Average Error: 0.1 → 0.1
Time: 10.8s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left({y}^{\frac{1}{3}}\right)\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\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(\left(x \cdot \left(2 \cdot \log \left({y}^{\frac{1}{3}}\right)\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
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r79872 = x;
        double r79873 = y;
        double r79874 = log(r79873);
        double r79875 = r79872 * r79874;
        double r79876 = z;
        double r79877 = r79875 + r79876;
        double r79878 = t;
        double r79879 = r79877 + r79878;
        double r79880 = a;
        double r79881 = r79879 + r79880;
        double r79882 = b;
        double r79883 = 0.5;
        double r79884 = r79882 - r79883;
        double r79885 = c;
        double r79886 = log(r79885);
        double r79887 = r79884 * r79886;
        double r79888 = r79881 + r79887;
        double r79889 = i;
        double r79890 = r79873 * r79889;
        double r79891 = r79888 + r79890;
        return r79891;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r79892 = x;
        double r79893 = 2.0;
        double r79894 = y;
        double r79895 = 0.3333333333333333;
        double r79896 = pow(r79894, r79895);
        double r79897 = log(r79896);
        double r79898 = r79893 * r79897;
        double r79899 = r79892 * r79898;
        double r79900 = cbrt(r79894);
        double r79901 = log(r79900);
        double r79902 = r79892 * r79901;
        double r79903 = r79899 + r79902;
        double r79904 = z;
        double r79905 = r79903 + r79904;
        double r79906 = t;
        double r79907 = r79905 + r79906;
        double r79908 = a;
        double r79909 = r79907 + r79908;
        double r79910 = b;
        double r79911 = 0.5;
        double r79912 = r79910 - r79911;
        double r79913 = c;
        double r79914 = log(r79913);
        double r79915 = r79912 * r79914;
        double r79916 = r79909 + r79915;
        double r79917 = i;
        double r79918 = r79894 * r79917;
        double r79919 = r79916 + r79918;
        return r79919;
}

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. Simplified0.1

    \[\leadsto \left(\left(\left(\left(\left(\color{blue}{x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right)} + x \cdot \log \left(\sqrt[3]{y}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
  7. Using strategy rm

  8. Applied pow1/30.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019352 
(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)))