Average Error: 0.1 → 0.0
Time: 12.2s
Precision: 64
\[\frac{\left(x + y\right) - z}{t \cdot 2.0}\]
↓
\[0.5 \cdot \left(\left(\frac{y}{t} + \frac{x}{t}\right) - \frac{z}{t}\right)\]
\frac{\left(x + y\right) - z}{t \cdot 2.0}
↓
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 r2243277 = x;
        double r2243278 = y;
        double r2243279 = r2243277 + r2243278;
        double r2243280 = z;
        double r2243281 = r2243279 - r2243280;
        double r2243282 = t;
        double r2243283 = 2.0;
        double r2243284 = r2243282 * r2243283;
        double r2243285 = r2243281 / r2243284;
        return r2243285;
}
↓
double f(double x, double y, double z, double t) {
        double r2243286 = 0.5;
        double r2243287 = y;
        double r2243288 = t;
        double r2243289 = r2243287 / r2243288;
        double r2243290 = x;
        double r2243291 = r2243290 / r2243288;
        double r2243292 = r2243289 + r2243291;
        double r2243293 = z;
        double r2243294 = r2243293 / r2243288;
        double r2243295 = r2243292 - r2243294;
        double r2243296 = r2243286 * r2243295;
        return r2243296;
}

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

    \[\frac{\left(x + y\right) - z}{t \cdot 2.0}\]

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 +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)))