Average Error: 0.0 → 0.0
Time: 3.2s
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 r125131 = 0.70711;
        double r125132 = 2.30753;
        double r125133 = x;
        double r125134 = 0.27061;
        double r125135 = r125133 * r125134;
        double r125136 = r125132 + r125135;
        double r125137 = 1.0;
        double r125138 = 0.99229;
        double r125139 = 0.04481;
        double r125140 = r125133 * r125139;
        double r125141 = r125138 + r125140;
        double r125142 = r125133 * r125141;
        double r125143 = r125137 + r125142;
        double r125144 = r125136 / r125143;
        double r125145 = r125144 - r125133;
        double r125146 = r125131 * r125145;
        return r125146;
}
↓
double f(double x) {
        double r125147 = 0.70711;
        double r125148 = 2.30753;
        double r125149 = x;
        double r125150 = 0.27061;
        double r125151 = r125149 * r125150;
        double r125152 = r125148 + r125151;
        double r125153 = 1.0;
        double r125154 = 0.99229;
        double r125155 = 0.04481;
        double r125156 = r125149 * r125155;
        double r125157 = r125154 + r125156;
        double r125158 = r125149 * r125157;
        double r125159 = r125153 + r125158;
        double r125160 = r125152 / r125159;
        double r125161 = r125160 - r125149;
        double r125162 = r125147 * r125161;
        return r125162;
}

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 2020046 
(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)))