Average Error: 0.1 → 0.1
Time: 9.2s
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 r78163 = x;
        double r78164 = y;
        double r78165 = r78163 + r78164;
        double r78166 = z;
        double r78167 = r78165 - r78166;
        double r78168 = t;
        double r78169 = 2.0;
        double r78170 = r78168 * r78169;
        double r78171 = r78167 / r78170;
        return r78171;
}
↓
double f(double x, double y, double z, double t) {
        double r78172 = 0.5;
        double r78173 = y;
        double r78174 = t;
        double r78175 = r78173 / r78174;
        double r78176 = x;
        double r78177 = r78176 / r78174;
        double r78178 = r78175 + r78177;
        double r78179 = z;
        double r78180 = r78179 / r78174;
        double r78181 = r78178 - r78180;
        double r78182 = r78172 * r78181;
        return r78182;
}

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 2020042 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2)))