Average Error: 0.2 → 0.2
Time: 28.9s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(y + x\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(y + x\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 r60961 = x;
        double r60962 = y;
        double r60963 = r60961 + r60962;
        double r60964 = log(r60963);
        double r60965 = z;
        double r60966 = log(r60965);
        double r60967 = r60964 + r60966;
        double r60968 = t;
        double r60969 = r60967 - r60968;
        double r60970 = a;
        double r60971 = 0.5;
        double r60972 = r60970 - r60971;
        double r60973 = log(r60968);
        double r60974 = r60972 * r60973;
        double r60975 = r60969 + r60974;
        return r60975;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r60976 = y;
        double r60977 = x;
        double r60978 = r60976 + r60977;
        double r60979 = log(r60978);
        double r60980 = z;
        double r60981 = log(r60980);
        double r60982 = t;
        double r60983 = r60981 - r60982;
        double r60984 = a;
        double r60985 = 0.5;
        double r60986 = r60984 - r60985;
        double r60987 = log(r60982);
        double r60988 = r60986 * r60987;
        double r60989 = r60983 + r60988;
        double r60990 = r60979 + r60989;
        return r60990;
}

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+0.2

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

  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. Simplified0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019174 
(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))))