Average Error: 7.1 → 3.8
Time: 4.6s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.669558449301389365130158102652756647247 \cdot 10^{171} \lor \neg \left(z \le 2315632523410916948049920\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.669558449301389365130158102652756647247 \cdot 10^{171} \lor \neg \left(z \le 2315632523410916948049920\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 r865666 = x;
        double r865667 = y;
        double r865668 = z;
        double r865669 = r865667 * r865668;
        double r865670 = r865669 - r865666;
        double r865671 = t;
        double r865672 = r865671 * r865668;
        double r865673 = r865672 - r865666;
        double r865674 = r865670 / r865673;
        double r865675 = r865666 + r865674;
        double r865676 = 1.0;
        double r865677 = r865666 + r865676;
        double r865678 = r865675 / r865677;
        return r865678;
}
↓
double f(double x, double y, double z, double t) {
        double r865679 = z;
        double r865680 = -2.6695584493013894e+171;
        bool r865681 = r865679 <= r865680;
        double r865682 = 2.315632523410917e+24;
        bool r865683 = r865679 <= r865682;
        double r865684 = !r865683;
        bool r865685 = r865681 || r865684;
        double r865686 = x;
        double r865687 = y;
        double r865688 = t;
        double r865689 = r865687 / r865688;
        double r865690 = r865686 + r865689;
        double r865691 = 1.0;
        double r865692 = r865686 + r865691;
        double r865693 = r865690 / r865692;
        double r865694 = 1.0;
        double r865695 = r865688 * r865679;
        double r865696 = r865695 - r865686;
        double r865697 = r865687 * r865679;
        double r865698 = r865697 - r865686;
        double r865699 = r865696 / r865698;
        double r865700 = r865694 / r865699;
        double r865701 = r865686 + r865700;
        double r865702 = r865701 / r865692;
        double r865703 = r865685 ? r865693 : r865702;
        return r865703;
}

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
Target0.3
Herbie3.8
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.6695584493013894e+171 or 2.315632523410917e+24 < z

    1. Initial program 18.2

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

    2. Taylor expanded around inf 8.2

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

    if -2.6695584493013894e+171 < z < 2.315632523410917e+24

    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-num1.8

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

  4. Final simplification3.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.669558449301389365130158102652756647247 \cdot 10^{171} \lor \neg \left(z \le 2315632523410916948049920\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2019362 
(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)))