Average Error: 0.0 → 0.2
Time: 3.9s
Precision: 64
\[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
↓
\[\frac{0.707110000000000016}{\frac{1 + \log \left(e^{x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)}{2.30753 + x \cdot 0.27061000000000002}} + 0.707110000000000016 \cdot \left(-x\right)\]
0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)
↓
\frac{0.707110000000000016}{\frac{1 + \log \left(e^{x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)}{2.30753 + x \cdot 0.27061000000000002}} + 0.707110000000000016 \cdot \left(-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) (((double) (0.70711 / ((double) (((double) (1.0 + ((double) log(((double) exp(((double) (x * ((double) (0.99229 + ((double) (x * 0.04481)))))))))))) / ((double) (2.30753 + ((double) (x * 0.27061)))))))) + ((double) (0.70711 * ((double) -(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 sub-neg0.0

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

  6. Applied distribute-lft-in0.0

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

  7. Simplified0.0

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

  9. Applied add-log-exp0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2020113 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  :precision binary64
  (* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* x (+ 0.99229 (* x 0.04481))))) x)))