Average Error: 0.1 → 0.1
Time: 8.3s
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 r22188 = x;
        double r22189 = y;
        double r22190 = r22188 + r22189;
        double r22191 = z;
        double r22192 = r22190 - r22191;
        double r22193 = t;
        double r22194 = 2.0;
        double r22195 = r22193 * r22194;
        double r22196 = r22192 / r22195;
        return r22196;
}
↓
double f(double x, double y, double z, double t) {
        double r22197 = 0.5;
        double r22198 = y;
        double r22199 = t;
        double r22200 = r22198 / r22199;
        double r22201 = x;
        double r22202 = r22201 / r22199;
        double r22203 = r22200 + r22202;
        double r22204 = z;
        double r22205 = r22204 / r22199;
        double r22206 = r22203 - r22205;
        double r22207 = r22197 * r22206;
        return r22207;
}

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 2019322 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2)))