Average Error: 0.3 → 0.3
Time: 35.8s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(x + y\right) + \left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \log t \cdot \left(a - 0.5\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\left(\log \left(x + y\right) + \left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \log t \cdot \left(a - 0.5\right)
double f(double x, double y, double z, double t, double a) {
        double r2105361 = x;
        double r2105362 = y;
        double r2105363 = r2105361 + r2105362;
        double r2105364 = log(r2105363);
        double r2105365 = z;
        double r2105366 = log(r2105365);
        double r2105367 = r2105364 + r2105366;
        double r2105368 = t;
        double r2105369 = r2105367 - r2105368;
        double r2105370 = a;
        double r2105371 = 0.5;
        double r2105372 = r2105370 - r2105371;
        double r2105373 = log(r2105368);
        double r2105374 = r2105372 * r2105373;
        double r2105375 = r2105369 + r2105374;
        return r2105375;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2105376 = x;
        double r2105377 = y;
        double r2105378 = r2105376 + r2105377;
        double r2105379 = log(r2105378);
        double r2105380 = z;
        double r2105381 = cbrt(r2105380);
        double r2105382 = log(r2105381);
        double r2105383 = r2105382 + r2105382;
        double r2105384 = r2105379 + r2105383;
        double r2105385 = r2105384 + r2105382;
        double r2105386 = t;
        double r2105387 = r2105385 - r2105386;
        double r2105388 = log(r2105386);
        double r2105389 = a;
        double r2105390 = 0.5;
        double r2105391 = r2105389 - r2105390;
        double r2105392 = r2105388 * r2105391;
        double r2105393 = r2105387 + r2105392;
        return r2105393;
}

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-cube-cbrt0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)}\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

  4. Applied log-prod0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \color{blue}{\left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)}\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

  5. Applied associate-+r+0.3

    \[\leadsto \left(\color{blue}{\left(\left(\log \left(x + y\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right)} - t\right) + \left(a - 0.5\right) \cdot \log t\]

  6. Simplified0.3

    \[\leadsto \left(\left(\color{blue}{\left(\log \left(y + x\right) + \left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)\right)} + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

  7. Final simplification0.3

    \[\leadsto \left(\left(\left(\log \left(x + y\right) + \left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \log t \cdot \left(a - 0.5\right)\]

Reproduce

herbie shell --seed 2019179 
(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))))