Average Error: 0.1 → 0.1
Time: 17.4s
Precision: 64
\[\frac{\left(x + y\right) - z}{t \cdot 2}\]
↓
\[\left(\frac{y}{t} + \left(\frac{x}{t} - \frac{z}{t}\right)\right) \cdot 0.5\]
\frac{\left(x + y\right) - z}{t \cdot 2}
↓
\left(\frac{y}{t} + \left(\frac{x}{t} - \frac{z}{t}\right)\right) \cdot 0.5
double f(double x, double y, double z, double t) {
        double r2104461 = x;
        double r2104462 = y;
        double r2104463 = r2104461 + r2104462;
        double r2104464 = z;
        double r2104465 = r2104463 - r2104464;
        double r2104466 = t;
        double r2104467 = 2.0;
        double r2104468 = r2104466 * r2104467;
        double r2104469 = r2104465 / r2104468;
        return r2104469;
}
↓
double f(double x, double y, double z, double t) {
        double r2104470 = y;
        double r2104471 = t;
        double r2104472 = r2104470 / r2104471;
        double r2104473 = x;
        double r2104474 = r2104473 / r2104471;
        double r2104475 = z;
        double r2104476 = r2104475 / r2104471;
        double r2104477 = r2104474 - r2104476;
        double r2104478 = r2104472 + r2104477;
        double r2104479 = 0.5;
        double r2104480 = r2104478 * r2104479;
        return r2104480;
}

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

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

  6. Final simplification0.1

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

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)))