Average Error: 0.1 → 0.1
Time: 34.4s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\log \left(\sqrt[3]{c}\right) + \log \left(\sqrt[3]{c}\right)\right) \cdot \left(b - 0.5\right) + \log \left(\sqrt[3]{c}\right) \cdot \left(b - 0.5\right)\right) + \left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right)\right) + i \cdot y\]
\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(\log \left(\sqrt[3]{c}\right) + \log \left(\sqrt[3]{c}\right)\right) \cdot \left(b - 0.5\right) + \log \left(\sqrt[3]{c}\right) \cdot \left(b - 0.5\right)\right) + \left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right)\right) + i \cdot y
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1480867 = x;
        double r1480868 = y;
        double r1480869 = log(r1480868);
        double r1480870 = r1480867 * r1480869;
        double r1480871 = z;
        double r1480872 = r1480870 + r1480871;
        double r1480873 = t;
        double r1480874 = r1480872 + r1480873;
        double r1480875 = a;
        double r1480876 = r1480874 + r1480875;
        double r1480877 = b;
        double r1480878 = 0.5;
        double r1480879 = r1480877 - r1480878;
        double r1480880 = c;
        double r1480881 = log(r1480880);
        double r1480882 = r1480879 * r1480881;
        double r1480883 = r1480876 + r1480882;
        double r1480884 = i;
        double r1480885 = r1480868 * r1480884;
        double r1480886 = r1480883 + r1480885;
        return r1480886;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1480887 = c;
        double r1480888 = cbrt(r1480887);
        double r1480889 = log(r1480888);
        double r1480890 = r1480889 + r1480889;
        double r1480891 = b;
        double r1480892 = 0.5;
        double r1480893 = r1480891 - r1480892;
        double r1480894 = r1480890 * r1480893;
        double r1480895 = r1480889 * r1480893;
        double r1480896 = r1480894 + r1480895;
        double r1480897 = x;
        double r1480898 = y;
        double r1480899 = log(r1480898);
        double r1480900 = r1480897 * r1480899;
        double r1480901 = z;
        double r1480902 = r1480900 + r1480901;
        double r1480903 = t;
        double r1480904 = r1480902 + r1480903;
        double r1480905 = a;
        double r1480906 = r1480904 + r1480905;
        double r1480907 = r1480896 + r1480906;
        double r1480908 = i;
        double r1480909 = r1480908 * r1480898;
        double r1480910 = r1480907 + r1480909;
        return r1480910;
}

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-rgt-in0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019156 
(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)))