Average Error: 0.1 → 0.1
Time: 6.6s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\log \left(1 \cdot {y}^{\frac{2}{3}}\right) \cdot x + \left(\left(\left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right) - z\right) + \log t\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\log \left(1 \cdot {y}^{\frac{2}{3}}\right) \cdot x + \left(\left(\left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right) - z\right) + \log t\right)
double f(double x, double y, double z, double t) {
        double r91475 = x;
        double r91476 = y;
        double r91477 = log(r91476);
        double r91478 = r91475 * r91477;
        double r91479 = r91478 - r91476;
        double r91480 = z;
        double r91481 = r91479 - r91480;
        double r91482 = t;
        double r91483 = log(r91482);
        double r91484 = r91481 + r91483;
        return r91484;
}
↓
double f(double x, double y, double z, double t) {
        double r91485 = 1.0;
        double r91486 = y;
        double r91487 = 0.6666666666666666;
        double r91488 = pow(r91486, r91487);
        double r91489 = r91485 * r91488;
        double r91490 = log(r91489);
        double r91491 = x;
        double r91492 = r91490 * r91491;
        double r91493 = cbrt(r91486);
        double r91494 = log(r91493);
        double r91495 = r91494 * r91491;
        double r91496 = r91495 - r91486;
        double r91497 = z;
        double r91498 = r91496 - r91497;
        double r91499 = t;
        double r91500 = log(r91499);
        double r91501 = r91498 + r91500;
        double r91502 = r91492 + r91501;
        return r91502;
}

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-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-rgt-in0.1

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

  6. Applied associate--l+0.1

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

  7. Applied associate--l+0.1

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

  8. Applied associate-+l+0.1

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

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

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

  11. Applied cbrt-prod0.1

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

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

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

  13. Applied cbrt-prod0.1

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

  14. Applied swap-sqr0.1

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

  15. Simplified0.1

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

  16. Simplified0.1

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

  17. Final simplification0.1

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

Reproduce

herbie shell --seed 2020027 
(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)))