Average Error: 0.5 → 0.4
Time: 40.0s
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 r11316373 = 1.0;
        double r11316374 = x;
        double r11316375 = exp(r11316374);
        double r11316376 = r11316373 + r11316375;
        double r11316377 = log(r11316376);
        double r11316378 = y;
        double r11316379 = r11316374 * r11316378;
        double r11316380 = r11316377 - r11316379;
        return r11316380;
}
↓
double f(double x, double y) {
        double r11316381 = x;
        double r11316382 = exp(r11316381);
        double r11316383 = log1p(r11316382);
        double r11316384 = y;
        double r11316385 = r11316384 * r11316381;
        double r11316386 = r11316383 - r11316385;
        return r11316386;
}

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

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

  3. Final simplification0.4

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

Reproduce

herbie shell --seed 2019128 +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)))