Average Error: 3.8 → 2.4
Time: 24.2s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -9.473153273384903490502724565303245723582 \cdot 10^{-244} \lor \neg \left(t \le 9.548444342446725028979639354139199225475 \cdot 10^{-247}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\\ \end{array}\]
\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 -9.473153273384903490502724565303245723582 \cdot 10^{-244} \lor \neg \left(t \le 9.548444342446725028979639354139199225475 \cdot 10^{-247}\right):\\
\;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\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)}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \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)}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \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 r63230 = x;
        double r63231 = y;
        double r63232 = 2.0;
        double r63233 = z;
        double r63234 = t;
        double r63235 = a;
        double r63236 = r63234 + r63235;
        double r63237 = sqrt(r63236);
        double r63238 = r63233 * r63237;
        double r63239 = r63238 / r63234;
        double r63240 = b;
        double r63241 = c;
        double r63242 = r63240 - r63241;
        double r63243 = 5.0;
        double r63244 = 6.0;
        double r63245 = r63243 / r63244;
        double r63246 = r63235 + r63245;
        double r63247 = 3.0;
        double r63248 = r63234 * r63247;
        double r63249 = r63232 / r63248;
        double r63250 = r63246 - r63249;
        double r63251 = r63242 * r63250;
        double r63252 = r63239 - r63251;
        double r63253 = r63232 * r63252;
        double r63254 = exp(r63253);
        double r63255 = r63231 * r63254;
        double r63256 = r63230 + r63255;
        double r63257 = r63230 / r63256;
        return r63257;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r63258 = t;
        double r63259 = -9.473153273384903e-244;
        bool r63260 = r63258 <= r63259;
        double r63261 = 9.548444342446725e-247;
        bool r63262 = r63258 <= r63261;
        double r63263 = !r63262;
        bool r63264 = r63260 || r63263;
        double r63265 = x;
        double r63266 = y;
        double r63267 = 2.0;
        double r63268 = z;
        double r63269 = cbrt(r63258);
        double r63270 = r63269 * r63269;
        double r63271 = r63268 / r63270;
        double r63272 = a;
        double r63273 = r63258 + r63272;
        double r63274 = sqrt(r63273);
        double r63275 = r63274 / r63269;
        double r63276 = r63271 * r63275;
        double r63277 = b;
        double r63278 = c;
        double r63279 = r63277 - r63278;
        double r63280 = 5.0;
        double r63281 = 6.0;
        double r63282 = r63280 / r63281;
        double r63283 = r63272 + r63282;
        double r63284 = 3.0;
        double r63285 = r63258 * r63284;
        double r63286 = r63267 / r63285;
        double r63287 = r63283 - r63286;
        double r63288 = r63279 * r63287;
        double r63289 = r63276 - r63288;
        double r63290 = r63267 * r63289;
        double r63291 = exp(r63290);
        double r63292 = r63266 * r63291;
        double r63293 = r63265 + r63292;
        double r63294 = r63265 / r63293;
        double r63295 = r63268 * r63275;
        double r63296 = r63272 - r63282;
        double r63297 = r63296 * r63285;
        double r63298 = r63295 * r63297;
        double r63299 = r63272 * r63272;
        double r63300 = r63282 * r63282;
        double r63301 = r63299 - r63300;
        double r63302 = r63301 * r63285;
        double r63303 = r63296 * r63267;
        double r63304 = r63302 - r63303;
        double r63305 = r63279 * r63304;
        double r63306 = r63270 * r63305;
        double r63307 = r63298 - r63306;
        double r63308 = r63270 * r63297;
        double r63309 = r63307 / r63308;
        double r63310 = r63267 * r63309;
        double r63311 = exp(r63310);
        double r63312 = r63266 * r63311;
        double r63313 = r63265 + r63312;
        double r63314 = r63265 / r63313;
        double r63315 = r63264 ? r63294 : r63314;
        return r63315;
}

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 < -9.473153273384903e-244 or 9.548444342446725e-247 < t

    1. Initial program 3.0

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

    3. Applied add-cube-cbrt3.0

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

    4. Applied times-frac1.8

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

    if -9.473153273384903e-244 < t < 9.548444342446725e-247

    1. Initial program 10.4

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

    3. Applied add-cube-cbrt10.4

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

    4. Applied times-frac10.5

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

    6. Applied flip-+13.9

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

    7. Applied frac-sub13.9

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

    8. Applied associate-*r/13.9

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

    9. Applied associate-*l/13.8

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

    10. Applied frac-sub7.9

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

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -9.473153273384903490502724565303245723582 \cdot 10^{-244} \lor \neg \left(t \le 9.548444342446725028979639354139199225475 \cdot 10^{-247}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(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)))))))))))