Average Error: 0.1 → 0.1
Time: 19.3s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\left(\log \left({\left(\sqrt[3]{y}\right)}^{\frac{5}{3}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot x + \left(\log \left({\left({y}^{\left(\sqrt{\frac{1}{3}}\right)}\right)}^{\left(\sqrt{\frac{1}{3}}\right)}\right) \cdot x - z\right)\right) - y\]
\left(x \cdot \log y - z\right) - y
↓
\left(\log \left({\left(\sqrt[3]{y}\right)}^{\frac{5}{3}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot x + \left(\log \left({\left({y}^{\left(\sqrt{\frac{1}{3}}\right)}\right)}^{\left(\sqrt{\frac{1}{3}}\right)}\right) \cdot x - z\right)\right) - y
double f(double x, double y, double z) {
        double r32637 = x;
        double r32638 = y;
        double r32639 = log(r32638);
        double r32640 = r32637 * r32639;
        double r32641 = z;
        double r32642 = r32640 - r32641;
        double r32643 = r32642 - r32638;
        return r32643;
}
↓
double f(double x, double y, double z) {
        double r32644 = y;
        double r32645 = cbrt(r32644);
        double r32646 = 1.6666666666666667;
        double r32647 = pow(r32645, r32646);
        double r32648 = cbrt(r32645);
        double r32649 = r32647 * r32648;
        double r32650 = log(r32649);
        double r32651 = x;
        double r32652 = r32650 * r32651;
        double r32653 = 0.3333333333333333;
        double r32654 = sqrt(r32653);
        double r32655 = pow(r32644, r32654);
        double r32656 = pow(r32655, r32654);
        double r32657 = log(r32656);
        double r32658 = r32657 * r32651;
        double r32659 = z;
        double r32660 = r32658 - r32659;
        double r32661 = r32652 + r32660;
        double r32662 = r32661 - r32644;
        return r32662;
}

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-rgt-in0.1

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

  6. Applied associate--l+0.1

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

  8. Applied pow1/30.1

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

  10. Applied add-cube-cbrt0.1

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

  11. Applied associate-*r*0.1

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

  12. Simplified0.1

    \[\leadsto \left(\log \left(\color{blue}{{\left(\sqrt[3]{y}\right)}^{\frac{5}{3}}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot x + \left(\log \left({y}^{\frac{1}{3}}\right) \cdot x - z\right)\right) - y\]
  13. Using strategy rm

  14. Applied add-sqr-sqrt0.1

    \[\leadsto \left(\log \left({\left(\sqrt[3]{y}\right)}^{\frac{5}{3}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot x + \left(\log \left({y}^{\color{blue}{\left(\sqrt{\frac{1}{3}} \cdot \sqrt{\frac{1}{3}}\right)}}\right) \cdot x - z\right)\right) - y\]

  15. Applied pow-unpow0.1

    \[\leadsto \left(\log \left({\left(\sqrt[3]{y}\right)}^{\frac{5}{3}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot x + \left(\log \color{blue}{\left({\left({y}^{\left(\sqrt{\frac{1}{3}}\right)}\right)}^{\left(\sqrt{\frac{1}{3}}\right)}\right)} \cdot x - z\right)\right) - y\]

  16. Final simplification0.1

    \[\leadsto \left(\log \left({\left(\sqrt[3]{y}\right)}^{\frac{5}{3}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot x + \left(\log \left({\left({y}^{\left(\sqrt{\frac{1}{3}}\right)}\right)}^{\left(\sqrt{\frac{1}{3}}\right)}\right) \cdot x - z\right)\right) - y\]

Reproduce

herbie shell --seed 2019306 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))