Average Error: 0.0 → 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 r52548 = x;
        double r52549 = y;
        double r52550 = r52548 + r52549;
        double r52551 = z;
        double r52552 = r52550 - r52551;
        double r52553 = t;
        double r52554 = 2.0;
        double r52555 = r52553 * r52554;
        double r52556 = r52552 / r52555;
        return r52556;
}
↓
double f(double x, double y, double z, double t) {
        double r52557 = 0.5;
        double r52558 = y;
        double r52559 = t;
        double r52560 = r52558 / r52559;
        double r52561 = x;
        double r52562 = r52561 / r52559;
        double r52563 = r52560 + r52562;
        double r52564 = z;
        double r52565 = r52564 / r52559;
        double r52566 = r52563 - r52565;
        double r52567 = r52557 * r52566;
        return r52567;
}

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 0.0

    \[\frac{\left(x + y\right) - z}{t \cdot 2}\]

  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 2020036 +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)))