Average Error: 0.1 → 0.1
Time: 13.2s
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 r61240 = x;
        double r61241 = y;
        double r61242 = r61240 + r61241;
        double r61243 = z;
        double r61244 = r61242 - r61243;
        double r61245 = t;
        double r61246 = 2.0;
        double r61247 = r61245 * r61246;
        double r61248 = r61244 / r61247;
        return r61248;
}
↓
double f(double x, double y, double z, double t) {
        double r61249 = 0.5;
        double r61250 = y;
        double r61251 = t;
        double r61252 = r61250 / r61251;
        double r61253 = x;
        double r61254 = r61253 / r61251;
        double r61255 = r61252 + r61254;
        double r61256 = z;
        double r61257 = r61256 / r61251;
        double r61258 = r61255 - r61257;
        double r61259 = r61249 * r61258;
        return r61259;
}

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