Average Error: 0.1 → 0.1
Time: 15.8s
Precision: 64
\[\frac{\left(x + y\right) - z}{t \cdot 2}\]
↓
\[0.5 \cdot \left(\left(\frac{y}{t} - \frac{z}{t}\right) + \frac{x}{t}\right)\]
\frac{\left(x + y\right) - z}{t \cdot 2}
↓
0.5 \cdot \left(\left(\frac{y}{t} - \frac{z}{t}\right) + \frac{x}{t}\right)
double f(double x, double y, double z, double t) {
        double r2512182 = x;
        double r2512183 = y;
        double r2512184 = r2512182 + r2512183;
        double r2512185 = z;
        double r2512186 = r2512184 - r2512185;
        double r2512187 = t;
        double r2512188 = 2.0;
        double r2512189 = r2512187 * r2512188;
        double r2512190 = r2512186 / r2512189;
        return r2512190;
}
↓
double f(double x, double y, double z, double t) {
        double r2512191 = 0.5;
        double r2512192 = y;
        double r2512193 = t;
        double r2512194 = r2512192 / r2512193;
        double r2512195 = z;
        double r2512196 = r2512195 / r2512193;
        double r2512197 = r2512194 - r2512196;
        double r2512198 = x;
        double r2512199 = r2512198 / r2512193;
        double r2512200 = r2512197 + r2512199;
        double r2512201 = r2512191 * r2512200;
        return r2512201;
}

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

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  (/ (- (+ x y) z) (* t 2.0)))