Average Error: 0.1 → 0.1
Time: 3.1s
Precision: 64
\[\frac{\left(x + y\right) - z}{t \cdot 2}\]
↓
\[\frac{\frac{x + y}{t} - \frac{z}{t}}{2}\]
\frac{\left(x + y\right) - z}{t \cdot 2}
↓
\frac{\frac{x + y}{t} - \frac{z}{t}}{2}
double f(double x, double y, double z, double t) {
        double r42990 = x;
        double r42991 = y;
        double r42992 = r42990 + r42991;
        double r42993 = z;
        double r42994 = r42992 - r42993;
        double r42995 = t;
        double r42996 = 2.0;
        double r42997 = r42995 * r42996;
        double r42998 = r42994 / r42997;
        return r42998;
}
↓
double f(double x, double y, double z, double t) {
        double r42999 = x;
        double r43000 = y;
        double r43001 = r42999 + r43000;
        double r43002 = t;
        double r43003 = r43001 / r43002;
        double r43004 = z;
        double r43005 = r43004 / r43002;
        double r43006 = r43003 - r43005;
        double r43007 = 2.0;
        double r43008 = r43006 / r43007;
        return r43008;
}

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. Using strategy rm

  3. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{\left(x + y\right) - z}{t}}{2}}\]
  4. Using strategy rm

  5. Applied div-sub0.1

    \[\leadsto \frac{\color{blue}{\frac{x + y}{t} - \frac{z}{t}}}{2}\]

  6. Final simplification0.1

    \[\leadsto \frac{\frac{x + y}{t} - \frac{z}{t}}{2}\]

Reproduce

herbie shell --seed 1978988140 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2)))