Average Error: 0.1 → 0.1
Time: 39.2s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(z + \left(\left(\log \left(\sqrt[3]{y}\right) \cdot x + \log \left(\sqrt[3]{y}\right) \cdot x\right) + \log \left({y}^{\frac{1}{3}}\right) \cdot x\right)\right) + t\right) + a\right) + \log c \cdot \left(b - 0.5\right)\right) + y \cdot i\]
\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(z + \left(\left(\log \left(\sqrt[3]{y}\right) \cdot x + \log \left(\sqrt[3]{y}\right) \cdot x\right) + \log \left({y}^{\frac{1}{3}}\right) \cdot x\right)\right) + t\right) + a\right) + \log c \cdot \left(b - 0.5\right)\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3932870 = x;
        double r3932871 = y;
        double r3932872 = log(r3932871);
        double r3932873 = r3932870 * r3932872;
        double r3932874 = z;
        double r3932875 = r3932873 + r3932874;
        double r3932876 = t;
        double r3932877 = r3932875 + r3932876;
        double r3932878 = a;
        double r3932879 = r3932877 + r3932878;
        double r3932880 = b;
        double r3932881 = 0.5;
        double r3932882 = r3932880 - r3932881;
        double r3932883 = c;
        double r3932884 = log(r3932883);
        double r3932885 = r3932882 * r3932884;
        double r3932886 = r3932879 + r3932885;
        double r3932887 = i;
        double r3932888 = r3932871 * r3932887;
        double r3932889 = r3932886 + r3932888;
        return r3932889;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3932890 = z;
        double r3932891 = y;
        double r3932892 = cbrt(r3932891);
        double r3932893 = log(r3932892);
        double r3932894 = x;
        double r3932895 = r3932893 * r3932894;
        double r3932896 = r3932895 + r3932895;
        double r3932897 = 0.3333333333333333;
        double r3932898 = pow(r3932891, r3932897);
        double r3932899 = log(r3932898);
        double r3932900 = r3932899 * r3932894;
        double r3932901 = r3932896 + r3932900;
        double r3932902 = r3932890 + r3932901;
        double r3932903 = t;
        double r3932904 = r3932902 + r3932903;
        double r3932905 = a;
        double r3932906 = r3932904 + r3932905;
        double r3932907 = c;
        double r3932908 = log(r3932907);
        double r3932909 = b;
        double r3932910 = 0.5;
        double r3932911 = r3932909 - r3932910;
        double r3932912 = r3932908 * r3932911;
        double r3932913 = r3932906 + r3932912;
        double r3932914 = i;
        double r3932915 = r3932891 * r3932914;
        double r3932916 = r3932913 + r3932915;
        return r3932916;
}

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-rgt-in0.1

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

  6. Simplified0.1

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

  8. Applied pow1/30.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))