Average Error: 7.3 → 3.7
Time: 19.1s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.0213726882368712246896067821148316655 \cdot 10^{81}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \le 2.653747744881045351380565842467581880116 \cdot 10^{131}:\\ \;\;\;\;\frac{x + \frac{1}{t \cdot z - x} \cdot \left(y \cdot z - x\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -5.0213726882368712246896067821148316655 \cdot 10^{81}:\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\

\mathbf{elif}\;z \le 2.653747744881045351380565842467581880116 \cdot 10^{131}:\\
\;\;\;\;\frac{x + \frac{1}{t \cdot z - x} \cdot \left(y \cdot z - x\right)}{x + 1}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r37018250 = x;
        double r37018251 = y;
        double r37018252 = z;
        double r37018253 = r37018251 * r37018252;
        double r37018254 = r37018253 - r37018250;
        double r37018255 = t;
        double r37018256 = r37018255 * r37018252;
        double r37018257 = r37018256 - r37018250;
        double r37018258 = r37018254 / r37018257;
        double r37018259 = r37018250 + r37018258;
        double r37018260 = 1.0;
        double r37018261 = r37018250 + r37018260;
        double r37018262 = r37018259 / r37018261;
        return r37018262;
}
↓
double f(double x, double y, double z, double t) {
        double r37018263 = z;
        double r37018264 = -5.021372688236871e+81;
        bool r37018265 = r37018263 <= r37018264;
        double r37018266 = x;
        double r37018267 = y;
        double r37018268 = t;
        double r37018269 = r37018267 / r37018268;
        double r37018270 = r37018266 + r37018269;
        double r37018271 = 1.0;
        double r37018272 = r37018266 + r37018271;
        double r37018273 = r37018270 / r37018272;
        double r37018274 = 2.6537477448810454e+131;
        bool r37018275 = r37018263 <= r37018274;
        double r37018276 = 1.0;
        double r37018277 = r37018268 * r37018263;
        double r37018278 = r37018277 - r37018266;
        double r37018279 = r37018276 / r37018278;
        double r37018280 = r37018267 * r37018263;
        double r37018281 = r37018280 - r37018266;
        double r37018282 = r37018279 * r37018281;
        double r37018283 = r37018266 + r37018282;
        double r37018284 = r37018283 / r37018272;
        double r37018285 = r37018275 ? r37018284 : r37018273;
        double r37018286 = r37018265 ? r37018273 : r37018285;
        return r37018286;
}

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

Original7.3
Target0.4
Herbie3.7
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -5.021372688236871e+81 or 2.6537477448810454e+131 < z

    1. Initial program 19.7

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

    2. Taylor expanded around inf 8.1

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

    if -5.021372688236871e+81 < z < 2.6537477448810454e+131

    1. Initial program 1.6

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

    3. Applied clear-num1.7

      \[\leadsto \frac{x + \color{blue}{\frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}}{x + 1}\]
    4. Using strategy rm

    5. Applied div-inv1.7

      \[\leadsto \frac{x + \frac{1}{\color{blue}{\left(t \cdot z - x\right) \cdot \frac{1}{y \cdot z - x}}}}{x + 1}\]

    6. Applied add-cube-cbrt1.7

      \[\leadsto \frac{x + \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\left(t \cdot z - x\right) \cdot \frac{1}{y \cdot z - x}}}{x + 1}\]

    7. Applied times-frac1.7

      \[\leadsto \frac{x + \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{t \cdot z - x} \cdot \frac{\sqrt[3]{1}}{\frac{1}{y \cdot z - x}}}}{x + 1}\]

    8. Simplified1.7

      \[\leadsto \frac{x + \color{blue}{\frac{1}{t \cdot z - x}} \cdot \frac{\sqrt[3]{1}}{\frac{1}{y \cdot z - x}}}{x + 1}\]

    9. Simplified1.7

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

  4. Final simplification3.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.0213726882368712246896067821148316655 \cdot 10^{81}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \le 2.653747744881045351380565842467581880116 \cdot 10^{131}:\\ \;\;\;\;\frac{x + \frac{1}{t \cdot z - x} \cdot \left(y \cdot z - x\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"

  :herbie-target
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1.0))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))