Average Error: 0.2 → 0.2
Time: 1.2s
Precision: binary64
\[\frac{\left({x}^{2} + {\left(x + \frac{1}{3}\right)}^{2}\right) \cdot \frac{1}{3}}{2}\]
↓
\[\frac{\left({x}^{2} + {\left(x + \frac{1}{3}\right)}^{2}\right) \cdot \frac{1}{3}}{2}\]
\frac{\left({x}^{2} + {\left(x + \frac{1}{3}\right)}^{2}\right) \cdot \frac{1}{3}}{2}
↓
\frac{\left({x}^{2} + {\left(x + \frac{1}{3}\right)}^{2}\right) \cdot \frac{1}{3}}{2}
double code(double x) {
	return ((double) (((double) (((double) (((double) pow(x, 2.0)) + ((double) pow(((double) (x + ((double) (1.0 / 3.0)))), 2.0)))) * ((double) (1.0 / 3.0)))) / 2.0));
}
↓
double code(double x) {
	return ((double) (((double) (((double) (((double) pow(x, 2.0)) + ((double) pow(((double) (x + ((double) (1.0 / 3.0)))), 2.0)))) * ((double) (1.0 / 3.0)))) / 2.0));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\frac{\left({x}^{2} + {\left(x + \frac{1}{3}\right)}^{2}\right) \cdot \frac{1}{3}}{2}\]

  2. Final simplification0.2

    \[\leadsto \frac{\left({x}^{2} + {\left(x + \frac{1}{3}\right)}^{2}\right) \cdot \frac{1}{3}}{2}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(/ (* (+ (pow x 2) (pow (+ x (/ 1 3)) 2)) (/ 1 3)) 2)"
  :precision binary64
  (/ (* (+ (pow x 2.0) (pow (+ x (/ 1.0 3.0)) 2.0)) (/ 1.0 3.0)) 2.0))