Average Error: 0.3 → 0.3
Time: 35.3s
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 r52206 = x;
        double r52207 = y;
        double r52208 = r52206 + r52207;
        double r52209 = log(r52208);
        double r52210 = z;
        double r52211 = log(r52210);
        double r52212 = r52209 + r52211;
        double r52213 = t;
        double r52214 = r52212 - r52213;
        double r52215 = a;
        double r52216 = 0.5;
        double r52217 = r52215 - r52216;
        double r52218 = log(r52213);
        double r52219 = r52217 * r52218;
        double r52220 = r52214 + r52219;
        return r52220;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r52221 = x;
        double r52222 = y;
        double r52223 = r52221 + r52222;
        double r52224 = log(r52223);
        double r52225 = z;
        double r52226 = log(r52225);
        double r52227 = t;
        double r52228 = r52226 - r52227;
        double r52229 = a;
        double r52230 = 0.5;
        double r52231 = r52229 - r52230;
        double r52232 = log(r52227);
        double r52233 = r52231 * r52232;
        double r52234 = r52228 + r52233;
        double r52235 = r52224 + r52234;
        return r52235;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019303 
(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))))