Average Error: 0.3 → 0.3
Time: 54.4s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log z + \log \left({\left(x + y\right)}^{\frac{1}{3}}\right)\right) + \log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\left(\log z + \log \left({\left(x + y\right)}^{\frac{1}{3}}\right)\right) + \log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\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 r2316704 = x;
        double r2316705 = y;
        double r2316706 = r2316704 + r2316705;
        double r2316707 = log(r2316706);
        double r2316708 = z;
        double r2316709 = log(r2316708);
        double r2316710 = r2316707 + r2316709;
        double r2316711 = t;
        double r2316712 = r2316710 - r2316711;
        double r2316713 = a;
        double r2316714 = 0.5;
        double r2316715 = r2316713 - r2316714;
        double r2316716 = log(r2316711);
        double r2316717 = r2316715 * r2316716;
        double r2316718 = r2316712 + r2316717;
        return r2316718;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2316719 = z;
        double r2316720 = log(r2316719);
        double r2316721 = x;
        double r2316722 = y;
        double r2316723 = r2316721 + r2316722;
        double r2316724 = 0.3333333333333333;
        double r2316725 = pow(r2316723, r2316724);
        double r2316726 = log(r2316725);
        double r2316727 = r2316720 + r2316726;
        double r2316728 = cbrt(r2316723);
        double r2316729 = r2316728 * r2316728;
        double r2316730 = log(r2316729);
        double r2316731 = r2316727 + r2316730;
        double r2316732 = t;
        double r2316733 = r2316731 - r2316732;
        double r2316734 = a;
        double r2316735 = 0.5;
        double r2316736 = r2316734 - r2316735;
        double r2316737 = log(r2316732);
        double r2316738 = r2316736 * r2316737;
        double r2316739 = r2316733 + r2316738;
        return r2316739;
}

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. Using strategy rm

  7. Applied pow1/30.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019200 
(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))))