Average Error: 0.0 → 0.0
Time: 14.3s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right)} - x\right)\]
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(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right)} - x\right)
double f(double x) {
        double r79950 = 0.70711;
        double r79951 = 2.30753;
        double r79952 = x;
        double r79953 = 0.27061;
        double r79954 = r79952 * r79953;
        double r79955 = r79951 + r79954;
        double r79956 = 1.0;
        double r79957 = 0.99229;
        double r79958 = 0.04481;
        double r79959 = r79952 * r79958;
        double r79960 = r79957 + r79959;
        double r79961 = r79952 * r79960;
        double r79962 = r79956 + r79961;
        double r79963 = r79955 / r79962;
        double r79964 = r79963 - r79952;
        double r79965 = r79950 * r79964;
        return r79965;
}
↓
double f(double x) {
        double r79966 = 0.70711;
        double r79967 = 2.30753;
        double r79968 = x;
        double r79969 = 0.27061;
        double r79970 = r79968 * r79969;
        double r79971 = r79967 + r79970;
        double r79972 = 1.0;
        double r79973 = 0.04481;
        double r79974 = r79968 * r79973;
        double r79975 = 0.99229;
        double r79976 = r79974 + r79975;
        double r79977 = r79968 * r79976;
        double r79978 = r79972 + r79977;
        double r79979 = r79971 / r79978;
        double r79980 = r79979 - r79968;
        double r79981 = r79966 * r79980;
        return r79981;
}

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

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  (* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)))