Average Error: 2.0 → 2.0
Time: 1.6s
Precision: binary64
\[\frac{x}{1 + {\left(1 - x\right)}^{\left(\frac{1}{3}\right)} \cdot \left(1 + {\left(1 - x\right)}^{\left(\frac{1}{3}\right)}\right)}\]
↓
\[\frac{x}{1 + {\left(1 - x\right)}^{\left(\frac{1}{3}\right)} \cdot \left(1 + {\left(1 - x\right)}^{\left(\frac{1}{3}\right)}\right)}\]
\frac{x}{1 + {\left(1 - x\right)}^{\left(\frac{1}{3}\right)} \cdot \left(1 + {\left(1 - x\right)}^{\left(\frac{1}{3}\right)}\right)}
↓
\frac{x}{1 + {\left(1 - x\right)}^{\left(\frac{1}{3}\right)} \cdot \left(1 + {\left(1 - x\right)}^{\left(\frac{1}{3}\right)}\right)}
double code(double x) {
	return ((double) (x / ((double) (1.0 + ((double) (((double) pow(((double) (1.0 - x)), ((double) (1.0 / 3.0)))) * ((double) (1.0 + ((double) pow(((double) (1.0 - x)), ((double) (1.0 / 3.0))))))))))));
}
↓
double code(double x) {
	return ((double) (x / ((double) (1.0 + ((double) (((double) pow(((double) (1.0 - x)), ((double) (1.0 / 3.0)))) * ((double) (1.0 + ((double) pow(((double) (1.0 - x)), ((double) (1.0 / 3.0))))))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 2.0

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

  2. Final simplification2.0

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

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(/ x (+ 1 (* (pow (- 1 x) (/ 1 3)) (+ 1 (pow (- 1 x) (/ 1 3))))))"
  :precision binary64
  (/ x (+ 1.0 (* (pow (- 1.0 x) (/ 1.0 3.0)) (+ 1.0 (pow (- 1.0 x) (/ 1.0 3.0)))))))