Average Error: 7.2 → 3.3
Time: 7.5s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.740851580023230491988514234119303951373 \cdot 10^{68} \lor \neg \left(z \le 8.572974683475893852965771329571608920798 \cdot 10^{137}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{\frac{y \cdot z - x}{t \cdot z - x} + x}}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -5.740851580023230491988514234119303951373 \cdot 10^{68} \lor \neg \left(z \le 8.572974683475893852965771329571608920798 \cdot 10^{137}\right):\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r496421 = x;
        double r496422 = y;
        double r496423 = z;
        double r496424 = r496422 * r496423;
        double r496425 = r496424 - r496421;
        double r496426 = t;
        double r496427 = r496426 * r496423;
        double r496428 = r496427 - r496421;
        double r496429 = r496425 / r496428;
        double r496430 = r496421 + r496429;
        double r496431 = 1.0;
        double r496432 = r496421 + r496431;
        double r496433 = r496430 / r496432;
        return r496433;
}
↓
double f(double x, double y, double z, double t) {
        double r496434 = z;
        double r496435 = -5.7408515800232305e+68;
        bool r496436 = r496434 <= r496435;
        double r496437 = 8.572974683475894e+137;
        bool r496438 = r496434 <= r496437;
        double r496439 = !r496438;
        bool r496440 = r496436 || r496439;
        double r496441 = x;
        double r496442 = y;
        double r496443 = t;
        double r496444 = r496442 / r496443;
        double r496445 = r496441 + r496444;
        double r496446 = 1.0;
        double r496447 = r496441 + r496446;
        double r496448 = r496445 / r496447;
        double r496449 = 1.0;
        double r496450 = r496442 * r496434;
        double r496451 = r496450 - r496441;
        double r496452 = r496443 * r496434;
        double r496453 = r496452 - r496441;
        double r496454 = r496451 / r496453;
        double r496455 = r496454 + r496441;
        double r496456 = r496447 / r496455;
        double r496457 = r496449 / r496456;
        double r496458 = r496440 ? r496448 : r496457;
        return r496458;
}

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

Derivation

  1. Split input into 2 regimes

  2. if z < -5.7408515800232305e+68 or 8.572974683475894e+137 < z

    1. Initial program 19.2

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

    2. Taylor expanded around inf 7.1

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

    if -5.7408515800232305e+68 < z < 8.572974683475894e+137

    1. Initial program 1.4

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

    3. Applied div-inv1.4

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

    5. Applied clear-num1.5

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

    6. Simplified1.4

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

  4. Final simplification3.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.740851580023230491988514234119303951373 \cdot 10^{68} \lor \neg \left(z \le 8.572974683475893852965771329571608920798 \cdot 10^{137}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{\frac{y \cdot z - x}{t \cdot z - x} + x}}\\ \end{array}\]

Reproduce

herbie shell --seed 1978988140 
(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)))