Average Error: 28.5 → 28.5
Time: 2.2m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{(\left((y \cdot \left((\left(y + a\right) \cdot y + b)_*\right) + c)_*\right) \cdot y + i)_*} \cdot (y \cdot \left((y \cdot \left((y \cdot \left((y \cdot x + z)_*\right) + 27464.7644705)_*\right) + 230661.510616)_*\right) + t)_*\]
\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 r11848744 = x;
        double r11848745 = y;
        double r11848746 = r11848744 * r11848745;
        double r11848747 = z;
        double r11848748 = r11848746 + r11848747;
        double r11848749 = r11848748 * r11848745;
        double r11848750 = 27464.7644705;
        double r11848751 = r11848749 + r11848750;
        double r11848752 = r11848751 * r11848745;
        double r11848753 = 230661.510616;
        double r11848754 = r11848752 + r11848753;
        double r11848755 = r11848754 * r11848745;
        double r11848756 = t;
        double r11848757 = r11848755 + r11848756;
        double r11848758 = a;
        double r11848759 = r11848745 + r11848758;
        double r11848760 = r11848759 * r11848745;
        double r11848761 = b;
        double r11848762 = r11848760 + r11848761;
        double r11848763 = r11848762 * r11848745;
        double r11848764 = c;
        double r11848765 = r11848763 + r11848764;
        double r11848766 = r11848765 * r11848745;
        double r11848767 = i;
        double r11848768 = r11848766 + r11848767;
        double r11848769 = r11848757 / r11848768;
        return r11848769;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r11848770 = 1.0;
        double r11848771 = y;
        double r11848772 = a;
        double r11848773 = r11848771 + r11848772;
        double r11848774 = b;
        double r11848775 = fma(r11848773, r11848771, r11848774);
        double r11848776 = c;
        double r11848777 = fma(r11848771, r11848775, r11848776);
        double r11848778 = i;
        double r11848779 = fma(r11848777, r11848771, r11848778);
        double r11848780 = r11848770 / r11848779;
        double r11848781 = x;
        double r11848782 = z;
        double r11848783 = fma(r11848771, r11848781, r11848782);
        double r11848784 = 27464.7644705;
        double r11848785 = fma(r11848771, r11848783, r11848784);
        double r11848786 = 230661.510616;
        double r11848787 = fma(r11848771, r11848785, r11848786);
        double r11848788 = t;
        double r11848789 = fma(r11848771, r11848787, r11848788);
        double r11848790 = r11848780 * r11848789;
        return r11848790;
}

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 28.5

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

  2. Simplified28.5

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

  4. Applied div-inv28.5

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

  5. Final simplification28.5

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

Reproduce

herbie shell --seed 2019112 +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)))