Average Error: 7.5 → 3.3
Time: 4.4s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.6579298446565844 \cdot 10^{132} \lor \neg \left(z \le 5.5896830212737893 \cdot 10^{76}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.6579298446565844 \cdot 10^{132} \lor \neg \left(z \le 5.5896830212737893 \cdot 10^{76}\right):\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r637458 = x;
        double r637459 = y;
        double r637460 = z;
        double r637461 = r637459 * r637460;
        double r637462 = r637461 - r637458;
        double r637463 = t;
        double r637464 = r637463 * r637460;
        double r637465 = r637464 - r637458;
        double r637466 = r637462 / r637465;
        double r637467 = r637458 + r637466;
        double r637468 = 1.0;
        double r637469 = r637458 + r637468;
        double r637470 = r637467 / r637469;
        return r637470;
}
↓
double f(double x, double y, double z, double t) {
        double r637471 = z;
        double r637472 = -1.6579298446565844e+132;
        bool r637473 = r637471 <= r637472;
        double r637474 = 5.589683021273789e+76;
        bool r637475 = r637471 <= r637474;
        double r637476 = !r637475;
        bool r637477 = r637473 || r637476;
        double r637478 = x;
        double r637479 = y;
        double r637480 = t;
        double r637481 = r637479 / r637480;
        double r637482 = r637478 + r637481;
        double r637483 = 1.0;
        double r637484 = r637478 + r637483;
        double r637485 = r637482 / r637484;
        double r637486 = 1.0;
        double r637487 = r637480 * r637471;
        double r637488 = r637487 - r637478;
        double r637489 = r637479 * r637471;
        double r637490 = r637489 - r637478;
        double r637491 = r637488 / r637490;
        double r637492 = r637486 / r637491;
        double r637493 = r637478 + r637492;
        double r637494 = r637493 / r637484;
        double r637495 = r637477 ? r637485 : r637494;
        return r637495;
}

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
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 < -1.6579298446565844e+132 or 5.589683021273789e+76 < z

    1. Initial program 20.5

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

    2. Taylor expanded around inf 7.6

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

    if -1.6579298446565844e+132 < z < 5.589683021273789e+76

    1. Initial program 1.3

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

    3. Applied clear-num1.3

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

  4. Final simplification3.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.6579298446565844 \cdot 10^{132} \lor \neg \left(z \le 5.5896830212737893 \cdot 10^{76}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(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)))