Average Error: 3.7 → 2.6
Time: 37.2s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.747646842184294811529008447013758285829 \cdot 10^{-63} \lor \neg \left(t \le 4.66119048674144283533835621815974643908 \cdot 10^{-116}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) \cdot \frac{z \cdot \sqrt{t + a}}{\sqrt[3]{t}} - \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\\ \end{array}\]
\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 -1.747646842184294811529008447013758285829 \cdot 10^{-63} \lor \neg \left(t \le 4.66119048674144283533835621815974643908 \cdot 10^{-116}\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(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) \cdot \frac{z \cdot \sqrt{t + a}}{\sqrt[3]{t}} - \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 r108887 = x;
        double r108888 = y;
        double r108889 = 2.0;
        double r108890 = z;
        double r108891 = t;
        double r108892 = a;
        double r108893 = r108891 + r108892;
        double r108894 = sqrt(r108893);
        double r108895 = r108890 * r108894;
        double r108896 = r108895 / r108891;
        double r108897 = b;
        double r108898 = c;
        double r108899 = r108897 - r108898;
        double r108900 = 5.0;
        double r108901 = 6.0;
        double r108902 = r108900 / r108901;
        double r108903 = r108892 + r108902;
        double r108904 = 3.0;
        double r108905 = r108891 * r108904;
        double r108906 = r108889 / r108905;
        double r108907 = r108903 - r108906;
        double r108908 = r108899 * r108907;
        double r108909 = r108896 - r108908;
        double r108910 = r108889 * r108909;
        double r108911 = exp(r108910);
        double r108912 = r108888 * r108911;
        double r108913 = r108887 + r108912;
        double r108914 = r108887 / r108913;
        return r108914;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r108915 = t;
        double r108916 = -1.7476468421842948e-63;
        bool r108917 = r108915 <= r108916;
        double r108918 = 4.661190486741443e-116;
        bool r108919 = r108915 <= r108918;
        double r108920 = !r108919;
        bool r108921 = r108917 || r108920;
        double r108922 = x;
        double r108923 = y;
        double r108924 = 2.0;
        double r108925 = z;
        double r108926 = cbrt(r108915);
        double r108927 = r108926 * r108926;
        double r108928 = r108925 / r108927;
        double r108929 = a;
        double r108930 = r108915 + r108929;
        double r108931 = sqrt(r108930);
        double r108932 = r108931 / r108926;
        double r108933 = r108928 * r108932;
        double r108934 = b;
        double r108935 = c;
        double r108936 = r108934 - r108935;
        double r108937 = 5.0;
        double r108938 = 6.0;
        double r108939 = r108937 / r108938;
        double r108940 = r108929 + r108939;
        double r108941 = 3.0;
        double r108942 = r108915 * r108941;
        double r108943 = r108924 / r108942;
        double r108944 = r108940 - r108943;
        double r108945 = r108936 * r108944;
        double r108946 = r108933 - r108945;
        double r108947 = r108924 * r108946;
        double r108948 = exp(r108947);
        double r108949 = r108923 * r108948;
        double r108950 = r108922 + r108949;
        double r108951 = r108922 / r108950;
        double r108952 = r108929 - r108939;
        double r108953 = r108952 * r108942;
        double r108954 = r108925 * r108931;
        double r108955 = r108954 / r108926;
        double r108956 = r108953 * r108955;
        double r108957 = r108929 * r108929;
        double r108958 = r108939 * r108939;
        double r108959 = r108957 - r108958;
        double r108960 = r108959 * r108942;
        double r108961 = r108952 * r108924;
        double r108962 = r108960 - r108961;
        double r108963 = r108936 * r108962;
        double r108964 = r108927 * r108963;
        double r108965 = r108956 - r108964;
        double r108966 = r108927 * r108953;
        double r108967 = r108965 / r108966;
        double r108968 = r108924 * r108967;
        double r108969 = exp(r108968);
        double r108970 = r108923 * r108969;
        double r108971 = r108922 + r108970;
        double r108972 = r108922 / r108971;
        double r108973 = r108921 ? r108951 : r108972;
        return r108973;
}

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 < -1.7476468421842948e-63 or 4.661190486741443e-116 < t

    1. Initial program 2.3

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

    3. Applied add-cube-cbrt2.3

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

    4. Applied times-frac0.5

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

    if -1.7476468421842948e-63 < t < 4.661190486741443e-116

    1. Initial program 6.6

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

    3. Applied add-cube-cbrt6.6

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

    4. Applied times-frac6.8

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

    6. Applied add-log-exp33.0

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

    8. Applied flip-+34.8

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

    9. Applied frac-sub34.8

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

    10. Applied associate-*r/34.8

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

    11. Applied associate-*l/34.8

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

    12. Applied frac-sub33.9

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

    13. Simplified6.7

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

  4. Final simplification2.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.747646842184294811529008447013758285829 \cdot 10^{-63} \lor \neg \left(t \le 4.66119048674144283533835621815974643908 \cdot 10^{-116}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) \cdot \frac{z \cdot \sqrt{t + a}}{\sqrt[3]{t}} - \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 
(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)))))))))))