Average Error: 0.0 → 0.0
Time: 1.9s
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 r95634 = 0.70711;
        double r95635 = 2.30753;
        double r95636 = x;
        double r95637 = 0.27061;
        double r95638 = r95636 * r95637;
        double r95639 = r95635 + r95638;
        double r95640 = 1.0;
        double r95641 = 0.99229;
        double r95642 = 0.04481;
        double r95643 = r95636 * r95642;
        double r95644 = r95641 + r95643;
        double r95645 = r95636 * r95644;
        double r95646 = r95640 + r95645;
        double r95647 = r95639 / r95646;
        double r95648 = r95647 - r95636;
        double r95649 = r95634 * r95648;
        return r95649;
}
↓
double f(double x) {
        double r95650 = 0.70711;
        double r95651 = 2.30753;
        double r95652 = x;
        double r95653 = 0.27061;
        double r95654 = r95652 * r95653;
        double r95655 = r95651 + r95654;
        double r95656 = 1.0;
        double r95657 = 0.99229;
        double r95658 = 0.04481;
        double r95659 = r95652 * r95658;
        double r95660 = r95657 + r95659;
        double r95661 = r95652 * r95660;
        double r95662 = r95656 + r95661;
        double r95663 = r95655 / r95662;
        double r95664 = r95663 - r95652;
        double r95665 = r95650 * r95664;
        return r95665;
}

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 2020024 
(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)))