Average Error: 0.1 → 0.1
Time: 5.4s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\left(x \cdot \log \left(\left({\left({\left({y}^{\frac{1}{3}}\right)}^{\left(\sqrt[3]{\frac{2}{3}} \cdot \sqrt[3]{\frac{2}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{2}{3}}\right)} \cdot {\left(\sqrt[3]{y}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{y}\right) + \left(\log \left(1 \cdot {y}^{\frac{1}{3}}\right) \cdot x - z\right)\right) - y\]
\left(x \cdot \log y - z\right) - y
↓
\left(x \cdot \log \left(\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 \sqrt[3]{y}\right) + \left(\log \left(1 \cdot {y}^{\frac{1}{3}}\right) \cdot x - z\right)\right) - y
double f(double x, double y, double z) {
        double r28393 = x;
        double r28394 = y;
        double r28395 = log(r28394);
        double r28396 = r28393 * r28395;
        double r28397 = z;
        double r28398 = r28396 - r28397;
        double r28399 = r28398 - r28394;
        return r28399;
}
↓
double f(double x, double y, double z) {
        double r28400 = x;
        double r28401 = y;
        double r28402 = 0.3333333333333333;
        double r28403 = pow(r28401, r28402);
        double r28404 = 0.6666666666666666;
        double r28405 = cbrt(r28404);
        double r28406 = r28405 * r28405;
        double r28407 = pow(r28403, r28406);
        double r28408 = pow(r28407, r28405);
        double r28409 = cbrt(r28401);
        double r28410 = pow(r28409, r28402);
        double r28411 = r28408 * r28410;
        double r28412 = r28411 * r28409;
        double r28413 = log(r28412);
        double r28414 = r28400 * r28413;
        double r28415 = 1.0;
        double r28416 = r28415 * r28403;
        double r28417 = log(r28416);
        double r28418 = r28417 * r28400;
        double r28419 = z;
        double r28420 = r28418 - r28419;
        double r28421 = r28414 + r28420;
        double r28422 = r28421 - r28401;
        return r28422;
}

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. Simplified0.1

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

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

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

  10. Applied cbrt-prod0.1

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

  11. Simplified0.1

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

  12. Simplified0.1

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

  14. Applied add-cube-cbrt0.1

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

  15. Simplified0.1

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

  16. Simplified0.2

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

  18. Applied add-cube-cbrt0.1

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

  19. Applied pow-unpow0.1

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

  20. Final simplification0.1

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

Reproduce

herbie shell --seed 2020057 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))