Average Error: 0.3 → 0.3
Time: 15.4s
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 r55277 = x;
        double r55278 = y;
        double r55279 = r55277 + r55278;
        double r55280 = log(r55279);
        double r55281 = z;
        double r55282 = log(r55281);
        double r55283 = r55280 + r55282;
        double r55284 = t;
        double r55285 = r55283 - r55284;
        double r55286 = a;
        double r55287 = 0.5;
        double r55288 = r55286 - r55287;
        double r55289 = log(r55284);
        double r55290 = r55288 * r55289;
        double r55291 = r55285 + r55290;
        return r55291;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r55292 = x;
        double r55293 = y;
        double r55294 = r55292 + r55293;
        double r55295 = log(r55294);
        double r55296 = z;
        double r55297 = log(r55296);
        double r55298 = t;
        double r55299 = r55297 - r55298;
        double r55300 = a;
        double r55301 = 0.5;
        double r55302 = r55300 - r55301;
        double r55303 = log(r55298);
        double r55304 = r55302 * r55303;
        double r55305 = r55299 + r55304;
        double r55306 = r55295 + r55305;
        return r55306;
}

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 2020047 
(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))))