Average Error: 0.1 → 0.1
Time: 10.9s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log \left({\left({y}^{\frac{2}{3}}\right)}^{1}\right) + \left(\log \left(\sqrt[3]{y}\right) \cdot x + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
↓
\left(\left(\left(\left(x \cdot \log \left({\left({y}^{\frac{2}{3}}\right)}^{1}\right) + \left(\log \left(\sqrt[3]{y}\right) \cdot x + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r58828 = x;
        double r58829 = y;
        double r58830 = log(r58829);
        double r58831 = r58828 * r58830;
        double r58832 = z;
        double r58833 = r58831 + r58832;
        double r58834 = t;
        double r58835 = r58833 + r58834;
        double r58836 = a;
        double r58837 = r58835 + r58836;
        double r58838 = b;
        double r58839 = 0.5;
        double r58840 = r58838 - r58839;
        double r58841 = c;
        double r58842 = log(r58841);
        double r58843 = r58840 * r58842;
        double r58844 = r58837 + r58843;
        double r58845 = i;
        double r58846 = r58829 * r58845;
        double r58847 = r58844 + r58846;
        return r58847;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r58848 = x;
        double r58849 = y;
        double r58850 = 0.6666666666666666;
        double r58851 = pow(r58849, r58850);
        double r58852 = 1.0;
        double r58853 = pow(r58851, r58852);
        double r58854 = log(r58853);
        double r58855 = r58848 * r58854;
        double r58856 = cbrt(r58849);
        double r58857 = log(r58856);
        double r58858 = r58857 * r58848;
        double r58859 = z;
        double r58860 = r58858 + r58859;
        double r58861 = r58855 + r58860;
        double r58862 = t;
        double r58863 = r58861 + r58862;
        double r58864 = a;
        double r58865 = r58863 + r58864;
        double r58866 = b;
        double r58867 = 0.5;
        double r58868 = r58866 - r58867;
        double r58869 = c;
        double r58870 = log(r58869);
        double r58871 = r58868 * r58870;
        double r58872 = r58865 + r58871;
        double r58873 = i;
        double r58874 = r58849 * r58873;
        double r58875 = r58872 + r58874;
        return r58875;
}

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

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  4. Applied log-prod0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right)} + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  5. Applied distribute-lft-in0.1

    \[\leadsto \left(\left(\left(\left(\color{blue}{\left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right)} + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  6. Applied associate-+l+0.1

    \[\leadsto \left(\left(\left(\color{blue}{\left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(x \cdot \log \left(\sqrt[3]{y}\right) + z\right)\right)} + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  7. Simplified0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \color{blue}{\left(\log \left(\sqrt[3]{y}\right) \cdot x + z\right)}\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
  8. Using strategy rm

  9. Applied pow10.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log \left(\sqrt[3]{y} \cdot \color{blue}{{\left(\sqrt[3]{y}\right)}^{1}}\right) + \left(\log \left(\sqrt[3]{y}\right) \cdot x + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  10. Applied pow10.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log \left(\color{blue}{{\left(\sqrt[3]{y}\right)}^{1}} \cdot {\left(\sqrt[3]{y}\right)}^{1}\right) + \left(\log \left(\sqrt[3]{y}\right) \cdot x + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  11. Applied pow-prod-down0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log \color{blue}{\left({\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)}^{1}\right)} + \left(\log \left(\sqrt[3]{y}\right) \cdot x + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  12. Simplified0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log \left({\color{blue}{\left({y}^{\frac{2}{3}}\right)}}^{1}\right) + \left(\log \left(\sqrt[3]{y}\right) \cdot x + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  13. Final simplification0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log \left({\left({y}^{\frac{2}{3}}\right)}^{1}\right) + \left(\log \left(\sqrt[3]{y}\right) \cdot x + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

Reproduce

herbie shell --seed 2020036 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))