Average Error: 7.2 → 3.4
Time: 19.1s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1.0}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.1409575287436362 \cdot 10^{+77}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1.0}\\ \mathbf{elif}\;z \le 1.2840647236389548 \cdot 10^{+57}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1.0}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1.0}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.1409575287436362 \cdot 10^{+77}:\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1.0}\\

\mathbf{elif}\;z \le 1.2840647236389548 \cdot 10^{+57}:\\
\;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1.0}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1.0}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r34567985 = x;
        double r34567986 = y;
        double r34567987 = z;
        double r34567988 = r34567986 * r34567987;
        double r34567989 = r34567988 - r34567985;
        double r34567990 = t;
        double r34567991 = r34567990 * r34567987;
        double r34567992 = r34567991 - r34567985;
        double r34567993 = r34567989 / r34567992;
        double r34567994 = r34567985 + r34567993;
        double r34567995 = 1.0;
        double r34567996 = r34567985 + r34567995;
        double r34567997 = r34567994 / r34567996;
        return r34567997;
}
↓
double f(double x, double y, double z, double t) {
        double r34567998 = z;
        double r34567999 = -1.1409575287436362e+77;
        bool r34568000 = r34567998 <= r34567999;
        double r34568001 = x;
        double r34568002 = y;
        double r34568003 = t;
        double r34568004 = r34568002 / r34568003;
        double r34568005 = r34568001 + r34568004;
        double r34568006 = 1.0;
        double r34568007 = r34568001 + r34568006;
        double r34568008 = r34568005 / r34568007;
        double r34568009 = 1.2840647236389548e+57;
        bool r34568010 = r34567998 <= r34568009;
        double r34568011 = 1.0;
        double r34568012 = r34568003 * r34567998;
        double r34568013 = r34568012 - r34568001;
        double r34568014 = r34568002 * r34567998;
        double r34568015 = r34568014 - r34568001;
        double r34568016 = r34568013 / r34568015;
        double r34568017 = r34568011 / r34568016;
        double r34568018 = r34568001 + r34568017;
        double r34568019 = r34568018 / r34568007;
        double r34568020 = r34568010 ? r34568019 : r34568008;
        double r34568021 = r34568000 ? r34568008 : r34568020;
        return r34568021;
}

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

Original7.2
Target0.4
Herbie3.4
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1.0}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.1409575287436362e+77 or 1.2840647236389548e+57 < z

    1. Initial program 18.0

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1.0}\]

    2. Taylor expanded around inf 7.7

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1.0}\]

    if -1.1409575287436362e+77 < z < 1.2840647236389548e+57

    1. Initial program 0.7

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1.0}\]
    2. Using strategy rm

    3. Applied clear-num0.8

      \[\leadsto \frac{x + \color{blue}{\frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}}{x + 1.0}\]
    4. Using strategy rm

    5. Applied *-un-lft-identity0.8

      \[\leadsto \frac{x + \frac{1}{\frac{t \cdot z - x}{\color{blue}{1 \cdot \left(y \cdot z - x\right)}}}}{x + 1.0}\]

    6. Applied associate-/r*0.8

      \[\leadsto \frac{x + \frac{1}{\color{blue}{\frac{\frac{t \cdot z - x}{1}}{y \cdot z - x}}}}{x + 1.0}\]

    7. Simplified0.8

      \[\leadsto \frac{x + \frac{1}{\frac{\color{blue}{z \cdot t - x}}{y \cdot z - x}}}{x + 1.0}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.1409575287436362 \cdot 10^{+77}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1.0}\\ \mathbf{elif}\;z \le 1.2840647236389548 \cdot 10^{+57}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1.0}\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(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)))