Average Error: 0.0 → 0.0
Time: 18.5s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[\left(-x\right) \cdot 0.7071100000000000163069557856942992657423 + \frac{0.7071100000000000163069557856942992657423}{\frac{\left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x + 1}{x \cdot 0.2706100000000000171951342053944244980812 + 2.307529999999999859028321225196123123169}}\]
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(-x\right) \cdot 0.7071100000000000163069557856942992657423 + \frac{0.7071100000000000163069557856942992657423}{\frac{\left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x + 1}{x \cdot 0.2706100000000000171951342053944244980812 + 2.307529999999999859028321225196123123169}}
double f(double x) {
        double r94951 = 0.70711;
        double r94952 = 2.30753;
        double r94953 = x;
        double r94954 = 0.27061;
        double r94955 = r94953 * r94954;
        double r94956 = r94952 + r94955;
        double r94957 = 1.0;
        double r94958 = 0.99229;
        double r94959 = 0.04481;
        double r94960 = r94953 * r94959;
        double r94961 = r94958 + r94960;
        double r94962 = r94953 * r94961;
        double r94963 = r94957 + r94962;
        double r94964 = r94956 / r94963;
        double r94965 = r94964 - r94953;
        double r94966 = r94951 * r94965;
        return r94966;
}
↓
double f(double x) {
        double r94967 = x;
        double r94968 = -r94967;
        double r94969 = 0.70711;
        double r94970 = r94968 * r94969;
        double r94971 = 0.99229;
        double r94972 = 0.04481;
        double r94973 = r94967 * r94972;
        double r94974 = r94971 + r94973;
        double r94975 = r94974 * r94967;
        double r94976 = 1.0;
        double r94977 = r94975 + r94976;
        double r94978 = 0.27061;
        double r94979 = r94967 * r94978;
        double r94980 = 2.30753;
        double r94981 = r94979 + r94980;
        double r94982 = r94977 / r94981;
        double r94983 = r94969 / r94982;
        double r94984 = r94970 + r94983;
        return r94984;
}

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. Simplified0.0

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

  4. Applied sub-neg0.0

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

  5. Applied distribute-lft-in0.0

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

  6. Simplified0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 
(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)))