Average Error: 0.1 → 0.1
Time: 7.5s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\log \left(1 \cdot {y}^{\frac{1}{3}}\right) \cdot x - y\right)\right) + \left(\log t - z\right)\]
\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(\log \left(1 \cdot {y}^{\frac{1}{3}}\right) \cdot x - y\right)\right) + \left(\log t - z\right)
double f(double x, double y, double z, double t) {
        double r115105 = x;
        double r115106 = y;
        double r115107 = log(r115106);
        double r115108 = r115105 * r115107;
        double r115109 = r115108 - r115106;
        double r115110 = z;
        double r115111 = r115109 - r115110;
        double r115112 = t;
        double r115113 = log(r115112);
        double r115114 = r115111 + r115113;
        return r115114;
}
↓
double f(double x, double y, double z, double t) {
        double r115115 = x;
        double r115116 = y;
        double r115117 = cbrt(r115116);
        double r115118 = r115117 * r115117;
        double r115119 = log(r115118);
        double r115120 = r115115 * r115119;
        double r115121 = 1.0;
        double r115122 = 0.3333333333333333;
        double r115123 = pow(r115116, r115122);
        double r115124 = r115121 * r115123;
        double r115125 = log(r115124);
        double r115126 = r115125 * r115115;
        double r115127 = r115126 - r115116;
        double r115128 = r115120 + r115127;
        double r115129 = t;
        double r115130 = log(r115129);
        double r115131 = z;
        double r115132 = r115130 - r115131;
        double r115133 = r115128 + r115132;
        return r115133;
}

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 sub-neg0.1

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

  4. Applied associate-+l+0.1

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

  5. Simplified0.1

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

  7. Applied add-cube-cbrt0.1

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

  8. Applied log-prod0.1

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

  9. Applied distribute-lft-in0.1

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

  10. Applied associate--l+0.1

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

  11. Simplified0.1

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

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

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

  14. Applied cbrt-prod0.1

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

  15. Simplified0.1

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

  16. Simplified0.1

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

  17. Final simplification0.1

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

Reproduce

herbie shell --seed 2020034 
(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)))