Average Error: 0.1 → 0.1
Time: 9.9s
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 r40109 = x;
        double r40110 = y;
        double r40111 = r40109 + r40110;
        double r40112 = z;
        double r40113 = r40111 - r40112;
        double r40114 = t;
        double r40115 = 2.0;
        double r40116 = r40114 * r40115;
        double r40117 = r40113 / r40116;
        return r40117;
}
↓
double f(double x, double y, double z, double t) {
        double r40118 = 0.5;
        double r40119 = y;
        double r40120 = t;
        double r40121 = r40119 / r40120;
        double r40122 = x;
        double r40123 = r40122 / r40120;
        double r40124 = r40121 + r40123;
        double r40125 = z;
        double r40126 = r40125 / r40120;
        double r40127 = r40124 - r40126;
        double r40128 = r40118 * r40127;
        return r40128;
}

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