Average Error: 29.2 → 29.3
Time: 9.4s
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 r71782 = x;
        double r71783 = y;
        double r71784 = r71782 * r71783;
        double r71785 = z;
        double r71786 = r71784 + r71785;
        double r71787 = r71786 * r71783;
        double r71788 = 27464.7644705;
        double r71789 = r71787 + r71788;
        double r71790 = r71789 * r71783;
        double r71791 = 230661.510616;
        double r71792 = r71790 + r71791;
        double r71793 = r71792 * r71783;
        double r71794 = t;
        double r71795 = r71793 + r71794;
        double r71796 = a;
        double r71797 = r71783 + r71796;
        double r71798 = r71797 * r71783;
        double r71799 = b;
        double r71800 = r71798 + r71799;
        double r71801 = r71800 * r71783;
        double r71802 = c;
        double r71803 = r71801 + r71802;
        double r71804 = r71803 * r71783;
        double r71805 = i;
        double r71806 = r71804 + r71805;
        double r71807 = r71795 / r71806;
        return r71807;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r71808 = x;
        double r71809 = y;
        double r71810 = r71808 * r71809;
        double r71811 = z;
        double r71812 = r71810 + r71811;
        double r71813 = r71812 * r71809;
        double r71814 = 27464.7644705;
        double r71815 = r71813 + r71814;
        double r71816 = r71815 * r71809;
        double r71817 = 230661.510616;
        double r71818 = r71816 + r71817;
        double r71819 = r71818 * r71809;
        double r71820 = t;
        double r71821 = r71819 + r71820;
        double r71822 = 1.0;
        double r71823 = a;
        double r71824 = r71809 + r71823;
        double r71825 = b;
        double r71826 = fma(r71824, r71809, r71825);
        double r71827 = c;
        double r71828 = fma(r71826, r71809, r71827);
        double r71829 = i;
        double r71830 = fma(r71828, r71809, r71829);
        double r71831 = r71830 * r71822;
        double r71832 = r71822 / r71831;
        double r71833 = r71821 * r71832;
        return r71833;
}

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 29.2

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

  3. Applied div-inv29.3

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

  4. Simplified29.3

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

  5. Final simplification29.3

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

Reproduce

herbie shell --seed 2019352 +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)))