Average Error: 0.1 → 0.0
Time: 18.2s
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 r2415367 = x;
        double r2415368 = y;
        double r2415369 = r2415367 + r2415368;
        double r2415370 = z;
        double r2415371 = r2415369 - r2415370;
        double r2415372 = t;
        double r2415373 = 2.0;
        double r2415374 = r2415372 * r2415373;
        double r2415375 = r2415371 / r2415374;
        return r2415375;
}
↓
double f(double x, double y, double z, double t) {
        double r2415376 = 0.5;
        double r2415377 = x;
        double r2415378 = t;
        double r2415379 = r2415377 / r2415378;
        double r2415380 = z;
        double r2415381 = r2415380 / r2415378;
        double r2415382 = r2415379 - r2415381;
        double r2415383 = y;
        double r2415384 = r2415383 / r2415378;
        double r2415385 = r2415382 + r2415384;
        double r2415386 = r2415376 * r2415385;
        return r2415386;
}

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)))