Average Error: 0.3 → 0.2
Time: 18.6s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]
\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(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)
double f(double x, double y, double z, double t, double a) {
        double r54100 = x;
        double r54101 = y;
        double r54102 = r54100 + r54101;
        double r54103 = log(r54102);
        double r54104 = z;
        double r54105 = log(r54104);
        double r54106 = r54103 + r54105;
        double r54107 = t;
        double r54108 = r54106 - r54107;
        double r54109 = a;
        double r54110 = 0.5;
        double r54111 = r54109 - r54110;
        double r54112 = log(r54107);
        double r54113 = r54111 * r54112;
        double r54114 = r54108 + r54113;
        return r54114;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r54115 = x;
        double r54116 = y;
        double r54117 = r54115 + r54116;
        double r54118 = log(r54117);
        double r54119 = z;
        double r54120 = log(r54119);
        double r54121 = t;
        double r54122 = r54120 - r54121;
        double r54123 = a;
        double r54124 = 0.5;
        double r54125 = r54123 - r54124;
        double r54126 = log(r54121);
        double r54127 = r54125 * r54126;
        double r54128 = r54122 + r54127;
        double r54129 = r54118 + r54128;
        return r54129;
}

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+0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020042 
(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))))