Average Error: 0.1 → 0.1
Time: 5.6s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\log \left(\sqrt[3]{y} \cdot \left(1 \cdot {y}^{\frac{1}{3}}\right)\right) \cdot x + \left(\left(\log \left({\left({\left({y}^{\frac{1}{3}}\right)}^{\left(\sqrt[3]{\frac{2}{3}} \cdot \sqrt[3]{\frac{2}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{2}{3}}\right)} \cdot {\left(\sqrt[3]{y}\right)}^{\frac{1}{3}}\right) \cdot x - z\right) - y\right)\]
\left(x \cdot \log y - z\right) - y
↓
\log \left(\sqrt[3]{y} \cdot \left(1 \cdot {y}^{\frac{1}{3}}\right)\right) \cdot x + \left(\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) - y\right)
double f(double x, double y, double z) {
        double r28095 = x;
        double r28096 = y;
        double r28097 = log(r28096);
        double r28098 = r28095 * r28097;
        double r28099 = z;
        double r28100 = r28098 - r28099;
        double r28101 = r28100 - r28096;
        return r28101;
}
↓
double f(double x, double y, double z) {
        double r28102 = y;
        double r28103 = cbrt(r28102);
        double r28104 = 1.0;
        double r28105 = 0.3333333333333333;
        double r28106 = pow(r28102, r28105);
        double r28107 = r28104 * r28106;
        double r28108 = r28103 * r28107;
        double r28109 = log(r28108);
        double r28110 = x;
        double r28111 = r28109 * r28110;
        double r28112 = 0.6666666666666666;
        double r28113 = cbrt(r28112);
        double r28114 = r28113 * r28113;
        double r28115 = pow(r28106, r28114);
        double r28116 = pow(r28115, r28113);
        double r28117 = pow(r28103, r28105);
        double r28118 = r28116 * r28117;
        double r28119 = log(r28118);
        double r28120 = r28119 * r28110;
        double r28121 = z;
        double r28122 = r28120 - r28121;
        double r28123 = r28122 - r28102;
        double r28124 = r28111 + r28123;
        return r28124;
}

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. Applied associate--l+0.1

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

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

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

  10. Applied cbrt-prod0.1

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

  11. Simplified0.1

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

  12. Simplified0.1

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

  14. Applied add-cube-cbrt0.1

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

  15. Simplified0.1

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

  16. Simplified0.1

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

  18. Applied add-cube-cbrt0.1

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

  19. Applied pow-unpow0.1

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

  20. Final simplification0.1

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

Reproduce

herbie shell --seed 2020033 +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))