Average Error: 0.0 → 0.1
Time: 53.4s
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 r45375 = x;
        double r45376 = y;
        double r45377 = r45375 + r45376;
        double r45378 = z;
        double r45379 = r45377 - r45378;
        double r45380 = t;
        double r45381 = 2.0;
        double r45382 = r45380 * r45381;
        double r45383 = r45379 / r45382;
        return r45383;
}
↓
double f(double x, double y, double z, double t) {
        double r45384 = 0.5;
        double r45385 = y;
        double r45386 = t;
        double r45387 = r45385 / r45386;
        double r45388 = x;
        double r45389 = r45388 / r45386;
        double r45390 = r45387 + r45389;
        double r45391 = z;
        double r45392 = r45391 / r45386;
        double r45393 = r45390 - r45392;
        double r45394 = r45384 * r45393;
        return r45394;
}

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 2019200 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  (/ (- (+ x y) z) (* t 2)))