Average Error: 0.1 → 0.0
Time: 18.1s
Precision: 64
\[\frac{\left(x + y\right) - z}{t \cdot 2.0}\]
↓
\[0.5 \cdot \left(\left(\frac{x}{t} - \frac{z}{t}\right) + \frac{y}{t}\right)\]
\frac{\left(x + y\right) - z}{t \cdot 2.0}
↓
0.5 \cdot \left(\left(\frac{x}{t} - \frac{z}{t}\right) + \frac{y}{t}\right)
double f(double x, double y, double z, double t) {
        double r2227599 = x;
        double r2227600 = y;
        double r2227601 = r2227599 + r2227600;
        double r2227602 = z;
        double r2227603 = r2227601 - r2227602;
        double r2227604 = t;
        double r2227605 = 2.0;
        double r2227606 = r2227604 * r2227605;
        double r2227607 = r2227603 / r2227606;
        return r2227607;
}
↓
double f(double x, double y, double z, double t) {
        double r2227608 = 0.5;
        double r2227609 = x;
        double r2227610 = t;
        double r2227611 = r2227609 / r2227610;
        double r2227612 = z;
        double r2227613 = r2227612 / r2227610;
        double r2227614 = r2227611 - r2227613;
        double r2227615 = y;
        double r2227616 = r2227615 / r2227610;
        double r2227617 = r2227614 + r2227616;
        double r2227618 = r2227608 * r2227617;
        return r2227618;
}

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

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

  4. Final simplification0.0

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

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)))