Average Error: 0.1 → 0.1
Time: 8.8s
Precision: 64
\[\frac{\left(x + y\right) - z}{t \cdot 2}\]
↓
\[0.5 \cdot \left(\left(\frac{y}{t} + \frac{x}{t}\right) - \frac{z}{t}\right)\]
\frac{\left(x + y\right) - z}{t \cdot 2}
↓
0.5 \cdot \left(\left(\frac{y}{t} + \frac{x}{t}\right) - \frac{z}{t}\right)
double f(double x, double y, double z, double t) {
        double r31861 = x;
        double r31862 = y;
        double r31863 = r31861 + r31862;
        double r31864 = z;
        double r31865 = r31863 - r31864;
        double r31866 = t;
        double r31867 = 2.0;
        double r31868 = r31866 * r31867;
        double r31869 = r31865 / r31868;
        return r31869;
}
↓
double f(double x, double y, double z, double t) {
        double r31870 = 0.5;
        double r31871 = y;
        double r31872 = t;
        double r31873 = r31871 / r31872;
        double r31874 = x;
        double r31875 = r31874 / r31872;
        double r31876 = r31873 + r31875;
        double r31877 = z;
        double r31878 = r31877 / r31872;
        double r31879 = r31876 - r31878;
        double r31880 = r31870 * r31879;
        return r31880;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\frac{\left(x + y\right) - z}{t \cdot 2}\]

  2. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{\left(0.5 \cdot \frac{y}{t} + 0.5 \cdot \frac{x}{t}\right) - 0.5 \cdot \frac{z}{t}}\]

  3. Simplified0.1

    \[\leadsto \color{blue}{0.5 \cdot \left(\left(\frac{y}{t} + \frac{x}{t}\right) - \frac{z}{t}\right)}\]

  4. Final simplification0.1

    \[\leadsto 0.5 \cdot \left(\left(\frac{y}{t} + \frac{x}{t}\right) - \frac{z}{t}\right)\]

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2)))