Average Error: 0.1 → 0.1
Time: 40.5s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(2 \cdot \log \left({c}^{\frac{1}{3}}\right)\right) \cdot \left(b - 0.5\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right)\right) + y \cdot i\]
\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(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(2 \cdot \log \left({c}^{\frac{1}{3}}\right)\right) \cdot \left(b - 0.5\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right)\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r67883 = x;
        double r67884 = y;
        double r67885 = log(r67884);
        double r67886 = r67883 * r67885;
        double r67887 = z;
        double r67888 = r67886 + r67887;
        double r67889 = t;
        double r67890 = r67888 + r67889;
        double r67891 = a;
        double r67892 = r67890 + r67891;
        double r67893 = b;
        double r67894 = 0.5;
        double r67895 = r67893 - r67894;
        double r67896 = c;
        double r67897 = log(r67896);
        double r67898 = r67895 * r67897;
        double r67899 = r67892 + r67898;
        double r67900 = i;
        double r67901 = r67884 * r67900;
        double r67902 = r67899 + r67901;
        return r67902;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r67903 = x;
        double r67904 = y;
        double r67905 = log(r67904);
        double r67906 = r67903 * r67905;
        double r67907 = z;
        double r67908 = r67906 + r67907;
        double r67909 = t;
        double r67910 = r67908 + r67909;
        double r67911 = a;
        double r67912 = r67910 + r67911;
        double r67913 = 2.0;
        double r67914 = c;
        double r67915 = 0.3333333333333333;
        double r67916 = pow(r67914, r67915);
        double r67917 = log(r67916);
        double r67918 = r67913 * r67917;
        double r67919 = b;
        double r67920 = 0.5;
        double r67921 = r67919 - r67920;
        double r67922 = r67918 * r67921;
        double r67923 = cbrt(r67914);
        double r67924 = log(r67923);
        double r67925 = r67921 * r67924;
        double r67926 = r67922 + r67925;
        double r67927 = r67912 + r67926;
        double r67928 = i;
        double r67929 = r67904 * r67928;
        double r67930 = r67927 + r67929;
        return r67930;
}

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

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Simplified0.1

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

  8. Applied pow1/30.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019325 
(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)))