Average Error: 0.6 → 0.6
Time: 4.9s
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 r229804 = 1.0;
        double r229805 = x;
        double r229806 = exp(r229805);
        double r229807 = r229804 + r229806;
        double r229808 = log(r229807);
        double r229809 = y;
        double r229810 = r229805 * r229809;
        double r229811 = r229808 - r229810;
        return r229811;
}
↓
double f(double x, double y) {
        double r229812 = 1.0;
        double r229813 = x;
        double r229814 = exp(r229813);
        double r229815 = r229812 + r229814;
        double r229816 = log(r229815);
        double r229817 = y;
        double r229818 = r229813 * r229817;
        double r229819 = r229816 - r229818;
        return r229819;
}

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 2020046 
(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)))