Average Error: 0.1 → 0.3
Time: 10.2s
Precision: 64
\[\frac{\left(x + y\right) - z}{t \cdot 2}\]
↓
\[\frac{\frac{1}{2}}{t} \cdot \left(y + \left(x - z\right)\right)\]
\frac{\left(x + y\right) - z}{t \cdot 2}
↓
\frac{\frac{1}{2}}{t} \cdot \left(y + \left(x - z\right)\right)
double f(double x, double y, double z, double t) {
        double r66150 = x;
        double r66151 = y;
        double r66152 = r66150 + r66151;
        double r66153 = z;
        double r66154 = r66152 - r66153;
        double r66155 = t;
        double r66156 = 2.0;
        double r66157 = r66155 * r66156;
        double r66158 = r66154 / r66157;
        return r66158;
}
↓
double f(double x, double y, double z, double t) {
        double r66159 = 1.0;
        double r66160 = 2.0;
        double r66161 = r66159 / r66160;
        double r66162 = t;
        double r66163 = r66161 / r66162;
        double r66164 = y;
        double r66165 = x;
        double r66166 = z;
        double r66167 = r66165 - r66166;
        double r66168 = r66164 + r66167;
        double r66169 = r66163 * r66168;
        return r66169;
}

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

    \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(\left(\frac{y}{t} + \frac{x}{t}\right) - \frac{z}{t}\right)}\]

  4. Final simplification0.3

    \[\leadsto \frac{\frac{1}{2}}{t} \cdot \left(y + \left(x - z\right)\right)\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2)))