Average Error: 0.2 → 0.1
Time: 1.6s
Precision: binary64
\[\left(\left(x - \frac{\left(x \cdot x\right) \cdot x}{6}\right) + \frac{\left(\left(\left(x \cdot x\right) \cdot x\right) \cdot x\right) \cdot x}{120}\right) - \frac{\left(\left(\left(\left(\left(x \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\right) \cdot x}{5040}\]
↓
\[\left(x - \frac{\left(x \cdot x\right) \cdot x}{6}\right) + {x}^{4} \cdot \left(\frac{x}{120} - \frac{{x}^{3}}{5040}\right)\]
\left(\left(x - \frac{\left(x \cdot x\right) \cdot x}{6}\right) + \frac{\left(\left(\left(x \cdot x\right) \cdot x\right) \cdot x\right) \cdot x}{120}\right) - \frac{\left(\left(\left(\left(\left(x \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\right) \cdot x}{5040}
↓
\left(x - \frac{\left(x \cdot x\right) \cdot x}{6}\right) + {x}^{4} \cdot \left(\frac{x}{120} - \frac{{x}^{3}}{5040}\right)
double code(double x) {
	return ((double) (((double) (((double) (x - ((double) (((double) (((double) (x * x)) * x)) / 6.0)))) + ((double) (((double) (((double) (((double) (((double) (x * x)) * x)) * x)) * x)) / 120.0)))) - ((double) (((double) (((double) (((double) (((double) (((double) (((double) (x * x)) * x)) * x)) * x)) * x)) * x)) / 5040.0))));
}
↓
double code(double x) {
	return ((double) (((double) (x - ((double) (((double) (((double) (x * x)) * x)) / 6.0)))) + ((double) (((double) pow(x, 4.0)) * ((double) (((double) (x / 120.0)) - ((double) (((double) pow(x, 3.0)) / 5040.0))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\left(\left(x - \frac{\left(x \cdot x\right) \cdot x}{6}\right) + \frac{\left(\left(\left(x \cdot x\right) \cdot x\right) \cdot x\right) \cdot x}{120}\right) - \frac{\left(\left(\left(\left(\left(x \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\right) \cdot x}{5040}\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\left(x - \frac{\left(x \cdot x\right) \cdot x}{6}\right) + {x}^{4} \cdot \left(\frac{x}{120} - \frac{{x}^{3}}{5040}\right)}\]

  3. Final simplification0.1

    \[\leadsto \left(x - \frac{\left(x \cdot x\right) \cdot x}{6}\right) + {x}^{4} \cdot \left(\frac{x}{120} - \frac{{x}^{3}}{5040}\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(- (+ (- x (/ (* (* x x) x) 6)) (/ (* (* (* (* x x) x) x) x) 120)) (/ (* (* (* (* (* (* x x) x) x) x) x) x) 5040))"
  :precision binary64
  (- (+ (- x (/ (* (* x x) x) 6.0)) (/ (* (* (* (* x x) x) x) x) 120.0)) (/ (* (* (* (* (* (* x x) x) x) x) x) x) 5040.0)))