Average Error: 0.3 → 0.3
Time: 39.7s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(a - 0.5\right) \cdot \log \left({t}^{\frac{1}{3}}\right) + \left(a - 0.5\right) \cdot \left(\log \left(\sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right)\right) + \left(\left(\log \left(y + x\right) + \log z\right) - t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(a - 0.5\right) \cdot \log \left({t}^{\frac{1}{3}}\right) + \left(a - 0.5\right) \cdot \left(\log \left(\sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\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 r2780631 = x;
        double r2780632 = y;
        double r2780633 = r2780631 + r2780632;
        double r2780634 = log(r2780633);
        double r2780635 = z;
        double r2780636 = log(r2780635);
        double r2780637 = r2780634 + r2780636;
        double r2780638 = t;
        double r2780639 = r2780637 - r2780638;
        double r2780640 = a;
        double r2780641 = 0.5;
        double r2780642 = r2780640 - r2780641;
        double r2780643 = log(r2780638);
        double r2780644 = r2780642 * r2780643;
        double r2780645 = r2780639 + r2780644;
        return r2780645;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2780646 = a;
        double r2780647 = 0.5;
        double r2780648 = r2780646 - r2780647;
        double r2780649 = t;
        double r2780650 = 0.3333333333333333;
        double r2780651 = pow(r2780649, r2780650);
        double r2780652 = log(r2780651);
        double r2780653 = r2780648 * r2780652;
        double r2780654 = cbrt(r2780649);
        double r2780655 = log(r2780654);
        double r2780656 = r2780655 + r2780655;
        double r2780657 = r2780648 * r2780656;
        double r2780658 = r2780653 + r2780657;
        double r2780659 = y;
        double r2780660 = x;
        double r2780661 = r2780659 + r2780660;
        double r2780662 = log(r2780661);
        double r2780663 = z;
        double r2780664 = log(r2780663);
        double r2780665 = r2780662 + r2780664;
        double r2780666 = r2780665 - r2780649;
        double r2780667 = r2780658 + r2780666;
        return r2780667;
}

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

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

  8. Applied pow1/30.3

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

  9. Final simplification0.3

    \[\leadsto \left(\left(a - 0.5\right) \cdot \log \left({t}^{\frac{1}{3}}\right) + \left(a - 0.5\right) \cdot \left(\log \left(\sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right)\right) + \left(\left(\log \left(y + x\right) + \log z\right) - t\right)\]

Reproduce

herbie shell --seed 2019163 
(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))))