Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, B

Average Error: 6.4 → 4.4

Time: 26.3s

Precision: 64

Math

\[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.9189385332046700050057097541866824030876\right) + \frac{\left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x}\]

↓

\[\begin{array}{l} \mathbf{if}\;x \le 210021393343397462016:\\ \;\;\;\;\left(\frac{\left(\left(7.936500793651000149400709382518925849581 \cdot 10^{-4} + y\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x} + 0.9189385332046700050057097541866824030876\right) + \left(\left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) - x\right) + \left(\left(x - 0.5\right) \cdot \left(\log \left({\left(\sqrt{x}\right)}^{\frac{1}{3}}\right) \cdot 2\right) + \left(x - 0.5\right) \cdot \log \left(\sqrt[3]{\sqrt{x}}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) - x\right) + \left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{\sqrt{x}}\right) + \left(x - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt{x}}\right)\right)\right)\right) + \left(\left(\left(\frac{\left(z \cdot z\right) \cdot 7.936500793651000149400709382518925849581 \cdot 10^{-4}}{x} - 0.002777777777777800001512975569539776188321 \cdot \frac{z}{x}\right) + \frac{z \cdot z}{\frac{x}{y}}\right) + 0.9189385332046700050057097541866824030876\right)\\ \end{array}\]

C

double f(double x, double y, double z) {
        double r286660 = x;
        double r286661 = 0.5;
        double r286662 = r286660 - r286661;
        double r286663 = log(r286660);
        double r286664 = r286662 * r286663;
        double r286665 = r286664 - r286660;
        double r286666 = 0.91893853320467;
        double r286667 = r286665 + r286666;
        double r286668 = y;
        double r286669 = 0.0007936500793651;
        double r286670 = r286668 + r286669;
        double r286671 = z;
        double r286672 = r286670 * r286671;
        double r286673 = 0.0027777777777778;
        double r286674 = r286672 - r286673;
        double r286675 = r286674 * r286671;
        double r286676 = 0.083333333333333;
        double r286677 = r286675 + r286676;
        double r286678 = r286677 / r286660;
        double r286679 = r286667 + r286678;
        return r286679;
}

↓

double f(double x, double y, double z) {
        double r286680 = x;
        double r286681 = 2.1002139334339746e+20;
        bool r286682 = r286680 <= r286681;
        double r286683 = 0.0007936500793651;
        double r286684 = y;
        double r286685 = r286683 + r286684;
        double r286686 = z;
        double r286687 = r286685 * r286686;
        double r286688 = 0.0027777777777778;
        double r286689 = r286687 - r286688;
        double r286690 = r286689 * r286686;
        double r286691 = 0.083333333333333;
        double r286692 = r286690 + r286691;
        double r286693 = r286692 / r286680;
        double r286694 = 0.91893853320467;
        double r286695 = r286693 + r286694;
        double r286696 = sqrt(r286680);
        double r286697 = log(r286696);
        double r286698 = 0.5;
        double r286699 = r286680 - r286698;
        double r286700 = r286697 * r286699;
        double r286701 = r286700 - r286680;
        double r286702 = 0.3333333333333333;
        double r286703 = pow(r286696, r286702);
        double r286704 = log(r286703);
        double r286705 = 2.0;
        double r286706 = r286704 * r286705;
        double r286707 = r286699 * r286706;
        double r286708 = cbrt(r286696);
        double r286709 = log(r286708);
        double r286710 = r286699 * r286709;
        double r286711 = r286707 + r286710;
        double r286712 = r286701 + r286711;
        double r286713 = r286695 + r286712;
        double r286714 = r286705 * r286709;
        double r286715 = r286699 * r286714;
        double r286716 = r286710 + r286715;
        double r286717 = r286701 + r286716;
        double r286718 = r286686 * r286686;
        double r286719 = r286718 * r286683;
        double r286720 = r286719 / r286680;
        double r286721 = r286686 / r286680;
        double r286722 = r286688 * r286721;
        double r286723 = r286720 - r286722;
        double r286724 = r286680 / r286684;
        double r286725 = r286718 / r286724;
        double r286726 = r286723 + r286725;
        double r286727 = r286726 + r286694;
        double r286728 = r286717 + r286727;
        double r286729 = r286682 ? r286713 : r286728;
        return r286729;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	6.4
Target	1.2
Herbie	4.4

\[\left(\left(\left(x - 0.5\right) \cdot \log x + \left(0.9189385332046700050057097541866824030876 - x\right)\right) + \frac{0.08333333333333299564049667651488562114537}{x}\right) + \frac{z}{x} \cdot \left(z \cdot \left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) - 0.002777777777777800001512975569539776188321\right)\]

Derivation

1. Split input into 2 regimes

2. if x < 2.1002139334339746e+20

   1. Initial program 0.2

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.9189385332046700050057097541866824030876\right) + \frac{\left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x}\]

   2. Simplified 0.2

      \[\leadsto \color{blue}{\left(\left(x - 0.5\right) \cdot \log x - x\right) + \left(0.9189385332046700050057097541866824030876 + \frac{0.08333333333333299564049667651488562114537 + z \cdot \left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right)}{x}\right)}\]
   3. Using strategy rm

   4. Applied add-sqr-sqrt 0.2

      \[\leadsto \left(\left(x - 0.5\right) \cdot \log \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} - x\right) + \left(0.9189385332046700050057097541866824030876 + \frac{0.08333333333333299564049667651488562114537 + z \cdot \left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right)}{x}\right)\]

   5. Applied log-prod 0.2

      \[\leadsto \left(\left(x - 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt{x}\right) + \log \left(\sqrt{x}\right)\right)} - x\right) + \left(0.9189385332046700050057097541866824030876 + \frac{0.08333333333333299564049667651488562114537 + z \cdot \left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right)}{x}\right)\]

   6. Applied distribute-lft-in 0.2

      \[\leadsto \left(\color{blue}{\left(\left(x - 0.5\right) \cdot \log \left(\sqrt{x}\right) + \left(x - 0.5\right) \cdot \log \left(\sqrt{x}\right)\right)} - x\right) + \left(0.9189385332046700050057097541866824030876 + \frac{0.08333333333333299564049667651488562114537 + z \cdot \left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right)}{x}\right)\]

   7. Applied associate--l+ 0.2

      \[\leadsto \color{blue}{\left(\left(x - 0.5\right) \cdot \log \left(\sqrt{x}\right) + \left(\left(x - 0.5\right) \cdot \log \left(\sqrt{x}\right) - x\right)\right)} + \left(0.9189385332046700050057097541866824030876 + \frac{0.08333333333333299564049667651488562114537 + z \cdot \left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right)}{x}\right)\]

   8. Simplified 0.2

      \[\leadsto \left(\left(x - 0.5\right) \cdot \log \left(\sqrt{x}\right) + \color{blue}{\left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) - x\right)}\right) + \left(0.9189385332046700050057097541866824030876 + \frac{0.08333333333333299564049667651488562114537 + z \cdot \left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right)}{x}\right)\]
   9. Using strategy rm

   10. Applied add-cube-cbrt 0.2

       \[\leadsto \left(\left(x - 0.5\right) \cdot \log \color{blue}{\left(\left(\sqrt[3]{\sqrt{x}} \cdot \sqrt[3]{\sqrt{x}}\right) \cdot \sqrt[3]{\sqrt{x}}\right)} + \left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) - x\right)\right) + \left(0.9189385332046700050057097541866824030876 + \frac{0.08333333333333299564049667651488562114537 + z \cdot \left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right)}{x}\right)\]

   11. Applied log-prod 0.2

       \[\leadsto \left(\left(x - 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt[3]{\sqrt{x}} \cdot \sqrt[3]{\sqrt{x}}\right) + \log \left(\sqrt[3]{\sqrt{x}}\right)\right)} + \left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) - x\right)\right) + \left(0.9189385332046700050057097541866824030876 + \frac{0.08333333333333299564049667651488562114537 + z \cdot \left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right)}{x}\right)\]

   12. Applied distribute-lft-in 0.2

       \[\leadsto \left(\color{blue}{\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{\sqrt{x}} \cdot \sqrt[3]{\sqrt{x}}\right) + \left(x - 0.5\right) \cdot \log \left(\sqrt[3]{\sqrt{x}}\right)\right)} + \left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) - x\right)\right) + \left(0.9189385332046700050057097541866824030876 + \frac{0.08333333333333299564049667651488562114537 + z \cdot \left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right)}{x}\right)\]

   13. Simplified 0.2

       \[\leadsto \left(\left(\color{blue}{\left(x - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt{x}}\right)\right)} + \left(x - 0.5\right) \cdot \log \left(\sqrt[3]{\sqrt{x}}\right)\right) + \left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) - x\right)\right) + \left(0.9189385332046700050057097541866824030876 + \frac{0.08333333333333299564049667651488562114537 + z \cdot \left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right)}{x}\right)\]

   14. Simplified 0.2

       \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt{x}}\right)\right) + \color{blue}{\log \left(\sqrt[3]{\sqrt{x}}\right) \cdot \left(x - 0.5\right)}\right) + \left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) - x\right)\right) + \left(0.9189385332046700050057097541866824030876 + \frac{0.08333333333333299564049667651488562114537 + z \cdot \left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right)}{x}\right)\]
   15. Using strategy rm

   16. Applied pow1/3 0.2

       \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \left(2 \cdot \log \color{blue}{\left({\left(\sqrt{x}\right)}^{\frac{1}{3}}\right)}\right) + \log \left(\sqrt[3]{\sqrt{x}}\right) \cdot \left(x - 0.5\right)\right) + \left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) - x\right)\right) + \left(0.9189385332046700050057097541866824030876 + \frac{0.08333333333333299564049667651488562114537 + z \cdot \left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right)}{x}\right)\]

   if 2.1002139334339746e+20 < x

   1. Initial program 11.3

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.9189385332046700050057097541866824030876\right) + \frac{\left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x}\]

   2. Simplified 11.3

      \[\leadsto \color{blue}{\left(\left(x - 0.5\right) \cdot \log x - x\right) + \left(0.9189385332046700050057097541866824030876 + \frac{0.08333333333333299564049667651488562114537 + z \cdot \left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right)}{x}\right)}\]
   3. Using strategy rm

   4. Applied add-sqr-sqrt 11.3

      \[\leadsto \left(\left(x - 0.5\right) \cdot \log \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} - x\right) + \left(0.9189385332046700050057097541866824030876 + \frac{0.08333333333333299564049667651488562114537 + z \cdot \left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right)}{x}\right)\]

   5. Applied log-prod 11.3

      \[\leadsto \left(\left(x - 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt{x}\right) + \log \left(\sqrt{x}\right)\right)} - x\right) + \left(0.9189385332046700050057097541866824030876 + \frac{0.08333333333333299564049667651488562114537 + z \cdot \left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right)}{x}\right)\]

   6. Applied distribute-lft-in 11.3

      \[\leadsto \left(\color{blue}{\left(\left(x - 0.5\right) \cdot \log \left(\sqrt{x}\right) + \left(x - 0.5\right) \cdot \log \left(\sqrt{x}\right)\right)} - x\right) + \left(0.9189385332046700050057097541866824030876 + \frac{0.08333333333333299564049667651488562114537 + z \cdot \left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right)}{x}\right)\]

   7. Applied associate--l+ 11.4

      \[\leadsto \color{blue}{\left(\left(x - 0.5\right) \cdot \log \left(\sqrt{x}\right) + \left(\left(x - 0.5\right) \cdot \log \left(\sqrt{x}\right) - x\right)\right)} + \left(0.9189385332046700050057097541866824030876 + \frac{0.08333333333333299564049667651488562114537 + z \cdot \left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right)}{x}\right)\]

   8. Simplified 11.4

      \[\leadsto \left(\left(x - 0.5\right) \cdot \log \left(\sqrt{x}\right) + \color{blue}{\left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) - x\right)}\right) + \left(0.9189385332046700050057097541866824030876 + \frac{0.08333333333333299564049667651488562114537 + z \cdot \left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right)}{x}\right)\]
   9. Using strategy rm

   10. Applied add-cube-cbrt 11.4

       \[\leadsto \left(\left(x - 0.5\right) \cdot \log \color{blue}{\left(\left(\sqrt[3]{\sqrt{x}} \cdot \sqrt[3]{\sqrt{x}}\right) \cdot \sqrt[3]{\sqrt{x}}\right)} + \left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) - x\right)\right) + \left(0.9189385332046700050057097541866824030876 + \frac{0.08333333333333299564049667651488562114537 + z \cdot \left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right)}{x}\right)\]

   11. Applied log-prod 11.4

       \[\leadsto \left(\left(x - 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt[3]{\sqrt{x}} \cdot \sqrt[3]{\sqrt{x}}\right) + \log \left(\sqrt[3]{\sqrt{x}}\right)\right)} + \left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) - x\right)\right) + \left(0.9189385332046700050057097541866824030876 + \frac{0.08333333333333299564049667651488562114537 + z \cdot \left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right)}{x}\right)\]

   12. Applied distribute-lft-in 11.3

       \[\leadsto \left(\color{blue}{\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{\sqrt{x}} \cdot \sqrt[3]{\sqrt{x}}\right) + \left(x - 0.5\right) \cdot \log \left(\sqrt[3]{\sqrt{x}}\right)\right)} + \left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) - x\right)\right) + \left(0.9189385332046700050057097541866824030876 + \frac{0.08333333333333299564049667651488562114537 + z \cdot \left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right)}{x}\right)\]

   13. Simplified 11.3

       \[\leadsto \left(\left(\color{blue}{\left(x - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt{x}}\right)\right)} + \left(x - 0.5\right) \cdot \log \left(\sqrt[3]{\sqrt{x}}\right)\right) + \left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) - x\right)\right) + \left(0.9189385332046700050057097541866824030876 + \frac{0.08333333333333299564049667651488562114537 + z \cdot \left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right)}{x}\right)\]

   14. Simplified 11.3

       \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt{x}}\right)\right) + \color{blue}{\log \left(\sqrt[3]{\sqrt{x}}\right) \cdot \left(x - 0.5\right)}\right) + \left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) - x\right)\right) + \left(0.9189385332046700050057097541866824030876 + \frac{0.08333333333333299564049667651488562114537 + z \cdot \left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right)}{x}\right)\]

   15. Taylor expanded around inf 11.4

       \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt{x}}\right)\right) + \log \left(\sqrt[3]{\sqrt{x}}\right) \cdot \left(x - 0.5\right)\right) + \left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) - x\right)\right) + \left(0.9189385332046700050057097541866824030876 + \color{blue}{\left(\left(7.936500793651000149400709382518925849581 \cdot 10^{-4} \cdot \frac{{z}^{2}}{x} + \frac{{z}^{2} \cdot y}{x}\right) - 0.002777777777777800001512975569539776188321 \cdot \frac{z}{x}\right)}\right)\]

   16. Simplified 7.8

       \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt{x}}\right)\right) + \log \left(\sqrt[3]{\sqrt{x}}\right) \cdot \left(x - 0.5\right)\right) + \left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) - x\right)\right) + \left(0.9189385332046700050057097541866824030876 + \color{blue}{\left(\frac{z \cdot z}{\frac{x}{y}} + \left(\frac{7.936500793651000149400709382518925849581 \cdot 10^{-4} \cdot \left(z \cdot z\right)}{x} - 0.002777777777777800001512975569539776188321 \cdot \frac{z}{x}\right)\right)}\right)\]
3. Recombined 2 regimes into one program.

4. Final simplification 4.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le 210021393343397462016:\\ \;\;\;\;\left(\frac{\left(\left(7.936500793651000149400709382518925849581 \cdot 10^{-4} + y\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x} + 0.9189385332046700050057097541866824030876\right) + \left(\left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) - x\right) + \left(\left(x - 0.5\right) \cdot \left(\log \left({\left(\sqrt{x}\right)}^{\frac{1}{3}}\right) \cdot 2\right) + \left(x - 0.5\right) \cdot \log \left(\sqrt[3]{\sqrt{x}}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\log \left(\sqrt{x}\right) \cdot \left(x - 0.5\right) - x\right) + \left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{\sqrt{x}}\right) + \left(x - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt{x}}\right)\right)\right)\right) + \left(\left(\left(\frac{\left(z \cdot z\right) \cdot 7.936500793651000149400709382518925849581 \cdot 10^{-4}}{x} - 0.002777777777777800001512975569539776188321 \cdot \frac{z}{x}\right) + \frac{z \cdot z}{\frac{x}{y}}\right) + 0.9189385332046700050057097541866824030876\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019195 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, B"

  :herbie-target
  (+ (+ (+ (* (- x 0.5) (log x)) (- 0.91893853320467 x)) (/ 0.083333333333333 x)) (* (/ z x) (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))

  (+ (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467) (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)))