Average Error: 0.0 → 0.0
Time: 2.1s
Precision: binary64
\[0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\right)\]
↓
\[\left(2.30753 + x \cdot 0.27061\right) \cdot \frac{0.70711}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \cdot 0.70711\]
0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\right)
↓
\left(2.30753 + x \cdot 0.27061\right) \cdot \frac{0.70711}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \cdot 0.70711
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) (((double) (((double) (2.30753 + ((double) (x * 0.27061)))) * (0.70711 / ((double) (1.0 + ((double) (x * ((double) (0.99229 + ((double) (x * 0.04481))))))))))) - ((double) (x * 0.70711))));
}

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 div-inv0.0

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

  5. Applied sub-neg0.0

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

  6. Applied distribute-lft-in0.0

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

  7. Simplified0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020199 
(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)))