Average Error: 29.0 → 29.1
Time: 37.0s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), t\right)}}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), t\right)}}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3819733 = x;
        double r3819734 = y;
        double r3819735 = r3819733 * r3819734;
        double r3819736 = z;
        double r3819737 = r3819735 + r3819736;
        double r3819738 = r3819737 * r3819734;
        double r3819739 = 27464.7644705;
        double r3819740 = r3819738 + r3819739;
        double r3819741 = r3819740 * r3819734;
        double r3819742 = 230661.510616;
        double r3819743 = r3819741 + r3819742;
        double r3819744 = r3819743 * r3819734;
        double r3819745 = t;
        double r3819746 = r3819744 + r3819745;
        double r3819747 = a;
        double r3819748 = r3819734 + r3819747;
        double r3819749 = r3819748 * r3819734;
        double r3819750 = b;
        double r3819751 = r3819749 + r3819750;
        double r3819752 = r3819751 * r3819734;
        double r3819753 = c;
        double r3819754 = r3819752 + r3819753;
        double r3819755 = r3819754 * r3819734;
        double r3819756 = i;
        double r3819757 = r3819755 + r3819756;
        double r3819758 = r3819746 / r3819757;
        return r3819758;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3819759 = 1.0;
        double r3819760 = y;
        double r3819761 = a;
        double r3819762 = r3819760 + r3819761;
        double r3819763 = b;
        double r3819764 = fma(r3819762, r3819760, r3819763);
        double r3819765 = c;
        double r3819766 = fma(r3819760, r3819764, r3819765);
        double r3819767 = i;
        double r3819768 = fma(r3819766, r3819760, r3819767);
        double r3819769 = x;
        double r3819770 = z;
        double r3819771 = fma(r3819760, r3819769, r3819770);
        double r3819772 = 27464.7644705;
        double r3819773 = fma(r3819760, r3819771, r3819772);
        double r3819774 = 230661.510616;
        double r3819775 = fma(r3819760, r3819773, r3819774);
        double r3819776 = t;
        double r3819777 = fma(r3819760, r3819775, r3819776);
        double r3819778 = r3819768 / r3819777;
        double r3819779 = r3819759 / r3819778;
        return r3819779;
}

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 29.0

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  2. Simplified29.0

    \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}}\]
  3. Using strategy rm

  4. Applied clear-num29.1

    \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), t\right)}}}\]

  5. Final simplification29.1

    \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), t\right)}}\]

Reproduce

herbie shell --seed 2019170 +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)))