Average Error: 0.1 → 0.1
Time: 6.0s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(\log \left({\left({\left({y}^{\frac{1}{3}}\right)}^{\left(\sqrt[3]{\frac{2}{3}} \cdot \sqrt[3]{\frac{2}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{2}{3}}\right)} \cdot {\left(\sqrt[3]{y}\right)}^{\frac{1}{3}}\right) \cdot x - z\right)\right) - y\]
\left(x \cdot \log y - z\right) - y
↓
\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \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 r43189 = x;
        double r43190 = y;
        double r43191 = log(r43190);
        double r43192 = r43189 * r43191;
        double r43193 = z;
        double r43194 = r43192 - r43193;
        double r43195 = r43194 - r43190;
        return r43195;
}
↓
double f(double x, double y, double z) {
        double r43196 = y;
        double r43197 = cbrt(r43196);
        double r43198 = r43197 * r43197;
        double r43199 = log(r43198);
        double r43200 = x;
        double r43201 = r43199 * r43200;
        double r43202 = 0.3333333333333333;
        double r43203 = pow(r43196, r43202);
        double r43204 = 0.6666666666666666;
        double r43205 = cbrt(r43204);
        double r43206 = r43205 * r43205;
        double r43207 = pow(r43203, r43206);
        double r43208 = pow(r43207, r43205);
        double r43209 = pow(r43197, r43202);
        double r43210 = r43208 * r43209;
        double r43211 = log(r43210);
        double r43212 = r43211 * r43200;
        double r43213 = z;
        double r43214 = r43212 - r43213;
        double r43215 = r43201 + r43214;
        double r43216 = r43215 - r43196;
        return r43216;
}

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

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

  11. Simplified0.1

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

  12. Simplified0.1

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

  14. Applied add-cube-cbrt0.1

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

  15. Applied pow-unpow0.1

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

  16. Final simplification0.1

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

Reproduce

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