Average Error: 0.1 → 0.1
Time: 19.4s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + x \cdot \log \left({\left(\frac{1}{y}\right)}^{\frac{-1}{3}}\right)\right) - y\right) - z\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + x \cdot \log \left({\left(\frac{1}{y}\right)}^{\frac{-1}{3}}\right)\right) - y\right) - z\right) + \log t
double f(double x, double y, double z, double t) {
        double r102788 = x;
        double r102789 = y;
        double r102790 = log(r102789);
        double r102791 = r102788 * r102790;
        double r102792 = r102791 - r102789;
        double r102793 = z;
        double r102794 = r102792 - r102793;
        double r102795 = t;
        double r102796 = log(r102795);
        double r102797 = r102794 + r102796;
        return r102797;
}
↓
double f(double x, double y, double z, double t) {
        double r102798 = 2.0;
        double r102799 = y;
        double r102800 = cbrt(r102799);
        double r102801 = log(r102800);
        double r102802 = r102798 * r102801;
        double r102803 = x;
        double r102804 = r102802 * r102803;
        double r102805 = 1.0;
        double r102806 = r102805 / r102799;
        double r102807 = -0.3333333333333333;
        double r102808 = pow(r102806, r102807);
        double r102809 = log(r102808);
        double r102810 = r102803 * r102809;
        double r102811 = r102804 + r102810;
        double r102812 = r102811 - r102799;
        double r102813 = z;
        double r102814 = r102812 - r102813;
        double r102815 = t;
        double r102816 = log(r102815);
        double r102817 = r102814 + r102816;
        return r102817;
}

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. Simplified0.1

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

  7. Taylor expanded around inf 0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019212 
(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)))