Average Error: 7.4 → 3.0
Time: 16.6s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \le -2.5121970162500594 \cdot 10^{206} \lor \neg \left(\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \le 1.9851270194247144 \cdot 10^{243}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{\sqrt[3]{y \cdot z - x} \cdot \sqrt[3]{y \cdot z - x}}{\sqrt[3]{t \cdot z - x} \cdot \sqrt[3]{t \cdot z - x}} \cdot \frac{\sqrt[3]{y \cdot z - x}}{\sqrt[3]{t \cdot z - x}}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \le -2.5121970162500594 \cdot 10^{206} \lor \neg \left(\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \le 1.9851270194247144 \cdot 10^{243}\right):\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + \frac{\sqrt[3]{y \cdot z - x} \cdot \sqrt[3]{y \cdot z - x}}{\sqrt[3]{t \cdot z - x} \cdot \sqrt[3]{t \cdot z - x}} \cdot \frac{\sqrt[3]{y \cdot z - x}}{\sqrt[3]{t \cdot z - x}}}{x + 1}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r449243 = x;
        double r449244 = y;
        double r449245 = z;
        double r449246 = r449244 * r449245;
        double r449247 = r449246 - r449243;
        double r449248 = t;
        double r449249 = r449248 * r449245;
        double r449250 = r449249 - r449243;
        double r449251 = r449247 / r449250;
        double r449252 = r449243 + r449251;
        double r449253 = 1.0;
        double r449254 = r449243 + r449253;
        double r449255 = r449252 / r449254;
        return r449255;
}
↓
double f(double x, double y, double z, double t) {
        double r449256 = x;
        double r449257 = y;
        double r449258 = z;
        double r449259 = r449257 * r449258;
        double r449260 = r449259 - r449256;
        double r449261 = t;
        double r449262 = r449261 * r449258;
        double r449263 = r449262 - r449256;
        double r449264 = r449260 / r449263;
        double r449265 = r449256 + r449264;
        double r449266 = 1.0;
        double r449267 = r449256 + r449266;
        double r449268 = r449265 / r449267;
        double r449269 = -2.5121970162500594e+206;
        bool r449270 = r449268 <= r449269;
        double r449271 = 1.9851270194247144e+243;
        bool r449272 = r449268 <= r449271;
        double r449273 = !r449272;
        bool r449274 = r449270 || r449273;
        double r449275 = r449257 / r449261;
        double r449276 = r449256 + r449275;
        double r449277 = r449276 / r449267;
        double r449278 = cbrt(r449260);
        double r449279 = r449278 * r449278;
        double r449280 = cbrt(r449263);
        double r449281 = r449280 * r449280;
        double r449282 = r449279 / r449281;
        double r449283 = r449278 / r449280;
        double r449284 = r449282 * r449283;
        double r449285 = r449256 + r449284;
        double r449286 = r449285 / r449267;
        double r449287 = r449274 ? r449277 : r449286;
        return r449287;
}

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
Herbie3.0
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)) < -2.5121970162500594e+206 or 1.9851270194247144e+243 < (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))

    1. Initial program 52.0

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

    2. Taylor expanded around inf 15.5

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

    if -2.5121970162500594e+206 < (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)) < 1.9851270194247144e+243

    1. Initial program 0.8

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

    3. Applied add-cube-cbrt1.2

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

    4. Applied add-cube-cbrt1.2

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

    5. Applied times-frac1.2

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

  4. Final simplification3.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \le -2.5121970162500594 \cdot 10^{206} \lor \neg \left(\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \le 1.9851270194247144 \cdot 10^{243}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{\sqrt[3]{y \cdot z - x} \cdot \sqrt[3]{y \cdot z - x}}{\sqrt[3]{t \cdot z - x} \cdot \sqrt[3]{t \cdot z - x}} \cdot \frac{\sqrt[3]{y \cdot z - x}}{\sqrt[3]{t \cdot z - x}}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2019198 
(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)))