Average Error: 16.2 → 16.2
Time: 686.0ms
Precision: binary64
\[\frac{\left(4 \cdot x\right) \cdot x}{1 + \frac{x}{1.1100000000000001} \cdot \frac{x}{1.1100000000000001}}\]
↓
\[\frac{\left(4 \cdot x\right) \cdot x}{1 + \frac{x}{1.1100000000000001} \cdot \frac{x}{1.1100000000000001}}\]
\frac{\left(4 \cdot x\right) \cdot x}{1 + \frac{x}{1.1100000000000001} \cdot \frac{x}{1.1100000000000001}}
↓
\frac{\left(4 \cdot x\right) \cdot x}{1 + \frac{x}{1.1100000000000001} \cdot \frac{x}{1.1100000000000001}}
double code(double x) {
	return ((double) (((double) (((double) (4.0 * x)) * x)) / ((double) (1.0 + ((double) (((double) (x / 1.11)) * ((double) (x / 1.11))))))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) (4.0 * x)) * x)) / ((double) (1.0 + ((double) (((double) (x / 1.11)) * ((double) (x / 1.11))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 16.2

    \[\frac{\left(4 \cdot x\right) \cdot x}{1 + \frac{x}{1.1100000000000001} \cdot \frac{x}{1.1100000000000001}}\]

  2. Final simplification16.2

    \[\leadsto \frac{\left(4 \cdot x\right) \cdot x}{1 + \frac{x}{1.1100000000000001} \cdot \frac{x}{1.1100000000000001}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(/ (* (* 4 x) x) (+ 1 (* (/ x 1.11) (/ x 1.11))))"
  :precision binary64
  (/ (* (* 4.0 x) x) (+ 1.0 (* (/ x 1.11) (/ x 1.11)))))