Average Error: 0.3 → 0.3
Time: 19.3s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\frac{{\left(\log \left(x + y\right)\right)}^{3} + {\left(\log z\right)}^{3}}{\log z \cdot \left(\log z - \log \left(x + y\right)\right) + \log \left(x + y\right) \cdot \log \left(x + y\right)} - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\frac{{\left(\log \left(x + y\right)\right)}^{3} + {\left(\log z\right)}^{3}}{\log z \cdot \left(\log z - \log \left(x + y\right)\right) + \log \left(x + y\right) \cdot \log \left(x + y\right)} - t\right) + \left(a - 0.5\right) \cdot \log t
double f(double x, double y, double z, double t, double a) {
        double r1751 = x;
        double r1752 = y;
        double r1753 = r1751 + r1752;
        double r1754 = log(r1753);
        double r1755 = z;
        double r1756 = log(r1755);
        double r1757 = r1754 + r1756;
        double r1758 = t;
        double r1759 = r1757 - r1758;
        double r1760 = a;
        double r1761 = 0.5;
        double r1762 = r1760 - r1761;
        double r1763 = log(r1758);
        double r1764 = r1762 * r1763;
        double r1765 = r1759 + r1764;
        return r1765;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1766 = x;
        double r1767 = y;
        double r1768 = r1766 + r1767;
        double r1769 = log(r1768);
        double r1770 = 3.0;
        double r1771 = pow(r1769, r1770);
        double r1772 = z;
        double r1773 = log(r1772);
        double r1774 = pow(r1773, r1770);
        double r1775 = r1771 + r1774;
        double r1776 = r1773 - r1769;
        double r1777 = r1773 * r1776;
        double r1778 = r1769 * r1769;
        double r1779 = r1777 + r1778;
        double r1780 = r1775 / r1779;
        double r1781 = t;
        double r1782 = r1780 - r1781;
        double r1783 = a;
        double r1784 = 0.5;
        double r1785 = r1783 - r1784;
        double r1786 = log(r1781);
        double r1787 = r1785 * r1786;
        double r1788 = r1782 + r1787;
        return r1788;
}

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

Target

Original0.3
Target0.3
Herbie0.3
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]

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 flip3-+0.3

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

  4. Simplified0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2020025 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (log t))))

  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))