Average Error: 16.3 → 16.3
Time: 1.0s
Precision: binary64
\[3 \cdot x - \left(0.10000000000000001 \cdot \sqrt{80}\right) \cdot \sqrt{5 \cdot {x}^{2} + 1}\]
↓
\[3 \cdot x - \left(0.10000000000000001 \cdot \sqrt{80}\right) \cdot \sqrt{5 \cdot {x}^{2} + 1}\]
3 \cdot x - \left(0.10000000000000001 \cdot \sqrt{80}\right) \cdot \sqrt{5 \cdot {x}^{2} + 1}
↓
3 \cdot x - \left(0.10000000000000001 \cdot \sqrt{80}\right) \cdot \sqrt{5 \cdot {x}^{2} + 1}
double code(double x) {
	return ((double) (((double) (3.0 * x)) - ((double) (((double) (0.1 * ((double) sqrt(80.0)))) * ((double) sqrt(((double) (((double) (5.0 * ((double) pow(x, 2.0)))) + 1.0))))))));
}
↓
double code(double x) {
	return ((double) (((double) (3.0 * x)) - ((double) (((double) (0.1 * ((double) sqrt(80.0)))) * ((double) sqrt(((double) (((double) (5.0 * ((double) pow(x, 2.0)))) + 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 16.3

    \[3 \cdot x - \left(0.10000000000000001 \cdot \sqrt{80}\right) \cdot \sqrt{5 \cdot {x}^{2} + 1}\]

  2. Final simplification16.3

    \[\leadsto 3 \cdot x - \left(0.10000000000000001 \cdot \sqrt{80}\right) \cdot \sqrt{5 \cdot {x}^{2} + 1}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(- (* 3 x) (* (* 0.1 (sqrt 80)) (sqrt (+ (* 5 (pow x 2)) 1))))"
  :precision binary64
  (- (* 3.0 x) (* (* 0.1 (sqrt 80.0)) (sqrt (+ (* 5.0 (pow x 2.0)) 1.0)))))