Average Error: 0.0 → 0.0
Time: 12.8s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
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 \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)
double f(double x) {
        double r88214 = 0.70711;
        double r88215 = 2.30753;
        double r88216 = x;
        double r88217 = 0.27061;
        double r88218 = r88216 * r88217;
        double r88219 = r88215 + r88218;
        double r88220 = 1.0;
        double r88221 = 0.99229;
        double r88222 = 0.04481;
        double r88223 = r88216 * r88222;
        double r88224 = r88221 + r88223;
        double r88225 = r88216 * r88224;
        double r88226 = r88220 + r88225;
        double r88227 = r88219 / r88226;
        double r88228 = r88227 - r88216;
        double r88229 = r88214 * r88228;
        return r88229;
}
↓
double f(double x) {
        double r88230 = 0.70711;
        double r88231 = 2.30753;
        double r88232 = x;
        double r88233 = 0.27061;
        double r88234 = r88232 * r88233;
        double r88235 = r88231 + r88234;
        double r88236 = 1.0;
        double r88237 = 0.99229;
        double r88238 = 0.04481;
        double r88239 = r88232 * r88238;
        double r88240 = r88237 + r88239;
        double r88241 = r88232 * r88240;
        double r88242 = r88236 + r88241;
        double r88243 = r88235 / r88242;
        double r88244 = r88243 - r88232;
        double r88245 = r88230 * r88244;
        return r88245;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019298 
(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)))