Average Error: 0.1 → 0.1
Time: 1.9s
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 r35011 = x;
        double r35012 = y;
        double r35013 = r35011 + r35012;
        double r35014 = z;
        double r35015 = r35013 - r35014;
        double r35016 = t;
        double r35017 = 2.0;
        double r35018 = r35016 * r35017;
        double r35019 = r35015 / r35018;
        return r35019;
}
↓
double f(double x, double y, double z, double t) {
        double r35020 = 0.5;
        double r35021 = y;
        double r35022 = t;
        double r35023 = r35021 / r35022;
        double r35024 = x;
        double r35025 = r35024 / r35022;
        double r35026 = r35023 + r35025;
        double r35027 = z;
        double r35028 = r35027 / r35022;
        double r35029 = r35026 - r35028;
        double r35030 = r35020 * r35029;
        return r35030;
}

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 2020065 +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)))