Average Error: 0.3 → 0.3
Time: 36.2s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(a - 0.5\right) \cdot \log t + \left(\frac{\left(\log z \cdot \log z\right) \cdot \log z + \log \left(x + y\right) \cdot \left(\log \left(x + y\right) \cdot \log \left(x + y\right)\right)}{\left(\log z - \log \left(x + y\right)\right) \cdot \log z + \log \left(x + y\right) \cdot \log \left(x + y\right)} - t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(a - 0.5\right) \cdot \log t + \left(\frac{\left(\log z \cdot \log z\right) \cdot \log z + \log \left(x + y\right) \cdot \left(\log \left(x + y\right) \cdot \log \left(x + y\right)\right)}{\left(\log z - \log \left(x + y\right)\right) \cdot \log z + \log \left(x + y\right) \cdot \log \left(x + y\right)} - t\right)
double f(double x, double y, double z, double t, double a) {
        double r1040046 = x;
        double r1040047 = y;
        double r1040048 = r1040046 + r1040047;
        double r1040049 = log(r1040048);
        double r1040050 = z;
        double r1040051 = log(r1040050);
        double r1040052 = r1040049 + r1040051;
        double r1040053 = t;
        double r1040054 = r1040052 - r1040053;
        double r1040055 = a;
        double r1040056 = 0.5;
        double r1040057 = r1040055 - r1040056;
        double r1040058 = log(r1040053);
        double r1040059 = r1040057 * r1040058;
        double r1040060 = r1040054 + r1040059;
        return r1040060;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1040061 = a;
        double r1040062 = 0.5;
        double r1040063 = r1040061 - r1040062;
        double r1040064 = t;
        double r1040065 = log(r1040064);
        double r1040066 = r1040063 * r1040065;
        double r1040067 = z;
        double r1040068 = log(r1040067);
        double r1040069 = r1040068 * r1040068;
        double r1040070 = r1040069 * r1040068;
        double r1040071 = x;
        double r1040072 = y;
        double r1040073 = r1040071 + r1040072;
        double r1040074 = log(r1040073);
        double r1040075 = r1040074 * r1040074;
        double r1040076 = r1040074 * r1040075;
        double r1040077 = r1040070 + r1040076;
        double r1040078 = r1040068 - r1040074;
        double r1040079 = r1040078 * r1040068;
        double r1040080 = r1040079 + r1040075;
        double r1040081 = r1040077 / r1040080;
        double r1040082 = r1040081 - r1040064;
        double r1040083 = r1040066 + r1040082;
        return r1040083;
}

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 flip3-+0.3

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

  4. Simplified0.3

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

  5. Simplified0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019153 
(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))))