Average Error: 6.2 → 1.3
Time: 8.0s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(z - x\right) \cdot y}{t} = -\infty:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;x + \frac{\left(z - x\right) \cdot y}{t} \le -8.469201958944395 \cdot 10^{-176}:\\ \;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right) + x\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(z - x\right) \cdot y}{t} = -\infty:\\
\;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\

\mathbf{elif}\;x + \frac{\left(z - x\right) \cdot y}{t} \le -8.469201958944395 \cdot 10^{-176}:\\
\;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\

\mathbf{else}:\\
\;\;\;\;\frac{y}{t} \cdot \left(z - x\right) + x\\

\end{array}
double f(double x, double y, double z, double t) {
        double r6815897 = x;
        double r6815898 = y;
        double r6815899 = z;
        double r6815900 = r6815899 - r6815897;
        double r6815901 = r6815898 * r6815900;
        double r6815902 = t;
        double r6815903 = r6815901 / r6815902;
        double r6815904 = r6815897 + r6815903;
        return r6815904;
}
↓
double f(double x, double y, double z, double t) {
        double r6815905 = x;
        double r6815906 = z;
        double r6815907 = r6815906 - r6815905;
        double r6815908 = y;
        double r6815909 = r6815907 * r6815908;
        double r6815910 = t;
        double r6815911 = r6815909 / r6815910;
        double r6815912 = r6815905 + r6815911;
        double r6815913 = -inf.0;
        bool r6815914 = r6815912 <= r6815913;
        double r6815915 = r6815910 / r6815907;
        double r6815916 = r6815908 / r6815915;
        double r6815917 = r6815905 + r6815916;
        double r6815918 = -8.469201958944395e-176;
        bool r6815919 = r6815912 <= r6815918;
        double r6815920 = r6815908 / r6815910;
        double r6815921 = r6815920 * r6815907;
        double r6815922 = r6815921 + r6815905;
        double r6815923 = r6815919 ? r6815912 : r6815922;
        double r6815924 = r6815914 ? r6815917 : r6815923;
        return r6815924;
}

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

Target

Original6.2
Target1.9
Herbie1.3
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

  2. if (+ x (/ (* y (- z x)) t)) < -inf.0

    1. Initial program 60.2

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

    3. Applied associate-/l*0.2

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

    if -inf.0 < (+ x (/ (* y (- z x)) t)) < -8.469201958944395e-176

    1. Initial program 0.4

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

    if -8.469201958944395e-176 < (+ x (/ (* y (- z x)) t))

    1. Initial program 5.9

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

    2. Taylor expanded around 0 5.9

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

    3. Simplified2.0

      \[\leadsto x + \color{blue}{\frac{y}{t} \cdot \left(z - x\right)}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(z - x\right) \cdot y}{t} = -\infty:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;x + \frac{\left(z - x\right) \cdot y}{t} \le -8.469201958944395 \cdot 10^{-176}:\\ \;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"

  :herbie-target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

  (+ x (/ (* y (- z x)) t)))