Average Error: 0.1 → 0.1
Time: 14.4s
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 r59364 = x;
        double r59365 = y;
        double r59366 = r59364 + r59365;
        double r59367 = z;
        double r59368 = r59366 - r59367;
        double r59369 = t;
        double r59370 = 2.0;
        double r59371 = r59369 * r59370;
        double r59372 = r59368 / r59371;
        return r59372;
}
↓
double f(double x, double y, double z, double t) {
        double r59373 = 0.5;
        double r59374 = y;
        double r59375 = t;
        double r59376 = r59374 / r59375;
        double r59377 = x;
        double r59378 = r59377 / r59375;
        double r59379 = r59376 + r59378;
        double r59380 = z;
        double r59381 = r59380 / r59375;
        double r59382 = r59379 - r59381;
        double r59383 = r59373 * r59382;
        return r59383;
}

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 2019303 +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)))