Average Error: 0.0 → 0.0
Time: 3.7s
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 r112044 = x;
        double r112045 = y;
        double r112046 = r112044 * r112045;
        double r112047 = 1.0;
        double r112048 = r112044 - r112047;
        double r112049 = z;
        double r112050 = r112048 * r112049;
        double r112051 = r112046 + r112050;
        return r112051;
}
↓
double f(double x, double y, double z) {
        double r112052 = x;
        double r112053 = y;
        double r112054 = 1.0;
        double r112055 = r112052 - r112054;
        double r112056 = z;
        double r112057 = r112055 * r112056;
        double r112058 = fma(r112052, r112053, r112057);
        return r112058;
}

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 2019322 +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)))