Average Error: 0.5 → 0.5
Time: 14.0s
Precision: 64
\[\log \left(1 + e^{x}\right) - x \cdot y\]
↓
\[\log \left(1 + e^{x}\right) - y \cdot x\]
\log \left(1 + e^{x}\right) - x \cdot y
↓
\log \left(1 + e^{x}\right) - y \cdot x
double f(double x, double y) {
        double r5182280 = 1.0;
        double r5182281 = x;
        double r5182282 = exp(r5182281);
        double r5182283 = r5182280 + r5182282;
        double r5182284 = log(r5182283);
        double r5182285 = y;
        double r5182286 = r5182281 * r5182285;
        double r5182287 = r5182284 - r5182286;
        return r5182287;
}
↓
double f(double x, double y) {
        double r5182288 = 1.0;
        double r5182289 = x;
        double r5182290 = exp(r5182289);
        double r5182291 = r5182288 + r5182290;
        double r5182292 = log(r5182291);
        double r5182293 = y;
        double r5182294 = r5182293 * r5182289;
        double r5182295 = r5182292 - r5182294;
        return r5182295;
}

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
\[\begin{array}{l} \mathbf{if}\;x \le 0.0:\\ \;\;\;\;\log \left(1 + e^{x}\right) - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\log \left(1 + e^{-x}\right) - \left(-x\right) \cdot \left(1 - y\right)\\ \end{array}\]

Derivation

  1. Initial program 0.5

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

  2. Final simplification0.5

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x y)
  :name "Logistic regression 2"

  :herbie-target
  (if (<= x 0.0) (- (log (+ 1.0 (exp x))) (* x y)) (- (log (+ 1.0 (exp (- x)))) (* (- x) (- 1.0 y))))

  (- (log (+ 1.0 (exp x))) (* x y)))