Average Error: 0.1 → 0.0
Time: 12.3s
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 r2168514 = x;
        double r2168515 = y;
        double r2168516 = r2168514 + r2168515;
        double r2168517 = z;
        double r2168518 = r2168516 - r2168517;
        double r2168519 = t;
        double r2168520 = 2.0;
        double r2168521 = r2168519 * r2168520;
        double r2168522 = r2168518 / r2168521;
        return r2168522;
}
↓
double f(double x, double y, double z, double t) {
        double r2168523 = 0.5;
        double r2168524 = y;
        double r2168525 = t;
        double r2168526 = r2168524 / r2168525;
        double r2168527 = x;
        double r2168528 = r2168527 / r2168525;
        double r2168529 = r2168526 + r2168528;
        double r2168530 = z;
        double r2168531 = r2168530 / r2168525;
        double r2168532 = r2168529 - r2168531;
        double r2168533 = r2168523 * r2168532;
        return r2168533;
}

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)))