0;
        double r2305026 = r2305022 - r2305025;
        double r2305027 = z;
        double r2305028 = r2305026 * r2305027;
        double r2305029 = r2305024 + r2305028;
        return r2305029;
}
↓
double f(double x, double y, double z) {
        double r2305030 = x;
        double r2305031 = y;
        double r2305032 = 1.0;
        double r2305033 = r2305030 - r2305032;
        double r2305034 = z;
        double r2305035 = r2305033 * r2305034;
        double r2305036 = fma(r2305030, r2305031, r2305035);
        return r2305036;
}

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 2019156 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  (+ (* x y) (* (- x 1.0) z)))