Average Error: 0.0 → 0.0
Time: 17.5s
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 r94217 = 0.70711;
        double r94218 = 2.30753;
        double r94219 = x;
        double r94220 = 0.27061;
        double r94221 = r94219 * r94220;
        double r94222 = r94218 + r94221;
        double r94223 = 1.0;
        double r94224 = 0.99229;
        double r94225 = 0.04481;
        double r94226 = r94219 * r94225;
        double r94227 = r94224 + r94226;
        double r94228 = r94219 * r94227;
        double r94229 = r94223 + r94228;
        double r94230 = r94222 / r94229;
        double r94231 = r94230 - r94219;
        double r94232 = r94217 * r94231;
        return r94232;
}
↓
double f(double x) {
        double r94233 = x;
        double r94234 = -r94233;
        double r94235 = 0.70711;
        double r94236 = r94234 * r94235;
        double r94237 = 0.99229;
        double r94238 = 0.04481;
        double r94239 = r94233 * r94238;
        double r94240 = r94237 + r94239;
        double r94241 = r94240 * r94233;
        double r94242 = 1.0;
        double r94243 = r94241 + r94242;
        double r94244 = 0.27061;
        double r94245 = r94233 * r94244;
        double r94246 = 2.30753;
        double r94247 = r94245 + r94246;
        double r94248 = r94243 / r94247;
        double r94249 = r94235 / r94248;
        double r94250 = r94236 + r94249;
        return r94250;
}

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)))