Average Error: 0.1 → 0.1
Time: 20.2s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\log \left({y}^{\frac{2}{3}}\right) \cdot x + \left(\left(\frac{x}{3} \cdot \log y - z\right) - y\right)\]
\left(x \cdot \log y - z\right) - y
↓
\log \left({y}^{\frac{2}{3}}\right) \cdot x + \left(\left(\frac{x}{3} \cdot \log y - z\right) - y\right)
double f(double x, double y, double z) {
        double r1402192 = x;
        double r1402193 = y;
        double r1402194 = log(r1402193);
        double r1402195 = r1402192 * r1402194;
        double r1402196 = z;
        double r1402197 = r1402195 - r1402196;
        double r1402198 = r1402197 - r1402193;
        return r1402198;
}
↓
double f(double x, double y, double z) {
        double r1402199 = y;
        double r1402200 = 0.6666666666666666;
        double r1402201 = pow(r1402199, r1402200);
        double r1402202 = log(r1402201);
        double r1402203 = x;
        double r1402204 = r1402202 * r1402203;
        double r1402205 = 3.0;
        double r1402206 = r1402203 / r1402205;
        double r1402207 = log(r1402199);
        double r1402208 = r1402206 * r1402207;
        double r1402209 = z;
        double r1402210 = r1402208 - r1402209;
        double r1402211 = r1402210 - r1402199;
        double r1402212 = r1402204 + r1402211;
        return r1402212;
}

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. Applied associate--l+0.1

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

  9. Applied pow1/30.1

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

  10. Applied pow1/30.1

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

  11. Applied pow-prod-up0.1

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

  12. Simplified0.1

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

  13. Taylor expanded around 0 0.2

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

  14. Simplified0.1

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

  15. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  (- (- (* x (log y)) z) y))