Average Error: 0.1 → 0.1
Time: 11.5s
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 r29809 = x;
        double r29810 = y;
        double r29811 = r29809 + r29810;
        double r29812 = z;
        double r29813 = r29811 - r29812;
        double r29814 = t;
        double r29815 = 2.0;
        double r29816 = r29814 * r29815;
        double r29817 = r29813 / r29816;
        return r29817;
}
↓
double f(double x, double y, double z, double t) {
        double r29818 = 0.5;
        double r29819 = y;
        double r29820 = t;
        double r29821 = r29819 / r29820;
        double r29822 = x;
        double r29823 = r29822 / r29820;
        double r29824 = r29821 + r29823;
        double r29825 = z;
        double r29826 = r29825 / r29820;
        double r29827 = r29824 - r29826;
        double r29828 = r29818 * r29827;
        return r29828;
}

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 2019235 +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)))