Average Error: 0.0 → 0.0
Time: 42.4s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[\left(\frac{0.2706100000000000171951342053944244980812 \cdot x + 2.307529999999999859028321225196123123169}{1 + \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right) \cdot x} - x\right) \cdot 0.7071100000000000163069557856942992657423\]
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{0.2706100000000000171951342053944244980812 \cdot x + 2.307529999999999859028321225196123123169}{1 + \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right) \cdot x} - x\right) \cdot 0.7071100000000000163069557856942992657423
double f(double x) {
        double r4351232 = 0.70711;
        double r4351233 = 2.30753;
        double r4351234 = x;
        double r4351235 = 0.27061;
        double r4351236 = r4351234 * r4351235;
        double r4351237 = r4351233 + r4351236;
        double r4351238 = 1.0;
        double r4351239 = 0.99229;
        double r4351240 = 0.04481;
        double r4351241 = r4351234 * r4351240;
        double r4351242 = r4351239 + r4351241;
        double r4351243 = r4351234 * r4351242;
        double r4351244 = r4351238 + r4351243;
        double r4351245 = r4351237 / r4351244;
        double r4351246 = r4351245 - r4351234;
        double r4351247 = r4351232 * r4351246;
        return r4351247;
}
↓
double f(double x) {
        double r4351248 = 0.27061;
        double r4351249 = x;
        double r4351250 = r4351248 * r4351249;
        double r4351251 = 2.30753;
        double r4351252 = r4351250 + r4351251;
        double r4351253 = 1.0;
        double r4351254 = 0.04481;
        double r4351255 = r4351254 * r4351249;
        double r4351256 = 0.99229;
        double r4351257 = r4351255 + r4351256;
        double r4351258 = r4351257 * r4351249;
        double r4351259 = r4351253 + r4351258;
        double r4351260 = r4351252 / r4351259;
        double r4351261 = r4351260 - r4351249;
        double r4351262 = 0.70711;
        double r4351263 = r4351261 * r4351262;
        return r4351263;
}

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 *-commutative0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 
(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)))