Average Error: 0.1 → 0.1
Time: 18.5s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(\log \left(\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{y}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}}\right)\right) \cdot x - y\right)\right) - z\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(\log \left(\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{y}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}}\right)\right) \cdot x - y\right)\right) - z\right) + \log t
double f(double x, double y, double z, double t) {
        double r4591999 = x;
        double r4592000 = y;
        double r4592001 = log(r4592000);
        double r4592002 = r4591999 * r4592001;
        double r4592003 = r4592002 - r4592000;
        double r4592004 = z;
        double r4592005 = r4592003 - r4592004;
        double r4592006 = t;
        double r4592007 = log(r4592006);
        double r4592008 = r4592005 + r4592007;
        return r4592008;
}
↓
double f(double x, double y, double z, double t) {
        double r4592009 = y;
        double r4592010 = cbrt(r4592009);
        double r4592011 = r4592010 * r4592010;
        double r4592012 = log(r4592011);
        double r4592013 = x;
        double r4592014 = r4592012 * r4592013;
        double r4592015 = cbrt(r4592010);
        double r4592016 = r4592015 * r4592015;
        double r4592017 = cbrt(r4592015);
        double r4592018 = cbrt(r4592016);
        double r4592019 = r4592017 * r4592018;
        double r4592020 = r4592016 * r4592019;
        double r4592021 = log(r4592020);
        double r4592022 = r4592021 * r4592013;
        double r4592023 = r4592022 - r4592009;
        double r4592024 = r4592014 + r4592023;
        double r4592025 = z;
        double r4592026 = r4592024 - r4592025;
        double r4592027 = t;
        double r4592028 = log(r4592027);
        double r4592029 = r4592026 + r4592028;
        return r4592029;
}

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. Using strategy rm

  8. Applied add-cube-cbrt0.1

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

  10. Applied add-cube-cbrt0.1

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

  11. Applied cbrt-prod0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  (+ (- (- (* x (log y)) y) z) (log t)))