Average Error: 0.3 → 0.3
Time: 43.2s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left({t}^{\frac{1}{3}}\right) \cdot \left(a - 0.5\right) + \left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right) + \left(\left(\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log z + \log \left(\sqrt[3]{y + x}\right)\right)\right) - t\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left({t}^{\frac{1}{3}}\right) \cdot \left(a - 0.5\right) + \left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right) + \left(\left(\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log z + \log \left(\sqrt[3]{y + x}\right)\right)\right) - t\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r2606719 = x;
        double r2606720 = y;
        double r2606721 = r2606719 + r2606720;
        double r2606722 = log(r2606721);
        double r2606723 = z;
        double r2606724 = log(r2606723);
        double r2606725 = r2606722 + r2606724;
        double r2606726 = t;
        double r2606727 = r2606725 - r2606726;
        double r2606728 = a;
        double r2606729 = 0.5;
        double r2606730 = r2606728 - r2606729;
        double r2606731 = log(r2606726);
        double r2606732 = r2606730 * r2606731;
        double r2606733 = r2606727 + r2606732;
        return r2606733;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2606734 = t;
        double r2606735 = 0.3333333333333333;
        double r2606736 = pow(r2606734, r2606735);
        double r2606737 = log(r2606736);
        double r2606738 = a;
        double r2606739 = 0.5;
        double r2606740 = r2606738 - r2606739;
        double r2606741 = r2606737 * r2606740;
        double r2606742 = cbrt(r2606734);
        double r2606743 = r2606742 * r2606742;
        double r2606744 = log(r2606743);
        double r2606745 = r2606744 * r2606740;
        double r2606746 = y;
        double r2606747 = x;
        double r2606748 = r2606746 + r2606747;
        double r2606749 = cbrt(r2606748);
        double r2606750 = r2606749 * r2606749;
        double r2606751 = log(r2606750);
        double r2606752 = z;
        double r2606753 = log(r2606752);
        double r2606754 = log(r2606749);
        double r2606755 = r2606753 + r2606754;
        double r2606756 = r2606751 + r2606755;
        double r2606757 = r2606756 - r2606734;
        double r2606758 = r2606745 + r2606757;
        double r2606759 = r2606741 + r2606758;
        return r2606759;
}

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 add-cube-cbrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied distribute-lft-in0.3

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

  6. Applied associate-+r+0.3

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

  8. Applied pow1/30.3

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

  10. Applied add-cube-cbrt0.3

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

  11. Applied log-prod0.3

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

  12. Applied associate-+l+0.3

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

  13. Final simplification0.3

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

Reproduce

herbie shell --seed 2019121 
(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))))