Average Error: 7.5 → 3.3
Time: 7.9s
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 r710282 = x;
        double r710283 = y;
        double r710284 = z;
        double r710285 = r710283 * r710284;
        double r710286 = r710285 - r710282;
        double r710287 = t;
        double r710288 = r710287 * r710284;
        double r710289 = r710288 - r710282;
        double r710290 = r710286 / r710289;
        double r710291 = r710282 + r710290;
        double r710292 = 1.0;
        double r710293 = r710282 + r710292;
        double r710294 = r710291 / r710293;
        return r710294;
}
↓
double f(double x, double y, double z, double t) {
        double r710295 = z;
        double r710296 = -1.6579298446565844e+132;
        bool r710297 = r710295 <= r710296;
        double r710298 = 5.589683021273789e+76;
        bool r710299 = r710295 <= r710298;
        double r710300 = !r710299;
        bool r710301 = r710297 || r710300;
        double r710302 = x;
        double r710303 = y;
        double r710304 = t;
        double r710305 = r710303 / r710304;
        double r710306 = r710302 + r710305;
        double r710307 = 1.0;
        double r710308 = r710302 + r710307;
        double r710309 = r710306 / r710308;
        double r710310 = 1.0;
        double r710311 = r710304 * r710295;
        double r710312 = r710311 - r710302;
        double r710313 = r710303 * r710295;
        double r710314 = r710313 - r710302;
        double r710315 = r710312 / r710314;
        double r710316 = r710310 / r710315;
        double r710317 = r710302 + r710316;
        double r710318 = r710317 / r710308;
        double r710319 = r710301 ? r710309 : r710318;
        return r710319;
}

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 
(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)))