Average Error: 0.4 → 0.4
Time: 14.9s
Precision: 64
\[\log \left(1 + e^{x}\right) - x \cdot y\]
↓
\[\log_* (1 + e^{x}) - y \cdot x\]
\log \left(1 + e^{x}\right) - x \cdot y
↓
\log_* (1 + e^{x}) - y \cdot x
double f(double x, double y) {
        double r3219693 = 1.0;
        double r3219694 = x;
        double r3219695 = exp(r3219694);
        double r3219696 = r3219693 + r3219695;
        double r3219697 = log(r3219696);
        double r3219698 = y;
        double r3219699 = r3219694 * r3219698;
        double r3219700 = r3219697 - r3219699;
        return r3219700;
}
↓
double f(double x, double y) {
        double r3219701 = x;
        double r3219702 = exp(r3219701);
        double r3219703 = log1p(r3219702);
        double r3219704 = y;
        double r3219705 = r3219704 * r3219701;
        double r3219706 = r3219703 - r3219705;
        return r3219706;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.4
Target0.1
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;x \le 0:\\ \;\;\;\;\log \left(1 + e^{x}\right) - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\log \left(1 + e^{-x}\right) - \left(-x\right) \cdot \left(1 - y\right)\\ \end{array}\]

Derivation

  1. Initial program 0.4

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

  2. Simplified0.4

    \[\leadsto \color{blue}{\log_* (1 + e^{x}) - y \cdot x}\]

  3. Final simplification0.4

    \[\leadsto \log_* (1 + e^{x}) - y \cdot x\]

Reproduce

herbie shell --seed 2019107 +o rules:numerics
(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)))