Average Error: 0.1 → 0.1
Time: 2.8s
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 r32423 = x;
        double r32424 = y;
        double r32425 = r32423 + r32424;
        double r32426 = z;
        double r32427 = r32425 - r32426;
        double r32428 = t;
        double r32429 = 2.0;
        double r32430 = r32428 * r32429;
        double r32431 = r32427 / r32430;
        return r32431;
}
↓
double f(double x, double y, double z, double t) {
        double r32432 = 0.5;
        double r32433 = y;
        double r32434 = t;
        double r32435 = r32433 / r32434;
        double r32436 = x;
        double r32437 = r32436 / r32434;
        double r32438 = r32435 + r32437;
        double r32439 = z;
        double r32440 = r32439 / r32434;
        double r32441 = r32438 - r32440;
        double r32442 = r32432 * r32441;
        return r32442;
}

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 2020083 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2)))