Average Error: 0.2 → 0.3
Time: 33.6s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r67030 = x;
        double r67031 = y;
        double r67032 = r67030 + r67031;
        double r67033 = log(r67032);
        double r67034 = z;
        double r67035 = log(r67034);
        double r67036 = r67033 + r67035;
        double r67037 = t;
        double r67038 = r67036 - r67037;
        double r67039 = a;
        double r67040 = 0.5;
        double r67041 = r67039 - r67040;
        double r67042 = log(r67037);
        double r67043 = r67041 * r67042;
        double r67044 = r67038 + r67043;
        return r67044;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r67045 = x;
        double r67046 = y;
        double r67047 = r67045 + r67046;
        double r67048 = log(r67047);
        double r67049 = z;
        double r67050 = log(r67049);
        double r67051 = r67048 + r67050;
        double r67052 = t;
        double r67053 = r67051 - r67052;
        double r67054 = 2.0;
        double r67055 = cbrt(r67052);
        double r67056 = log(r67055);
        double r67057 = r67054 * r67056;
        double r67058 = a;
        double r67059 = 0.5;
        double r67060 = r67058 - r67059;
        double r67061 = r67057 * r67060;
        double r67062 = r67060 * r67056;
        double r67063 = r67061 + r67062;
        double r67064 = r67053 + r67063;
        return r67064;
}

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-cbrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied distribute-lft-in0.3

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

  6. Simplified0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\color{blue}{\left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right)} + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)\]

  7. Final simplification0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)\]

Reproduce

herbie shell --seed 2019347 
(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))))