Average Error: 25.7 → 25.7
Time: 1.1s
Precision: binary64
\[\frac{1 - \left(x - y\right) \cdot \left(x - y\right)}{\left(4 \cdot x\right) \cdot y}\]
↓
\[\frac{1 - \left(x - y\right) \cdot \left(x - y\right)}{\left(4 \cdot x\right) \cdot y}\]
\frac{1 - \left(x - y\right) \cdot \left(x - y\right)}{\left(4 \cdot x\right) \cdot y}
↓
\frac{1 - \left(x - y\right) \cdot \left(x - y\right)}{\left(4 \cdot x\right) \cdot y}
double code(double x, double y) {
	return ((double) (((double) (1.0 - ((double) (((double) (x - y)) * ((double) (x - y)))))) / ((double) (((double) (4.0 * x)) * y))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (1.0 - ((double) (((double) (x - y)) * ((double) (x - y)))))) / ((double) (((double) (4.0 * x)) * y))));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 25.7

    \[\frac{1 - \left(x - y\right) \cdot \left(x - y\right)}{\left(4 \cdot x\right) \cdot y}\]

  2. Final simplification25.7

    \[\leadsto \frac{1 - \left(x - y\right) \cdot \left(x - y\right)}{\left(4 \cdot x\right) \cdot y}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x y)
  :name "(/ (- 1 (* (- x y) (- x y))) (* (* 4 x) y))"
  :precision binary64
  (/ (- 1.0 (* (- x y) (- x y))) (* (* 4.0 x) y)))