Average Error: 0.0 → 0.0
Time: 3.7s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)\right) - x\]
\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
↓
\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)\right) - x
double f(double x) {
        double r102242 = 2.30753;
        double r102243 = x;
        double r102244 = 0.27061;
        double r102245 = r102243 * r102244;
        double r102246 = r102242 + r102245;
        double r102247 = 1.0;
        double r102248 = 0.99229;
        double r102249 = 0.04481;
        double r102250 = r102243 * r102249;
        double r102251 = r102248 + r102250;
        double r102252 = r102243 * r102251;
        double r102253 = r102247 + r102252;
        double r102254 = r102246 / r102253;
        double r102255 = r102254 - r102243;
        return r102255;
}
↓
double f(double x) {
        double r102256 = 2.30753;
        double r102257 = x;
        double r102258 = 0.27061;
        double r102259 = r102257 * r102258;
        double r102260 = r102256 + r102259;
        double r102261 = 1.0;
        double r102262 = 0.99229;
        double r102263 = 0.04481;
        double r102264 = r102257 * r102263;
        double r102265 = r102262 + r102264;
        double r102266 = r102257 * r102265;
        double r102267 = r102261 + r102266;
        double r102268 = r102260 / r102267;
        double r102269 = log1p(r102268);
        double r102270 = expm1(r102269);
        double r102271 = r102270 - r102257;
        return r102271;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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 expm1-log1p-u0.0

    \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)\right)} - x\]

  4. Final simplification0.0

    \[\leadsto \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)\right) - x\]

Reproduce

herbie shell --seed 2020081 +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))