Average Error: 0.3 → 0.3
Time: 18.1s
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 r55017 = x;
        double r55018 = y;
        double r55019 = r55017 + r55018;
        double r55020 = log(r55019);
        double r55021 = z;
        double r55022 = log(r55021);
        double r55023 = r55020 + r55022;
        double r55024 = t;
        double r55025 = r55023 - r55024;
        double r55026 = a;
        double r55027 = 0.5;
        double r55028 = r55026 - r55027;
        double r55029 = log(r55024);
        double r55030 = r55028 * r55029;
        double r55031 = r55025 + r55030;
        return r55031;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r55032 = x;
        double r55033 = y;
        double r55034 = r55032 + r55033;
        double r55035 = log(r55034);
        double r55036 = z;
        double r55037 = log(r55036);
        double r55038 = t;
        double r55039 = r55037 - r55038;
        double r55040 = a;
        double r55041 = 0.5;
        double r55042 = r55040 - r55041;
        double r55043 = log(r55038);
        double r55044 = r55042 * r55043;
        double r55045 = r55039 + r55044;
        double r55046 = r55035 + r55045;
        return r55046;
}

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 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+0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2020047 
(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))))