Average Error: 0.1 → 0.1
Time: 16.9s
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 r8123369 = x;
        double r8123370 = y;
        double r8123371 = r8123369 + r8123370;
        double r8123372 = z;
        double r8123373 = r8123371 - r8123372;
        double r8123374 = t;
        double r8123375 = 2.0;
        double r8123376 = r8123374 * r8123375;
        double r8123377 = r8123373 / r8123376;
        return r8123377;
}
↓
double f(double x, double y, double z, double t) {
        double r8123378 = 0.5;
        double r8123379 = y;
        double r8123380 = t;
        double r8123381 = r8123379 / r8123380;
        double r8123382 = x;
        double r8123383 = r8123382 / r8123380;
        double r8123384 = r8123381 + r8123383;
        double r8123385 = z;
        double r8123386 = r8123385 / r8123380;
        double r8123387 = r8123384 - r8123386;
        double r8123388 = r8123378 * r8123387;
        return r8123388;
}

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 2019173 +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)))