Average Error: 0.1 → 0.1
Time: 16.0s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\log \left({\left(\sqrt[3]{y}\right)}^{\frac{5}{3}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot x + \left(\log \left({y}^{\frac{1}{3}}\right) \cdot x - y\right)\right) - z\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\log \left({\left(\sqrt[3]{y}\right)}^{\frac{5}{3}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot x + \left(\log \left({y}^{\frac{1}{3}}\right) \cdot x - y\right)\right) - z\right) + \log t
double f(double x, double y, double z, double t) {
        double r152473 = x;
        double r152474 = y;
        double r152475 = log(r152474);
        double r152476 = r152473 * r152475;
        double r152477 = r152476 - r152474;
        double r152478 = z;
        double r152479 = r152477 - r152478;
        double r152480 = t;
        double r152481 = log(r152480);
        double r152482 = r152479 + r152481;
        return r152482;
}
↓
double f(double x, double y, double z, double t) {
        double r152483 = y;
        double r152484 = cbrt(r152483);
        double r152485 = 1.6666666666666667;
        double r152486 = pow(r152484, r152485);
        double r152487 = cbrt(r152484);
        double r152488 = r152486 * r152487;
        double r152489 = log(r152488);
        double r152490 = x;
        double r152491 = r152489 * r152490;
        double r152492 = 0.3333333333333333;
        double r152493 = pow(r152483, r152492);
        double r152494 = log(r152493);
        double r152495 = r152494 * r152490;
        double r152496 = r152495 - r152483;
        double r152497 = r152491 + r152496;
        double r152498 = z;
        double r152499 = r152497 - r152498;
        double r152500 = t;
        double r152501 = log(r152500);
        double r152502 = r152499 + r152501;
        return r152502;
}

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. Using strategy rm

  8. Applied pow1/30.1

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

  10. Applied add-cube-cbrt0.1

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

  11. Applied associate-*r*0.1

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

  12. Simplified0.1

    \[\leadsto \left(\left(\log \left(\color{blue}{{\left(\sqrt[3]{y}\right)}^{\frac{5}{3}}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot x + \left(\log \left({y}^{\frac{1}{3}}\right) \cdot x - y\right)\right) - z\right) + \log t\]

  13. Final simplification0.1

    \[\leadsto \left(\left(\log \left({\left(\sqrt[3]{y}\right)}^{\frac{5}{3}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot x + \left(\log \left({y}^{\frac{1}{3}}\right) \cdot x - y\right)\right) - z\right) + \log t\]

Reproduce

herbie shell --seed 2019350 
(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)))