Average Error: 0.0 → 0.0
Time: 1.9s
Precision: binary64
\[\left(\left(x - \frac{1}{2} \cdot {x}^{2}\right) - \frac{1}{3} \cdot {x}^{3}\right) - \frac{1}{4} \cdot {x}^{4}\]
↓
\[\left(x - \frac{1}{4} \cdot {x}^{4}\right) - 1 \cdot \left(\frac{{x}^{3}}{3} + \frac{{x}^{2}}{2}\right)\]
\left(\left(x - \frac{1}{2} \cdot {x}^{2}\right) - \frac{1}{3} \cdot {x}^{3}\right) - \frac{1}{4} \cdot {x}^{4}
↓
\left(x - \frac{1}{4} \cdot {x}^{4}\right) - 1 \cdot \left(\frac{{x}^{3}}{3} + \frac{{x}^{2}}{2}\right)
double code(double x) {
	return ((double) (((double) (((double) (x - ((double) (((double) (1.0 / 2.0)) * ((double) pow(x, 2.0)))))) - ((double) (((double) (1.0 / 3.0)) * ((double) pow(x, 3.0)))))) - ((double) (((double) (1.0 / 4.0)) * ((double) pow(x, 4.0))))));
}
↓
double code(double x) {
	return ((double) (((double) (x - ((double) (((double) (1.0 / 4.0)) * ((double) pow(x, 4.0)))))) - ((double) (1.0 * ((double) (((double) (((double) pow(x, 3.0)) / 3.0)) + ((double) (((double) pow(x, 2.0)) / 2.0))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(- (- (- x (* (/ 1 2) (pow x 2))) (* (/ 1 3) (pow x 3))) (* (/ 1 4) (pow x 4)))"
  :precision binary64
  (- (- (- x (* (/ 1.0 2.0) (pow x 2.0))) (* (/ 1.0 3.0) (pow x 3.0))) (* (/ 1.0 4.0) (pow x 4.0))))