Average Error: 0.0 → 0.0
Time: 2.7s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right) \cdot 1} - x\]
\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
↓
\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right) \cdot 1} - x
double f(double x) {
        double r239 = 2.30753;
        double r240 = x;
        double r241 = 0.27061;
        double r242 = r240 * r241;
        double r243 = r239 + r242;
        double r244 = 1.0;
        double r245 = 0.99229;
        double r246 = 0.04481;
        double r247 = r240 * r246;
        double r248 = r245 + r247;
        double r249 = r240 * r248;
        double r250 = r244 + r249;
        double r251 = r243 / r250;
        double r252 = r251 - r240;
        return r252;
}
↓
double f(double x) {
        double r253 = 2.30753;
        double r254 = x;
        double r255 = 0.27061;
        double r256 = r254 * r255;
        double r257 = r253 + r256;
        double r258 = 1.0;
        double r259 = 0.04481;
        double r260 = 0.99229;
        double r261 = fma(r259, r254, r260);
        double r262 = 1.0;
        double r263 = fma(r254, r261, r262);
        double r264 = r263 * r258;
        double r265 = r258 / r264;
        double r266 = r257 * r265;
        double r267 = r266 - r254;
        return r267;
}

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. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020025 +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))