Average Error: 16.4 → 16.4
Time: 784.0ms
Precision: binary64
\[\frac{\left(4 \cdot x\right) \cdot x}{\frac{x}{\frac{111}{100}} \cdot \frac{x}{\frac{111}{100}} + 1}\]
↓
\[\frac{\left(4 \cdot x\right) \cdot x}{\frac{x}{\frac{111}{100}} \cdot \frac{x}{\frac{111}{100}} + 1}\]
\frac{\left(4 \cdot x\right) \cdot x}{\frac{x}{\frac{111}{100}} \cdot \frac{x}{\frac{111}{100}} + 1}
↓
\frac{\left(4 \cdot x\right) \cdot x}{\frac{x}{\frac{111}{100}} \cdot \frac{x}{\frac{111}{100}} + 1}
double code(double x) {
	return ((double) (((double) (((double) (4.0 * x)) * x)) / ((double) (((double) (((double) (x / ((double) (111.0 / 100.0)))) * ((double) (x / ((double) (111.0 / 100.0)))))) + 1.0))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) (4.0 * x)) * x)) / ((double) (((double) (((double) (x / ((double) (111.0 / 100.0)))) * ((double) (x / ((double) (111.0 / 100.0)))))) + 1.0))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 16.4

    \[\frac{\left(4 \cdot x\right) \cdot x}{\frac{x}{\frac{111}{100}} \cdot \frac{x}{\frac{111}{100}} + 1}\]

  2. Final simplification16.4

    \[\leadsto \frac{\left(4 \cdot x\right) \cdot x}{\frac{x}{\frac{111}{100}} \cdot \frac{x}{\frac{111}{100}} + 1}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(/ (* (* 4 x) x) (+ (* (/ x (/ 111 100)) (/ x (/ 111 100))) 1))"
  :precision binary64
  (/ (* (* 4.0 x) x) (+ (* (/ x (/ 111.0 100.0)) (/ x (/ 111.0 100.0))) 1.0)))