Average Error: 0.5 → 0.5
Time: 6.0s
Precision: 64
\[\log \left(1 + e^{x}\right) - x \cdot y\]
↓
\[\sqrt[3]{{\left(\log \left(1 + e^{x}\right)\right)}^{3}} - x \cdot y\]
\log \left(1 + e^{x}\right) - x \cdot y
↓
\sqrt[3]{{\left(\log \left(1 + e^{x}\right)\right)}^{3}} - x \cdot y
double code(double x, double y) {
	return (log((1.0 + exp(x))) - (x * y));
}
↓
double code(double x, double y) {
	return (cbrt(pow(log((1.0 + exp(x))), 3.0)) - (x * y));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.5
Target0.1
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;x \le 0.0:\\ \;\;\;\;\log \left(1 + e^{x}\right) - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\log \left(1 + e^{-x}\right) - \left(-x\right) \cdot \left(1 - y\right)\\ \end{array}\]

Derivation

  1. Initial program 0.5

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

  3. Applied add-cbrt-cube0.5

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

  4. Simplified0.5

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

  5. Final simplification0.5

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

Reproduce

herbie shell --seed 2020078 
(FPCore (x y)
  :name "Logistic regression 2"
  :precision binary64

  :herbie-target
  (if (<= x 0.0) (- (log (+ 1 (exp x))) (* x y)) (- (log (+ 1 (exp (- x)))) (* (- x) (- 1 y))))

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