Average Error: 0.3 → 0.3
Time: 11.1s
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 r58318 = x;
        double r58319 = y;
        double r58320 = r58318 + r58319;
        double r58321 = log(r58320);
        double r58322 = z;
        double r58323 = log(r58322);
        double r58324 = r58321 + r58323;
        double r58325 = t;
        double r58326 = r58324 - r58325;
        double r58327 = a;
        double r58328 = 0.5;
        double r58329 = r58327 - r58328;
        double r58330 = log(r58325);
        double r58331 = r58329 * r58330;
        double r58332 = r58326 + r58331;
        return r58332;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r58333 = x;
        double r58334 = y;
        double r58335 = r58333 + r58334;
        double r58336 = log(r58335);
        double r58337 = z;
        double r58338 = log(r58337);
        double r58339 = t;
        double r58340 = r58338 - r58339;
        double r58341 = a;
        double r58342 = 0.5;
        double r58343 = r58341 - r58342;
        double r58344 = log(r58339);
        double r58345 = r58343 * r58344;
        double r58346 = r58340 + r58345;
        double r58347 = r58336 + r58346;
        return r58347;
}

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 2020027 
(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))))