Average Error: 7.4 → 3.6
Time: 5.8s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.705275441028536951824571425223078003263 \cdot 10^{46} \lor \neg \left(z \le 3.409532601960749253424962145421535262975 \cdot 10^{120}\right):\\ \;\;\;\;\frac{\left(-x\right) - \frac{y}{t}}{-\left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-x\right) - \frac{y \cdot z - x}{t \cdot z - x}}{-\left(x + 1\right)}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.705275441028536951824571425223078003263 \cdot 10^{46} \lor \neg \left(z \le 3.409532601960749253424962145421535262975 \cdot 10^{120}\right):\\
\;\;\;\;\frac{\left(-x\right) - \frac{y}{t}}{-\left(x + 1\right)}\\

\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 r662355 = x;
        double r662356 = y;
        double r662357 = z;
        double r662358 = r662356 * r662357;
        double r662359 = r662358 - r662355;
        double r662360 = t;
        double r662361 = r662360 * r662357;
        double r662362 = r662361 - r662355;
        double r662363 = r662359 / r662362;
        double r662364 = r662355 + r662363;
        double r662365 = 1.0;
        double r662366 = r662355 + r662365;
        double r662367 = r662364 / r662366;
        return r662367;
}
↓
double f(double x, double y, double z, double t) {
        double r662368 = z;
        double r662369 = -2.705275441028537e+46;
        bool r662370 = r662368 <= r662369;
        double r662371 = 3.409532601960749e+120;
        bool r662372 = r662368 <= r662371;
        double r662373 = !r662372;
        bool r662374 = r662370 || r662373;
        double r662375 = x;
        double r662376 = -r662375;
        double r662377 = y;
        double r662378 = t;
        double r662379 = r662377 / r662378;
        double r662380 = r662376 - r662379;
        double r662381 = 1.0;
        double r662382 = r662375 + r662381;
        double r662383 = -r662382;
        double r662384 = r662380 / r662383;
        double r662385 = r662377 * r662368;
        double r662386 = r662385 - r662375;
        double r662387 = r662378 * r662368;
        double r662388 = r662387 - r662375;
        double r662389 = r662386 / r662388;
        double r662390 = r662376 - r662389;
        double r662391 = r662390 / r662383;
        double r662392 = r662374 ? r662384 : r662391;
        return r662392;
}

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

Original7.4
Target0.4
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 < -2.705275441028537e+46 or 3.409532601960749e+120 < z

    1. Initial program 19.1

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

    3. Applied clear-num19.1

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

    5. Applied frac-2neg19.1

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

    6. Simplified19.1

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

    7. Taylor expanded around inf 8.2

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

    if -2.705275441028537e+46 < z < 3.409532601960749e+120

    1. Initial program 1.0

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

    3. Applied clear-num1.0

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

    5. Applied frac-2neg1.0

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

    6. Simplified1.0

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

  4. Final simplification3.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.705275441028536951824571425223078003263 \cdot 10^{46} \lor \neg \left(z \le 3.409532601960749253424962145421535262975 \cdot 10^{120}\right):\\ \;\;\;\;\frac{\left(-x\right) - \frac{y}{t}}{-\left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-x\right) - \frac{y \cdot z - x}{t \cdot z - x}}{-\left(x + 1\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019356 
(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)))