Average Error: 0.0 → 0.0
Time: 4.8s
Precision: 64
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]
↓
\[\frac{\mathsf{fma}\left(x, 0.2706100000000000171951342053944244980812, 2.307529999999999859028321225196123123169\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.04481000000000000260680366181986755691469, x, 0.992290000000000005364597654988756403327\right), 1\right)} - x\]
\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x
↓
\frac{\mathsf{fma}\left(x, 0.2706100000000000171951342053944244980812, 2.307529999999999859028321225196123123169\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.04481000000000000260680366181986755691469, x, 0.992290000000000005364597654988756403327\right), 1\right)} - x
double f(double x) {
        double r44913 = 2.30753;
        double r44914 = x;
        double r44915 = 0.27061;
        double r44916 = r44914 * r44915;
        double r44917 = r44913 + r44916;
        double r44918 = 1.0;
        double r44919 = 0.99229;
        double r44920 = 0.04481;
        double r44921 = r44914 * r44920;
        double r44922 = r44919 + r44921;
        double r44923 = r44914 * r44922;
        double r44924 = r44918 + r44923;
        double r44925 = r44917 / r44924;
        double r44926 = r44925 - r44914;
        return r44926;
}
↓
double f(double x) {
        double r44927 = x;
        double r44928 = 0.27061;
        double r44929 = 2.30753;
        double r44930 = fma(r44927, r44928, r44929);
        double r44931 = 0.04481;
        double r44932 = 0.99229;
        double r44933 = fma(r44931, r44927, r44932);
        double r44934 = 1.0;
        double r44935 = fma(r44927, r44933, r44934);
        double r44936 = r44930 / r44935;
        double r44937 = r44936 - r44927;
        return r44937;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.0

    \[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 0.2706100000000000171951342053944244980812, 2.307529999999999859028321225196123123169\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.04481000000000000260680366181986755691469, x, 0.992290000000000005364597654988756403327\right), 1\right)} - x}\]

  3. Final simplification0.0

    \[\leadsto \frac{\mathsf{fma}\left(x, 0.2706100000000000171951342053944244980812, 2.307529999999999859028321225196123123169\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.04481000000000000260680366181986755691469, x, 0.992290000000000005364597654988756403327\right), 1\right)} - x\]

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C"
  :precision binary64
  (- (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* x (+ 0.99229 (* x 0.04481))))) x))