Average Error: 0.3 → 0.3
Time: 38.0s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right) + \left(\left(\left(\log \left(y + x\right) + \log z\right) - t\right) + \log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right) + \left(\left(\left(\log \left(y + x\right) + \log z\right) - t\right) + \log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r1688315 = x;
        double r1688316 = y;
        double r1688317 = r1688315 + r1688316;
        double r1688318 = log(r1688317);
        double r1688319 = z;
        double r1688320 = log(r1688319);
        double r1688321 = r1688318 + r1688320;
        double r1688322 = t;
        double r1688323 = r1688321 - r1688322;
        double r1688324 = a;
        double r1688325 = 0.5;
        double r1688326 = r1688324 - r1688325;
        double r1688327 = log(r1688322);
        double r1688328 = r1688326 * r1688327;
        double r1688329 = r1688323 + r1688328;
        return r1688329;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1688330 = t;
        double r1688331 = sqrt(r1688330);
        double r1688332 = log(r1688331);
        double r1688333 = a;
        double r1688334 = 0.5;
        double r1688335 = r1688333 - r1688334;
        double r1688336 = r1688332 * r1688335;
        double r1688337 = y;
        double r1688338 = x;
        double r1688339 = r1688337 + r1688338;
        double r1688340 = log(r1688339);
        double r1688341 = z;
        double r1688342 = log(r1688341);
        double r1688343 = r1688340 + r1688342;
        double r1688344 = r1688343 - r1688330;
        double r1688345 = r1688344 + r1688336;
        double r1688346 = r1688336 + r1688345;
        return r1688346;
}

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 add-sqr-sqrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied distribute-rgt-in0.3

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

  6. Applied associate-+r+0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019143 +o rules:numerics
(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))))