Average Error: 23.2 → 23.2
Time: 590.0ms
Precision: binary64
\[\frac{1 - x \cdot x}{1 - \left(\left(x \cdot x\right) \cdot x\right) \cdot x}\]
↓
\[\frac{1 - x \cdot x}{1 - \left(\left(x \cdot x\right) \cdot x\right) \cdot x}\]
\frac{1 - x \cdot x}{1 - \left(\left(x \cdot x\right) \cdot x\right) \cdot x}
↓
\frac{1 - x \cdot x}{1 - \left(\left(x \cdot x\right) \cdot x\right) \cdot x}
double code(double x) {
	return ((double) (((double) (1.0 - ((double) (x * x)))) / ((double) (1.0 - ((double) (((double) (((double) (x * x)) * x)) * x))))));
}
↓
double code(double x) {
	return ((double) (((double) (1.0 - ((double) (x * x)))) / ((double) (1.0 - ((double) (((double) (((double) (x * x)) * x)) * x))))));
}

Error

Bits error versus x

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 23.2

    \[\frac{1 - x \cdot x}{1 - \left(\left(x \cdot x\right) \cdot x\right) \cdot x}\]

  2. Final simplification23.2

    \[\leadsto \frac{1 - x \cdot x}{1 - \left(\left(x \cdot x\right) \cdot x\right) \cdot x}\]

Reproduce

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