Average Error: 24.1 → 24.1
Time: 2.4s
Precision: binary64
\[{\left(\sqrt{16 \cdot {x}^{2} + 1} - 4 \cdot x\right)}^{\left(\frac{1}{3}\right)}\]
↓
\[{\left(\sqrt{16 \cdot {x}^{2} + 1} - 4 \cdot x\right)}^{\left(\frac{1}{3}\right)}\]
{\left(\sqrt{16 \cdot {x}^{2} + 1} - 4 \cdot x\right)}^{\left(\frac{1}{3}\right)}
↓
{\left(\sqrt{16 \cdot {x}^{2} + 1} - 4 \cdot x\right)}^{\left(\frac{1}{3}\right)}
double code(double x) {
	return ((double) pow(((double) (((double) sqrt(((double) (((double) (16.0 * ((double) pow(x, 2.0)))) + 1.0)))) - ((double) (4.0 * x)))), ((double) (1.0 / 3.0))));
}
↓
double code(double x) {
	return ((double) pow(((double) (((double) sqrt(((double) (((double) (16.0 * ((double) pow(x, 2.0)))) + 1.0)))) - ((double) (4.0 * x)))), ((double) (1.0 / 3.0))));
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 24.1

    \[{\left(\sqrt{16 \cdot {x}^{2} + 1} - 4 \cdot x\right)}^{\left(\frac{1}{3}\right)}\]

  2. Final simplification24.1

    \[\leadsto {\left(\sqrt{16 \cdot {x}^{2} + 1} - 4 \cdot x\right)}^{\left(\frac{1}{3}\right)}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(pow (- (sqrt (+ (* 16 (pow x 2)) 1)) (* 4 x)) (/ 1 3))"
  :precision binary64
  (pow (- (sqrt (+ (* 16.0 (pow x 2.0)) 1.0)) (* 4.0 x)) (/ 1.0 3.0)))