Average Error: 0.1 → 0.1
Time: 14.4s
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 r47279 = x;
        double r47280 = y;
        double r47281 = r47279 + r47280;
        double r47282 = z;
        double r47283 = r47281 - r47282;
        double r47284 = t;
        double r47285 = 2.0;
        double r47286 = r47284 * r47285;
        double r47287 = r47283 / r47286;
        return r47287;
}
↓
double f(double x, double y, double z, double t) {
        double r47288 = 0.5;
        double r47289 = y;
        double r47290 = t;
        double r47291 = r47289 / r47290;
        double r47292 = x;
        double r47293 = r47292 / r47290;
        double r47294 = r47291 + r47293;
        double r47295 = z;
        double r47296 = r47295 / r47290;
        double r47297 = r47294 - r47296;
        double r47298 = r47288 * r47297;
        return r47298;
}

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)))