Average Error: 0.3 → 0.3
Time: 31.4s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(y + x\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\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(y + x\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 r1817925 = x;
        double r1817926 = y;
        double r1817927 = r1817925 + r1817926;
        double r1817928 = log(r1817927);
        double r1817929 = z;
        double r1817930 = log(r1817929);
        double r1817931 = r1817928 + r1817930;
        double r1817932 = t;
        double r1817933 = r1817931 - r1817932;
        double r1817934 = a;
        double r1817935 = 0.5;
        double r1817936 = r1817934 - r1817935;
        double r1817937 = log(r1817932);
        double r1817938 = r1817936 * r1817937;
        double r1817939 = r1817933 + r1817938;
        return r1817939;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1817940 = y;
        double r1817941 = x;
        double r1817942 = r1817940 + r1817941;
        double r1817943 = log(r1817942);
        double r1817944 = z;
        double r1817945 = cbrt(r1817944);
        double r1817946 = r1817945 * r1817945;
        double r1817947 = log(r1817946);
        double r1817948 = r1817943 + r1817947;
        double r1817949 = log(r1817945);
        double r1817950 = r1817948 + r1817949;
        double r1817951 = t;
        double r1817952 = r1817950 - r1817951;
        double r1817953 = a;
        double r1817954 = 0.5;
        double r1817955 = r1817953 - r1817954;
        double r1817956 = log(r1817951);
        double r1817957 = r1817955 * r1817956;
        double r1817958 = r1817952 + r1817957;
        return r1817958;
}

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

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

Reproduce

herbie shell --seed 2019171 
(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))))