Average Error: 0.6 → 0.5
Time: 15.7s
Precision: 64
\[\log \left(1 + e^{x}\right) - x \cdot y\]
↓
\[\mathsf{log1p}\left(e^{x}\right) - y \cdot x\]
\log \left(1 + e^{x}\right) - x \cdot y
↓
\mathsf{log1p}\left(e^{x}\right) - y \cdot x
double f(double x, double y) {
        double r2530633 = 1.0;
        double r2530634 = x;
        double r2530635 = exp(r2530634);
        double r2530636 = r2530633 + r2530635;
        double r2530637 = log(r2530636);
        double r2530638 = y;
        double r2530639 = r2530634 * r2530638;
        double r2530640 = r2530637 - r2530639;
        return r2530640;
}
↓
double f(double x, double y) {
        double r2530641 = x;
        double r2530642 = exp(r2530641);
        double r2530643 = log1p(r2530642);
        double r2530644 = y;
        double r2530645 = r2530644 * r2530641;
        double r2530646 = r2530643 - r2530645;
        return r2530646;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.6
Target0.1
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 0.6

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

  2. Simplified0.5

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

  3. Final simplification0.5

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

Reproduce

herbie shell --seed 2019151 +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)))