Average Error: 0.0 → 0.0
Time: 1.4s
Precision: binary64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]
↓
\[\left(x \cdot y + \left(\left(-1\right) \cdot x - y \cdot 0.5\right)\right) + 0.918938533204673003\]

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]
  2. Using strategy rm

  3. Applied sub-neg0.0

    \[\leadsto \left(x \cdot \color{blue}{\left(y + \left(-1\right)\right)} - y \cdot 0.5\right) + 0.918938533204673003\]

  4. Applied distribute-lft-in0.0

    \[\leadsto \left(\color{blue}{\left(x \cdot y + x \cdot \left(-1\right)\right)} - y \cdot 0.5\right) + 0.918938533204673003\]

  5. Applied associate--l+0.0

    \[\leadsto \color{blue}{\left(x \cdot y + \left(x \cdot \left(-1\right) - y \cdot 0.5\right)\right)} + 0.918938533204673003\]

  6. Simplified0.0

    \[\leadsto \left(x \cdot y + \color{blue}{\left(\left(-1\right) \cdot x - y \cdot 0.5\right)}\right) + 0.918938533204673003\]

  7. Final simplification0.0

    \[\leadsto \left(x \cdot y + \left(\left(-1\right) \cdot x - y \cdot 0.5\right)\right) + 0.918938533204673003\]

Reproduce

herbie shell --seed 2020150 
(FPCore (x y)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (* x (- y 1.0)) (* y 0.5)) 0.918938533204673))