Average Error: 0.0 → 0.0
Time: 3.0s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\frac{1}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right)}{\mathsf{fma}\left(0.27061000000000002, x, 2.30753\right)}} - x\]
\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
↓
\frac{1}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right)}{\mathsf{fma}\left(0.27061000000000002, x, 2.30753\right)}} - x
double f(double x) {
        double r52078 = 2.30753;
        double r52079 = x;
        double r52080 = 0.27061;
        double r52081 = r52079 * r52080;
        double r52082 = r52078 + r52081;
        double r52083 = 1.0;
        double r52084 = 0.99229;
        double r52085 = 0.04481;
        double r52086 = r52079 * r52085;
        double r52087 = r52084 + r52086;
        double r52088 = r52079 * r52087;
        double r52089 = r52083 + r52088;
        double r52090 = r52082 / r52089;
        double r52091 = r52090 - r52079;
        return r52091;
}
↓
double f(double x) {
        double r52092 = 1.0;
        double r52093 = x;
        double r52094 = 0.04481;
        double r52095 = 0.99229;
        double r52096 = fma(r52094, r52093, r52095);
        double r52097 = 1.0;
        double r52098 = fma(r52093, r52096, r52097);
        double r52099 = 0.27061;
        double r52100 = 2.30753;
        double r52101 = fma(r52099, r52093, r52100);
        double r52102 = r52098 / r52101;
        double r52103 = r52092 / r52102;
        double r52104 = r52103 - r52093;
        return r52104;
}

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 clear-num0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020089 +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))