Average Error: 0.1 → 0.1
Time: 2.6s
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 r37076 = x;
        double r37077 = y;
        double r37078 = r37076 + r37077;
        double r37079 = z;
        double r37080 = r37078 - r37079;
        double r37081 = t;
        double r37082 = 2.0;
        double r37083 = r37081 * r37082;
        double r37084 = r37080 / r37083;
        return r37084;
}
↓
double f(double x, double y, double z, double t) {
        double r37085 = 0.5;
        double r37086 = y;
        double r37087 = t;
        double r37088 = r37086 / r37087;
        double r37089 = x;
        double r37090 = r37089 / r37087;
        double r37091 = r37088 + r37090;
        double r37092 = z;
        double r37093 = r37092 / r37087;
        double r37094 = r37091 - r37093;
        double r37095 = r37085 * r37094;
        return r37095;
}

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 2020001 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2)))