Average Error: 0.1 → 0.1
Time: 11.8s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\log \left(\sqrt{\sqrt{y}}\right) \cdot x + \left(x \cdot \left(\log \left(\sqrt{\sqrt{y}}\right) + \log \left(\sqrt{y}\right)\right) - \left(y + \left(z - \log t\right)\right)\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\log \left(\sqrt{\sqrt{y}}\right) \cdot x + \left(x \cdot \left(\log \left(\sqrt{\sqrt{y}}\right) + \log \left(\sqrt{y}\right)\right) - \left(y + \left(z - \log t\right)\right)\right)
double f(double x, double y, double z, double t) {
        double r105606 = x;
        double r105607 = y;
        double r105608 = log(r105607);
        double r105609 = r105606 * r105608;
        double r105610 = r105609 - r105607;
        double r105611 = z;
        double r105612 = r105610 - r105611;
        double r105613 = t;
        double r105614 = log(r105613);
        double r105615 = r105612 + r105614;
        return r105615;
}
↓
double f(double x, double y, double z, double t) {
        double r105616 = y;
        double r105617 = sqrt(r105616);
        double r105618 = sqrt(r105617);
        double r105619 = log(r105618);
        double r105620 = x;
        double r105621 = r105619 * r105620;
        double r105622 = log(r105617);
        double r105623 = r105619 + r105622;
        double r105624 = r105620 * r105623;
        double r105625 = z;
        double r105626 = t;
        double r105627 = log(r105626);
        double r105628 = r105625 - r105627;
        double r105629 = r105616 + r105628;
        double r105630 = r105624 - r105629;
        double r105631 = r105621 + r105630;
        return r105631;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Applied associate--l+0.1

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

  7. Applied associate--l+0.1

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

  8. Applied associate-+l+0.1

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

  9. Simplified0.1

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

  11. Applied add-sqr-sqrt0.1

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

  12. Applied sqrt-prod0.1

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

  13. Applied log-prod0.1

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

  14. Applied distribute-rgt-in0.1

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

  15. Applied associate-+l+0.1

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

  16. Simplified0.1

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

  17. Final simplification0.1

    \[\leadsto \log \left(\sqrt{\sqrt{y}}\right) \cdot x + \left(x \cdot \left(\log \left(\sqrt{\sqrt{y}}\right) + \log \left(\sqrt{y}\right)\right) - \left(y + \left(z - \log t\right)\right)\right)\]

Reproduce

herbie shell --seed 2020045 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))