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

Average Error: 31.8 → 0

Time: 790.0ms

Precision: binary64

Math

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

↓

\[\left|x\right| + \left(-\left|y\right|\right)\]

Error

Bits error versus x

Bits error versus y

Derivation

1. Initial program 31.8

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

2. Simplified 0

   \[\leadsto \color{blue}{\left|x\right| + \left(-\left|y\right|\right)}\]

3. Final simplification 0

   \[\leadsto \left|x\right| + \left(-\left|y\right|\right)\]

Reproduce

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