Average Error: 0.3 → 0.3
Time: 27.6s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(y + x\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\left(\log \left(y + x\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{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 r910757 = x;
        double r910758 = y;
        double r910759 = r910757 + r910758;
        double r910760 = log(r910759);
        double r910761 = z;
        double r910762 = log(r910761);
        double r910763 = r910760 + r910762;
        double r910764 = t;
        double r910765 = r910763 - r910764;
        double r910766 = a;
        double r910767 = 0.5;
        double r910768 = r910766 - r910767;
        double r910769 = log(r910764);
        double r910770 = r910768 * r910769;
        double r910771 = r910765 + r910770;
        return r910771;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r910772 = y;
        double r910773 = x;
        double r910774 = r910772 + r910773;
        double r910775 = log(r910774);
        double r910776 = z;
        double r910777 = cbrt(r910776);
        double r910778 = r910777 * r910777;
        double r910779 = log(r910778);
        double r910780 = r910775 + r910779;
        double r910781 = log(r910777);
        double r910782 = r910780 + r910781;
        double r910783 = t;
        double r910784 = r910782 - r910783;
        double r910785 = a;
        double r910786 = 0.5;
        double r910787 = r910785 - r910786;
        double r910788 = log(r910783);
        double r910789 = r910787 * r910788;
        double r910790 = r910784 + r910789;
        return r910790;
}

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

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

  4. Applied log-prod0.3

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

  5. Applied associate-+r+0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(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))))