Average Error: 7.6 → 3.7
Time: 11.5s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.168113515321289505231587010261632652554 \cdot 10^{196} \lor \neg \left(z \le 6.161388123871168091398241911862244333833 \cdot 10^{118}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -3.168113515321289505231587010261632652554 \cdot 10^{196} \lor \neg \left(z \le 6.161388123871168091398241911862244333833 \cdot 10^{118}\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 r447623 = x;
        double r447624 = y;
        double r447625 = z;
        double r447626 = r447624 * r447625;
        double r447627 = r447626 - r447623;
        double r447628 = t;
        double r447629 = r447628 * r447625;
        double r447630 = r447629 - r447623;
        double r447631 = r447627 / r447630;
        double r447632 = r447623 + r447631;
        double r447633 = 1.0;
        double r447634 = r447623 + r447633;
        double r447635 = r447632 / r447634;
        return r447635;
}
↓
double f(double x, double y, double z, double t) {
        double r447636 = z;
        double r447637 = -3.1681135153212895e+196;
        bool r447638 = r447636 <= r447637;
        double r447639 = 6.161388123871168e+118;
        bool r447640 = r447636 <= r447639;
        double r447641 = !r447640;
        bool r447642 = r447638 || r447641;
        double r447643 = x;
        double r447644 = y;
        double r447645 = t;
        double r447646 = r447644 / r447645;
        double r447647 = r447643 + r447646;
        double r447648 = 1.0;
        double r447649 = r447643 + r447648;
        double r447650 = r447647 / r447649;
        double r447651 = 1.0;
        double r447652 = r447645 * r447636;
        double r447653 = r447652 - r447643;
        double r447654 = r447644 * r447636;
        double r447655 = r447654 - r447643;
        double r447656 = r447653 / r447655;
        double r447657 = r447651 / r447656;
        double r447658 = r447643 + r447657;
        double r447659 = r447658 / r447649;
        double r447660 = r447642 ? r447650 : r447659;
        return r447660;
}

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

Original7.6
Target0.3
Herbie3.7
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -3.1681135153212895e+196 or 6.161388123871168e+118 < z

    1. Initial program 23.1

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

    2. Taylor expanded around inf 6.7

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

    if -3.1681135153212895e+196 < z < 6.161388123871168e+118

    1. Initial program 2.7

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

    3. Applied clear-num2.7

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

  4. Final simplification3.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.168113515321289505231587010261632652554 \cdot 10^{196} \lor \neg \left(z \le 6.161388123871168091398241911862244333833 \cdot 10^{118}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2019297 
(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)))