Average Error: 0.5 → 0.5
Time: 15.8s
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 r6233751 = 1.0;
        double r6233752 = x;
        double r6233753 = exp(r6233752);
        double r6233754 = r6233751 + r6233753;
        double r6233755 = log(r6233754);
        double r6233756 = y;
        double r6233757 = r6233752 * r6233756;
        double r6233758 = r6233755 - r6233757;
        return r6233758;
}
↓
double f(double x, double y) {
        double r6233759 = 1.0;
        double r6233760 = x;
        double r6233761 = exp(r6233760);
        double r6233762 = r6233759 + r6233761;
        double r6233763 = log(r6233762);
        double r6233764 = y;
        double r6233765 = r6233764 * r6233760;
        double r6233766 = r6233763 - r6233765;
        return r6233766;
}

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 2019172 
(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)))