Average Error: 0.3 → 0.3
Time: 2.6s
Precision: binary64
\[\left(\left(\left(a + \frac{1}{2} \cdot a\right) + \frac{1}{6} \cdot {a}^{2}\right) + \frac{1}{24} \cdot {a}^{3}\right) + \frac{1}{120} \cdot {a}^{4}\]
↓
\[\left(\left(\left(a + \frac{1}{2} \cdot a\right) + \frac{1}{6} \cdot {a}^{2}\right) + \frac{1}{24} \cdot {a}^{3}\right) + \frac{1}{120} \cdot {a}^{4}\]
\left(\left(\left(a + \frac{1}{2} \cdot a\right) + \frac{1}{6} \cdot {a}^{2}\right) + \frac{1}{24} \cdot {a}^{3}\right) + \frac{1}{120} \cdot {a}^{4}
↓
\left(\left(\left(a + \frac{1}{2} \cdot a\right) + \frac{1}{6} \cdot {a}^{2}\right) + \frac{1}{24} \cdot {a}^{3}\right) + \frac{1}{120} \cdot {a}^{4}
double code(double a) {
	return ((double) (((double) (((double) (((double) (a + ((double) (((double) (1.0 / 2.0)) * a)))) + ((double) (((double) (1.0 / 6.0)) * ((double) pow(a, 2.0)))))) + ((double) (((double) (1.0 / 24.0)) * ((double) pow(a, 3.0)))))) + ((double) (((double) (1.0 / 120.0)) * ((double) pow(a, 4.0))))));
}
↓
double code(double a) {
	return ((double) (((double) (((double) (((double) (a + ((double) (((double) (1.0 / 2.0)) * a)))) + ((double) (((double) (1.0 / 6.0)) * ((double) pow(a, 2.0)))))) + ((double) (((double) (1.0 / 24.0)) * ((double) pow(a, 3.0)))))) + ((double) (((double) (1.0 / 120.0)) * ((double) pow(a, 4.0))))));
}

Error

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

    \[\left(\left(\left(a + \frac{1}{2} \cdot a\right) + \frac{1}{6} \cdot {a}^{2}\right) + \frac{1}{24} \cdot {a}^{3}\right) + \frac{1}{120} \cdot {a}^{4}\]

  2. Final simplification0.3

    \[\leadsto \left(\left(\left(a + \frac{1}{2} \cdot a\right) + \frac{1}{6} \cdot {a}^{2}\right) + \frac{1}{24} \cdot {a}^{3}\right) + \frac{1}{120} \cdot {a}^{4}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (a)
  :name "(+ (+ (+ (+ a (* (/ 1 2) a)) (* (/ 1 6) (pow a 2))) (* (/ 1 24) (pow a 3))) (* (/ 1 120) (pow a 4)))"
  :precision binary64
  (+ (+ (+ (+ a (* (/ 1.0 2.0) a)) (* (/ 1.0 6.0) (pow a 2.0))) (* (/ 1.0 24.0) (pow a 3.0))) (* (/ 1.0 120.0) (pow a 4.0))))