Average Error: 0.3 → 0.3
Time: 12.4s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\log \left(\sqrt[3]{x + y}\right) + \log z\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\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]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\log \left(\sqrt[3]{x + y}\right) + \log z\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t
double f(double x, double y, double z, double t, double a) {
        double r51604 = x;
        double r51605 = y;
        double r51606 = r51604 + r51605;
        double r51607 = log(r51606);
        double r51608 = z;
        double r51609 = log(r51608);
        double r51610 = r51607 + r51609;
        double r51611 = t;
        double r51612 = r51610 - r51611;
        double r51613 = a;
        double r51614 = 0.5;
        double r51615 = r51613 - r51614;
        double r51616 = log(r51611);
        double r51617 = r51615 * r51616;
        double r51618 = r51612 + r51617;
        return r51618;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r51619 = x;
        double r51620 = y;
        double r51621 = r51619 + r51620;
        double r51622 = cbrt(r51621);
        double r51623 = r51622 * r51622;
        double r51624 = log(r51623);
        double r51625 = log(r51622);
        double r51626 = z;
        double r51627 = log(r51626);
        double r51628 = r51625 + r51627;
        double r51629 = r51624 + r51628;
        double r51630 = t;
        double r51631 = r51629 - r51630;
        double r51632 = a;
        double r51633 = 0.5;
        double r51634 = r51632 - r51633;
        double r51635 = log(r51630);
        double r51636 = r51634 * r51635;
        double r51637 = r51631 + r51636;
        return r51637;
}

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

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

  4. Applied log-prod0.3

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

  5. Applied associate-+l+0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2020018 +o rules:numerics
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))