Average Error: 7.3 → 3.4
Time: 4.1s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -6.6316489725122158 \cdot 10^{38} \lor \neg \left(z \le 1.13775010509918027 \cdot 10^{117}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 \cdot \left(\frac{y \cdot z - x}{t \cdot z - x} + x\right)}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -6.6316489725122158 \cdot 10^{38} \lor \neg \left(z \le 1.13775010509918027 \cdot 10^{117}\right):\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r726394 = x;
        double r726395 = y;
        double r726396 = z;
        double r726397 = r726395 * r726396;
        double r726398 = r726397 - r726394;
        double r726399 = t;
        double r726400 = r726399 * r726396;
        double r726401 = r726400 - r726394;
        double r726402 = r726398 / r726401;
        double r726403 = r726394 + r726402;
        double r726404 = 1.0;
        double r726405 = r726394 + r726404;
        double r726406 = r726403 / r726405;
        return r726406;
}
↓
double f(double x, double y, double z, double t) {
        double r726407 = z;
        double r726408 = -6.631648972512216e+38;
        bool r726409 = r726407 <= r726408;
        double r726410 = 1.1377501050991803e+117;
        bool r726411 = r726407 <= r726410;
        double r726412 = !r726411;
        bool r726413 = r726409 || r726412;
        double r726414 = x;
        double r726415 = y;
        double r726416 = t;
        double r726417 = r726415 / r726416;
        double r726418 = r726414 + r726417;
        double r726419 = 1.0;
        double r726420 = r726414 + r726419;
        double r726421 = r726418 / r726420;
        double r726422 = 1.0;
        double r726423 = r726415 * r726407;
        double r726424 = r726423 - r726414;
        double r726425 = r726416 * r726407;
        double r726426 = r726425 - r726414;
        double r726427 = r726424 / r726426;
        double r726428 = r726427 + r726414;
        double r726429 = r726422 * r726428;
        double r726430 = r726429 / r726420;
        double r726431 = r726413 ? r726421 : r726430;
        return r726431;
}

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
Target0.4
Herbie3.4
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -6.631648972512216e+38 or 1.1377501050991803e+117 < z

    1. Initial program 18.3

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

    3. Applied clear-num18.3

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

    5. Applied clear-num18.3

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

    6. Taylor expanded around inf 7.7

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

    if -6.631648972512216e+38 < z < 1.1377501050991803e+117

    1. Initial program 1.1

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

    3. Applied clear-num1.1

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

    5. Applied *-un-lft-identity1.1

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

    6. Applied *-un-lft-identity1.1

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

    7. Applied distribute-lft-out1.1

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

    8. Simplified1.1

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

  4. Final simplification3.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -6.6316489725122158 \cdot 10^{38} \lor \neg \left(z \le 1.13775010509918027 \cdot 10^{117}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 \cdot \left(\frac{y \cdot z - x}{t \cdot z - x} + x\right)}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020039 
(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)))