(- (sqrt (+ (* x x) (* y y))) x)

Average Error: 35.5 → 35.5

Time: 947.0ms

Precision: binary64

Math

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

↓

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

C

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

Derivation

1. Initial program 35.5

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

2. Final simplification 35.5

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

Reproduce

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