Average Error: 1.8 → 1.2
Time: 13.7s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{1}{\frac{y}{\left({\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1}\right)}^{1} \cdot x\right) \cdot \frac{{\left(\frac{\sqrt[3]{1}}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{1}{\frac{y}{\left({\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1}\right)}^{1} \cdot x\right) \cdot \frac{{\left(\frac{\sqrt[3]{1}}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}
double f(double x, double y, double z, double t, double a, double b) {
        double r99863 = x;
        double r99864 = y;
        double r99865 = z;
        double r99866 = log(r99865);
        double r99867 = r99864 * r99866;
        double r99868 = t;
        double r99869 = 1.0;
        double r99870 = r99868 - r99869;
        double r99871 = a;
        double r99872 = log(r99871);
        double r99873 = r99870 * r99872;
        double r99874 = r99867 + r99873;
        double r99875 = b;
        double r99876 = r99874 - r99875;
        double r99877 = exp(r99876);
        double r99878 = r99863 * r99877;
        double r99879 = r99878 / r99864;
        return r99879;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r99880 = 1.0;
        double r99881 = y;
        double r99882 = cbrt(r99880);
        double r99883 = r99882 * r99882;
        double r99884 = r99883 / r99880;
        double r99885 = 1.0;
        double r99886 = pow(r99884, r99885);
        double r99887 = x;
        double r99888 = r99886 * r99887;
        double r99889 = a;
        double r99890 = r99882 / r99889;
        double r99891 = pow(r99890, r99885);
        double r99892 = z;
        double r99893 = r99880 / r99892;
        double r99894 = log(r99893);
        double r99895 = r99881 * r99894;
        double r99896 = r99880 / r99889;
        double r99897 = log(r99896);
        double r99898 = t;
        double r99899 = r99897 * r99898;
        double r99900 = b;
        double r99901 = r99899 + r99900;
        double r99902 = r99895 + r99901;
        double r99903 = exp(r99902);
        double r99904 = r99891 / r99903;
        double r99905 = r99888 * r99904;
        double r99906 = r99881 / r99905;
        double r99907 = r99880 / r99906;
        return r99907;
}

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 1.8

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

  2. Taylor expanded around inf 1.9

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

  3. Simplified1.1

    \[\leadsto \frac{x \cdot \color{blue}{\frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}{y}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity1.1

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

  6. Applied *-un-lft-identity1.1

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

  7. Applied add-cube-cbrt1.1

    \[\leadsto \frac{x \cdot \frac{{\left(\frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{1 \cdot a}\right)}^{1}}{1 \cdot e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y}\]

  8. Applied times-frac1.1

    \[\leadsto \frac{x \cdot \frac{{\color{blue}{\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1} \cdot \frac{\sqrt[3]{1}}{a}\right)}}^{1}}{1 \cdot e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y}\]

  9. Applied unpow-prod-down1.1

    \[\leadsto \frac{x \cdot \frac{\color{blue}{{\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1}\right)}^{1} \cdot {\left(\frac{\sqrt[3]{1}}{a}\right)}^{1}}}{1 \cdot e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y}\]

  10. Applied times-frac1.1

    \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{{\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1}\right)}^{1}}{1} \cdot \frac{{\left(\frac{\sqrt[3]{1}}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}\right)}}{y}\]

  11. Applied associate-*r*1.1

    \[\leadsto \frac{\color{blue}{\left(x \cdot \frac{{\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1}\right)}^{1}}{1}\right) \cdot \frac{{\left(\frac{\sqrt[3]{1}}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}{y}\]

  12. Simplified1.1

    \[\leadsto \frac{\color{blue}{\left({\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1}\right)}^{1} \cdot x\right)} \cdot \frac{{\left(\frac{\sqrt[3]{1}}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y}\]
  13. Using strategy rm

  14. Applied clear-num1.2

    \[\leadsto \color{blue}{\frac{1}{\frac{y}{\left({\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1}\right)}^{1} \cdot x\right) \cdot \frac{{\left(\frac{\sqrt[3]{1}}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}}\]

  15. Final simplification1.2

    \[\leadsto \frac{1}{\frac{y}{\left({\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1}\right)}^{1} \cdot x\right) \cdot \frac{{\left(\frac{\sqrt[3]{1}}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}\]

Reproduce

herbie shell --seed 2020065 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  :precision binary64
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1) (log a))) b))) y))