Average Error: 0.1 → 0.1
Time: 2.0s
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 r52482 = x;
        double r52483 = y;
        double r52484 = r52482 + r52483;
        double r52485 = z;
        double r52486 = r52484 - r52485;
        double r52487 = t;
        double r52488 = 2.0;
        double r52489 = r52487 * r52488;
        double r52490 = r52486 / r52489;
        return r52490;
}
↓
double f(double x, double y, double z, double t) {
        double r52491 = 0.5;
        double r52492 = y;
        double r52493 = t;
        double r52494 = r52492 / r52493;
        double r52495 = x;
        double r52496 = r52495 / r52493;
        double r52497 = r52494 + r52496;
        double r52498 = z;
        double r52499 = r52498 / r52493;
        double r52500 = r52497 - r52499;
        double r52501 = r52491 * r52500;
        return r52501;
}

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