Average Error: 0.4 → 0.4
Time: 19.6s
Precision: 64
Internal Precision: 576
\[\log \left(1 + e^{x}\right) - x \cdot y\]
↓
\[e^{\left(\sqrt[3]{\log \left(\log \left(1 + e^{x}\right)\right)} \cdot \sqrt[3]{\log \left(\log \left(1 + e^{x}\right)\right)}\right) \cdot \sqrt[3]{\log \left(\log \left(1 + e^{x}\right)\right)}} - x \cdot y\]

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.4
Target0.0
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;x \le 0:\\ \;\;\;\;\log \left(1 + e^{x}\right) - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\log \left(1 + e^{-x}\right) - \left(-x\right) \cdot \left(1 - y\right)\\ \end{array}\]

Derivation

  1. Initial program 0.4

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

  3. Applied add-exp-log0.4

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

  5. Applied add-cube-cbrt0.4

    \[\leadsto e^{\color{blue}{\left(\sqrt[3]{\log \left(\log \left(1 + e^{x}\right)\right)} \cdot \sqrt[3]{\log \left(\log \left(1 + e^{x}\right)\right)}\right) \cdot \sqrt[3]{\log \left(\log \left(1 + e^{x}\right)\right)}}} - x \cdot y\]

Runtime

Time bar (total: 19.6s)Debug logProfile

herbie shell --seed 2018167 
(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)))