Average Error: 38.7 → 38.7
Time: 1.7s
Precision: binary64
\[\sqrt{x \cdot x - y \cdot y} - x\]
↓
\[\sqrt{x \cdot x - y \cdot y} - x\]
\sqrt{x \cdot x - y \cdot y} - x
↓
\sqrt{x \cdot x - y \cdot y} - x
double code(double x, double y) {
	return ((double) (((double) sqrt(((double) (((double) (x * x)) - ((double) (y * y)))))) - x));
}
↓
double code(double x, double y) {
	return ((double) (((double) sqrt(((double) (((double) (x * x)) - ((double) (y * y)))))) - x));
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 38.7

    \[\sqrt{x \cdot x - y \cdot y} - x\]

  2. Final simplification38.7

    \[\leadsto \sqrt{x \cdot x - y \cdot y} - x\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x y)
  :name "(- (sqrt (- (* x x) (* y y))) x)"
  :precision binary64
  (- (sqrt (- (* x x) (* y y))) x))