Average Error: 0.1 → 0.1
Time: 15.2s
Precision: 64
\[\frac{\left(x + y\right) - z}{t \cdot 2}\]
↓
\[\left(\left(\frac{x}{t} + \frac{y}{t}\right) - \frac{z}{t}\right) \cdot 0.5\]
\frac{\left(x + y\right) - z}{t \cdot 2}
↓
\left(\left(\frac{x}{t} + \frac{y}{t}\right) - \frac{z}{t}\right) \cdot 0.5
double f(double x, double y, double z, double t) {
        double r2675034 = x;
        double r2675035 = y;
        double r2675036 = r2675034 + r2675035;
        double r2675037 = z;
        double r2675038 = r2675036 - r2675037;
        double r2675039 = t;
        double r2675040 = 2.0;
        double r2675041 = r2675039 * r2675040;
        double r2675042 = r2675038 / r2675041;
        return r2675042;
}
↓
double f(double x, double y, double z, double t) {
        double r2675043 = x;
        double r2675044 = t;
        double r2675045 = r2675043 / r2675044;
        double r2675046 = y;
        double r2675047 = r2675046 / r2675044;
        double r2675048 = r2675045 + r2675047;
        double r2675049 = z;
        double r2675050 = r2675049 / r2675044;
        double r2675051 = r2675048 - r2675050;
        double r2675052 = 0.5;
        double r2675053 = r2675051 * r2675052;
        return r2675053;
}

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. 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

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 +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)))