Average Error: 0.3 → 0.3
Time: 39.7s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(y + x\right) + \left(\left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \left(\log \left(\sqrt[3]{z}\right) - t\right)\right) + \log t \cdot \left(a - 0.5\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(y + x\right) + \left(\left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \left(\log \left(\sqrt[3]{z}\right) - t\right)\right) + \log t \cdot \left(a - 0.5\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r2706994 = x;
        double r2706995 = y;
        double r2706996 = r2706994 + r2706995;
        double r2706997 = log(r2706996);
        double r2706998 = z;
        double r2706999 = log(r2706998);
        double r2707000 = r2706997 + r2706999;
        double r2707001 = t;
        double r2707002 = r2707000 - r2707001;
        double r2707003 = a;
        double r2707004 = 0.5;
        double r2707005 = r2707003 - r2707004;
        double r2707006 = log(r2707001);
        double r2707007 = r2707005 * r2707006;
        double r2707008 = r2707002 + r2707007;
        return r2707008;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2707009 = y;
        double r2707010 = x;
        double r2707011 = r2707009 + r2707010;
        double r2707012 = log(r2707011);
        double r2707013 = z;
        double r2707014 = cbrt(r2707013);
        double r2707015 = r2707014 * r2707014;
        double r2707016 = log(r2707015);
        double r2707017 = log(r2707014);
        double r2707018 = t;
        double r2707019 = r2707017 - r2707018;
        double r2707020 = r2707016 + r2707019;
        double r2707021 = log(r2707018);
        double r2707022 = a;
        double r2707023 = 0.5;
        double r2707024 = r2707022 - r2707023;
        double r2707025 = r2707021 * r2707024;
        double r2707026 = r2707020 + r2707025;
        double r2707027 = r2707012 + r2707026;
        return r2707027;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019172 
(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))))