Average Error: 0.6 → 0.6
Time: 4.1s
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 r184281 = 1.0;
        double r184282 = x;
        double r184283 = exp(r184282);
        double r184284 = r184281 + r184283;
        double r184285 = log(r184284);
        double r184286 = y;
        double r184287 = r184282 * r184286;
        double r184288 = r184285 - r184287;
        return r184288;
}
↓
double f(double x, double y) {
        double r184289 = 1.0;
        double r184290 = x;
        double r184291 = exp(r184290);
        double r184292 = r184289 + r184291;
        double r184293 = log(r184292);
        double r184294 = y;
        double r184295 = r184290 * r184294;
        double r184296 = r184293 - r184295;
        return r184296;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.6
Target0.1
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;x \le 0.0:\\ \;\;\;\;\log \left(1 + e^{x}\right) - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\log \left(1 + e^{-x}\right) - \left(-x\right) \cdot \left(1 - y\right)\\ \end{array}\]

Derivation

  1. Initial program 0.6

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

  2. Final simplification0.6

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

Reproduce

herbie shell --seed 2020059 
(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)))