Average Error: 0.0 → 0.0
Time: 6.6s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\mathsf{fma}\left(2.30753 + x \cdot 0.27061000000000002, \frac{1}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}, -x\right)\]
\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
↓
\mathsf{fma}\left(2.30753 + x \cdot 0.27061000000000002, \frac{1}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}, -x\right)
double f(double x) {
        double r187965 = 2.30753;
        double r187966 = x;
        double r187967 = 0.27061;
        double r187968 = r187966 * r187967;
        double r187969 = r187965 + r187968;
        double r187970 = 1.0;
        double r187971 = 0.99229;
        double r187972 = 0.04481;
        double r187973 = r187966 * r187972;
        double r187974 = r187971 + r187973;
        double r187975 = r187966 * r187974;
        double r187976 = r187970 + r187975;
        double r187977 = r187969 / r187976;
        double r187978 = r187977 - r187966;
        return r187978;
}
↓
double f(double x) {
        double r187979 = 2.30753;
        double r187980 = x;
        double r187981 = 0.27061;
        double r187982 = r187980 * r187981;
        double r187983 = r187979 + r187982;
        double r187984 = 1.0;
        double r187985 = 1.0;
        double r187986 = 0.99229;
        double r187987 = 0.04481;
        double r187988 = r187980 * r187987;
        double r187989 = r187986 + r187988;
        double r187990 = r187980 * r187989;
        double r187991 = r187985 + r187990;
        double r187992 = r187984 / r187991;
        double r187993 = -r187980;
        double r187994 = fma(r187983, r187992, r187993);
        return r187994;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.0

    \[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
  2. Using strategy rm

  3. Applied div-inv0.0

    \[\leadsto \color{blue}{\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} - x\]

  4. Applied fma-neg0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(2.30753 + x \cdot 0.27061000000000002, \frac{1}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}, -x\right)}\]

  5. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(2.30753 + x \cdot 0.27061000000000002, \frac{1}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}, -x\right)\]

Reproduce

herbie shell --seed 2020043 +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))