Average Error: 0.1 → 0.1
Time: 6.3s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\left(\left(\log \left({y}^{\frac{1}{3}}\right) \cdot x - y\right) - z\right) + \log t\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\left(\left(\log \left({y}^{\frac{1}{3}}\right) \cdot x - y\right) - z\right) + \log t\right)
double f(double x, double y, double z, double t) {
        double r85795 = x;
        double r85796 = y;
        double r85797 = log(r85796);
        double r85798 = r85795 * r85797;
        double r85799 = r85798 - r85796;
        double r85800 = z;
        double r85801 = r85799 - r85800;
        double r85802 = t;
        double r85803 = log(r85802);
        double r85804 = r85801 + r85803;
        return r85804;
}
↓
double f(double x, double y, double z, double t) {
        double r85805 = x;
        double r85806 = y;
        double r85807 = cbrt(r85806);
        double r85808 = r85807 * r85807;
        double r85809 = log(r85808);
        double r85810 = r85805 * r85809;
        double r85811 = 0.3333333333333333;
        double r85812 = pow(r85806, r85811);
        double r85813 = log(r85812);
        double r85814 = r85813 * r85805;
        double r85815 = r85814 - r85806;
        double r85816 = z;
        double r85817 = r85815 - r85816;
        double r85818 = t;
        double r85819 = log(r85818);
        double r85820 = r85817 + r85819;
        double r85821 = r85810 + r85820;
        return r85821;
}

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. Using strategy rm

  3. Applied add-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Applied associate--l+0.1

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

  7. Applied associate--l+0.1

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

  8. Applied associate-+l+0.1

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

  9. Simplified0.1

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

  11. Applied pow1/30.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2020056 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))