Average Error: 0.5 → 0.4
Time: 13.4s
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 r2385138 = 1.0;
        double r2385139 = x;
        double r2385140 = exp(r2385139);
        double r2385141 = r2385138 + r2385140;
        double r2385142 = log(r2385141);
        double r2385143 = y;
        double r2385144 = r2385139 * r2385143;
        double r2385145 = r2385142 - r2385144;
        return r2385145;
}
↓
double f(double x, double y) {
        double r2385146 = x;
        double r2385147 = exp(r2385146);
        double r2385148 = log1p(r2385147);
        double r2385149 = y;
        double r2385150 = r2385149 * r2385146;
        double r2385151 = r2385148 - r2385150;
        return r2385151;
}

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
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;x \le 0:\\ \;\;\;\;\log \left(1 + e^{x}\right) - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\log \left(1 + e^{-x}\right) - \left(-x\right) \cdot \left(1 - y\right)\\ \end{array}\]

Derivation

  1. Initial program 0.5

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

  2. Simplified0.4

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

  3. Final simplification0.4

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

Reproduce

herbie shell --seed 2019155 +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)))