Average Error: 0.5 → 0.5
Time: 9.6s
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 r2414708 = 1.0;
        double r2414709 = x;
        double r2414710 = exp(r2414709);
        double r2414711 = r2414708 + r2414710;
        double r2414712 = log(r2414711);
        double r2414713 = y;
        double r2414714 = r2414709 * r2414713;
        double r2414715 = r2414712 - r2414714;
        return r2414715;
}
↓
double f(double x, double y) {
        double r2414716 = 1.0;
        double r2414717 = x;
        double r2414718 = exp(r2414717);
        double r2414719 = r2414716 + r2414718;
        double r2414720 = log(r2414719);
        double r2414721 = y;
        double r2414722 = r2414721 * r2414717;
        double r2414723 = r2414720 - r2414722;
        return r2414723;
}

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
\[\begin{array}{l} \mathbf{if}\;x \le 0:\\ \;\;\;\;\log \left(1 + e^{x}\right) - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\log \left(1 + e^{-x}\right) - \left(-x\right) \cdot \left(1 - y\right)\\ \end{array}\]

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 2019152 
(FPCore (x y)
  :name "Logistic regression 2"

  :herbie-target
  (if (<= x 0) (- (log (+ 1 (exp x))) (* x y)) (- (log (+ 1 (exp (- x)))) (* (- x) (- 1 y))))

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