Derivation

Initial program 45.4
\[(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
Initial simplification34.9
\[\leadsto \left((x \cdot y + z)_* - x \cdot y\right) - \left(z - -1\right)\]
Using strategy rm
Applied sub-neg34.9
\[\leadsto \left((x \cdot y + z)_* - x \cdot y\right) - \color{blue}{\left(z + \left(--1\right)\right)}\]
Applied associate--r+14.0
\[\leadsto \color{blue}{\left(\left((x \cdot y + z)_* - x \cdot y\right) - z\right) - \left(--1\right)}\]
Simplified14.0
\[\leadsto \left(\left((x \cdot y + z)_* - x \cdot y\right) - z\right) - \color{blue}{1}\]
Using strategy rm
Applied flip--31.8
\[\leadsto \left(\color{blue}{\frac{(x \cdot y + z)_* \cdot (x \cdot y + z)_* - \left(x \cdot y\right) \cdot \left(x \cdot y\right)}{(x \cdot y + z)_* + x \cdot y}} - z\right) - 1\]
Taylor expanded around -inf 8.6
\[\leadsto \color{blue}{\left((x \cdot y + z)_* - \left(z + x \cdot y\right)\right)} - 1\]
Final simplification8.6
\[\leadsto \left((x \cdot y + z)_* - \left(z + x \cdot y\right)\right) - 1\]

Runtime

herbie shell --seed 2018304 
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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