Average Error: 0.3 → 0.3
Time: 30.5s
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 r61304 = x;
        double r61305 = y;
        double r61306 = r61304 + r61305;
        double r61307 = log(r61306);
        double r61308 = z;
        double r61309 = log(r61308);
        double r61310 = r61307 + r61309;
        double r61311 = t;
        double r61312 = r61310 - r61311;
        double r61313 = a;
        double r61314 = 0.5;
        double r61315 = r61313 - r61314;
        double r61316 = log(r61311);
        double r61317 = r61315 * r61316;
        double r61318 = r61312 + r61317;
        return r61318;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r61319 = x;
        double r61320 = y;
        double r61321 = r61319 + r61320;
        double r61322 = log(r61321);
        double r61323 = z;
        double r61324 = log(r61323);
        double r61325 = t;
        double r61326 = r61324 - r61325;
        double r61327 = a;
        double r61328 = 0.5;
        double r61329 = r61327 - r61328;
        double r61330 = log(r61325);
        double r61331 = r61329 * r61330;
        double r61332 = r61326 + r61331;
        double r61333 = r61322 + r61332;
        return r61333;
}

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 2019212 
(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))))