Error

Target

Derivation

1. Initial program 45.3

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

3. Applied add-log-exp47.1

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

4. Applied add-log-exp47.6

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

5. Applied diff-log47.6

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

6. Simplified30.9

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

8. Applied associate-+l-15.2

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

9. Applied exp-diff15.2

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

10. Taylor expanded around 0 8.1

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

11. Final simplification8.1

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

Reproduce

herbie shell --seed 2019016 
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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

Details

Time bar (total: 25.8s)Debug log