Average Error: 7.8 → 3.9
Time: 3.8s
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 r838237 = x;
        double r838238 = y;
        double r838239 = z;
        double r838240 = r838238 * r838239;
        double r838241 = r838240 - r838237;
        double r838242 = t;
        double r838243 = r838242 * r838239;
        double r838244 = r838243 - r838237;
        double r838245 = r838241 / r838244;
        double r838246 = r838237 + r838245;
        double r838247 = 1.0;
        double r838248 = r838237 + r838247;
        double r838249 = r838246 / r838248;
        return r838249;
}
↓
double f(double x, double y, double z, double t) {
        double r838250 = z;
        double r838251 = -1.6086847956254996e+72;
        bool r838252 = r838250 <= r838251;
        double r838253 = 1.15942617022607e+58;
        bool r838254 = r838250 <= r838253;
        double r838255 = !r838254;
        bool r838256 = r838252 || r838255;
        double r838257 = x;
        double r838258 = y;
        double r838259 = t;
        double r838260 = r838258 / r838259;
        double r838261 = r838257 + r838260;
        double r838262 = 1.0;
        double r838263 = r838257 + r838262;
        double r838264 = r838261 / r838263;
        double r838265 = 1.0;
        double r838266 = r838259 * r838250;
        double r838267 = r838266 - r838257;
        double r838268 = r838258 * r838250;
        double r838269 = r838268 - r838257;
        double r838270 = r838267 / r838269;
        double r838271 = r838265 / r838270;
        double r838272 = r838257 + r838271;
        double r838273 = r838272 / r838263;
        double r838274 = r838256 ? r838264 : r838273;
        return r838274;
}

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)))