Average Error: 0.1 → 0.1
Time: 45.9s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + \log \left(\sqrt[3]{y}\right) \cdot x\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\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(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\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
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r68913 = x;
        double r68914 = y;
        double r68915 = log(r68914);
        double r68916 = r68913 * r68915;
        double r68917 = z;
        double r68918 = r68916 + r68917;
        double r68919 = t;
        double r68920 = r68918 + r68919;
        double r68921 = a;
        double r68922 = r68920 + r68921;
        double r68923 = b;
        double r68924 = 0.5;
        double r68925 = r68923 - r68924;
        double r68926 = c;
        double r68927 = log(r68926);
        double r68928 = r68925 * r68927;
        double r68929 = r68922 + r68928;
        double r68930 = i;
        double r68931 = r68914 * r68930;
        double r68932 = r68929 + r68931;
        return r68932;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r68933 = 2.0;
        double r68934 = y;
        double r68935 = cbrt(r68934);
        double r68936 = log(r68935);
        double r68937 = r68933 * r68936;
        double r68938 = x;
        double r68939 = r68937 * r68938;
        double r68940 = r68936 * r68938;
        double r68941 = r68939 + r68940;
        double r68942 = z;
        double r68943 = r68941 + r68942;
        double r68944 = t;
        double r68945 = r68943 + r68944;
        double r68946 = a;
        double r68947 = r68945 + r68946;
        double r68948 = b;
        double r68949 = 0.5;
        double r68950 = r68948 - r68949;
        double r68951 = c;
        double r68952 = log(r68951);
        double r68953 = r68950 * r68952;
        double r68954 = r68947 + r68953;
        double r68955 = i;
        double r68956 = r68934 * r68955;
        double r68957 = r68954 + r68956;
        return r68957;
}

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

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 
(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)))