Average Error: 7.3 → 3.6
Time: 4.8s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.26827066007243838 \cdot 10^{97} \lor \neg \left(z \le 5.84421128900095789 \cdot 10^{44}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-x\right) - \frac{y \cdot z - x}{t \cdot z - x}}{-\left(x + 1\right)}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.26827066007243838 \cdot 10^{97} \lor \neg \left(z \le 5.84421128900095789 \cdot 10^{44}\right):\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r689494 = x;
        double r689495 = y;
        double r689496 = z;
        double r689497 = r689495 * r689496;
        double r689498 = r689497 - r689494;
        double r689499 = t;
        double r689500 = r689499 * r689496;
        double r689501 = r689500 - r689494;
        double r689502 = r689498 / r689501;
        double r689503 = r689494 + r689502;
        double r689504 = 1.0;
        double r689505 = r689494 + r689504;
        double r689506 = r689503 / r689505;
        return r689506;
}
↓
double f(double x, double y, double z, double t) {
        double r689507 = z;
        double r689508 = -1.2682706600724384e+97;
        bool r689509 = r689507 <= r689508;
        double r689510 = 5.844211289000958e+44;
        bool r689511 = r689507 <= r689510;
        double r689512 = !r689511;
        bool r689513 = r689509 || r689512;
        double r689514 = x;
        double r689515 = y;
        double r689516 = t;
        double r689517 = r689515 / r689516;
        double r689518 = r689514 + r689517;
        double r689519 = 1.0;
        double r689520 = r689514 + r689519;
        double r689521 = r689518 / r689520;
        double r689522 = -r689514;
        double r689523 = r689515 * r689507;
        double r689524 = r689523 - r689514;
        double r689525 = r689516 * r689507;
        double r689526 = r689525 - r689514;
        double r689527 = r689524 / r689526;
        double r689528 = r689522 - r689527;
        double r689529 = -r689520;
        double r689530 = r689528 / r689529;
        double r689531 = r689513 ? r689521 : r689530;
        return r689531;
}

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

Original7.3
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 < -1.2682706600724384e+97 or 5.844211289000958e+44 < z

    1. Initial program 18.2

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

    3. Applied clear-num18.2

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

    5. Applied div-sub18.2

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

    6. Taylor expanded around inf 8.2

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

    if -1.2682706600724384e+97 < z < 5.844211289000958e+44

    1. Initial program 0.8

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

    3. Applied clear-num0.8

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

    5. Applied frac-2neg0.8

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

    6. Simplified0.8

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

  4. Final simplification3.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.26827066007243838 \cdot 10^{97} \lor \neg \left(z \le 5.84421128900095789 \cdot 10^{44}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-x\right) - \frac{y \cdot z - x}{t \cdot z - x}}{-\left(x + 1\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020081 
(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)))