Average Error: 7.1 → 3.5
Time: 14.1s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.161757018370643750541095776788235057033 \cdot 10^{52} \lor \neg \left(z \le 5.898617430808727721691772880269426008307 \cdot 10^{139}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -5.161757018370643750541095776788235057033 \cdot 10^{52} \lor \neg \left(z \le 5.898617430808727721691772880269426008307 \cdot 10^{139}\right):\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r536843 = x;
        double r536844 = y;
        double r536845 = z;
        double r536846 = r536844 * r536845;
        double r536847 = r536846 - r536843;
        double r536848 = t;
        double r536849 = r536848 * r536845;
        double r536850 = r536849 - r536843;
        double r536851 = r536847 / r536850;
        double r536852 = r536843 + r536851;
        double r536853 = 1.0;
        double r536854 = r536843 + r536853;
        double r536855 = r536852 / r536854;
        return r536855;
}
↓
double f(double x, double y, double z, double t) {
        double r536856 = z;
        double r536857 = -5.161757018370644e+52;
        bool r536858 = r536856 <= r536857;
        double r536859 = 5.898617430808728e+139;
        bool r536860 = r536856 <= r536859;
        double r536861 = !r536860;
        bool r536862 = r536858 || r536861;
        double r536863 = x;
        double r536864 = y;
        double r536865 = t;
        double r536866 = r536864 / r536865;
        double r536867 = r536863 + r536866;
        double r536868 = 1.0;
        double r536869 = r536863 + r536868;
        double r536870 = r536867 / r536869;
        double r536871 = 1.0;
        double r536872 = r536865 * r536856;
        double r536873 = r536872 - r536863;
        double r536874 = r536864 * r536856;
        double r536875 = r536874 - r536863;
        double r536876 = r536873 / r536875;
        double r536877 = r536871 / r536876;
        double r536878 = r536863 + r536877;
        double r536879 = r536878 / r536869;
        double r536880 = r536862 ? r536870 : r536879;
        return r536880;
}

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

Original7.1
Target0.4
Herbie3.5
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -5.161757018370644e+52 or 5.898617430808728e+139 < z

    1. Initial program 19.2

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]

    2. Taylor expanded around inf 8.1

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1}\]

    if -5.161757018370644e+52 < z < 5.898617430808728e+139

    1. Initial program 1.2

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
    2. Using strategy rm

    3. Applied clear-num1.2

      \[\leadsto \frac{x + \color{blue}{\frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}}{x + 1}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.161757018370643750541095776788235057033 \cdot 10^{52} \lor \neg \left(z \le 5.898617430808727721691772880269426008307 \cdot 10^{139}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2019298 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1)))