Average Error: 0.1 → 0.1
Time: 11.1s
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 r36332 = x;
        double r36333 = y;
        double r36334 = r36332 + r36333;
        double r36335 = z;
        double r36336 = r36334 - r36335;
        double r36337 = t;
        double r36338 = 2.0;
        double r36339 = r36337 * r36338;
        double r36340 = r36336 / r36339;
        return r36340;
}
↓
double f(double x, double y, double z, double t) {
        double r36341 = 0.5;
        double r36342 = y;
        double r36343 = t;
        double r36344 = r36342 / r36343;
        double r36345 = x;
        double r36346 = r36345 / r36343;
        double r36347 = r36344 + r36346;
        double r36348 = z;
        double r36349 = r36348 / r36343;
        double r36350 = r36347 - r36349;
        double r36351 = r36341 * r36350;
        return r36351;
}

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 2020042 +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)))