Average Error: 0.3 → 0.3
Time: 11.1s
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 r55936 = x;
        double r55937 = y;
        double r55938 = r55936 + r55937;
        double r55939 = log(r55938);
        double r55940 = z;
        double r55941 = log(r55940);
        double r55942 = r55939 + r55941;
        double r55943 = t;
        double r55944 = r55942 - r55943;
        double r55945 = a;
        double r55946 = 0.5;
        double r55947 = r55945 - r55946;
        double r55948 = log(r55943);
        double r55949 = r55947 * r55948;
        double r55950 = r55944 + r55949;
        return r55950;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r55951 = x;
        double r55952 = y;
        double r55953 = r55951 + r55952;
        double r55954 = log(r55953);
        double r55955 = z;
        double r55956 = cbrt(r55955);
        double r55957 = r55956 * r55956;
        double r55958 = log(r55957);
        double r55959 = r55954 + r55958;
        double r55960 = log(r55956);
        double r55961 = r55959 + r55960;
        double r55962 = t;
        double r55963 = r55961 - r55962;
        double r55964 = a;
        double r55965 = 0.5;
        double r55966 = r55964 - r55965;
        double r55967 = log(r55962);
        double r55968 = r55966 * r55967;
        double r55969 = r55963 + r55968;
        return r55969;
}

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 add-cube-cbrt0.3

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

  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 2020065 
(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))))