Average Error: 0.0 → 0.0
Time: 9.3s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[0.7071100000000000163069557856942992657423 \cdot \left(\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{1}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)
↓
0.7071100000000000163069557856942992657423 \cdot \left(\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{1}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)
double f(double x) {
        double r43171 = 0.70711;
        double r43172 = 2.30753;
        double r43173 = x;
        double r43174 = 0.27061;
        double r43175 = r43173 * r43174;
        double r43176 = r43172 + r43175;
        double r43177 = 1.0;
        double r43178 = 0.99229;
        double r43179 = 0.04481;
        double r43180 = r43173 * r43179;
        double r43181 = r43178 + r43180;
        double r43182 = r43173 * r43181;
        double r43183 = r43177 + r43182;
        double r43184 = r43176 / r43183;
        double r43185 = r43184 - r43173;
        double r43186 = r43171 * r43185;
        return r43186;
}
↓
double f(double x) {
        double r43187 = 0.70711;
        double r43188 = 2.30753;
        double r43189 = x;
        double r43190 = 0.27061;
        double r43191 = r43189 * r43190;
        double r43192 = r43188 + r43191;
        double r43193 = 1.0;
        double r43194 = 1.0;
        double r43195 = 0.99229;
        double r43196 = 0.04481;
        double r43197 = r43189 * r43196;
        double r43198 = r43195 + r43197;
        double r43199 = r43189 * r43198;
        double r43200 = r43194 + r43199;
        double r43201 = r43193 / r43200;
        double r43202 = r43192 * r43201;
        double r43203 = r43202 - r43189;
        double r43204 = r43187 * r43203;
        return r43204;
}

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

    \[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
  2. Using strategy rm

  3. Applied div-inv0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\color{blue}{\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{1}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)}} - x\right)\]

  4. Final simplification0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{1}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]

Reproduce

herbie shell --seed 2019305 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  :precision binary64
  (* 0.707110000000000016 (- (/ (+ 2.30753 (* x 0.27061000000000002)) (+ 1 (* x (+ 0.992290000000000005 (* x 0.044810000000000003))))) x)))