Average Error: 0.1 → 0.1
Time: 14.7s
Precision: 64
\[\frac{\left(x + y\right) - z}{t \cdot 2}\]
↓
\[\left(\frac{x}{t} + \left(\frac{y}{t} - \frac{z}{t}\right)\right) \cdot 0.5\]
\frac{\left(x + y\right) - z}{t \cdot 2}
↓
\left(\frac{x}{t} + \left(\frac{y}{t} - \frac{z}{t}\right)\right) \cdot 0.5
double f(double x, double y, double z, double t) {
        double r2974701 = x;
        double r2974702 = y;
        double r2974703 = r2974701 + r2974702;
        double r2974704 = z;
        double r2974705 = r2974703 - r2974704;
        double r2974706 = t;
        double r2974707 = 2.0;
        double r2974708 = r2974706 * r2974707;
        double r2974709 = r2974705 / r2974708;
        return r2974709;
}
↓
double f(double x, double y, double z, double t) {
        double r2974710 = x;
        double r2974711 = t;
        double r2974712 = r2974710 / r2974711;
        double r2974713 = y;
        double r2974714 = r2974713 / r2974711;
        double r2974715 = z;
        double r2974716 = r2974715 / r2974711;
        double r2974717 = r2974714 - r2974716;
        double r2974718 = r2974712 + r2974717;
        double r2974719 = 0.5;
        double r2974720 = r2974718 * r2974719;
        return r2974720;
}

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

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  (/ (- (+ x y) z) (* t 2.0)))