Error

Target

Derivation

1. Initial program 45.9

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

3. Applied add-log-exp47.7

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

4. Applied add-log-exp48.2

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

5. Applied diff-log48.2

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

6. Simplified31.1

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

8. Applied associate-+l-14.7

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

9. Taylor expanded around -inf 8.2

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

10. Final simplification8.2

    \[\leadsto \log \left(e^{-1 - \left(\left(z + x \cdot y\right) - (x \cdot y + z)_*\right)}\right)\]

Reproduce

herbie shell --seed 2019004 
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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

Details

Time bar (total: 15.5s)Debug log