Average Error: 0.1 → 0.1
Time: 18.1s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\log t + x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right) + \left(\log \left(\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) + \log \left(\sqrt[3]{\sqrt[3]{y}}\right)\right)\right)\right) - \left(y + z\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\log t + x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right) + \left(\log \left(\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) + \log \left(\sqrt[3]{\sqrt[3]{y}}\right)\right)\right)\right) - \left(y + z\right)
double f(double x, double y, double z, double t) {
        double r88077 = x;
        double r88078 = y;
        double r88079 = log(r88078);
        double r88080 = r88077 * r88079;
        double r88081 = r88080 - r88078;
        double r88082 = z;
        double r88083 = r88081 - r88082;
        double r88084 = t;
        double r88085 = log(r88084);
        double r88086 = r88083 + r88085;
        return r88086;
}
↓
double f(double x, double y, double z, double t) {
        double r88087 = t;
        double r88088 = log(r88087);
        double r88089 = x;
        double r88090 = 2.0;
        double r88091 = y;
        double r88092 = cbrt(r88091);
        double r88093 = log(r88092);
        double r88094 = r88090 * r88093;
        double r88095 = r88092 * r88092;
        double r88096 = cbrt(r88095);
        double r88097 = log(r88096);
        double r88098 = cbrt(r88092);
        double r88099 = log(r88098);
        double r88100 = r88097 + r88099;
        double r88101 = r88094 + r88100;
        double r88102 = r88089 * r88101;
        double r88103 = r88088 + r88102;
        double r88104 = z;
        double r88105 = r88091 + r88104;
        double r88106 = r88103 - r88105;
        return r88106;
}

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

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

  8. Applied add-cube-cbrt0.1

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

  9. Applied cbrt-prod0.1

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

  10. Applied log-prod0.1

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

  11. Applied distribute-lft-in0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 
(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)))