Average Error: 0.0 → 0.0
Time: 3.7s
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 r50921 = x;
        double r50922 = y;
        double r50923 = r50921 + r50922;
        double r50924 = z;
        double r50925 = r50923 - r50924;
        double r50926 = t;
        double r50927 = 2.0;
        double r50928 = r50926 * r50927;
        double r50929 = r50925 / r50928;
        return r50929;
}
↓
double f(double x, double y, double z, double t) {
        double r50930 = 0.5;
        double r50931 = y;
        double r50932 = t;
        double r50933 = r50931 / r50932;
        double r50934 = x;
        double r50935 = r50934 / r50932;
        double r50936 = r50933 + r50935;
        double r50937 = z;
        double r50938 = r50937 / r50932;
        double r50939 = r50936 - r50938;
        double r50940 = r50930 * r50939;
        return r50940;
}

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 0.0

    \[\leadsto \color{blue}{\left(0.5 \cdot \frac{y}{t} + 0.5 \cdot \frac{x}{t}\right) - 0.5 \cdot \frac{z}{t}}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{0.5 \cdot \left(\left(\frac{y}{t} + \frac{x}{t}\right) - \frac{z}{t}\right)}\]

  4. Final simplification0.0

    \[\leadsto 0.5 \cdot \left(\left(\frac{y}{t} + \frac{x}{t}\right) - \frac{z}{t}\right)\]

Reproduce

herbie shell --seed 2019352 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2)))