Average Error: 0.1 → 0.1
Time: 2.3s
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 r31889 = x;
        double r31890 = y;
        double r31891 = r31889 + r31890;
        double r31892 = z;
        double r31893 = r31891 - r31892;
        double r31894 = t;
        double r31895 = 2.0;
        double r31896 = r31894 * r31895;
        double r31897 = r31893 / r31896;
        return r31897;
}
↓
double f(double x, double y, double z, double t) {
        double r31898 = 0.5;
        double r31899 = y;
        double r31900 = t;
        double r31901 = r31899 / r31900;
        double r31902 = x;
        double r31903 = r31902 / r31900;
        double r31904 = r31901 + r31903;
        double r31905 = z;
        double r31906 = r31905 / r31900;
        double r31907 = r31904 - r31906;
        double r31908 = r31898 * r31907;
        return r31908;
}

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 2019353 +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)))