Average Error: 0.3 → 0.3
Time: 33.5s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(\left(\log \left(y + x\right) + \log z\right) - t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\log \left(\sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(\left(\log \left(y + x\right) + \log z\right) - t\right)
double f(double x, double y, double z, double t, double a) {
        double r2167600 = x;
        double r2167601 = y;
        double r2167602 = r2167600 + r2167601;
        double r2167603 = log(r2167602);
        double r2167604 = z;
        double r2167605 = log(r2167604);
        double r2167606 = r2167603 + r2167605;
        double r2167607 = t;
        double r2167608 = r2167606 - r2167607;
        double r2167609 = a;
        double r2167610 = 0.5;
        double r2167611 = r2167609 - r2167610;
        double r2167612 = log(r2167607);
        double r2167613 = r2167611 * r2167612;
        double r2167614 = r2167608 + r2167613;
        return r2167614;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2167615 = t;
        double r2167616 = cbrt(r2167615);
        double r2167617 = log(r2167616);
        double r2167618 = r2167617 + r2167617;
        double r2167619 = a;
        double r2167620 = 0.5;
        double r2167621 = r2167619 - r2167620;
        double r2167622 = r2167618 * r2167621;
        double r2167623 = r2167621 * r2167617;
        double r2167624 = r2167622 + r2167623;
        double r2167625 = y;
        double r2167626 = x;
        double r2167627 = r2167625 + r2167626;
        double r2167628 = log(r2167627);
        double r2167629 = z;
        double r2167630 = log(r2167629);
        double r2167631 = r2167628 + r2167630;
        double r2167632 = r2167631 - r2167615;
        double r2167633 = r2167624 + r2167632;
        return r2167633;
}

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

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

  4. Applied log-prod0.3

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

  5. Applied distribute-lft-in0.3

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

  6. Simplified0.3

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

  8. Applied pow1/30.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(a - 0.5\right) \cdot \left(\log \left(\sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot \log \color{blue}{\left({t}^{\frac{1}{3}}\right)}\right)\]
  9. Using strategy rm

  10. Applied unpow1/30.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2019192 
(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))))