Average Error: 0.0 → 0.0
Time: 2.2s
Precision: 64
\[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
↓
\[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
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 \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)
double f(double x) {
        double r109975 = 0.70711;
        double r109976 = 2.30753;
        double r109977 = x;
        double r109978 = 0.27061;
        double r109979 = r109977 * r109978;
        double r109980 = r109976 + r109979;
        double r109981 = 1.0;
        double r109982 = 0.99229;
        double r109983 = 0.04481;
        double r109984 = r109977 * r109983;
        double r109985 = r109982 + r109984;
        double r109986 = r109977 * r109985;
        double r109987 = r109981 + r109986;
        double r109988 = r109980 / r109987;
        double r109989 = r109988 - r109977;
        double r109990 = r109975 * r109989;
        return r109990;
}
↓
double f(double x) {
        double r109991 = 0.70711;
        double r109992 = 2.30753;
        double r109993 = x;
        double r109994 = 0.27061;
        double r109995 = r109993 * r109994;
        double r109996 = r109992 + r109995;
        double r109997 = 1.0;
        double r109998 = 0.99229;
        double r109999 = 0.04481;
        double r110000 = r109993 * r109999;
        double r110001 = r109998 + r110000;
        double r110002 = r109993 * r110001;
        double r110003 = r109997 + r110002;
        double r110004 = r109996 / r110003;
        double r110005 = r110004 - r109993;
        double r110006 = r109991 * r110005;
        return r110006;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020036 
(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)))