Error

Target

Derivation

1. Initial program 45.2

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

3. Applied add-log-exp47.0

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

4. Applied add-log-exp47.5

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

5. Applied diff-log47.5

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

6. Simplified7.9

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

7. Final simplification7.9

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

Reproduce

herbie shell --seed 2019050 
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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