Average Error: 15.1 → 15.1
Time: 1.1s
Precision: binary64
\[\frac{1}{1 + 2 \cdot x} - \frac{1 - x}{1 + x}\]
↓
\[\frac{1}{1 + 2 \cdot x} - \frac{1 - x}{1 + x}\]
\frac{1}{1 + 2 \cdot x} - \frac{1 - x}{1 + x}
↓
\frac{1}{1 + 2 \cdot x} - \frac{1 - x}{1 + x}
double code(double x) {
	return ((double) (((double) (1.0 / ((double) (1.0 + ((double) (2.0 * x)))))) - ((double) (((double) (1.0 - x)) / ((double) (1.0 + x))))));
}
↓
double code(double x) {
	return ((double) (((double) (1.0 / ((double) (1.0 + ((double) (2.0 * x)))))) - ((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 15.1

    \[\frac{1}{1 + 2 \cdot x} - \frac{1 - x}{1 + x}\]

  2. Final simplification15.1

    \[\leadsto \frac{1}{1 + 2 \cdot x} - \frac{1 - x}{1 + x}\]

Reproduce

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