Average Error: 0.0 → 0.0
Time: 20.2s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{0.2706100000000000171951342053944244980812 \cdot x + 2.307529999999999859028321225196123123169}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
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{0.2706100000000000171951342053944244980812 \cdot x + 2.307529999999999859028321225196123123169}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)
double f(double x) {
        double r7718945 = 0.70711;
        double r7718946 = 2.30753;
        double r7718947 = x;
        double r7718948 = 0.27061;
        double r7718949 = r7718947 * r7718948;
        double r7718950 = r7718946 + r7718949;
        double r7718951 = 1.0;
        double r7718952 = 0.99229;
        double r7718953 = 0.04481;
        double r7718954 = r7718947 * r7718953;
        double r7718955 = r7718952 + r7718954;
        double r7718956 = r7718947 * r7718955;
        double r7718957 = r7718951 + r7718956;
        double r7718958 = r7718950 / r7718957;
        double r7718959 = r7718958 - r7718947;
        double r7718960 = r7718945 * r7718959;
        return r7718960;
}
↓
double f(double x) {
        double r7718961 = 0.70711;
        double r7718962 = 0.27061;
        double r7718963 = x;
        double r7718964 = r7718962 * r7718963;
        double r7718965 = 2.30753;
        double r7718966 = r7718964 + r7718965;
        double r7718967 = 1.0;
        double r7718968 = 0.99229;
        double r7718969 = 0.04481;
        double r7718970 = r7718963 * r7718969;
        double r7718971 = r7718968 + r7718970;
        double r7718972 = r7718963 * r7718971;
        double r7718973 = r7718967 + r7718972;
        double r7718974 = r7718966 / r7718973;
        double r7718975 = r7718974 - r7718963;
        double r7718976 = r7718961 * r7718975;
        return r7718976;
}

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. Taylor expanded around 0 0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(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)))