Average Error: 0.0 → 0.0
Time: 2.2s
Precision: 64
Internal Precision: 128
\[a \cdot a - b \cdot b\]
↓
\[(a \cdot a + \left(-b \cdot b\right))_*\]

Error

Bits error versus a

Bits error versus b

Target

Original0.0
Target0.0
Herbie0.0
\[\left(a + b\right) \cdot \left(a - b\right)\]

Derivation

  1. Initial program 0.0

    \[a \cdot a - b \cdot b\]
  2. Using strategy rm

  3. Applied fma-neg0.0

    \[\leadsto \color{blue}{(a \cdot a + \left(-b \cdot b\right))_*}\]

  4. Final simplification0.0

    \[\leadsto (a \cdot a + \left(-b \cdot b\right))_*\]

Reproduce

herbie shell --seed 2019089 +o rules:numerics
(FPCore (a b)
  :name "Difference of squares"

  :herbie-target
  (* (+ a b) (- a b))

  (- (* a a) (* b b)))