Average Error: 0.0 → 0.0
Time: 10.9s
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 r7325588 = x;
        double r7325589 = y;
        double r7325590 = r7325588 * r7325589;
        double r7325591 = 1.0;
        double r7325592 = r7325588 - r7325591;
        double r7325593 = z;
        double r7325594 = r7325592 * r7325593;
        double r7325595 = r7325590 + r7325594;
        return r7325595;
}
↓
double f(double x, double y, double z) {
        double r7325596 = x;
        double r7325597 = y;
        double r7325598 = 1.0;
        double r7325599 = r7325596 - r7325598;
        double r7325600 = z;
        double r7325601 = r7325599 * r7325600;
        double r7325602 = fma(r7325596, r7325597, r7325601);
        return r7325602;
}

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 2019158 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  (+ (* x y) (* (- x 1.0) z)))