Average Error: 0.0 → 0.1
Time: 2.4s
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 r48343 = x;
        double r48344 = y;
        double r48345 = r48343 + r48344;
        double r48346 = z;
        double r48347 = r48345 - r48346;
        double r48348 = t;
        double r48349 = 2.0;
        double r48350 = r48348 * r48349;
        double r48351 = r48347 / r48350;
        return r48351;
}
↓
double f(double x, double y, double z, double t) {
        double r48352 = 0.5;
        double r48353 = y;
        double r48354 = t;
        double r48355 = r48353 / r48354;
        double r48356 = x;
        double r48357 = r48356 / r48354;
        double r48358 = r48355 + r48357;
        double r48359 = z;
        double r48360 = r48359 / r48354;
        double r48361 = r48358 - r48360;
        double r48362 = r48352 * r48361;
        return r48362;
}

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 simplification0.1

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

Reproduce

herbie shell --seed 2020036 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2)))