Average Error: 0.1 → 0.1
Time: 16.8s
Precision: 64
\[\frac{\left(x + y\right) - z}{t \cdot 2}\]
↓
\[\left(\frac{y}{t} + \left(\frac{x}{t} - \frac{z}{t}\right)\right) \cdot 0.5\]
\frac{\left(x + y\right) - z}{t \cdot 2}
↓
\left(\frac{y}{t} + \left(\frac{x}{t} - \frac{z}{t}\right)\right) \cdot 0.5
double f(double x, double y, double z, double t) {
        double r2434692 = x;
        double r2434693 = y;
        double r2434694 = r2434692 + r2434693;
        double r2434695 = z;
        double r2434696 = r2434694 - r2434695;
        double r2434697 = t;
        double r2434698 = 2.0;
        double r2434699 = r2434697 * r2434698;
        double r2434700 = r2434696 / r2434699;
        return r2434700;
}
↓
double f(double x, double y, double z, double t) {
        double r2434701 = y;
        double r2434702 = t;
        double r2434703 = r2434701 / r2434702;
        double r2434704 = x;
        double r2434705 = r2434704 / r2434702;
        double r2434706 = z;
        double r2434707 = r2434706 / r2434702;
        double r2434708 = r2434705 - r2434707;
        double r2434709 = r2434703 + r2434708;
        double r2434710 = 0.5;
        double r2434711 = r2434709 * r2434710;
        return r2434711;
}

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

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019192 +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)))