Average Error: 40.9 → 40.9
Time: 5.8s
Precision: binary64
\[\left(0.5 - 0.5 \cdot {\left(\gamma - \alpha\right)}^{\left(\frac{1}{3}\right)}\right) + 0.5 \cdot {\left(\gamma + \alpha\right)}^{\left(\frac{1}{3}\right)}\]
↓
\[\left(0.5 - 0.5 \cdot {\left(\gamma - \alpha\right)}^{\left(\frac{1}{3}\right)}\right) + 0.5 \cdot {\left(\gamma + \alpha\right)}^{\left(\frac{1}{3}\right)}\]
\left(0.5 - 0.5 \cdot {\left(\gamma - \alpha\right)}^{\left(\frac{1}{3}\right)}\right) + 0.5 \cdot {\left(\gamma + \alpha\right)}^{\left(\frac{1}{3}\right)}
↓
\left(0.5 - 0.5 \cdot {\left(\gamma - \alpha\right)}^{\left(\frac{1}{3}\right)}\right) + 0.5 \cdot {\left(\gamma + \alpha\right)}^{\left(\frac{1}{3}\right)}
double code(double gamma, double alpha) {
	return ((double) (((double) (0.5 - ((double) (0.5 * ((double) pow(((double) (gamma - alpha)), ((double) (1.0 / 3.0)))))))) + ((double) (0.5 * ((double) pow(((double) (gamma + alpha)), ((double) (1.0 / 3.0))))))));
}
↓
double code(double gamma, double alpha) {
	return ((double) (((double) (0.5 - ((double) (0.5 * ((double) pow(((double) (gamma - alpha)), ((double) (1.0 / 3.0)))))))) + ((double) (0.5 * ((double) pow(((double) (gamma + alpha)), ((double) (1.0 / 3.0))))))));
}

Error

Bits error versus gamma

Bits error versus alpha

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 40.9

    \[\left(0.5 - 0.5 \cdot {\left(\gamma - \alpha\right)}^{\left(\frac{1}{3}\right)}\right) + 0.5 \cdot {\left(\gamma + \alpha\right)}^{\left(\frac{1}{3}\right)}\]

  2. Final simplification40.9

    \[\leadsto \left(0.5 - 0.5 \cdot {\left(\gamma - \alpha\right)}^{\left(\frac{1}{3}\right)}\right) + 0.5 \cdot {\left(\gamma + \alpha\right)}^{\left(\frac{1}{3}\right)}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (gamma alpha)
  :name "(+ (- 0.5 (* 0.5 (pow (- gamma alpha) (/ 1 3)))) (* 0.5 (pow (+ gamma alpha) (/ 1 3))))"
  :precision binary64
  (+ (- 0.5 (* 0.5 (pow (- gamma alpha) (/ 1.0 3.0)))) (* 0.5 (pow (+ gamma alpha) (/ 1.0 3.0)))))