Average Error: 0.0 → 0.0
Time: 3.9s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[\left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right) \cdot 0.7071100000000000163069557856942992657423\]
0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)
↓
\left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right) \cdot 0.7071100000000000163069557856942992657423
double f(double x) {
        double r81898 = 0.70711;
        double r81899 = 2.30753;
        double r81900 = x;
        double r81901 = 0.27061;
        double r81902 = r81900 * r81901;
        double r81903 = r81899 + r81902;
        double r81904 = 1.0;
        double r81905 = 0.99229;
        double r81906 = 0.04481;
        double r81907 = r81900 * r81906;
        double r81908 = r81905 + r81907;
        double r81909 = r81900 * r81908;
        double r81910 = r81904 + r81909;
        double r81911 = r81903 / r81910;
        double r81912 = r81911 - r81900;
        double r81913 = r81898 * r81912;
        return r81913;
}
↓
double f(double x) {
        double r81914 = 2.30753;
        double r81915 = x;
        double r81916 = 0.27061;
        double r81917 = r81915 * r81916;
        double r81918 = r81914 + r81917;
        double r81919 = 1.0;
        double r81920 = 0.99229;
        double r81921 = 0.04481;
        double r81922 = r81915 * r81921;
        double r81923 = r81920 + r81922;
        double r81924 = r81915 * r81923;
        double r81925 = r81919 + r81924;
        double r81926 = r81918 / r81925;
        double r81927 = r81926 - r81915;
        double r81928 = 0.70711;
        double r81929 = r81927 * r81928;
        return r81929;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 1978988140 
(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)))