Average Error: 0.1 → 0.1
Time: 1.6s
Precision: binary64
\[\left(\left(x + \frac{{x}^{2}}{2}\right) + \frac{{x}^{3}}{6}\right) + \frac{{x}^{4}}{24}\]
↓
\[\left(\left(x + \frac{{x}^{2}}{2}\right) + \frac{{x}^{3}}{6}\right) + \frac{{x}^{4}}{24}\]
\left(\left(x + \frac{{x}^{2}}{2}\right) + \frac{{x}^{3}}{6}\right) + \frac{{x}^{4}}{24}
↓
\left(\left(x + \frac{{x}^{2}}{2}\right) + \frac{{x}^{3}}{6}\right) + \frac{{x}^{4}}{24}
double code(double x) {
	return ((double) (((double) (((double) (x + ((double) (((double) pow(x, 2.0)) / 2.0)))) + ((double) (((double) pow(x, 3.0)) / 6.0)))) + ((double) (((double) pow(x, 4.0)) / 24.0))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) (x + ((double) (((double) pow(x, 2.0)) / 2.0)))) + ((double) (((double) pow(x, 3.0)) / 6.0)))) + ((double) (((double) pow(x, 4.0)) / 24.0))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(x + \frac{{x}^{2}}{2}\right) + \frac{{x}^{3}}{6}\right) + \frac{{x}^{4}}{24}\]

  2. Final simplification0.1

    \[\leadsto \left(\left(x + \frac{{x}^{2}}{2}\right) + \frac{{x}^{3}}{6}\right) + \frac{{x}^{4}}{24}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(+ (+ (+ x (/ (pow x 2) 2)) (/ (pow x 3) 6)) (/ (pow x 4) 24))"
  :precision binary64
  (+ (+ (+ x (/ (pow x 2.0) 2.0)) (/ (pow x 3.0) 6.0)) (/ (pow x 4.0) 24.0)))