Average Error: 0.0 → 0.0
Time: 23.6s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[0.7071100000000000163069557856942992657423 \cdot \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} + \left(-x\right) \cdot 0.7071100000000000163069557856942992657423\]
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 \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} + \left(-x\right) \cdot 0.7071100000000000163069557856942992657423
double f(double x) {
        double r90960 = 0.70711;
        double r90961 = 2.30753;
        double r90962 = x;
        double r90963 = 0.27061;
        double r90964 = r90962 * r90963;
        double r90965 = r90961 + r90964;
        double r90966 = 1.0;
        double r90967 = 0.99229;
        double r90968 = 0.04481;
        double r90969 = r90962 * r90968;
        double r90970 = r90967 + r90969;
        double r90971 = r90962 * r90970;
        double r90972 = r90966 + r90971;
        double r90973 = r90965 / r90972;
        double r90974 = r90973 - r90962;
        double r90975 = r90960 * r90974;
        return r90975;
}
↓
double f(double x) {
        double r90976 = 0.70711;
        double r90977 = 2.30753;
        double r90978 = x;
        double r90979 = 0.27061;
        double r90980 = r90978 * r90979;
        double r90981 = r90977 + r90980;
        double r90982 = 1.0;
        double r90983 = 0.99229;
        double r90984 = 0.04481;
        double r90985 = r90978 * r90984;
        double r90986 = r90983 + r90985;
        double r90987 = r90978 * r90986;
        double r90988 = r90982 + r90987;
        double r90989 = r90981 / r90988;
        double r90990 = r90976 * r90989;
        double r90991 = -r90978;
        double r90992 = r90991 * r90976;
        double r90993 = r90990 + r90992;
        return r90993;
}

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 sub-neg0.0

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

  4. Applied distribute-lft-in0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  :precision binary64
  (* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* x (+ 0.99229 (* x 0.04481))))) x)))