Average Error: 7.2 → 3.6
Time: 5.5s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.1155458979184906 \cdot 10^{207} \lor \neg \left(z \le 2.2142226299666923 \cdot 10^{124}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z}{y \cdot z - x} - \frac{1}{\frac{y \cdot z - x}{x}}}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.1155458979184906 \cdot 10^{207} \lor \neg \left(z \le 2.2142226299666923 \cdot 10^{124}\right):\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r733028 = x;
        double r733029 = y;
        double r733030 = z;
        double r733031 = r733029 * r733030;
        double r733032 = r733031 - r733028;
        double r733033 = t;
        double r733034 = r733033 * r733030;
        double r733035 = r733034 - r733028;
        double r733036 = r733032 / r733035;
        double r733037 = r733028 + r733036;
        double r733038 = 1.0;
        double r733039 = r733028 + r733038;
        double r733040 = r733037 / r733039;
        return r733040;
}
↓
double f(double x, double y, double z, double t) {
        double r733041 = z;
        double r733042 = -1.1155458979184906e+207;
        bool r733043 = r733041 <= r733042;
        double r733044 = 2.2142226299666923e+124;
        bool r733045 = r733041 <= r733044;
        double r733046 = !r733045;
        bool r733047 = r733043 || r733046;
        double r733048 = x;
        double r733049 = y;
        double r733050 = t;
        double r733051 = r733049 / r733050;
        double r733052 = r733048 + r733051;
        double r733053 = 1.0;
        double r733054 = r733048 + r733053;
        double r733055 = r733052 / r733054;
        double r733056 = 1.0;
        double r733057 = r733050 * r733041;
        double r733058 = r733049 * r733041;
        double r733059 = r733058 - r733048;
        double r733060 = r733057 / r733059;
        double r733061 = r733059 / r733048;
        double r733062 = r733056 / r733061;
        double r733063 = r733060 - r733062;
        double r733064 = r733056 / r733063;
        double r733065 = r733048 + r733064;
        double r733066 = r733065 / r733054;
        double r733067 = r733047 ? r733055 : r733066;
        return r733067;
}

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

Derivation

  1. Split input into 2 regimes

  2. if z < -1.1155458979184906e+207 or 2.2142226299666923e+124 < z

    1. Initial program 22.5

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

    2. Taylor expanded around inf 6.3

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

    if -1.1155458979184906e+207 < z < 2.2142226299666923e+124

    1. Initial program 2.8

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

    3. Applied clear-num2.8

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

    5. Applied div-sub2.8

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

    7. Applied clear-num2.8

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

  4. Final simplification3.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.1155458979184906 \cdot 10^{207} \lor \neg \left(z \le 2.2142226299666923 \cdot 10^{124}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z}{y \cdot z - x} - \frac{1}{\frac{y \cdot z - x}{x}}}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020003 
(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)))