Average Error: 0.5 → 0.5
Time: 17.1s
Precision: 64
\[\log \left(1 + e^{x}\right) - x \cdot y\]
↓
\[\log \left(1 + e^{x}\right) - x \cdot y\]
\log \left(1 + e^{x}\right) - x \cdot y
↓
\log \left(1 + e^{x}\right) - x \cdot y
double f(double x, double y) {
        double r135686 = 1.0;
        double r135687 = x;
        double r135688 = exp(r135687);
        double r135689 = r135686 + r135688;
        double r135690 = log(r135689);
        double r135691 = y;
        double r135692 = r135687 * r135691;
        double r135693 = r135690 - r135692;
        return r135693;
}
↓
double f(double x, double y) {
        double r135694 = 1.0;
        double r135695 = x;
        double r135696 = exp(r135695);
        double r135697 = r135694 + r135696;
        double r135698 = log(r135697);
        double r135699 = y;
        double r135700 = r135695 * r135699;
        double r135701 = r135698 - r135700;
        return r135701;
}

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. Final simplification0.5

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

Reproduce

herbie shell --seed 2019323 
(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)))