Average Error: 0.2 → 0.3
Time: 10.8s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(x + y\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\left(\log \left(x + y\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t
double f(double x, double y, double z, double t, double a) {
        double r50038 = x;
        double r50039 = y;
        double r50040 = r50038 + r50039;
        double r50041 = log(r50040);
        double r50042 = z;
        double r50043 = log(r50042);
        double r50044 = r50041 + r50043;
        double r50045 = t;
        double r50046 = r50044 - r50045;
        double r50047 = a;
        double r50048 = 0.5;
        double r50049 = r50047 - r50048;
        double r50050 = log(r50045);
        double r50051 = r50049 * r50050;
        double r50052 = r50046 + r50051;
        return r50052;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r50053 = x;
        double r50054 = y;
        double r50055 = r50053 + r50054;
        double r50056 = log(r50055);
        double r50057 = z;
        double r50058 = cbrt(r50057);
        double r50059 = r50058 * r50058;
        double r50060 = log(r50059);
        double r50061 = r50056 + r50060;
        double r50062 = log(r50058);
        double r50063 = r50061 + r50062;
        double r50064 = t;
        double r50065 = r50063 - r50064;
        double r50066 = a;
        double r50067 = 0.5;
        double r50068 = r50066 - r50067;
        double r50069 = log(r50064);
        double r50070 = r50068 * r50069;
        double r50071 = r50065 + r50070;
        return r50071;
}

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 add-cube-cbrt0.2

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

  4. Applied log-prod0.3

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

  5. Applied associate-+r+0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2020056 
(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))))