Error

Target

Derivation

1. Initial program 0.5

   \[\log \left(1 + e^{x}\right) - x \cdot y\]
2. Using strategy rm

3. Applied add-sqr-sqrt1.3

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

4. Applied log-prod1.0

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

5. Applied associate--l+1.0

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

7. Applied add-sqr-sqrt1.0

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

8. Applied fma-def0.5

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

9. Final simplification0.5

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

Reproduce

herbie shell --seed 2019004 +o rules:numerics
(FPCore (x y)
  :name "Logistic regression 2"

  :herbie-target
  (if (<= x 0) (- (log (+ 1 (exp x))) (* x y)) (- (log (+ 1 (exp (- x)))) (* (- x) (- 1 y))))

  (- (log (+ 1 (exp x))) (* x y)))

Details

Time bar (total: 22.1s)Debug log