Average Error: 0.1 → 0.1
Time: 2.9s
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 r31173 = x;
        double r31174 = y;
        double r31175 = r31173 + r31174;
        double r31176 = z;
        double r31177 = r31175 - r31176;
        double r31178 = t;
        double r31179 = 2.0;
        double r31180 = r31178 * r31179;
        double r31181 = r31177 / r31180;
        return r31181;
}
↓
double f(double x, double y, double z, double t) {
        double r31182 = 0.5;
        double r31183 = y;
        double r31184 = t;
        double r31185 = r31183 / r31184;
        double r31186 = x;
        double r31187 = r31186 / r31184;
        double r31188 = r31185 + r31187;
        double r31189 = z;
        double r31190 = r31189 / r31184;
        double r31191 = r31188 - r31190;
        double r31192 = r31182 * r31191;
        return r31192;
}

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 +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)))