Average Error: 0.1 → 0.1
Time: 2.0s
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 r56162 = x;
        double r56163 = y;
        double r56164 = r56162 + r56163;
        double r56165 = z;
        double r56166 = r56164 - r56165;
        double r56167 = t;
        double r56168 = 2.0;
        double r56169 = r56167 * r56168;
        double r56170 = r56166 / r56169;
        return r56170;
}
↓
double f(double x, double y, double z, double t) {
        double r56171 = 0.5;
        double r56172 = y;
        double r56173 = t;
        double r56174 = r56172 / r56173;
        double r56175 = x;
        double r56176 = r56175 / r56173;
        double r56177 = r56174 + r56176;
        double r56178 = z;
        double r56179 = r56178 / r56173;
        double r56180 = r56177 - r56179;
        double r56181 = r56171 * r56180;
        return r56181;
}

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 2019353 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2)))