Average Error: 29.5 → 29.5
Time: 25.8s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\]
\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)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r71781 = x;
        double r71782 = y;
        double r71783 = r71781 * r71782;
        double r71784 = z;
        double r71785 = r71783 + r71784;
        double r71786 = r71785 * r71782;
        double r71787 = 27464.7644705;
        double r71788 = r71786 + r71787;
        double r71789 = r71788 * r71782;
        double r71790 = 230661.510616;
        double r71791 = r71789 + r71790;
        double r71792 = r71791 * r71782;
        double r71793 = t;
        double r71794 = r71792 + r71793;
        double r71795 = a;
        double r71796 = r71782 + r71795;
        double r71797 = r71796 * r71782;
        double r71798 = b;
        double r71799 = r71797 + r71798;
        double r71800 = r71799 * r71782;
        double r71801 = c;
        double r71802 = r71800 + r71801;
        double r71803 = r71802 * r71782;
        double r71804 = i;
        double r71805 = r71803 + r71804;
        double r71806 = r71794 / r71805;
        return r71806;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r71807 = x;
        double r71808 = y;
        double r71809 = r71807 * r71808;
        double r71810 = z;
        double r71811 = r71809 + r71810;
        double r71812 = r71811 * r71808;
        double r71813 = 27464.7644705;
        double r71814 = r71812 + r71813;
        double r71815 = r71814 * r71808;
        double r71816 = 230661.510616;
        double r71817 = r71815 + r71816;
        double r71818 = r71817 * r71808;
        double r71819 = t;
        double r71820 = r71818 + r71819;
        double r71821 = 1.0;
        double r71822 = a;
        double r71823 = r71808 + r71822;
        double r71824 = b;
        double r71825 = fma(r71823, r71808, r71824);
        double r71826 = c;
        double r71827 = fma(r71825, r71808, r71826);
        double r71828 = i;
        double r71829 = fma(r71827, r71808, r71828);
        double r71830 = r71821 / r71829;
        double r71831 = r71820 * r71830;
        return r71831;
}

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 29.5

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

  3. Applied div-inv29.5

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

  4. Simplified29.5

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

  5. Final simplification29.5

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

Reproduce

herbie shell --seed 2019209 +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) 27464.764470499998) y) 230661.510616000014) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))