Average Error: 0.0 → 0.0
Time: 16.0s
Precision: 64
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]
↓
\[\frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(0.04481000000000000260680366181986755691469, x, 0.992290000000000005364597654988756403327\right), x, 1\right)}{\mathsf{fma}\left(0.2706100000000000171951342053944244980812, x, 2.307529999999999859028321225196123123169\right)}} - x\]
\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x
↓
\frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(0.04481000000000000260680366181986755691469, x, 0.992290000000000005364597654988756403327\right), x, 1\right)}{\mathsf{fma}\left(0.2706100000000000171951342053944244980812, x, 2.307529999999999859028321225196123123169\right)}} - x
double f(double x) {
        double r64890 = 2.30753;
        double r64891 = x;
        double r64892 = 0.27061;
        double r64893 = r64891 * r64892;
        double r64894 = r64890 + r64893;
        double r64895 = 1.0;
        double r64896 = 0.99229;
        double r64897 = 0.04481;
        double r64898 = r64891 * r64897;
        double r64899 = r64896 + r64898;
        double r64900 = r64891 * r64899;
        double r64901 = r64895 + r64900;
        double r64902 = r64894 / r64901;
        double r64903 = r64902 - r64891;
        return r64903;
}
↓
double f(double x) {
        double r64904 = 1.0;
        double r64905 = 0.04481;
        double r64906 = x;
        double r64907 = 0.99229;
        double r64908 = fma(r64905, r64906, r64907);
        double r64909 = 1.0;
        double r64910 = fma(r64908, r64906, r64909);
        double r64911 = 0.27061;
        double r64912 = 2.30753;
        double r64913 = fma(r64911, r64906, r64912);
        double r64914 = r64910 / r64913;
        double r64915 = r64904 / r64914;
        double r64916 = r64915 - r64906;
        return r64916;
}

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. Using strategy rm

  3. Applied clear-num0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 +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))