Average Error: 0.0 → 0.1
Time: 2.0s
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 r42877 = x;
        double r42878 = y;
        double r42879 = r42877 + r42878;
        double r42880 = z;
        double r42881 = r42879 - r42880;
        double r42882 = t;
        double r42883 = 2.0;
        double r42884 = r42882 * r42883;
        double r42885 = r42881 / r42884;
        return r42885;
}
↓
double f(double x, double y, double z, double t) {
        double r42886 = 0.5;
        double r42887 = y;
        double r42888 = t;
        double r42889 = r42887 / r42888;
        double r42890 = x;
        double r42891 = r42890 / r42888;
        double r42892 = r42889 + r42891;
        double r42893 = z;
        double r42894 = r42893 / r42888;
        double r42895 = r42892 - r42894;
        double r42896 = r42886 * r42895;
        return r42896;
}

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 0.0

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

  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 2020036 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2)))