Average Error: 0.1 → 0.1
Time: 19.0s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\left(\log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot 2 + \log \left(\sqrt[3]{y}\right)\right) \cdot x + \left(\log \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot 2\right) \cdot x\right) - z\right) + \left(\log t - y\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\left(\log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot 2 + \log \left(\sqrt[3]{y}\right)\right) \cdot x + \left(\log \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot 2\right) \cdot x\right) - z\right) + \left(\log t - y\right)
double f(double x, double y, double z, double t) {
        double r74631 = x;
        double r74632 = y;
        double r74633 = log(r74632);
        double r74634 = r74631 * r74633;
        double r74635 = r74634 - r74632;
        double r74636 = z;
        double r74637 = r74635 - r74636;
        double r74638 = t;
        double r74639 = log(r74638);
        double r74640 = r74637 + r74639;
        return r74640;
}
↓
double f(double x, double y, double z, double t) {
        double r74641 = y;
        double r74642 = cbrt(r74641);
        double r74643 = cbrt(r74642);
        double r74644 = log(r74643);
        double r74645 = 2.0;
        double r74646 = r74644 * r74645;
        double r74647 = log(r74642);
        double r74648 = r74646 + r74647;
        double r74649 = x;
        double r74650 = r74648 * r74649;
        double r74651 = r74643 * r74643;
        double r74652 = log(r74651);
        double r74653 = r74652 * r74645;
        double r74654 = r74653 * r74649;
        double r74655 = r74650 + r74654;
        double r74656 = z;
        double r74657 = r74655 - r74656;
        double r74658 = t;
        double r74659 = log(r74658);
        double r74660 = r74659 - r74641;
        double r74661 = r74657 + r74660;
        return r74661;
}

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. Simplified0.1

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

  4. Applied add-cube-cbrt0.1

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

  5. Applied log-prod0.1

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

  6. Applied distribute-lft-in0.1

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

  7. Simplified0.1

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

  9. Applied add-cube-cbrt0.1

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

  10. Applied log-prod0.1

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

  11. Applied distribute-rgt-in0.1

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

  12. Applied distribute-lft-in0.1

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

  13. Applied associate-+l+0.1

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

  14. Simplified0.1

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

  15. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  (+ (- (- (* x (log y)) y) z) (log t)))