Average Error: 0.0 → 0.0
Time: 17.6s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{1}{\frac{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)}{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}} - x\right)\]
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{1}{\frac{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)}{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}} - x\right)
double f(double x) {
        double r100007 = 0.70711;
        double r100008 = 2.30753;
        double r100009 = x;
        double r100010 = 0.27061;
        double r100011 = r100009 * r100010;
        double r100012 = r100008 + r100011;
        double r100013 = 1.0;
        double r100014 = 0.99229;
        double r100015 = 0.04481;
        double r100016 = r100009 * r100015;
        double r100017 = r100014 + r100016;
        double r100018 = r100009 * r100017;
        double r100019 = r100013 + r100018;
        double r100020 = r100012 / r100019;
        double r100021 = r100020 - r100009;
        double r100022 = r100007 * r100021;
        return r100022;
}
↓
double f(double x) {
        double r100023 = 0.70711;
        double r100024 = 1.0;
        double r100025 = 1.0;
        double r100026 = x;
        double r100027 = 0.99229;
        double r100028 = 0.04481;
        double r100029 = r100026 * r100028;
        double r100030 = r100027 + r100029;
        double r100031 = r100026 * r100030;
        double r100032 = r100025 + r100031;
        double r100033 = 2.30753;
        double r100034 = 0.27061;
        double r100035 = r100026 * r100034;
        double r100036 = r100033 + r100035;
        double r100037 = r100032 / r100036;
        double r100038 = r100024 / r100037;
        double r100039 = r100038 - r100026;
        double r100040 = r100023 * r100039;
        return r100040;
}

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 clear-num0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019350 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  :precision binary64
  (* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* x (+ 0.99229 (* x 0.04481))))) x)))