Average Error: 0.1 → 0.0
Time: 11.2s
Precision: 64
\[\frac{\left(x + y\right) - z}{t \cdot 2.0}\]
↓
\[0.5 \cdot \left(\left(\frac{y}{t} + \frac{x}{t}\right) - \frac{z}{t}\right)\]
\frac{\left(x + y\right) - z}{t \cdot 2.0}
↓
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 r2272188 = x;
        double r2272189 = y;
        double r2272190 = r2272188 + r2272189;
        double r2272191 = z;
        double r2272192 = r2272190 - r2272191;
        double r2272193 = t;
        double r2272194 = 2.0;
        double r2272195 = r2272193 * r2272194;
        double r2272196 = r2272192 / r2272195;
        return r2272196;
}
↓
double f(double x, double y, double z, double t) {
        double r2272197 = 0.5;
        double r2272198 = y;
        double r2272199 = t;
        double r2272200 = r2272198 / r2272199;
        double r2272201 = x;
        double r2272202 = r2272201 / r2272199;
        double r2272203 = r2272200 + r2272202;
        double r2272204 = z;
        double r2272205 = r2272204 / r2272199;
        double r2272206 = r2272203 - r2272205;
        double r2272207 = r2272197 * r2272206;
        return r2272207;
}

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

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

  4. Final simplification0.0

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

Reproduce

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