Average Error: 28.3 → 28.3
Time: 56.9s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{(\left((y \cdot \left((\left(y + a\right) \cdot y + b)_*\right) + c)_*\right) \cdot y + i)_*} \cdot (y \cdot \left((y \cdot \left((y \cdot \left((y \cdot x + z)_*\right) + 27464.7644705)_*\right) + 230661.510616)_*\right) + t)_*\]
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r5563760 = x;
        double r5563761 = y;
        double r5563762 = r5563760 * r5563761;
        double r5563763 = z;
        double r5563764 = r5563762 + r5563763;
        double r5563765 = r5563764 * r5563761;
        double r5563766 = 27464.7644705;
        double r5563767 = r5563765 + r5563766;
        double r5563768 = r5563767 * r5563761;
        double r5563769 = 230661.510616;
        double r5563770 = r5563768 + r5563769;
        double r5563771 = r5563770 * r5563761;
        double r5563772 = t;
        double r5563773 = r5563771 + r5563772;
        double r5563774 = a;
        double r5563775 = r5563761 + r5563774;
        double r5563776 = r5563775 * r5563761;
        double r5563777 = b;
        double r5563778 = r5563776 + r5563777;
        double r5563779 = r5563778 * r5563761;
        double r5563780 = c;
        double r5563781 = r5563779 + r5563780;
        double r5563782 = r5563781 * r5563761;
        double r5563783 = i;
        double r5563784 = r5563782 + r5563783;
        double r5563785 = r5563773 / r5563784;
        return r5563785;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r5563786 = 1.0;
        double r5563787 = y;
        double r5563788 = a;
        double r5563789 = r5563787 + r5563788;
        double r5563790 = b;
        double r5563791 = fma(r5563789, r5563787, r5563790);
        double r5563792 = c;
        double r5563793 = fma(r5563787, r5563791, r5563792);
        double r5563794 = i;
        double r5563795 = fma(r5563793, r5563787, r5563794);
        double r5563796 = r5563786 / r5563795;
        double r5563797 = x;
        double r5563798 = z;
        double r5563799 = fma(r5563787, r5563797, r5563798);
        double r5563800 = 27464.7644705;
        double r5563801 = fma(r5563787, r5563799, r5563800);
        double r5563802 = 230661.510616;
        double r5563803 = fma(r5563787, r5563801, r5563802);
        double r5563804 = t;
        double r5563805 = fma(r5563787, r5563803, r5563804);
        double r5563806 = r5563796 * r5563805;
        return r5563806;
}


\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{1}{(\left((y \cdot \left((\left(y + a\right) \cdot y + b)_*\right) + c)_*\right) \cdot y + i)_*} \cdot (y \cdot \left((y \cdot \left((y \cdot \left((y \cdot x + z)_*\right) + 27464.7644705)_*\right) + 230661.510616)_*\right) + t)_*

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Derivation

  1. Initial program 28.3

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  2. Simplified28.2

    \[\leadsto \color{blue}{\frac{(y \cdot \left((y \cdot \left((y \cdot \left((y \cdot x + z)_*\right) + 27464.7644705)_*\right) + 230661.510616)_*\right) + t)_*}{(\left((y \cdot \left((\left(y + a\right) \cdot y + b)_*\right) + c)_*\right) \cdot y + i)_*}}\]
  3. Using strategy rm

  4. Applied div-inv28.3

    \[\leadsto \color{blue}{(y \cdot \left((y \cdot \left((y \cdot \left((y \cdot x + z)_*\right) + 27464.7644705)_*\right) + 230661.510616)_*\right) + t)_* \cdot \frac{1}{(\left((y \cdot \left((\left(y + a\right) \cdot y + b)_*\right) + c)_*\right) \cdot y + i)_*}}\]

  5. Final simplification28.3

    \[\leadsto \frac{1}{(\left((y \cdot \left((\left(y + a\right) \cdot y + b)_*\right) + c)_*\right) \cdot y + i)_*} \cdot (y \cdot \left((y \cdot \left((y \cdot \left((y \cdot x + z)_*\right) + 27464.7644705)_*\right) + 230661.510616)_*\right) + t)_*\]

Reproduce

herbie shell --seed 2019102 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))