(- (* (sqrt (/ mu x)) (- (sqrt (/ (* 2 y) (+ x y))) 1)) (* (- timout) 5.0))

Average Error: 11.2 → 11.2

Time: 2.9s

Precision: binary64

Math

\[\sqrt{\frac{mu}{x}} \cdot \left(\sqrt{\frac{2 \cdot y}{x + y}} - 1\right) - \left(-timout\right) \cdot 5\]

↓

\[timout \cdot 5 + \sqrt{\frac{mu}{x}} \cdot \left(\sqrt{\frac{2 \cdot y}{x + y}} - 1\right)\]

Error

Bits error versus mu

Bits error versus x

Bits error versus y

Bits error versus timout

Derivation

1. Initial program 11.2

   \[\sqrt{\frac{mu}{x}} \cdot \left(\sqrt{\frac{2 \cdot y}{x + y}} - 1\right) - \left(-timout\right) \cdot 5\]

2. Simplified 11.2

   \[\leadsto \color{blue}{timout \cdot 5 + \sqrt{\frac{mu}{x}} \cdot \left(\sqrt{\frac{2 \cdot y}{x + y}} - 1\right)}\]

3. Final simplification 11.2

   \[\leadsto timout \cdot 5 + \sqrt{\frac{mu}{x}} \cdot \left(\sqrt{\frac{2 \cdot y}{x + y}} - 1\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (mu x y timout)
  :name "(- (* (sqrt (/ mu x)) (- (sqrt (/ (* 2 y) (+ x y))) 1)) (* (- timout) 5.0))"
  :precision binary64
  (- (* (sqrt (/ mu x)) (- (sqrt (/ (* 2.0 y) (+ x y))) 1.0)) (* (neg timout) 5.0)))