Average Error: 0.0 → 0.0
Time: 19.1s
Precision: 64
\[0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\right)\]
↓
\[\left(-x\right) \cdot 0.70711 + \frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(x \cdot 0.04481 + 0.99229\right)} \cdot 0.70711\]
0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\right)
↓
\left(-x\right) \cdot 0.70711 + \frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(x \cdot 0.04481 + 0.99229\right)} \cdot 0.70711
double f(double x) {
        double r6982041 = 0.70711;
        double r6982042 = 2.30753;
        double r6982043 = x;
        double r6982044 = 0.27061;
        double r6982045 = r6982043 * r6982044;
        double r6982046 = r6982042 + r6982045;
        double r6982047 = 1.0;
        double r6982048 = 0.99229;
        double r6982049 = 0.04481;
        double r6982050 = r6982043 * r6982049;
        double r6982051 = r6982048 + r6982050;
        double r6982052 = r6982043 * r6982051;
        double r6982053 = r6982047 + r6982052;
        double r6982054 = r6982046 / r6982053;
        double r6982055 = r6982054 - r6982043;
        double r6982056 = r6982041 * r6982055;
        return r6982056;
}
↓
double f(double x) {
        double r6982057 = x;
        double r6982058 = -r6982057;
        double r6982059 = 0.70711;
        double r6982060 = r6982058 * r6982059;
        double r6982061 = 2.30753;
        double r6982062 = 0.27061;
        double r6982063 = r6982057 * r6982062;
        double r6982064 = r6982061 + r6982063;
        double r6982065 = 1.0;
        double r6982066 = 0.04481;
        double r6982067 = r6982057 * r6982066;
        double r6982068 = 0.99229;
        double r6982069 = r6982067 + r6982068;
        double r6982070 = r6982057 * r6982069;
        double r6982071 = r6982065 + r6982070;
        double r6982072 = r6982064 / r6982071;
        double r6982073 = r6982072 * r6982059;
        double r6982074 = r6982060 + r6982073;
        return r6982074;
}

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

    \[0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.0

    \[\leadsto 0.70711 \cdot \color{blue}{\left(\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} + \left(-x\right)\right)}\]

  4. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{0.70711 \cdot \frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} + 0.70711 \cdot \left(-x\right)}\]

  5. Final simplification0.0

    \[\leadsto \left(-x\right) \cdot 0.70711 + \frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(x \cdot 0.04481 + 0.99229\right)} \cdot 0.70711\]

Reproduce

herbie shell --seed 2019163 
(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)))