Average Error: 0.1 → 0.1
Time: 44.7s
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 r1193387 = x;
        double r1193388 = y;
        double r1193389 = log(r1193388);
        double r1193390 = r1193387 * r1193389;
        double r1193391 = z;
        double r1193392 = r1193390 - r1193391;
        double r1193393 = r1193392 - r1193388;
        return r1193393;
}
↓
double f(double x, double y, double z) {
        double r1193394 = y;
        double r1193395 = 0.6666666666666666;
        double r1193396 = pow(r1193394, r1193395);
        double r1193397 = log(r1193396);
        double r1193398 = x;
        double r1193399 = r1193397 * r1193398;
        double r1193400 = 3.0;
        double r1193401 = r1193398 / r1193400;
        double r1193402 = log(r1193394);
        double r1193403 = r1193401 * r1193402;
        double r1193404 = z;
        double r1193405 = r1193403 - r1193404;
        double r1193406 = r1193405 - r1193394;
        double r1193407 = r1193399 + r1193406;
        return r1193407;
}

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