Average Error: 0.0 → 0.1
Time: 59.9s
Precision: 64
\[\frac{\left(x + y\right) - z}{t \cdot 2}\]
↓
\[0.5 \cdot \left(\frac{x}{t} + \left(\frac{y}{t} - \frac{z}{t}\right)\right)\]
\frac{\left(x + y\right) - z}{t \cdot 2}
↓
0.5 \cdot \left(\frac{x}{t} + \left(\frac{y}{t} - \frac{z}{t}\right)\right)
double f(double x, double y, double z, double t) {
        double r3105987 = x;
        double r3105988 = y;
        double r3105989 = r3105987 + r3105988;
        double r3105990 = z;
        double r3105991 = r3105989 - r3105990;
        double r3105992 = t;
        double r3105993 = 2.0;
        double r3105994 = r3105992 * r3105993;
        double r3105995 = r3105991 / r3105994;
        return r3105995;
}
↓
double f(double x, double y, double z, double t) {
        double r3105996 = 0.5;
        double r3105997 = x;
        double r3105998 = t;
        double r3105999 = r3105997 / r3105998;
        double r3106000 = y;
        double r3106001 = r3106000 / r3105998;
        double r3106002 = z;
        double r3106003 = r3106002 / r3105998;
        double r3106004 = r3106001 - r3106003;
        double r3106005 = r3105999 + r3106004;
        double r3106006 = r3105996 * r3106005;
        return r3106006;
}

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. Using strategy rm

  3. Applied associate--l+0.0

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

  4. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{\left(0.5 \cdot \frac{y}{t} + 0.5 \cdot \frac{x}{t}\right) - 0.5 \cdot \frac{z}{t}}\]

  5. Simplified0.1

    \[\leadsto \color{blue}{\left(\frac{x}{t} + \left(\frac{y}{t} - \frac{z}{t}\right)\right) \cdot 0.5}\]

  6. Final simplification0.1

    \[\leadsto 0.5 \cdot \left(\frac{x}{t} + \left(\frac{y}{t} - \frac{z}{t}\right)\right)\]

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  (/ (- (+ x y) z) (* t 2.0)))