Average Error: 0.1 → 0.1
Time: 22.9s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\log \left(\left(\sqrt[3]{{y}^{\frac{2}{3}}} \cdot \sqrt[3]{{y}^{\frac{2}{3}}}\right) \cdot {\left(\sqrt[3]{\sqrt[3]{y}}\right)}^{2}\right) \cdot x + \left(\left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right) - z\right)\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\log \left(\left(\sqrt[3]{{y}^{\frac{2}{3}}} \cdot \sqrt[3]{{y}^{\frac{2}{3}}}\right) \cdot {\left(\sqrt[3]{\sqrt[3]{y}}\right)}^{2}\right) \cdot x + \left(\left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right) - z\right)\right) + \log t
double f(double x, double y, double z, double t) {
        double r75628 = x;
        double r75629 = y;
        double r75630 = log(r75629);
        double r75631 = r75628 * r75630;
        double r75632 = r75631 - r75629;
        double r75633 = z;
        double r75634 = r75632 - r75633;
        double r75635 = t;
        double r75636 = log(r75635);
        double r75637 = r75634 + r75636;
        return r75637;
}
↓
double f(double x, double y, double z, double t) {
        double r75638 = y;
        double r75639 = 0.6666666666666666;
        double r75640 = pow(r75638, r75639);
        double r75641 = cbrt(r75640);
        double r75642 = r75641 * r75641;
        double r75643 = cbrt(r75638);
        double r75644 = cbrt(r75643);
        double r75645 = 2.0;
        double r75646 = pow(r75644, r75645);
        double r75647 = r75642 * r75646;
        double r75648 = log(r75647);
        double r75649 = x;
        double r75650 = r75648 * r75649;
        double r75651 = log(r75643);
        double r75652 = r75651 * r75649;
        double r75653 = r75652 - r75638;
        double r75654 = z;
        double r75655 = r75653 - r75654;
        double r75656 = r75650 + r75655;
        double r75657 = t;
        double r75658 = log(r75657);
        double r75659 = r75656 + r75658;
        return r75659;
}

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-rgt-in0.1

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

  6. Applied associate--l+0.1

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

  7. Applied associate--l+0.1

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

  9. Applied add-cube-cbrt0.1

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

  10. Applied cbrt-prod0.1

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

  11. Applied add-cube-cbrt0.1

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

  12. Applied cbrt-prod0.1

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

  13. Applied swap-sqr0.1

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

  14. Simplified0.1

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

  15. Simplified0.1

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

  16. Final simplification0.1

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

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(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)))