Average Error: 0.3 → 0.3
Time: 34.3s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\log t \cdot \left(a - 0.5\right) + \left(\left(\log \left(\sqrt{z}\right) - t\right) + \log \left(\sqrt{z}\right)\right)\right) + \log \left(y + x\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\log t \cdot \left(a - 0.5\right) + \left(\left(\log \left(\sqrt{z}\right) - t\right) + \log \left(\sqrt{z}\right)\right)\right) + \log \left(y + x\right)
double f(double x, double y, double z, double t, double a) {
        double r2834308 = x;
        double r2834309 = y;
        double r2834310 = r2834308 + r2834309;
        double r2834311 = log(r2834310);
        double r2834312 = z;
        double r2834313 = log(r2834312);
        double r2834314 = r2834311 + r2834313;
        double r2834315 = t;
        double r2834316 = r2834314 - r2834315;
        double r2834317 = a;
        double r2834318 = 0.5;
        double r2834319 = r2834317 - r2834318;
        double r2834320 = log(r2834315);
        double r2834321 = r2834319 * r2834320;
        double r2834322 = r2834316 + r2834321;
        return r2834322;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2834323 = t;
        double r2834324 = log(r2834323);
        double r2834325 = a;
        double r2834326 = 0.5;
        double r2834327 = r2834325 - r2834326;
        double r2834328 = r2834324 * r2834327;
        double r2834329 = z;
        double r2834330 = sqrt(r2834329);
        double r2834331 = log(r2834330);
        double r2834332 = r2834331 - r2834323;
        double r2834333 = r2834332 + r2834331;
        double r2834334 = r2834328 + r2834333;
        double r2834335 = y;
        double r2834336 = x;
        double r2834337 = r2834335 + r2834336;
        double r2834338 = log(r2834337);
        double r2834339 = r2834334 + r2834338;
        return r2834339;
}

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+0.2

    \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)}\]
  5. Using strategy rm

  6. Applied add-sqr-sqrt0.2

    \[\leadsto \log \left(x + y\right) + \left(\left(\log \color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)} - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]

  7. Applied log-prod0.2

    \[\leadsto \log \left(x + y\right) + \left(\left(\color{blue}{\left(\log \left(\sqrt{z}\right) + \log \left(\sqrt{z}\right)\right)} - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]

  8. Applied associate--l+0.3

    \[\leadsto \log \left(x + y\right) + \left(\color{blue}{\left(\log \left(\sqrt{z}\right) + \left(\log \left(\sqrt{z}\right) - t\right)\right)} + \left(a - 0.5\right) \cdot \log t\right)\]

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019164 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))