Average Error: 0.1 → 0.1
Time: 2.8s
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 r59735 = x;
        double r59736 = y;
        double r59737 = r59735 + r59736;
        double r59738 = z;
        double r59739 = r59737 - r59738;
        double r59740 = t;
        double r59741 = 2.0;
        double r59742 = r59740 * r59741;
        double r59743 = r59739 / r59742;
        return r59743;
}
↓
double f(double x, double y, double z, double t) {
        double r59744 = 0.5;
        double r59745 = y;
        double r59746 = t;
        double r59747 = r59745 / r59746;
        double r59748 = x;
        double r59749 = r59748 / r59746;
        double r59750 = r59747 + r59749;
        double r59751 = z;
        double r59752 = r59751 / r59746;
        double r59753 = r59750 - r59752;
        double r59754 = r59744 * r59753;
        return r59754;
}

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 2020065 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2)))