Average Error: 0.0 → 0.0
Time: 16.1s
Precision: 64
\[\frac{\left(x + y\right) - z}{t \cdot 2.0}\]
↓
\[\left(\frac{y}{t} + \left(\frac{x}{t} - \frac{z}{t}\right)\right) \cdot 0.5\]
\frac{\left(x + y\right) - z}{t \cdot 2.0}
↓
\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 r2555840 = x;
        double r2555841 = y;
        double r2555842 = r2555840 + r2555841;
        double r2555843 = z;
        double r2555844 = r2555842 - r2555843;
        double r2555845 = t;
        double r2555846 = 2.0;
        double r2555847 = r2555845 * r2555846;
        double r2555848 = r2555844 / r2555847;
        return r2555848;
}
↓
double f(double x, double y, double z, double t) {
        double r2555849 = y;
        double r2555850 = t;
        double r2555851 = r2555849 / r2555850;
        double r2555852 = x;
        double r2555853 = r2555852 / r2555850;
        double r2555854 = z;
        double r2555855 = r2555854 / r2555850;
        double r2555856 = r2555853 - r2555855;
        double r2555857 = r2555851 + r2555856;
        double r2555858 = 0.5;
        double r2555859 = r2555857 * r2555858;
        return r2555859;
}

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 0.0

    \[\frac{\left(x + y\right) - z}{t \cdot 2.0}\]

  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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  (/ (- (+ x y) z) (* t 2.0)))