Average Error: 0.6 → 0.6
Time: 10.3s
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 r21245257 = 1.0;
        double r21245258 = x;
        double r21245259 = exp(r21245258);
        double r21245260 = r21245257 + r21245259;
        double r21245261 = log(r21245260);
        double r21245262 = y;
        double r21245263 = r21245258 * r21245262;
        double r21245264 = r21245261 - r21245263;
        return r21245264;
}
↓
double f(double x, double y) {
        double r21245265 = 1.0;
        double r21245266 = x;
        double r21245267 = exp(r21245266);
        double r21245268 = r21245265 + r21245267;
        double r21245269 = log(r21245268);
        double r21245270 = y;
        double r21245271 = r21245270 * r21245266;
        double r21245272 = r21245269 - r21245271;
        return r21245272;
}

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

Derivation

  1. Initial program 0.6

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

  2. Final simplification0.6

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

Reproduce

herbie shell --seed 2019124 +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)))