Average Error: 0.0 → 0.0
Time: 2.3s
Precision: 64
\[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
↓
\[0.707110000000000016 \cdot \left(\frac{1}{\frac{1 + \left(x \cdot 0.992290000000000005 + x \cdot \left(x \cdot 0.044810000000000003\right)\right)}{2.30753 + x \cdot 0.27061000000000002}} - x\right)\]
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{1}{\frac{1 + \left(x \cdot 0.992290000000000005 + x \cdot \left(x \cdot 0.044810000000000003\right)\right)}{2.30753 + x \cdot 0.27061000000000002}} - x\right)
double code(double x) {
	return ((double) (0.70711 * ((double) (((double) (((double) (2.30753 + ((double) (x * 0.27061)))) / ((double) (1.0 + ((double) (x * ((double) (0.99229 + ((double) (x * 0.04481)))))))))) - x))));
}
↓
double code(double x) {
	return ((double) (0.70711 * ((double) (((double) (1.0 / ((double) (((double) (1.0 + ((double) (((double) (x * 0.99229)) + ((double) (x * ((double) (x * 0.04481)))))))) / ((double) (2.30753 + ((double) (x * 0.27061)))))))) - x))));
}

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. Using strategy rm

  3. Applied clear-num0.0

    \[\leadsto 0.707110000000000016 \cdot \left(\color{blue}{\frac{1}{\frac{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}{2.30753 + x \cdot 0.27061000000000002}}} - x\right)\]
  4. Using strategy rm

  5. Applied distribute-lft-in0.0

    \[\leadsto 0.707110000000000016 \cdot \left(\frac{1}{\frac{1 + \color{blue}{\left(x \cdot 0.992290000000000005 + x \cdot \left(x \cdot 0.044810000000000003\right)\right)}}{2.30753 + x \cdot 0.27061000000000002}} - x\right)\]

  6. Final simplification0.0

    \[\leadsto 0.707110000000000016 \cdot \left(\frac{1}{\frac{1 + \left(x \cdot 0.992290000000000005 + x \cdot \left(x \cdot 0.044810000000000003\right)\right)}{2.30753 + x \cdot 0.27061000000000002}} - x\right)\]

Reproduce

herbie shell --seed 2020124 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  :precision binary64
  (* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)))