Average Error: 3.7 → 2.0
Time: 1.0m
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.208395080102709112792128783245881603461 \cdot 10^{-212} \lor \neg \left(t \le 2.337263817047334211087764408008483118108 \cdot 10^{-101}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{a + t}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - t \cdot \left(\left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{t \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\\ \end{array}\]
\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.208395080102709112792128783245881603461 \cdot 10^{-212} \lor \neg \left(t \le 2.337263817047334211087764408008483118108 \cdot 10^{-101}\right):\\
\;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{a + t}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - t \cdot \left(\left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{t \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r168258 = x;
        double r168259 = y;
        double r168260 = 2.0;
        double r168261 = z;
        double r168262 = t;
        double r168263 = a;
        double r168264 = r168262 + r168263;
        double r168265 = sqrt(r168264);
        double r168266 = r168261 * r168265;
        double r168267 = r168266 / r168262;
        double r168268 = b;
        double r168269 = c;
        double r168270 = r168268 - r168269;
        double r168271 = 5.0;
        double r168272 = 6.0;
        double r168273 = r168271 / r168272;
        double r168274 = r168263 + r168273;
        double r168275 = 3.0;
        double r168276 = r168262 * r168275;
        double r168277 = r168260 / r168276;
        double r168278 = r168274 - r168277;
        double r168279 = r168270 * r168278;
        double r168280 = r168267 - r168279;
        double r168281 = r168260 * r168280;
        double r168282 = exp(r168281);
        double r168283 = r168259 * r168282;
        double r168284 = r168258 + r168283;
        double r168285 = r168258 / r168284;
        return r168285;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r168286 = t;
        double r168287 = -1.208395080102709e-212;
        bool r168288 = r168286 <= r168287;
        double r168289 = 2.3372638170473342e-101;
        bool r168290 = r168286 <= r168289;
        double r168291 = !r168290;
        bool r168292 = r168288 || r168291;
        double r168293 = x;
        double r168294 = y;
        double r168295 = 2.0;
        double r168296 = z;
        double r168297 = cbrt(r168286);
        double r168298 = r168297 * r168297;
        double r168299 = r168296 / r168298;
        double r168300 = a;
        double r168301 = r168300 + r168286;
        double r168302 = sqrt(r168301);
        double r168303 = r168302 / r168297;
        double r168304 = r168299 * r168303;
        double r168305 = b;
        double r168306 = c;
        double r168307 = r168305 - r168306;
        double r168308 = 5.0;
        double r168309 = 6.0;
        double r168310 = r168308 / r168309;
        double r168311 = r168300 + r168310;
        double r168312 = 3.0;
        double r168313 = r168286 * r168312;
        double r168314 = r168295 / r168313;
        double r168315 = r168311 - r168314;
        double r168316 = r168307 * r168315;
        double r168317 = r168304 - r168316;
        double r168318 = r168295 * r168317;
        double r168319 = exp(r168318);
        double r168320 = r168294 * r168319;
        double r168321 = r168293 + r168320;
        double r168322 = r168293 / r168321;
        double r168323 = r168286 + r168300;
        double r168324 = sqrt(r168323);
        double r168325 = r168296 * r168324;
        double r168326 = r168300 - r168310;
        double r168327 = r168326 * r168313;
        double r168328 = r168325 * r168327;
        double r168329 = r168311 * r168327;
        double r168330 = r168326 * r168295;
        double r168331 = r168329 - r168330;
        double r168332 = r168307 * r168331;
        double r168333 = r168286 * r168332;
        double r168334 = r168328 - r168333;
        double r168335 = r168286 * r168327;
        double r168336 = r168334 / r168335;
        double r168337 = r168295 * r168336;
        double r168338 = exp(r168337);
        double r168339 = r168294 * r168338;
        double r168340 = r168293 + r168339;
        double r168341 = r168293 / r168340;
        double r168342 = r168292 ? r168322 : r168341;
        return r168342;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if t < -1.208395080102709e-212 or 2.3372638170473342e-101 < t

    1. Initial program 2.7

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt2.7

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]

    4. Applied times-frac1.2

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]

    5. Simplified1.2

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \color{blue}{\frac{\sqrt{a + t}}{\sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]

    if -1.208395080102709e-212 < t < 2.3372638170473342e-101

    1. Initial program 6.5

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
    2. Using strategy rm

    3. Applied flip-+9.9

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\color{blue}{\frac{a \cdot a - \frac{5}{6} \cdot \frac{5}{6}}{a - \frac{5}{6}}} - \frac{2}{t \cdot 3}\right)\right)}}\]

    4. Applied frac-sub9.9

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \color{blue}{\frac{\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2}{\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)}}\right)}}\]

    5. Applied associate-*r/9.9

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \color{blue}{\frac{\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)}{\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)}}\right)}}\]

    6. Applied frac-sub7.4

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - t \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{t \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}}\]
    7. Using strategy rm

    8. Applied difference-of-squares7.4

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - t \cdot \left(\left(b - c\right) \cdot \left(\color{blue}{\left(\left(a + \frac{5}{6}\right) \cdot \left(a - \frac{5}{6}\right)\right)} \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{t \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\]

    9. Applied associate-*l*4.2

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - t \cdot \left(\left(b - c\right) \cdot \left(\color{blue}{\left(a + \frac{5}{6}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)} - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{t \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.208395080102709112792128783245881603461 \cdot 10^{-212} \lor \neg \left(t \le 2.337263817047334211087764408008483118108 \cdot 10^{-101}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{a + t}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - t \cdot \left(\left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{t \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019291 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2"
  :precision binary64
  (/ x (+ x (* y (exp (* 2 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5 6)) (/ 2 (* t 3)))))))))))