Average Error: 29.6 → 29.6
Time: 1.2s
Precision: binary64
\[\left(\frac{1}{2} \cdot x + 1\right) - \frac{1 - x}{1 + x}\]
↓
\[\left(\frac{1}{2} \cdot x + 1\right) - \frac{1 - x}{1 + x}\]
\left(\frac{1}{2} \cdot x + 1\right) - \frac{1 - x}{1 + x}
↓
\left(\frac{1}{2} \cdot x + 1\right) - \frac{1 - x}{1 + x}
double code(double x) {
	return ((double) (((double) (((double) (((double) (1.0 / 2.0)) * x)) + 1.0)) - ((double) (((double) (1.0 - x)) / ((double) (1.0 + x))))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) (((double) (1.0 / 2.0)) * x)) + 1.0)) - ((double) (((double) (1.0 - x)) / ((double) (1.0 + x))))));
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 29.6

    \[\left(\frac{1}{2} \cdot x + 1\right) - \frac{1 - x}{1 + x}\]

  2. Final simplification29.6

    \[\leadsto \left(\frac{1}{2} \cdot x + 1\right) - \frac{1 - x}{1 + x}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(- (+ (* (/ 1 2) x) 1) (/ (- 1 x) (+ 1 x)))"
  :precision binary64
  (- (+ (* (/ 1.0 2.0) x) 1.0) (/ (- 1.0 x) (+ 1.0 x))))