Average Error: 0.3 → 0.3
Time: 30.7s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(x + y\right) + \left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \left(\left(\log \left(\sqrt[3]{z}\right) - t\right) + \left(a - 0.5\right) \cdot \log t\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(x + y\right) + \left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \left(\left(\log \left(\sqrt[3]{z}\right) - t\right) + \left(a - 0.5\right) \cdot \log t\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r54025 = x;
        double r54026 = y;
        double r54027 = r54025 + r54026;
        double r54028 = log(r54027);
        double r54029 = z;
        double r54030 = log(r54029);
        double r54031 = r54028 + r54030;
        double r54032 = t;
        double r54033 = r54031 - r54032;
        double r54034 = a;
        double r54035 = 0.5;
        double r54036 = r54034 - r54035;
        double r54037 = log(r54032);
        double r54038 = r54036 * r54037;
        double r54039 = r54033 + r54038;
        return r54039;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r54040 = x;
        double r54041 = y;
        double r54042 = r54040 + r54041;
        double r54043 = log(r54042);
        double r54044 = z;
        double r54045 = cbrt(r54044);
        double r54046 = r54045 * r54045;
        double r54047 = log(r54046);
        double r54048 = log(r54045);
        double r54049 = t;
        double r54050 = r54048 - r54049;
        double r54051 = a;
        double r54052 = 0.5;
        double r54053 = r54051 - r54052;
        double r54054 = log(r54049);
        double r54055 = r54053 * r54054;
        double r54056 = r54050 + r54055;
        double r54057 = r54047 + r54056;
        double r54058 = r54043 + r54057;
        return r54058;
}

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 associate--l+0.3

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

  4. Applied associate-+l+0.3

    \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt0.3

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

  7. Applied log-prod0.3

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

  8. Applied associate--l+0.3

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

  9. Applied associate-+l+0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019195 
(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))))