Average Error: 7.4 → 3.3
Time: 4.7s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.9907923277987659 \cdot 10^{139} \lor \neg \left(z \le 3.0023821461350899 \cdot 10^{139}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(y \cdot z - x\right) \cdot \frac{1}{t \cdot z - x}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.9907923277987659 \cdot 10^{139} \lor \neg \left(z \le 3.0023821461350899 \cdot 10^{139}\right):\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r623287 = x;
        double r623288 = y;
        double r623289 = z;
        double r623290 = r623288 * r623289;
        double r623291 = r623290 - r623287;
        double r623292 = t;
        double r623293 = r623292 * r623289;
        double r623294 = r623293 - r623287;
        double r623295 = r623291 / r623294;
        double r623296 = r623287 + r623295;
        double r623297 = 1.0;
        double r623298 = r623287 + r623297;
        double r623299 = r623296 / r623298;
        return r623299;
}
↓
double f(double x, double y, double z, double t) {
        double r623300 = z;
        double r623301 = -2.990792327798766e+139;
        bool r623302 = r623300 <= r623301;
        double r623303 = 3.00238214613509e+139;
        bool r623304 = r623300 <= r623303;
        double r623305 = !r623304;
        bool r623306 = r623302 || r623305;
        double r623307 = x;
        double r623308 = y;
        double r623309 = t;
        double r623310 = r623308 / r623309;
        double r623311 = r623307 + r623310;
        double r623312 = 1.0;
        double r623313 = r623307 + r623312;
        double r623314 = r623311 / r623313;
        double r623315 = r623308 * r623300;
        double r623316 = r623315 - r623307;
        double r623317 = 1.0;
        double r623318 = r623309 * r623300;
        double r623319 = r623318 - r623307;
        double r623320 = r623317 / r623319;
        double r623321 = r623316 * r623320;
        double r623322 = r623307 + r623321;
        double r623323 = r623322 / r623313;
        double r623324 = r623306 ? r623314 : r623323;
        return r623324;
}

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

Original7.4
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 < -2.990792327798766e+139 or 3.00238214613509e+139 < z

    1. Initial program 22.1

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

    2. Taylor expanded around inf 6.6

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

    if -2.990792327798766e+139 < z < 3.00238214613509e+139

    1. Initial program 2.0

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

    3. Applied div-inv2.1

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

  4. Final simplification3.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.9907923277987659 \cdot 10^{139} \lor \neg \left(z \le 3.0023821461350899 \cdot 10^{139}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(y \cdot z - x\right) \cdot \frac{1}{t \cdot z - x}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020021 
(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)))