Average Error: 0.1 → 0.1
Time: 21.5s
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 r46413 = x;
        double r46414 = y;
        double r46415 = r46413 + r46414;
        double r46416 = z;
        double r46417 = r46415 - r46416;
        double r46418 = t;
        double r46419 = 2.0;
        double r46420 = r46418 * r46419;
        double r46421 = r46417 / r46420;
        return r46421;
}
↓
double f(double x, double y, double z, double t) {
        double r46422 = 0.5;
        double r46423 = y;
        double r46424 = t;
        double r46425 = r46423 / r46424;
        double r46426 = x;
        double r46427 = r46426 / r46424;
        double r46428 = r46425 + r46427;
        double r46429 = z;
        double r46430 = r46429 / r46424;
        double r46431 = r46428 - r46430;
        double r46432 = r46422 * r46431;
        return r46432;
}

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 2019199 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  (/ (- (+ x y) z) (* t 2.0)))