Average Error: 0.0 → 0.0
Time: 7.5s
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 r61525 = 0.70711;
        double r61526 = 2.30753;
        double r61527 = x;
        double r61528 = 0.27061;
        double r61529 = r61527 * r61528;
        double r61530 = r61526 + r61529;
        double r61531 = 1.0;
        double r61532 = 0.99229;
        double r61533 = 0.04481;
        double r61534 = r61527 * r61533;
        double r61535 = r61532 + r61534;
        double r61536 = r61527 * r61535;
        double r61537 = r61531 + r61536;
        double r61538 = r61530 / r61537;
        double r61539 = r61538 - r61527;
        double r61540 = r61525 * r61539;
        return r61540;
}
↓
double f(double x) {
        double r61541 = 0.70711;
        double r61542 = 2.30753;
        double r61543 = x;
        double r61544 = 0.27061;
        double r61545 = r61543 * r61544;
        double r61546 = r61542 + r61545;
        double r61547 = 1.0;
        double r61548 = 0.99229;
        double r61549 = 0.04481;
        double r61550 = r61543 * r61549;
        double r61551 = r61548 + r61550;
        double r61552 = r61543 * r61551;
        double r61553 = r61547 + r61552;
        double r61554 = r61546 / r61553;
        double r61555 = r61554 - r61543;
        double r61556 = r61541 * r61555;
        return r61556;
}

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 2019199 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  (* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)))