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
(FPCore (x)
 :precision binary64
 (*
  0.70711
  (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)))
↓
(FPCore (x)
 :precision binary64
 (+
  (*
   (+ 2.30753 (* x 0.27061))
   (/ 0.70711 (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
  (* x -0.70711)))
double code(double x) {
	return 0.70711 * (((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x);
}
↓
double code(double x) {
	return ((2.30753 + (x * 0.27061)) * (0.70711 / (1.0 + (x * (0.99229 + (x * 0.04481)))))) + (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 sub-neg_binary640.0

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

  4. Applied distribute-lft-in_binary640.0

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

  5. Simplified0.0

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

  6. Simplified0.0

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

  8. Applied div-inv_binary640.0

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

  9. Applied associate-*l*_binary640.0

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

  10. Simplified0.0

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

  11. 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 2020224 
(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)))