Average Error: 0.1 → 0.1
Time: 23.3s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(x \cdot \log \left({\left(\frac{1}{y}\right)}^{\frac{-1}{3}}\right) - z\right) + \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x\right) + \left(\log t - y\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(x \cdot \log \left({\left(\frac{1}{y}\right)}^{\frac{-1}{3}}\right) - z\right) + \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x\right) + \left(\log t - y\right)
double f(double x, double y, double z, double t) {
        double r85855 = x;
        double r85856 = y;
        double r85857 = log(r85856);
        double r85858 = r85855 * r85857;
        double r85859 = r85858 - r85856;
        double r85860 = z;
        double r85861 = r85859 - r85860;
        double r85862 = t;
        double r85863 = log(r85862);
        double r85864 = r85861 + r85863;
        return r85864;
}
↓
double f(double x, double y, double z, double t) {
        double r85865 = x;
        double r85866 = 1.0;
        double r85867 = y;
        double r85868 = r85866 / r85867;
        double r85869 = -0.3333333333333333;
        double r85870 = pow(r85868, r85869);
        double r85871 = log(r85870);
        double r85872 = r85865 * r85871;
        double r85873 = z;
        double r85874 = r85872 - r85873;
        double r85875 = cbrt(r85867);
        double r85876 = r85875 * r85875;
        double r85877 = log(r85876);
        double r85878 = r85877 * r85865;
        double r85879 = r85874 + r85878;
        double r85880 = t;
        double r85881 = log(r85880);
        double r85882 = r85881 - r85867;
        double r85883 = r85879 + r85882;
        return r85883;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\left(x \cdot \log y - z\right) + \left(\log t - y\right)}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt0.1

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

  5. Applied log-prod0.1

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

  6. Applied distribute-lft-in0.1

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

  7. Applied associate--l+0.1

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

  8. Taylor expanded around inf 0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  (+ (- (- (* x (log y)) y) z) (log t)))