Average Error: 0.0 → 0.0
Time: 6.9s
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 r5678133 = x;
        double r5678134 = y;
        double r5678135 = r5678133 * r5678134;
        double r5678136 = 1.0;
        double r5678137 = r5678133 - r5678136;
        double r5678138 = z;
        double r5678139 = r5678137 * r5678138;
        double r5678140 = r5678135 + r5678139;
        return r5678140;
}
↓
double f(double x, double y, double z) {
        double r5678141 = x;
        double r5678142 = y;
        double r5678143 = 1.0;
        double r5678144 = r5678141 - r5678143;
        double r5678145 = z;
        double r5678146 = r5678144 * r5678145;
        double r5678147 = fma(r5678141, r5678142, r5678146);
        return r5678147;
}

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 2019169 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  (+ (* x y) (* (- x 1.0) z)))