Error

Target

Derivation

1. Initial program 0.5

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

2. Initial simplification0.4

   \[\leadsto \log_* (1 + e^{x}) - y \cdot x\]
3. Using strategy rm

4. Applied *-un-lft-identity0.4

   \[\leadsto \color{blue}{1 \cdot \log_* (1 + e^{x})} - y \cdot x\]

5. Applied prod-diff0.4

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

6. Simplified0.4

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

8. Applied add-sqr-sqrt1.0

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

9. Applied prod-diff1.0

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

10. Simplified0.4

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

11. Final simplification0.4

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

Runtime

Time bar (total: 8.1s)Debug logProfile

herbie shell --seed 2018339 +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)))