Average Error: 29.1 → 29.2
Time: 30.4s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), i\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), y, t\right)\]
\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}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), i\right)} \cdot \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)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r61817 = x;
        double r61818 = y;
        double r61819 = r61817 * r61818;
        double r61820 = z;
        double r61821 = r61819 + r61820;
        double r61822 = r61821 * r61818;
        double r61823 = 27464.7644705;
        double r61824 = r61822 + r61823;
        double r61825 = r61824 * r61818;
        double r61826 = 230661.510616;
        double r61827 = r61825 + r61826;
        double r61828 = r61827 * r61818;
        double r61829 = t;
        double r61830 = r61828 + r61829;
        double r61831 = a;
        double r61832 = r61818 + r61831;
        double r61833 = r61832 * r61818;
        double r61834 = b;
        double r61835 = r61833 + r61834;
        double r61836 = r61835 * r61818;
        double r61837 = c;
        double r61838 = r61836 + r61837;
        double r61839 = r61838 * r61818;
        double r61840 = i;
        double r61841 = r61839 + r61840;
        double r61842 = r61830 / r61841;
        return r61842;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r61843 = 1.0;
        double r61844 = y;
        double r61845 = a;
        double r61846 = r61844 + r61845;
        double r61847 = b;
        double r61848 = fma(r61846, r61844, r61847);
        double r61849 = c;
        double r61850 = fma(r61844, r61848, r61849);
        double r61851 = i;
        double r61852 = fma(r61844, r61850, r61851);
        double r61853 = r61843 / r61852;
        double r61854 = x;
        double r61855 = z;
        double r61856 = fma(r61844, r61854, r61855);
        double r61857 = 27464.7644705;
        double r61858 = fma(r61844, r61856, r61857);
        double r61859 = 230661.510616;
        double r61860 = fma(r61844, r61858, r61859);
        double r61861 = t;
        double r61862 = fma(r61860, r61844, r61861);
        double r61863 = r61853 * r61862;
        return r61863;
}

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. Simplified29.1

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

  4. Applied div-inv29.2

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

  5. Simplified29.2

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

  6. Final simplification29.2

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

Reproduce

herbie shell --seed 2019194 +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)))