Average Error: 0.3 → 0.3
Time: 1.2m
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(y + x\right) + \left(\log \left({\left({t}^{\left(\sqrt{\frac{1}{3}}\right)}\right)}^{\left(\sqrt{\frac{1}{3}}\right)}\right) \cdot \left(a - 0.5\right) + \left(\left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) + \left(\log z - t\right)\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(y + x\right) + \left(\log \left({\left({t}^{\left(\sqrt{\frac{1}{3}}\right)}\right)}^{\left(\sqrt{\frac{1}{3}}\right)}\right) \cdot \left(a - 0.5\right) + \left(\left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) + \left(\log z - t\right)\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r2948739 = x;
        double r2948740 = y;
        double r2948741 = r2948739 + r2948740;
        double r2948742 = log(r2948741);
        double r2948743 = z;
        double r2948744 = log(r2948743);
        double r2948745 = r2948742 + r2948744;
        double r2948746 = t;
        double r2948747 = r2948745 - r2948746;
        double r2948748 = a;
        double r2948749 = 0.5;
        double r2948750 = r2948748 - r2948749;
        double r2948751 = log(r2948746);
        double r2948752 = r2948750 * r2948751;
        double r2948753 = r2948747 + r2948752;
        return r2948753;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2948754 = y;
        double r2948755 = x;
        double r2948756 = r2948754 + r2948755;
        double r2948757 = log(r2948756);
        double r2948758 = t;
        double r2948759 = 0.3333333333333333;
        double r2948760 = sqrt(r2948759);
        double r2948761 = pow(r2948758, r2948760);
        double r2948762 = pow(r2948761, r2948760);
        double r2948763 = log(r2948762);
        double r2948764 = a;
        double r2948765 = 0.5;
        double r2948766 = r2948764 - r2948765;
        double r2948767 = r2948763 * r2948766;
        double r2948768 = cbrt(r2948758);
        double r2948769 = r2948768 * r2948768;
        double r2948770 = log(r2948769);
        double r2948771 = r2948766 * r2948770;
        double r2948772 = z;
        double r2948773 = log(r2948772);
        double r2948774 = r2948773 - r2948758;
        double r2948775 = r2948771 + r2948774;
        double r2948776 = r2948767 + r2948775;
        double r2948777 = r2948757 + r2948776;
        return r2948777;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

    \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
  2. Using strategy rm

  3. Applied associate--l+0.3

    \[\leadsto \color{blue}{\left(\log \left(x + y\right) + \left(\log z - t\right)\right)} + \left(a - 0.5\right) \cdot \log t\]

  4. Applied associate-+l+0.3

    \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt0.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log \color{blue}{\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)}\right)\]

  7. Applied log-prod0.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right)}\right)\]

  8. Applied distribute-lft-in0.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\log z - t\right) + \color{blue}{\left(\left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)}\right)\]

  9. Applied associate-+r+0.3

    \[\leadsto \log \left(x + y\right) + \color{blue}{\left(\left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)}\]
  10. Using strategy rm

  11. Applied pow1/30.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot \log \color{blue}{\left({t}^{\frac{1}{3}}\right)}\right)\]
  12. Using strategy rm

  13. Applied add-sqr-sqrt0.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot \log \left({t}^{\color{blue}{\left(\sqrt{\frac{1}{3}} \cdot \sqrt{\frac{1}{3}}\right)}}\right)\right)\]

  14. Applied pow-unpow0.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot \log \color{blue}{\left({\left({t}^{\left(\sqrt{\frac{1}{3}}\right)}\right)}^{\left(\sqrt{\frac{1}{3}}\right)}\right)}\right)\]

  15. Final simplification0.3

    \[\leadsto \log \left(y + x\right) + \left(\log \left({\left({t}^{\left(\sqrt{\frac{1}{3}}\right)}\right)}^{\left(\sqrt{\frac{1}{3}}\right)}\right) \cdot \left(a - 0.5\right) + \left(\left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) + \left(\log z - t\right)\right)\right)\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))