Average Error: 0.1 → 0.1
Time: 13.2s
Precision: 64
\[\frac{\left(x + y\right) - z}{t \cdot 2}\]
↓
\[\left(\frac{x}{t} + \left(\frac{y}{t} - \frac{z}{t}\right)\right) \cdot 0.5\]
\frac{\left(x + y\right) - z}{t \cdot 2}
↓
\left(\frac{x}{t} + \left(\frac{y}{t} - \frac{z}{t}\right)\right) \cdot 0.5
double f(double x, double y, double z, double t) {
        double r3080897 = x;
        double r3080898 = y;
        double r3080899 = r3080897 + r3080898;
        double r3080900 = z;
        double r3080901 = r3080899 - r3080900;
        double r3080902 = t;
        double r3080903 = 2.0;
        double r3080904 = r3080902 * r3080903;
        double r3080905 = r3080901 / r3080904;
        return r3080905;
}
↓
double f(double x, double y, double z, double t) {
        double r3080906 = x;
        double r3080907 = t;
        double r3080908 = r3080906 / r3080907;
        double r3080909 = y;
        double r3080910 = r3080909 / r3080907;
        double r3080911 = z;
        double r3080912 = r3080911 / r3080907;
        double r3080913 = r3080910 - r3080912;
        double r3080914 = r3080908 + r3080913;
        double r3080915 = 0.5;
        double r3080916 = r3080914 * r3080915;
        return r3080916;
}

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. Using strategy rm

  3. Applied associate-/r*0.1

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

  4. Taylor expanded around 0 0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  (/ (- (+ x y) z) (* t 2.0)))