Average Error: 29.0 → 29.2
Time: 29.0s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), y, t\right)}{\mathsf{fma}\left(\sqrt[3]{\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right)} \cdot \left(\sqrt[3]{\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right)} \cdot \sqrt[3]{\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right)}\right), y, i\right)}\]
\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{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), y, t\right)}{\mathsf{fma}\left(\sqrt[3]{\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right)} \cdot \left(\sqrt[3]{\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right)} \cdot \sqrt[3]{\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right)}\right), y, i\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2340747 = x;
        double r2340748 = y;
        double r2340749 = r2340747 * r2340748;
        double r2340750 = z;
        double r2340751 = r2340749 + r2340750;
        double r2340752 = r2340751 * r2340748;
        double r2340753 = 27464.7644705;
        double r2340754 = r2340752 + r2340753;
        double r2340755 = r2340754 * r2340748;
        double r2340756 = 230661.510616;
        double r2340757 = r2340755 + r2340756;
        double r2340758 = r2340757 * r2340748;
        double r2340759 = t;
        double r2340760 = r2340758 + r2340759;
        double r2340761 = a;
        double r2340762 = r2340748 + r2340761;
        double r2340763 = r2340762 * r2340748;
        double r2340764 = b;
        double r2340765 = r2340763 + r2340764;
        double r2340766 = r2340765 * r2340748;
        double r2340767 = c;
        double r2340768 = r2340766 + r2340767;
        double r2340769 = r2340768 * r2340748;
        double r2340770 = i;
        double r2340771 = r2340769 + r2340770;
        double r2340772 = r2340760 / r2340771;
        return r2340772;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2340773 = y;
        double r2340774 = x;
        double r2340775 = z;
        double r2340776 = fma(r2340773, r2340774, r2340775);
        double r2340777 = 27464.7644705;
        double r2340778 = fma(r2340773, r2340776, r2340777);
        double r2340779 = 230661.510616;
        double r2340780 = fma(r2340773, r2340778, r2340779);
        double r2340781 = t;
        double r2340782 = fma(r2340780, r2340773, r2340781);
        double r2340783 = a;
        double r2340784 = r2340773 + r2340783;
        double r2340785 = b;
        double r2340786 = fma(r2340784, r2340773, r2340785);
        double r2340787 = c;
        double r2340788 = fma(r2340773, r2340786, r2340787);
        double r2340789 = cbrt(r2340788);
        double r2340790 = r2340789 * r2340789;
        double r2340791 = r2340789 * r2340790;
        double r2340792 = i;
        double r2340793 = fma(r2340791, r2340773, r2340792);
        double r2340794 = r2340782 / r2340793;
        return r2340794;
}

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

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

  4. Applied add-cube-cbrt29.2

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

  5. Final simplification29.2

    \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), y, t\right)}{\mathsf{fma}\left(\sqrt[3]{\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right)} \cdot \left(\sqrt[3]{\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right)} \cdot \sqrt[3]{\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right)}\right), y, i\right)}\]

Reproduce

herbie shell --seed 2019192 +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)))