Average Error: 0.3 → 0.3
Time: 36.6s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log z + \log \left(\sqrt[3]{y + x}\right)\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\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) + \left(a - 0.5\right) \cdot \log t
double f(double x, double y, double z, double t, double a) {
        double r2516729 = x;
        double r2516730 = y;
        double r2516731 = r2516729 + r2516730;
        double r2516732 = log(r2516731);
        double r2516733 = z;
        double r2516734 = log(r2516733);
        double r2516735 = r2516732 + r2516734;
        double r2516736 = t;
        double r2516737 = r2516735 - r2516736;
        double r2516738 = a;
        double r2516739 = 0.5;
        double r2516740 = r2516738 - r2516739;
        double r2516741 = log(r2516736);
        double r2516742 = r2516740 * r2516741;
        double r2516743 = r2516737 + r2516742;
        return r2516743;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2516744 = y;
        double r2516745 = x;
        double r2516746 = r2516744 + r2516745;
        double r2516747 = cbrt(r2516746);
        double r2516748 = r2516747 * r2516747;
        double r2516749 = log(r2516748);
        double r2516750 = z;
        double r2516751 = log(r2516750);
        double r2516752 = log(r2516747);
        double r2516753 = r2516751 + r2516752;
        double r2516754 = r2516749 + r2516753;
        double r2516755 = t;
        double r2516756 = r2516754 - r2516755;
        double r2516757 = a;
        double r2516758 = 0.5;
        double r2516759 = r2516757 - r2516758;
        double r2516760 = log(r2516755);
        double r2516761 = r2516759 * r2516760;
        double r2516762 = r2516756 + r2516761;
        return r2516762;
}

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

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

  4. Applied log-prod0.3

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

  5. Applied associate-+l+0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019170 
(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))))