Error

Target

Derivation

1. Initial program 45.1

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

2. Initial simplification34.4

   \[\leadsto \left((x \cdot y + z)_* - x \cdot y\right) - \left(z - -1\right)\]
3. Using strategy rm

4. Applied sub-neg34.4

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

5. Applied associate--r+13.4

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

6. Simplified13.4

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

8. Applied flip--31.8

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

9. Taylor expanded around inf 8.1

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

10. Final simplification8.1

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

Reproduce

herbie shell --seed 2018362 
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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

Details

Time bar (total: 12.6s)Debug log