Derivation

Initial program 44.8
\[(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
Initial simplification34.0
\[\leadsto \left((x \cdot y + z)_* - x \cdot y\right) - \left(z - -1\right)\]
Using strategy rm
Applied sub-neg34.0
\[\leadsto \left((x \cdot y + z)_* - x \cdot y\right) - \color{blue}{\left(z + \left(--1\right)\right)}\]
Applied associate--r+13.4
\[\leadsto \color{blue}{\left(\left((x \cdot y + z)_* - x \cdot y\right) - z\right) - \left(--1\right)}\]
Simplified13.4
\[\leadsto \left(\left((x \cdot y + z)_* - x \cdot y\right) - z\right) - \color{blue}{1}\]
Using strategy rm
Applied add-cube-cbrt30.4
\[\leadsto \left(\color{blue}{\left(\sqrt[3]{(x \cdot y + z)_* - x \cdot y} \cdot \sqrt[3]{(x \cdot y + z)_* - x \cdot y}\right) \cdot \sqrt[3]{(x \cdot y + z)_* - x \cdot y}} - z\right) - 1\]
Taylor expanded around inf 8.0
\[\leadsto \color{blue}{\left((x \cdot y + z)_* - \left(z + x \cdot y\right)\right)} - 1\]
Final simplification8.0
\[\leadsto \left((x \cdot y + z)_* - \left(z + x \cdot y\right)\right) - 1\]

Runtime

herbie shell --seed 2018274 
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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