Average Error: 0.3 → 0.3
Time: 36.1s
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 r74240 = x;
        double r74241 = y;
        double r74242 = r74240 + r74241;
        double r74243 = log(r74242);
        double r74244 = z;
        double r74245 = log(r74244);
        double r74246 = r74243 + r74245;
        double r74247 = t;
        double r74248 = r74246 - r74247;
        double r74249 = a;
        double r74250 = 0.5;
        double r74251 = r74249 - r74250;
        double r74252 = log(r74247);
        double r74253 = r74251 * r74252;
        double r74254 = r74248 + r74253;
        return r74254;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r74255 = x;
        double r74256 = y;
        double r74257 = r74255 + r74256;
        double r74258 = log(r74257);
        double r74259 = z;
        double r74260 = log(r74259);
        double r74261 = t;
        double r74262 = r74260 - r74261;
        double r74263 = a;
        double r74264 = 0.5;
        double r74265 = r74263 - r74264;
        double r74266 = log(r74261);
        double r74267 = r74265 * r74266;
        double r74268 = r74262 + r74267;
        double r74269 = r74258 + r74268;
        return r74269;
}

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 2019304 
(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))))