Average Error: 0.0 → 0.1
Time: 48.1s
Precision: 64
\[\frac{\left(x + y\right) - z}{t \cdot 2}\]
↓
\[0.5 \cdot \left(\frac{x}{t} + \left(\frac{y}{t} - \frac{z}{t}\right)\right)\]
\frac{\left(x + y\right) - z}{t \cdot 2}
↓
0.5 \cdot \left(\frac{x}{t} + \left(\frac{y}{t} - \frac{z}{t}\right)\right)
double f(double x, double y, double z, double t) {
        double r3235337 = x;
        double r3235338 = y;
        double r3235339 = r3235337 + r3235338;
        double r3235340 = z;
        double r3235341 = r3235339 - r3235340;
        double r3235342 = t;
        double r3235343 = 2.0;
        double r3235344 = r3235342 * r3235343;
        double r3235345 = r3235341 / r3235344;
        return r3235345;
}
↓
double f(double x, double y, double z, double t) {
        double r3235346 = 0.5;
        double r3235347 = x;
        double r3235348 = t;
        double r3235349 = r3235347 / r3235348;
        double r3235350 = y;
        double r3235351 = r3235350 / r3235348;
        double r3235352 = z;
        double r3235353 = r3235352 / r3235348;
        double r3235354 = r3235351 - r3235353;
        double r3235355 = r3235349 + r3235354;
        double r3235356 = r3235346 * r3235355;
        return r3235356;
}

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

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  (/ (- (+ x y) z) (* t 2.0)))