Average Error: 0.0 → 0.1
Time: 37.6s
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 r2701980 = x;
        double r2701981 = y;
        double r2701982 = r2701980 + r2701981;
        double r2701983 = z;
        double r2701984 = r2701982 - r2701983;
        double r2701985 = t;
        double r2701986 = 2.0;
        double r2701987 = r2701985 * r2701986;
        double r2701988 = r2701984 / r2701987;
        return r2701988;
}
↓
double f(double x, double y, double z, double t) {
        double r2701989 = y;
        double r2701990 = t;
        double r2701991 = r2701989 / r2701990;
        double r2701992 = x;
        double r2701993 = r2701992 / r2701990;
        double r2701994 = z;
        double r2701995 = r2701994 / r2701990;
        double r2701996 = r2701993 - r2701995;
        double r2701997 = r2701991 + r2701996;
        double r2701998 = 0.5;
        double r2701999 = r2701997 * r2701998;
        return r2701999;
}

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

    \[\frac{\left(x + y\right) - z}{t \cdot 2}\]

  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

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

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