Average Error: 0.0 → 0.1
Time: 37.1s
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 r46080 = x;
        double r46081 = y;
        double r46082 = r46080 + r46081;
        double r46083 = z;
        double r46084 = r46082 - r46083;
        double r46085 = t;
        double r46086 = 2.0;
        double r46087 = r46085 * r46086;
        double r46088 = r46084 / r46087;
        return r46088;
}
↓
double f(double x, double y, double z, double t) {
        double r46089 = 0.5;
        double r46090 = y;
        double r46091 = t;
        double r46092 = r46090 / r46091;
        double r46093 = x;
        double r46094 = r46093 / r46091;
        double r46095 = r46092 + r46094;
        double r46096 = z;
        double r46097 = r46096 / r46091;
        double r46098 = r46095 - r46097;
        double r46099 = r46089 * r46098;
        return r46099;
}

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 0.0

    \[\frac{\left(x + y\right) - z}{t \cdot 2}\]

  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 2019200 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  (/ (- (+ x y) z) (* t 2)))