Average Error: 0.0 → 0.0
Time: 4.2s
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 r98082 = 0.70711;
        double r98083 = 2.30753;
        double r98084 = x;
        double r98085 = 0.27061;
        double r98086 = r98084 * r98085;
        double r98087 = r98083 + r98086;
        double r98088 = 1.0;
        double r98089 = 0.99229;
        double r98090 = 0.04481;
        double r98091 = r98084 * r98090;
        double r98092 = r98089 + r98091;
        double r98093 = r98084 * r98092;
        double r98094 = r98088 + r98093;
        double r98095 = r98087 / r98094;
        double r98096 = r98095 - r98084;
        double r98097 = r98082 * r98096;
        return r98097;
}
↓
double f(double x) {
        double r98098 = 0.70711;
        double r98099 = 2.30753;
        double r98100 = x;
        double r98101 = 0.27061;
        double r98102 = r98100 * r98101;
        double r98103 = r98099 + r98102;
        double r98104 = 1.0;
        double r98105 = 0.99229;
        double r98106 = 0.04481;
        double r98107 = r98100 * r98106;
        double r98108 = r98105 + r98107;
        double r98109 = r98100 * r98108;
        double r98110 = r98104 + r98109;
        double r98111 = r98103 / r98110;
        double r98112 = r98111 - r98100;
        double r98113 = r98098 * r98112;
        return r98113;
}

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 2020083 
(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)))