Average Error: 0.1 → 0.1
Time: 5.9s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\log \left({\left({\left({y}^{\frac{1}{3}}\right)}^{\left(\sqrt[3]{\frac{2}{3}} \cdot \sqrt[3]{\frac{2}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{2}{3}}\right)} \cdot {\left(\sqrt[3]{y}\right)}^{\frac{1}{3}}\right) \cdot x - z\right)\right) - y\]
\left(x \cdot \log y - z\right) - y
↓
\left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\log \left({\left({\left({y}^{\frac{1}{3}}\right)}^{\left(\sqrt[3]{\frac{2}{3}} \cdot \sqrt[3]{\frac{2}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{2}{3}}\right)} \cdot {\left(\sqrt[3]{y}\right)}^{\frac{1}{3}}\right) \cdot x - z\right)\right) - y
double f(double x, double y, double z) {
        double r43509 = x;
        double r43510 = y;
        double r43511 = log(r43510);
        double r43512 = r43509 * r43511;
        double r43513 = z;
        double r43514 = r43512 - r43513;
        double r43515 = r43514 - r43510;
        return r43515;
}
↓
double f(double x, double y, double z) {
        double r43516 = x;
        double r43517 = y;
        double r43518 = cbrt(r43517);
        double r43519 = r43518 * r43518;
        double r43520 = log(r43519);
        double r43521 = r43516 * r43520;
        double r43522 = 0.3333333333333333;
        double r43523 = pow(r43517, r43522);
        double r43524 = 0.6666666666666666;
        double r43525 = cbrt(r43524);
        double r43526 = r43525 * r43525;
        double r43527 = pow(r43523, r43526);
        double r43528 = pow(r43527, r43525);
        double r43529 = pow(r43518, r43522);
        double r43530 = r43528 * r43529;
        double r43531 = log(r43530);
        double r43532 = r43531 * r43516;
        double r43533 = z;
        double r43534 = r43532 - r43533;
        double r43535 = r43521 + r43534;
        double r43536 = r43535 - r43517;
        return r43536;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(x \cdot \log y - z\right) - y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Applied associate--l+0.1

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

  7. Simplified0.1

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

  9. Applied pow1/30.1

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

  11. Applied add-cube-cbrt0.1

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

  12. Simplified0.1

    \[\leadsto \left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\log \left(\color{blue}{{\left({y}^{\frac{1}{3}}\right)}^{\frac{2}{3}}} \cdot \sqrt[3]{{y}^{\frac{1}{3}}}\right) \cdot x - z\right)\right) - y\]

  13. Simplified0.1

    \[\leadsto \left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\log \left({\left({y}^{\frac{1}{3}}\right)}^{\frac{2}{3}} \cdot \color{blue}{{\left(\sqrt[3]{y}\right)}^{\frac{1}{3}}}\right) \cdot x - z\right)\right) - y\]
  14. Using strategy rm

  15. Applied add-cube-cbrt0.1

    \[\leadsto \left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\log \left({\left({y}^{\frac{1}{3}}\right)}^{\color{blue}{\left(\left(\sqrt[3]{\frac{2}{3}} \cdot \sqrt[3]{\frac{2}{3}}\right) \cdot \sqrt[3]{\frac{2}{3}}\right)}} \cdot {\left(\sqrt[3]{y}\right)}^{\frac{1}{3}}\right) \cdot x - z\right)\right) - y\]

  16. Applied pow-unpow0.1

    \[\leadsto \left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\log \left(\color{blue}{{\left({\left({y}^{\frac{1}{3}}\right)}^{\left(\sqrt[3]{\frac{2}{3}} \cdot \sqrt[3]{\frac{2}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{2}{3}}\right)}} \cdot {\left(\sqrt[3]{y}\right)}^{\frac{1}{3}}\right) \cdot x - z\right)\right) - y\]

  17. Final simplification0.1

    \[\leadsto \left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\log \left({\left({\left({y}^{\frac{1}{3}}\right)}^{\left(\sqrt[3]{\frac{2}{3}} \cdot \sqrt[3]{\frac{2}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{2}{3}}\right)} \cdot {\left(\sqrt[3]{y}\right)}^{\frac{1}{3}}\right) \cdot x - z\right)\right) - y\]

Reproduce

herbie shell --seed 2020035 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))