Average Error: 0.5 → 0.5
Time: 24.4s
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 r81841 = 1.0;
        double r81842 = x;
        double r81843 = exp(r81842);
        double r81844 = r81841 + r81843;
        double r81845 = log(r81844);
        double r81846 = y;
        double r81847 = r81842 * r81846;
        double r81848 = r81845 - r81847;
        return r81848;
}
↓
double f(double x, double y) {
        double r81849 = 1.0;
        double r81850 = x;
        double r81851 = exp(r81850);
        double r81852 = r81849 + r81851;
        double r81853 = log(r81852);
        double r81854 = y;
        double r81855 = r81850 * r81854;
        double r81856 = r81853 - r81855;
        return r81856;
}

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 2019323 
(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)))