Average Error: 1.9 → 1.1
Time: 40.3s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}{\sqrt[3]{\sqrt[3]{y}} \cdot \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)} \cdot \left(x \cdot \frac{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right)\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\frac{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}{\sqrt[3]{\sqrt[3]{y}} \cdot \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)} \cdot \left(x \cdot \frac{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r1306905 = x;
        double r1306906 = y;
        double r1306907 = z;
        double r1306908 = log(r1306907);
        double r1306909 = r1306906 * r1306908;
        double r1306910 = t;
        double r1306911 = 1.0;
        double r1306912 = r1306910 - r1306911;
        double r1306913 = a;
        double r1306914 = log(r1306913);
        double r1306915 = r1306912 * r1306914;
        double r1306916 = r1306909 + r1306915;
        double r1306917 = b;
        double r1306918 = r1306916 - r1306917;
        double r1306919 = exp(r1306918);
        double r1306920 = r1306905 * r1306919;
        double r1306921 = r1306920 / r1306906;
        return r1306921;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1306922 = a;
        double r1306923 = log(r1306922);
        double r1306924 = t;
        double r1306925 = 1.0;
        double r1306926 = r1306924 - r1306925;
        double r1306927 = r1306923 * r1306926;
        double r1306928 = z;
        double r1306929 = log(r1306928);
        double r1306930 = y;
        double r1306931 = r1306929 * r1306930;
        double r1306932 = r1306927 + r1306931;
        double r1306933 = b;
        double r1306934 = r1306932 - r1306933;
        double r1306935 = exp(r1306934);
        double r1306936 = cbrt(r1306935);
        double r1306937 = cbrt(r1306930);
        double r1306938 = cbrt(r1306937);
        double r1306939 = r1306938 * r1306938;
        double r1306940 = r1306938 * r1306939;
        double r1306941 = r1306936 / r1306940;
        double r1306942 = x;
        double r1306943 = r1306936 * r1306936;
        double r1306944 = r1306937 * r1306937;
        double r1306945 = r1306943 / r1306944;
        double r1306946 = r1306942 * r1306945;
        double r1306947 = r1306941 * r1306946;
        return r1306947;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.9

    \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity1.9

    \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{\color{blue}{1 \cdot y}}\]

  4. Applied times-frac2.0

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\]

  5. Simplified2.0

    \[\leadsto \color{blue}{x} \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt2.0

    \[\leadsto x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}\]

  8. Applied add-cube-cbrt2.0

    \[\leadsto x \cdot \frac{\color{blue}{\left(\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}\right) \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}\]

  9. Applied times-frac2.0

    \[\leadsto x \cdot \color{blue}{\left(\frac{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}{\sqrt[3]{y}}\right)}\]

  10. Applied associate-*r*1.1

    \[\leadsto \color{blue}{\left(x \cdot \frac{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot \frac{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}{\sqrt[3]{y}}}\]
  11. Using strategy rm

  12. Applied add-cube-cbrt1.1

    \[\leadsto \left(x \cdot \frac{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot \frac{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}{\color{blue}{\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \sqrt[3]{\sqrt[3]{y}}}}\]

  13. Final simplification1.1

    \[\leadsto \frac{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}{\sqrt[3]{\sqrt[3]{y}} \cdot \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)} \cdot \left(x \cdot \frac{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right)\]

Reproduce

herbie shell --seed 2019152 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))