Average Error: 0.5 → 0.5
Time: 20.8s
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 r6668755 = 1.0;
        double r6668756 = x;
        double r6668757 = exp(r6668756);
        double r6668758 = r6668755 + r6668757;
        double r6668759 = log(r6668758);
        double r6668760 = y;
        double r6668761 = r6668756 * r6668760;
        double r6668762 = r6668759 - r6668761;
        return r6668762;
}
↓
double f(double x, double y) {
        double r6668763 = x;
        double r6668764 = exp(r6668763);
        double r6668765 = log1p(r6668764);
        double r6668766 = y;
        double r6668767 = r6668766 * r6668763;
        double r6668768 = r6668765 - r6668767;
        return r6668768;
}

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

Derivation

  1. Initial program 0.5

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

  2. Simplified0.5

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

  3. Final simplification0.5

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

Reproduce

herbie shell --seed 2019130 +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)))