Average Error: 0.0 → 0.0
Time: 3.8s
Precision: 64
\[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
↓
\[0.707110000000000016 \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} + 0.707110000000000016 \cdot \left(-x\right)\]
0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)
↓
0.707110000000000016 \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} + 0.707110000000000016 \cdot \left(-x\right)
double f(double x) {
        double r131989 = 0.70711;
        double r131990 = 2.30753;
        double r131991 = x;
        double r131992 = 0.27061;
        double r131993 = r131991 * r131992;
        double r131994 = r131990 + r131993;
        double r131995 = 1.0;
        double r131996 = 0.99229;
        double r131997 = 0.04481;
        double r131998 = r131991 * r131997;
        double r131999 = r131996 + r131998;
        double r132000 = r131991 * r131999;
        double r132001 = r131995 + r132000;
        double r132002 = r131994 / r132001;
        double r132003 = r132002 - r131991;
        double r132004 = r131989 * r132003;
        return r132004;
}
↓
double f(double x) {
        double r132005 = 0.70711;
        double r132006 = 2.30753;
        double r132007 = x;
        double r132008 = 0.27061;
        double r132009 = r132007 * r132008;
        double r132010 = r132006 + r132009;
        double r132011 = 1.0;
        double r132012 = 0.99229;
        double r132013 = 0.04481;
        double r132014 = r132007 * r132013;
        double r132015 = r132012 + r132014;
        double r132016 = r132007 * r132015;
        double r132017 = r132011 + r132016;
        double r132018 = r132010 / r132017;
        double r132019 = r132005 * r132018;
        double r132020 = -r132007;
        double r132021 = r132005 * r132020;
        double r132022 = r132019 + r132021;
        return r132022;
}

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

    \[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.0

    \[\leadsto 0.707110000000000016 \cdot \color{blue}{\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} + \left(-x\right)\right)}\]

  4. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{0.707110000000000016 \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} + 0.707110000000000016 \cdot \left(-x\right)}\]

  5. Final simplification0.0

    \[\leadsto 0.707110000000000016 \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} + 0.707110000000000016 \cdot \left(-x\right)\]

Reproduce

herbie shell --seed 2020057 
(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)))