Average Error: 0.1 → 0.1
Time: 15.3s
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 r8098314 = x;
        double r8098315 = y;
        double r8098316 = r8098314 + r8098315;
        double r8098317 = z;
        double r8098318 = r8098316 - r8098317;
        double r8098319 = t;
        double r8098320 = 2.0;
        double r8098321 = r8098319 * r8098320;
        double r8098322 = r8098318 / r8098321;
        return r8098322;
}
↓
double f(double x, double y, double z, double t) {
        double r8098323 = 0.5;
        double r8098324 = y;
        double r8098325 = t;
        double r8098326 = r8098324 / r8098325;
        double r8098327 = x;
        double r8098328 = r8098327 / r8098325;
        double r8098329 = r8098326 + r8098328;
        double r8098330 = z;
        double r8098331 = r8098330 / r8098325;
        double r8098332 = r8098329 - r8098331;
        double r8098333 = r8098323 * r8098332;
        return r8098333;
}

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 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  (/ (- (+ x y) z) (* t 2.0)))