Average Error: 0.5 → 0.5
Time: 6.6s
Precision: 64
Internal precision: 640
\[\log \left(1 + e^{x}\right) - x \cdot y\]
⬇
\[\log \left(1 + e^{x}\right) - x \cdot y\]

Error

Bits error versus x

Bits error versus y

Target

Original0.5
Comparison0.1
Herbie0.5
\[ \begin{array}{l} \mathbf{if}\;x \le 0:\\ \;\;\;\;\log \left(1 + e^{x}\right) - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\log \left(1 + e^{-x}\right) - \left(-x\right) \cdot \left(1 - y\right)\\ \end{array} \]

Derivation

  1. Initial program 0.5

    \[\log \left(1 + e^{x}\right) - x \cdot y\]
  2. Removed slow pow expressions

Runtime

Time bar (total: 6.6s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1064524629 4159152179 2999149171 575749698 4006532819 692958815)'
(FPCore (x y)
  :name "Logistic regression 2"

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

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