Average Error: 0.1 → 0.0
Time: 16.6s
Precision: 64
\[\frac{\left(x + y\right) - z}{t \cdot 2.0}\]
↓
\[\left(\frac{y}{t} + \left(\frac{x}{t} - \frac{z}{t}\right)\right) \cdot 0.5\]
\frac{\left(x + y\right) - z}{t \cdot 2.0}
↓
\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 r2582636 = x;
        double r2582637 = y;
        double r2582638 = r2582636 + r2582637;
        double r2582639 = z;
        double r2582640 = r2582638 - r2582639;
        double r2582641 = t;
        double r2582642 = 2.0;
        double r2582643 = r2582641 * r2582642;
        double r2582644 = r2582640 / r2582643;
        return r2582644;
}
↓
double f(double x, double y, double z, double t) {
        double r2582645 = y;
        double r2582646 = t;
        double r2582647 = r2582645 / r2582646;
        double r2582648 = x;
        double r2582649 = r2582648 / r2582646;
        double r2582650 = z;
        double r2582651 = r2582650 / r2582646;
        double r2582652 = r2582649 - r2582651;
        double r2582653 = r2582647 + r2582652;
        double r2582654 = 0.5;
        double r2582655 = r2582653 * r2582654;
        return r2582655;
}

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

    \[\frac{\left(x + y\right) - z}{t \cdot 2.0}\]

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  (/ (- (+ x y) z) (* t 2.0)))