Average Error: 7.8 → 3.9
Time: 4.1s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.6086847956254996 \cdot 10^{72} \lor \neg \left(z \le 1.15942617022607004 \cdot 10^{58}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.6086847956254996 \cdot 10^{72} \lor \neg \left(z \le 1.15942617022607004 \cdot 10^{58}\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 r804492 = x;
        double r804493 = y;
        double r804494 = z;
        double r804495 = r804493 * r804494;
        double r804496 = r804495 - r804492;
        double r804497 = t;
        double r804498 = r804497 * r804494;
        double r804499 = r804498 - r804492;
        double r804500 = r804496 / r804499;
        double r804501 = r804492 + r804500;
        double r804502 = 1.0;
        double r804503 = r804492 + r804502;
        double r804504 = r804501 / r804503;
        return r804504;
}
↓
double f(double x, double y, double z, double t) {
        double r804505 = z;
        double r804506 = -1.6086847956254996e+72;
        bool r804507 = r804505 <= r804506;
        double r804508 = 1.15942617022607e+58;
        bool r804509 = r804505 <= r804508;
        double r804510 = !r804509;
        bool r804511 = r804507 || r804510;
        double r804512 = x;
        double r804513 = y;
        double r804514 = t;
        double r804515 = r804513 / r804514;
        double r804516 = r804512 + r804515;
        double r804517 = 1.0;
        double r804518 = r804512 + r804517;
        double r804519 = r804516 / r804518;
        double r804520 = 1.0;
        double r804521 = r804514 * r804505;
        double r804522 = r804521 - r804512;
        double r804523 = r804513 * r804505;
        double r804524 = r804523 - r804512;
        double r804525 = r804522 / r804524;
        double r804526 = r804520 / r804525;
        double r804527 = r804512 + r804526;
        double r804528 = r804527 / r804518;
        double r804529 = r804511 ? r804519 : r804528;
        return r804529;
}

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

Original7.8
Target0.5
Herbie3.9
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.6086847956254996e+72 or 1.15942617022607e+58 < z

    1. Initial program 19.6

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

    2. Taylor expanded around inf 9.2

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

    if -1.6086847956254996e+72 < z < 1.15942617022607e+58

    1. Initial program 0.5

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

    3. Applied clear-num0.6

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

  4. Final simplification3.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.6086847956254996 \cdot 10^{72} \lor \neg \left(z \le 1.15942617022607004 \cdot 10^{58}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(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)))