Average Error: 0.2 → 0.2
Time: 13.6s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)
double f(double x, double y, double z, double t, double a) {
        double r79701 = x;
        double r79702 = y;
        double r79703 = r79701 + r79702;
        double r79704 = log(r79703);
        double r79705 = z;
        double r79706 = log(r79705);
        double r79707 = r79704 + r79706;
        double r79708 = t;
        double r79709 = r79707 - r79708;
        double r79710 = a;
        double r79711 = 0.5;
        double r79712 = r79710 - r79711;
        double r79713 = log(r79708);
        double r79714 = r79712 * r79713;
        double r79715 = r79709 + r79714;
        return r79715;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r79716 = x;
        double r79717 = y;
        double r79718 = r79716 + r79717;
        double r79719 = log(r79718);
        double r79720 = z;
        double r79721 = log(r79720);
        double r79722 = t;
        double r79723 = r79721 - r79722;
        double r79724 = a;
        double r79725 = 0.5;
        double r79726 = r79724 - r79725;
        double r79727 = log(r79722);
        double r79728 = r79726 * r79727;
        double r79729 = r79723 + r79728;
        double r79730 = r79719 + r79729;
        return r79730;
}

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 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+0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020100 
(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))))