Average Error: 0.1 → 0.3
Time: 4.2s
Precision: 64
\[\frac{\left(x + y\right) - z}{t \cdot 2}\]
↓
\[\frac{0.5}{t} \cdot \left(y + \left(x - z\right)\right)\]
\frac{\left(x + y\right) - z}{t \cdot 2}
↓
\frac{0.5}{t} \cdot \left(y + \left(x - z\right)\right)
double f(double x, double y, double z, double t) {
        double r42056 = x;
        double r42057 = y;
        double r42058 = r42056 + r42057;
        double r42059 = z;
        double r42060 = r42058 - r42059;
        double r42061 = t;
        double r42062 = 2.0;
        double r42063 = r42061 * r42062;
        double r42064 = r42060 / r42063;
        return r42064;
}
↓
double f(double x, double y, double z, double t) {
        double r42065 = 0.5;
        double r42066 = t;
        double r42067 = r42065 / r42066;
        double r42068 = y;
        double r42069 = x;
        double r42070 = z;
        double r42071 = r42069 - r42070;
        double r42072 = r42068 + r42071;
        double r42073 = r42067 * r42072;
        return r42073;
}

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 simplification0.3

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

Reproduce

herbie shell --seed 2019308 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2)))