Average Error: 0.0 → 0.3
Time: 12.5s
Precision: 64
\[\frac{\left(x + y\right) - z}{t \cdot 2}\]
↓
\[\frac{0.5}{t} \cdot \left(y + \left(x - z\right)\right)\]
\frac{\left(x + y\right) - z}{t \cdot 2}
↓
\frac{0.5}{t} \cdot \left(y + \left(x - z\right)\right)
double f(double x, double y, double z, double t) {
        double r48258 = x;
        double r48259 = y;
        double r48260 = r48258 + r48259;
        double r48261 = z;
        double r48262 = r48260 - r48261;
        double r48263 = t;
        double r48264 = 2.0;
        double r48265 = r48263 * r48264;
        double r48266 = r48262 / r48265;
        return r48266;
}
↓
double f(double x, double y, double z, double t) {
        double r48267 = 0.5;
        double r48268 = t;
        double r48269 = r48267 / r48268;
        double r48270 = y;
        double r48271 = x;
        double r48272 = z;
        double r48273 = r48271 - r48272;
        double r48274 = r48270 + r48273;
        double r48275 = r48269 * r48274;
        return r48275;
}

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 simplification0.3

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

Reproduce

herbie shell --seed 2019297 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2)))