Average Error: 0.2 → 0.3
Time: 11.4s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\log \left(\sqrt[3]{x + y}\right) + \log z\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\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]{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
double f(double x, double y, double z, double t, double a) {
        double r73733 = x;
        double r73734 = y;
        double r73735 = r73733 + r73734;
        double r73736 = log(r73735);
        double r73737 = z;
        double r73738 = log(r73737);
        double r73739 = r73736 + r73738;
        double r73740 = t;
        double r73741 = r73739 - r73740;
        double r73742 = a;
        double r73743 = 0.5;
        double r73744 = r73742 - r73743;
        double r73745 = log(r73740);
        double r73746 = r73744 * r73745;
        double r73747 = r73741 + r73746;
        return r73747;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r73748 = x;
        double r73749 = y;
        double r73750 = r73748 + r73749;
        double r73751 = cbrt(r73750);
        double r73752 = r73751 * r73751;
        double r73753 = log(r73752);
        double r73754 = log(r73751);
        double r73755 = z;
        double r73756 = log(r73755);
        double r73757 = r73754 + r73756;
        double r73758 = r73753 + r73757;
        double r73759 = t;
        double r73760 = r73758 - r73759;
        double r73761 = a;
        double r73762 = 0.5;
        double r73763 = r73761 - r73762;
        double r73764 = log(r73759);
        double r73765 = r73763 * r73764;
        double r73766 = r73760 + r73765;
        return r73766;
}

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 0.2

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

  3. Applied add-cube-cbrt0.2

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

  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

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

Reproduce

herbie shell --seed 2020024 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))