Average Error: 22.4 → 22.4
Time: 3.0s
Precision: binary64
\[\frac{x}{\frac{2 \cdot \left(y + 1\right)}{y - 1}} - \frac{x}{2}\]
↓
\[\frac{x \cdot \left(\frac{y - 1}{y + 1} - 1\right)}{2}\]
\frac{x}{\frac{2 \cdot \left(y + 1\right)}{y - 1}} - \frac{x}{2}
↓
\frac{x \cdot \left(\frac{y - 1}{y + 1} - 1\right)}{2}
double code(double x, double y) {
	return ((double) (((double) (x / ((double) (((double) (2.0 * ((double) (y + 1.0)))) / ((double) (y - 1.0)))))) - ((double) (x / 2.0))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (x * ((double) (((double) (((double) (y - 1.0)) / ((double) (y + 1.0)))) - 1.0)))) / 2.0));
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 22.4

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

  2. Simplified22.4

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

  3. Final simplification22.4

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

Reproduce

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