Average Error: 29.1 → 29.2
Time: 9.9s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right) \cdot 1}\]
\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}
↓
\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right) \cdot 1}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r71768 = x;
        double r71769 = y;
        double r71770 = r71768 * r71769;
        double r71771 = z;
        double r71772 = r71770 + r71771;
        double r71773 = r71772 * r71769;
        double r71774 = 27464.7644705;
        double r71775 = r71773 + r71774;
        double r71776 = r71775 * r71769;
        double r71777 = 230661.510616;
        double r71778 = r71776 + r71777;
        double r71779 = r71778 * r71769;
        double r71780 = t;
        double r71781 = r71779 + r71780;
        double r71782 = a;
        double r71783 = r71769 + r71782;
        double r71784 = r71783 * r71769;
        double r71785 = b;
        double r71786 = r71784 + r71785;
        double r71787 = r71786 * r71769;
        double r71788 = c;
        double r71789 = r71787 + r71788;
        double r71790 = r71789 * r71769;
        double r71791 = i;
        double r71792 = r71790 + r71791;
        double r71793 = r71781 / r71792;
        return r71793;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r71794 = x;
        double r71795 = y;
        double r71796 = r71794 * r71795;
        double r71797 = z;
        double r71798 = r71796 + r71797;
        double r71799 = r71798 * r71795;
        double r71800 = 27464.7644705;
        double r71801 = r71799 + r71800;
        double r71802 = r71801 * r71795;
        double r71803 = 230661.510616;
        double r71804 = r71802 + r71803;
        double r71805 = r71804 * r71795;
        double r71806 = t;
        double r71807 = r71805 + r71806;
        double r71808 = 1.0;
        double r71809 = a;
        double r71810 = r71795 + r71809;
        double r71811 = b;
        double r71812 = fma(r71810, r71795, r71811);
        double r71813 = c;
        double r71814 = fma(r71812, r71795, r71813);
        double r71815 = i;
        double r71816 = fma(r71814, r71795, r71815);
        double r71817 = r71816 * r71808;
        double r71818 = r71808 / r71817;
        double r71819 = r71807 * r71818;
        return r71819;
}

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 29.1

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

  3. Applied div-inv29.2

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

  4. Simplified29.2

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

  5. Final simplification29.2

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))