Average Error: 0.0 → 0.0
Time: 6.8s
Precision: binary64
\[\left(x + y\right) \cdot \left(1 - z\right)\]
↓
\[\left(\left(x + y\right) \cdot 1 - x \cdot z\right) + \left(-z\right) \cdot y\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

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

  3. Applied sub-neg0.0

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

  4. Applied distribute-lft-in0.0

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

  5. Simplified0.0

    \[\leadsto \left(x + y\right) \cdot 1 + \color{blue}{\left(-z\right) \cdot \left(x + y\right)}\]
  6. Using strategy rm

  7. Applied distribute-lft-in0.0

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

  8. Applied associate-+r+0.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020182 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))