Average Error: 0.0 → 0.1
Time: 2.9s
Precision: binary64
\[0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\right)\]
↓
\[0.70711 \cdot \left(\frac{\frac{2.30753 + x \cdot 0.27061}{\sqrt{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}}}{\sqrt{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}} - x\right)\]
0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\right)
↓
0.70711 \cdot \left(\frac{\frac{2.30753 + x \cdot 0.27061}{\sqrt{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}}}{\sqrt{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}} - x\right)
double code(double x) {
	return ((double) (0.70711 * ((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) (2.30753 + ((double) (x * 0.27061)))) / ((double) sqrt(((double) (1.0 + ((double) (x * ((double) (0.99229 + ((double) (x * 0.04481))))))))))) / ((double) sqrt(((double) (1.0 + ((double) (x * ((double) (0.99229 + ((double) (x * 0.04481))))))))))) - 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

    \[0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\right)\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.1

    \[\leadsto 0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{\color{blue}{\sqrt{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} \cdot \sqrt{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}}} - x\right)\]

  4. Applied associate-/r*0.1

    \[\leadsto 0.70711 \cdot \left(\color{blue}{\frac{\frac{2.30753 + x \cdot 0.27061}{\sqrt{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}}}{\sqrt{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}}} - x\right)\]

  5. Final simplification0.1

    \[\leadsto 0.70711 \cdot \left(\frac{\frac{2.30753 + x \cdot 0.27061}{\sqrt{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}}}{\sqrt{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}} - x\right)\]

Reproduce

herbie shell --seed 2020196 
(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)))