Average Error: 0.5 → 0.5
Time: 15.5s
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 r2544132 = 1.0;
        double r2544133 = x;
        double r2544134 = exp(r2544133);
        double r2544135 = r2544132 + r2544134;
        double r2544136 = log(r2544135);
        double r2544137 = y;
        double r2544138 = r2544133 * r2544137;
        double r2544139 = r2544136 - r2544138;
        return r2544139;
}
↓
double f(double x, double y) {
        double r2544140 = x;
        double r2544141 = exp(r2544140);
        double r2544142 = log1p(r2544141);
        double r2544143 = y;
        double r2544144 = r2544143 * r2544140;
        double r2544145 = r2544142 - r2544144;
        return r2544145;
}

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
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;x \le 0:\\ \;\;\;\;\log \left(1 + e^{x}\right) - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\log \left(1 + e^{-x}\right) - \left(-x\right) \cdot \left(1 - y\right)\\ \end{array}\]

Derivation

  1. Initial program 0.5

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

  2. Simplified0.5

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

  3. Final simplification0.5

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

Reproduce

herbie shell --seed 2019153 +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)))