Average Error: 0.1 → 0.1
Time: 7.4s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\left(\log \left(1 \cdot {y}^{\frac{1}{3}}\right) \cdot x - y\right) - z\right)\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\left(\log \left(1 \cdot {y}^{\frac{1}{3}}\right) \cdot x - y\right) - z\right)\right) + \log t
double f(double x, double y, double z, double t) {
        double r92764 = x;
        double r92765 = y;
        double r92766 = log(r92765);
        double r92767 = r92764 * r92766;
        double r92768 = r92767 - r92765;
        double r92769 = z;
        double r92770 = r92768 - r92769;
        double r92771 = t;
        double r92772 = log(r92771);
        double r92773 = r92770 + r92772;
        return r92773;
}
↓
double f(double x, double y, double z, double t) {
        double r92774 = x;
        double r92775 = y;
        double r92776 = cbrt(r92775);
        double r92777 = r92776 * r92776;
        double r92778 = log(r92777);
        double r92779 = r92774 * r92778;
        double r92780 = 1.0;
        double r92781 = 0.3333333333333333;
        double r92782 = pow(r92775, r92781);
        double r92783 = r92780 * r92782;
        double r92784 = log(r92783);
        double r92785 = r92784 * r92774;
        double r92786 = r92785 - r92775;
        double r92787 = z;
        double r92788 = r92786 - r92787;
        double r92789 = r92779 + r92788;
        double r92790 = t;
        double r92791 = log(r92790);
        double r92792 = r92789 + r92791;
        return r92792;
}

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. Simplified0.1

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

  10. Applied *-un-lft-identity0.1

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

  11. Applied cbrt-prod0.1

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

  12. Simplified0.1

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

  13. Simplified0.1

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

  14. Final simplification0.1

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

Reproduce

herbie shell --seed 2019353 
(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)))