Average Error: 23.7 → 23.7
Time: 807.0ms
Precision: binary64
\[\sqrt{x \cdot x + 0.20000000000000001 \cdot 0.20000000000000001} - x\]
↓
\[\sqrt{x \cdot x + 0.20000000000000001 \cdot 0.20000000000000001} - x\]
\sqrt{x \cdot x + 0.20000000000000001 \cdot 0.20000000000000001} - x
↓
\sqrt{x \cdot x + 0.20000000000000001 \cdot 0.20000000000000001} - x
double code(double x) {
	return ((double) (((double) sqrt(((double) (((double) (x * x)) + ((double) (0.2 * 0.2)))))) - x));
}
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) (((double) (x * x)) + ((double) (0.2 * 0.2)))))) - x));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 23.7

    \[\sqrt{x \cdot x + 0.20000000000000001 \cdot 0.20000000000000001} - x\]

  2. Final simplification23.7

    \[\leadsto \sqrt{x \cdot x + 0.20000000000000001 \cdot 0.20000000000000001} - x\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(- (sqrt (+ (* x x) (* 0.2 0.2))) x)"
  :precision binary64
  (- (sqrt (+ (* x x) (* 0.2 0.2))) x))