Average Error: 0.1 → 0.1
Time: 3.4s
Precision: 64
\[\frac{\left(x + y\right) - z}{t \cdot 2}\]
↓
\[0.5 \cdot \left(\left(\frac{y}{t} + \frac{x}{t}\right) - \frac{z}{t}\right)\]
\frac{\left(x + y\right) - z}{t \cdot 2}
↓
0.5 \cdot \left(\left(\frac{y}{t} + \frac{x}{t}\right) - \frac{z}{t}\right)
double f(double x, double y, double z, double t) {
        double r32732 = x;
        double r32733 = y;
        double r32734 = r32732 + r32733;
        double r32735 = z;
        double r32736 = r32734 - r32735;
        double r32737 = t;
        double r32738 = 2.0;
        double r32739 = r32737 * r32738;
        double r32740 = r32736 / r32739;
        return r32740;
}
↓
double f(double x, double y, double z, double t) {
        double r32741 = 0.5;
        double r32742 = y;
        double r32743 = t;
        double r32744 = r32742 / r32743;
        double r32745 = x;
        double r32746 = r32745 / r32743;
        double r32747 = r32744 + r32746;
        double r32748 = z;
        double r32749 = r32748 / r32743;
        double r32750 = r32747 - r32749;
        double r32751 = r32741 * r32750;
        return r32751;
}

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 simplification0.1

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

Reproduce

herbie shell --seed 2020083 +o rules:numerics
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2)))