Average Error: 45.2 → 0
Time: 19.0s
Precision: 64
Internal Precision: 2368
\[(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
↓
\[-1\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.2
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.2

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

  2. Initial simplification45.2

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

  3. Taylor expanded around 0 0

    \[\leadsto \color{blue}{-1}\]

  4. Final simplification0

    \[\leadsto -1\]

Runtime

Time bar (total: 19.0s)Debug logProfile

herbie shell --seed 2018214 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

  (- (fma x y z) (+ 1 (+ (* x y) z))))