Average Error: 0.5 → 0.4
Time: 18.5s
Precision: 64
\[\log \left(1 + e^{x}\right) - x \cdot y\]
↓
\[\mathsf{log1p}\left(\left(e^{x}\right)\right) - y \cdot x\]
\log \left(1 + e^{x}\right) - x \cdot y
↓
\mathsf{log1p}\left(\left(e^{x}\right)\right) - y \cdot x
double f(double x, double y) {
        double r4908922 = 1.0;
        double r4908923 = x;
        double r4908924 = exp(r4908923);
        double r4908925 = r4908922 + r4908924;
        double r4908926 = log(r4908925);
        double r4908927 = y;
        double r4908928 = r4908923 * r4908927;
        double r4908929 = r4908926 - r4908928;
        return r4908929;
}
↓
double f(double x, double y) {
        double r4908930 = x;
        double r4908931 = exp(r4908930);
        double r4908932 = log1p(r4908931);
        double r4908933 = y;
        double r4908934 = r4908933 * r4908930;
        double r4908935 = r4908932 - r4908934;
        return r4908935;
}

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
Target0.0
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 0.5

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

  2. Simplified0.4

    \[\leadsto \color{blue}{\mathsf{log1p}\left(\left(e^{x}\right)\right) - y \cdot x}\]

  3. Final simplification0.4

    \[\leadsto \mathsf{log1p}\left(\left(e^{x}\right)\right) - y \cdot x\]

Reproduce

herbie shell --seed 2019133 +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)))