Average Error: 0.1 → 0.1
Time: 2.1s
Precision: binary64
\[\left(\left(x - \left(\left(\frac{1}{6} \cdot x\right) \cdot x\right) \cdot x\right) + \left(\left(\left(\left(\frac{1}{120} \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\right) - \left(\left(\left(\left(\left(\left(\frac{1}{5040} \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\]
↓
\[\left({x}^{4} \cdot \left(\left(\frac{1}{120} - \left(\frac{1}{5040} \cdot x\right) \cdot x\right) \cdot x\right) - {x}^{3} \cdot \frac{1}{6}\right) + x\]
\left(\left(x - \left(\left(\frac{1}{6} \cdot x\right) \cdot x\right) \cdot x\right) + \left(\left(\left(\left(\frac{1}{120} \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\right) - \left(\left(\left(\left(\left(\left(\frac{1}{5040} \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\right) \cdot x
↓
\left({x}^{4} \cdot \left(\left(\frac{1}{120} - \left(\frac{1}{5040} \cdot x\right) \cdot x\right) \cdot x\right) - {x}^{3} \cdot \frac{1}{6}\right) + x
double code(double x) {
	return ((double) (((double) (((double) (x - ((double) (((double) (((double) (((double) (1.0 / 6.0)) * x)) * x)) * x)))) + ((double) (((double) (((double) (((double) (((double) (((double) (1.0 / 120.0)) * x)) * x)) * x)) * x)) * x)))) - ((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (1.0 / 5040.0)) * x)) * x)) * x)) * x)) * x)) * x)) * x))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) (((double) pow(x, 4.0)) * ((double) (((double) (((double) (1.0 / 120.0)) - ((double) (((double) (((double) (1.0 / 5040.0)) * x)) * x)))) * x)))) - ((double) (((double) pow(x, 3.0)) * ((double) (1.0 / 6.0)))))) + x));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(x - \left(\left(\frac{1}{6} \cdot x\right) \cdot x\right) \cdot x\right) + \left(\left(\left(\left(\frac{1}{120} \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\right) - \left(\left(\left(\left(\left(\left(\frac{1}{5040} \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\right) \cdot x\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\left({x}^{4} \cdot \left(\left(\frac{1}{120} - \left(\frac{1}{5040} \cdot x\right) \cdot x\right) \cdot x\right) - {x}^{3} \cdot \frac{1}{6}\right) + x}\]

  3. Final simplification0.1

    \[\leadsto \left({x}^{4} \cdot \left(\left(\frac{1}{120} - \left(\frac{1}{5040} \cdot x\right) \cdot x\right) \cdot x\right) - {x}^{3} \cdot \frac{1}{6}\right) + x\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(- (+ (- x (* (* (* (/ 1 6) x) x) x)) (* (* (* (* (* (/ 1 120) x) x) x) x) x)) (* (* (* (* (* (* (* (/ 1 5040) x) x) x) x) x) x) x))"
  :precision binary64
  (- (+ (- x (* (* (* (/ 1.0 6.0) x) x) x)) (* (* (* (* (* (/ 1.0 120.0) x) x) x) x) x)) (* (* (* (* (* (* (* (/ 1.0 5040.0) x) x) x) x) x) x) x)))