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 r99540 = 0.70711;
        double r99541 = 2.30753;
        double r99542 = x;
        double r99543 = 0.27061;
        double r99544 = r99542 * r99543;
        double r99545 = r99541 + r99544;
        double r99546 = 1.0;
        double r99547 = 0.99229;
        double r99548 = 0.04481;
        double r99549 = r99542 * r99548;
        double r99550 = r99547 + r99549;
        double r99551 = r99542 * r99550;
        double r99552 = r99546 + r99551;
        double r99553 = r99545 / r99552;
        double r99554 = r99553 - r99542;
        double r99555 = r99540 * r99554;
        return r99555;
}
↓
double f(double x) {
        double r99556 = 0.70711;
        double r99557 = 2.30753;
        double r99558 = x;
        double r99559 = 0.27061;
        double r99560 = r99558 * r99559;
        double r99561 = r99557 + r99560;
        double r99562 = 1.0;
        double r99563 = 0.99229;
        double r99564 = 0.04481;
        double r99565 = r99558 * r99564;
        double r99566 = r99563 + r99565;
        double r99567 = r99558 * r99566;
        double r99568 = r99562 + r99567;
        double r99569 = r99561 / r99568;
        double r99570 = r99569 - r99558;
        double r99571 = r99556 * r99570;
        return r99571;
}

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 2020049 
(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)))