Average Error: 0.3 → 0.3
Time: 38.8s
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 r55051 = x;
        double r55052 = y;
        double r55053 = r55051 + r55052;
        double r55054 = log(r55053);
        double r55055 = z;
        double r55056 = log(r55055);
        double r55057 = r55054 + r55056;
        double r55058 = t;
        double r55059 = r55057 - r55058;
        double r55060 = a;
        double r55061 = 0.5;
        double r55062 = r55060 - r55061;
        double r55063 = log(r55058);
        double r55064 = r55062 * r55063;
        double r55065 = r55059 + r55064;
        return r55065;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r55066 = x;
        double r55067 = y;
        double r55068 = r55066 + r55067;
        double r55069 = log(r55068);
        double r55070 = z;
        double r55071 = log(r55070);
        double r55072 = t;
        double r55073 = r55071 - r55072;
        double r55074 = a;
        double r55075 = 0.5;
        double r55076 = r55074 - r55075;
        double r55077 = log(r55072);
        double r55078 = r55076 * r55077;
        double r55079 = r55073 + r55078;
        double r55080 = r55069 + r55079;
        return r55080;
}

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 2019323 
(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))))