Average Error: 0.1 → 0.1
Time: 2.1s
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 r43435 = x;
        double r43436 = y;
        double r43437 = r43435 + r43436;
        double r43438 = z;
        double r43439 = r43437 - r43438;
        double r43440 = t;
        double r43441 = 2.0;
        double r43442 = r43440 * r43441;
        double r43443 = r43439 / r43442;
        return r43443;
}
↓
double f(double x, double y, double z, double t) {
        double r43444 = 0.5;
        double r43445 = y;
        double r43446 = t;
        double r43447 = r43445 / r43446;
        double r43448 = x;
        double r43449 = r43448 / r43446;
        double r43450 = r43447 + r43449;
        double r43451 = z;
        double r43452 = r43451 / r43446;
        double r43453 = r43450 - r43452;
        double r43454 = r43444 * r43453;
        return r43454;
}

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 2019353 +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)))