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 r38671 = x;
        double r38672 = y;
        double r38673 = r38671 + r38672;
        double r38674 = z;
        double r38675 = r38673 - r38674;
        double r38676 = t;
        double r38677 = 2.0;
        double r38678 = r38676 * r38677;
        double r38679 = r38675 / r38678;
        return r38679;
}
↓
double f(double x, double y, double z, double t) {
        double r38680 = 0.5;
        double r38681 = y;
        double r38682 = t;
        double r38683 = r38681 / r38682;
        double r38684 = x;
        double r38685 = r38684 / r38682;
        double r38686 = r38683 + r38685;
        double r38687 = z;
        double r38688 = r38687 / r38682;
        double r38689 = r38686 - r38688;
        double r38690 = r38680 * r38689;
        return r38690;
}

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 2020020 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2)))