Average Error: 0.1 → 0.1
Time: 14.2s
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 r38884 = x;
        double r38885 = y;
        double r38886 = r38884 + r38885;
        double r38887 = z;
        double r38888 = r38886 - r38887;
        double r38889 = t;
        double r38890 = 2.0;
        double r38891 = r38889 * r38890;
        double r38892 = r38888 / r38891;
        return r38892;
}
↓
double f(double x, double y, double z, double t) {
        double r38893 = 0.5;
        double r38894 = y;
        double r38895 = t;
        double r38896 = r38894 / r38895;
        double r38897 = x;
        double r38898 = r38897 / r38895;
        double r38899 = r38896 + r38898;
        double r38900 = z;
        double r38901 = r38900 / r38895;
        double r38902 = r38899 - r38901;
        double r38903 = r38893 * r38902;
        return r38903;
}

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 2019303 +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)))