Average Error: 23.2 → 23.2
Time: 637.0ms
Precision: binary64
\[\frac{x \cdot x + 1}{\left(\left(x \cdot x\right) \cdot x\right) \cdot x + 10^{5}}\]
↓
\[\frac{x \cdot x + 1}{\left(\left(x \cdot x\right) \cdot x\right) \cdot x + 10^{5}}\]
\frac{x \cdot x + 1}{\left(\left(x \cdot x\right) \cdot x\right) \cdot x + 10^{5}}
↓
\frac{x \cdot x + 1}{\left(\left(x \cdot x\right) \cdot x\right) \cdot x + 10^{5}}
double code(double x) {
	return ((double) (((double) (((double) (x * x)) + 1.0)) / ((double) (((double) (((double) (((double) (x * x)) * x)) * x)) + 100000.0))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) (x * x)) + 1.0)) / ((double) (((double) (((double) (((double) (x * x)) * x)) * x)) + 100000.0))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 23.2

    \[\frac{x \cdot x + 1}{\left(\left(x \cdot x\right) \cdot x\right) \cdot x + 10^{5}}\]

  2. Final simplification23.2

    \[\leadsto \frac{x \cdot x + 1}{\left(\left(x \cdot x\right) \cdot x\right) \cdot x + 10^{5}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(/ (+ (* x x) 1) (+ (* (* (* x x) x) x) 100000))"
  :precision binary64
  (/ (+ (* x x) 1.0) (+ (* (* (* x x) x) x) 100000.0)))