Average Error: 0.0 → 0.0
Time: 19.7s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
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(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)
double f(double x) {
        double r74155 = 0.70711;
        double r74156 = 2.30753;
        double r74157 = x;
        double r74158 = 0.27061;
        double r74159 = r74157 * r74158;
        double r74160 = r74156 + r74159;
        double r74161 = 1.0;
        double r74162 = 0.99229;
        double r74163 = 0.04481;
        double r74164 = r74157 * r74163;
        double r74165 = r74162 + r74164;
        double r74166 = r74157 * r74165;
        double r74167 = r74161 + r74166;
        double r74168 = r74160 / r74167;
        double r74169 = r74168 - r74157;
        double r74170 = r74155 * r74169;
        return r74170;
}
↓
double f(double x) {
        double r74171 = 0.70711;
        double r74172 = 2.30753;
        double r74173 = x;
        double r74174 = 0.27061;
        double r74175 = r74173 * r74174;
        double r74176 = r74172 + r74175;
        double r74177 = 1.0;
        double r74178 = 0.99229;
        double r74179 = 0.04481;
        double r74180 = r74173 * r74179;
        double r74181 = r74178 + r74180;
        double r74182 = r74173 * r74181;
        double r74183 = r74177 + r74182;
        double r74184 = r74176 / r74183;
        double r74185 = r74184 - r74173;
        double r74186 = r74171 * r74185;
        return r74186;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019304 
(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)))