Average Error: 7.5 → 4.0
Time: 20.7s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -80570587.88156504929065704345703125:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \le 9.261161175855565389212509968548170125786 \cdot 10^{162}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -80570587.88156504929065704345703125:\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\

\mathbf{elif}\;z \le 9.261161175855565389212509968548170125786 \cdot 10^{162}:\\
\;\;\;\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r33018466 = x;
        double r33018467 = y;
        double r33018468 = z;
        double r33018469 = r33018467 * r33018468;
        double r33018470 = r33018469 - r33018466;
        double r33018471 = t;
        double r33018472 = r33018471 * r33018468;
        double r33018473 = r33018472 - r33018466;
        double r33018474 = r33018470 / r33018473;
        double r33018475 = r33018466 + r33018474;
        double r33018476 = 1.0;
        double r33018477 = r33018466 + r33018476;
        double r33018478 = r33018475 / r33018477;
        return r33018478;
}
↓
double f(double x, double y, double z, double t) {
        double r33018479 = z;
        double r33018480 = -80570587.88156505;
        bool r33018481 = r33018479 <= r33018480;
        double r33018482 = x;
        double r33018483 = y;
        double r33018484 = t;
        double r33018485 = r33018483 / r33018484;
        double r33018486 = r33018482 + r33018485;
        double r33018487 = 1.0;
        double r33018488 = r33018482 + r33018487;
        double r33018489 = r33018486 / r33018488;
        double r33018490 = 9.261161175855565e+162;
        bool r33018491 = r33018479 <= r33018490;
        double r33018492 = r33018483 * r33018479;
        double r33018493 = r33018492 - r33018482;
        double r33018494 = r33018484 * r33018479;
        double r33018495 = r33018494 - r33018482;
        double r33018496 = r33018493 / r33018495;
        double r33018497 = r33018482 + r33018496;
        double r33018498 = r33018497 / r33018488;
        double r33018499 = r33018491 ? r33018498 : r33018489;
        double r33018500 = r33018481 ? r33018489 : r33018499;
        return r33018500;
}

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

Original7.5
Target0.4
Herbie4.0
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -80570587.88156505 or 9.261161175855565e+162 < z

    1. Initial program 18.0

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

    2. Taylor expanded around inf 8.1

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

    if -80570587.88156505 < z < 9.261161175855565e+162

    1. Initial program 1.7

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

    3. Applied clear-num1.7

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

    5. Applied *-un-lft-identity1.7

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

    6. Applied associate-/r*1.7

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

    7. Simplified1.7

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

  4. Final simplification4.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -80570587.88156504929065704345703125:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \le 9.261161175855565389212509968548170125786 \cdot 10^{162}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(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)))