Average Error: 0.5 → 0.5
Time: 4.3s
Precision: 64
\[\log \left(1 + e^{x}\right) - x \cdot y\]
↓
\[\log \left(1 + e^{x}\right) - x \cdot y\]
\log \left(1 + e^{x}\right) - x \cdot y
↓
\log \left(1 + e^{x}\right) - x \cdot y
double f(double x, double y) {
        double r128281 = 1.0;
        double r128282 = x;
        double r128283 = exp(r128282);
        double r128284 = r128281 + r128283;
        double r128285 = log(r128284);
        double r128286 = y;
        double r128287 = r128282 * r128286;
        double r128288 = r128285 - r128287;
        return r128288;
}
↓
double f(double x, double y) {
        double r128289 = 1.0;
        double r128290 = x;
        double r128291 = exp(r128290);
        double r128292 = r128289 + r128291;
        double r128293 = log(r128292);
        double r128294 = y;
        double r128295 = r128290 * r128294;
        double r128296 = r128293 - r128295;
        return r128296;
}

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

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

Reproduce

herbie shell --seed 2020002 
(FPCore (x y)
  :name "Logistic regression 2"
  :precision binary64

  :herbie-target
  (if (<= x 0.0) (- (log (+ 1 (exp x))) (* x y)) (- (log (+ 1 (exp (- x)))) (* (- x) (- 1 y))))

  (- (log (+ 1 (exp x))) (* x y)))