Average Error: 7.5 → 4.0
Time: 20.6s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -80570587.88156504929065704345703125:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \le 9.261161175855565389212509968548170125786 \cdot 10^{162}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -80570587.88156504929065704345703125:\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\

\mathbf{elif}\;z \le 9.261161175855565389212509968548170125786 \cdot 10^{162}:\\
\;\;\;\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r30571774 = x;
        double r30571775 = y;
        double r30571776 = z;
        double r30571777 = r30571775 * r30571776;
        double r30571778 = r30571777 - r30571774;
        double r30571779 = t;
        double r30571780 = r30571779 * r30571776;
        double r30571781 = r30571780 - r30571774;
        double r30571782 = r30571778 / r30571781;
        double r30571783 = r30571774 + r30571782;
        double r30571784 = 1.0;
        double r30571785 = r30571774 + r30571784;
        double r30571786 = r30571783 / r30571785;
        return r30571786;
}
↓
double f(double x, double y, double z, double t) {
        double r30571787 = z;
        double r30571788 = -80570587.88156505;
        bool r30571789 = r30571787 <= r30571788;
        double r30571790 = x;
        double r30571791 = y;
        double r30571792 = t;
        double r30571793 = r30571791 / r30571792;
        double r30571794 = r30571790 + r30571793;
        double r30571795 = 1.0;
        double r30571796 = r30571790 + r30571795;
        double r30571797 = r30571794 / r30571796;
        double r30571798 = 9.261161175855565e+162;
        bool r30571799 = r30571787 <= r30571798;
        double r30571800 = r30571791 * r30571787;
        double r30571801 = r30571800 - r30571790;
        double r30571802 = r30571792 * r30571787;
        double r30571803 = r30571802 - r30571790;
        double r30571804 = r30571801 / r30571803;
        double r30571805 = r30571790 + r30571804;
        double r30571806 = r30571805 / r30571796;
        double r30571807 = r30571799 ? r30571806 : r30571797;
        double r30571808 = r30571789 ? r30571797 : r30571807;
        return r30571808;
}

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

Original7.5
Target0.4
Herbie4.0
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -80570587.88156505 or 9.261161175855565e+162 < z

    1. Initial program 18.0

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

    2. Taylor expanded around inf 8.1

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

    if -80570587.88156505 < z < 9.261161175855565e+162

    1. Initial program 1.7

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

    3. Applied clear-num1.7

      \[\leadsto \frac{x + \color{blue}{\frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}}{x + 1}\]
    4. Using strategy rm

    5. Applied *-un-lft-identity1.7

      \[\leadsto \frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{\color{blue}{1 \cdot \left(x + 1\right)}}\]

    6. Applied associate-/r*1.7

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

    7. Simplified1.7

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

  4. Final simplification4.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -80570587.88156504929065704345703125:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \le 9.261161175855565389212509968548170125786 \cdot 10^{162}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"

  :herbie-target
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1.0))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))