Average Error: 0.1 → 0.1
Time: 2.5s
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 r46387 = x;
        double r46388 = y;
        double r46389 = r46387 + r46388;
        double r46390 = z;
        double r46391 = r46389 - r46390;
        double r46392 = t;
        double r46393 = 2.0;
        double r46394 = r46392 * r46393;
        double r46395 = r46391 / r46394;
        return r46395;
}
↓
double f(double x, double y, double z, double t) {
        double r46396 = 0.5;
        double r46397 = y;
        double r46398 = t;
        double r46399 = r46397 / r46398;
        double r46400 = x;
        double r46401 = r46400 / r46398;
        double r46402 = r46399 + r46401;
        double r46403 = z;
        double r46404 = r46403 / r46398;
        double r46405 = r46402 - r46404;
        double r46406 = r46396 * r46405;
        return r46406;
}

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 2019322 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2)))