Average Error: 0.3 → 0.3
Time: 29.6s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\left(\log \left(\sqrt[3]{x + y}\right) - t\right) + \left(\log t \cdot \left(a - 0.5\right) + \log z\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\left(\log \left(\sqrt[3]{x + y}\right) - t\right) + \left(\log t \cdot \left(a - 0.5\right) + \log z\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r53031 = x;
        double r53032 = y;
        double r53033 = r53031 + r53032;
        double r53034 = log(r53033);
        double r53035 = z;
        double r53036 = log(r53035);
        double r53037 = r53034 + r53036;
        double r53038 = t;
        double r53039 = r53037 - r53038;
        double r53040 = a;
        double r53041 = 0.5;
        double r53042 = r53040 - r53041;
        double r53043 = log(r53038);
        double r53044 = r53042 * r53043;
        double r53045 = r53039 + r53044;
        return r53045;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r53046 = x;
        double r53047 = y;
        double r53048 = r53046 + r53047;
        double r53049 = cbrt(r53048);
        double r53050 = r53049 * r53049;
        double r53051 = log(r53050);
        double r53052 = log(r53049);
        double r53053 = t;
        double r53054 = r53052 - r53053;
        double r53055 = log(r53053);
        double r53056 = a;
        double r53057 = 0.5;
        double r53058 = r53056 - r53057;
        double r53059 = r53055 * r53058;
        double r53060 = z;
        double r53061 = log(r53060);
        double r53062 = r53059 + r53061;
        double r53063 = r53054 + r53062;
        double r53064 = r53051 + r53063;
        return r53064;
}

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. Simplified0.3

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

  4. Applied add-cube-cbrt0.3

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

  5. Applied log-prod0.3

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

  6. Applied associate--l+0.3

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

  7. Simplified0.3

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

  8. Final simplification0.3

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

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))))