Average Error: 0.5 → 0.5
Time: 16.7s
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 r7283381 = 1.0;
        double r7283382 = x;
        double r7283383 = exp(r7283382);
        double r7283384 = r7283381 + r7283383;
        double r7283385 = log(r7283384);
        double r7283386 = y;
        double r7283387 = r7283382 * r7283386;
        double r7283388 = r7283385 - r7283387;
        return r7283388;
}
↓
double f(double x, double y) {
        double r7283389 = 1.0;
        double r7283390 = x;
        double r7283391 = exp(r7283390);
        double r7283392 = r7283389 + r7283391;
        double r7283393 = log(r7283392);
        double r7283394 = y;
        double r7283395 = r7283394 * r7283390;
        double r7283396 = r7283393 - r7283395;
        return r7283396;
}

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
Target0.0
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 2019179 
(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)))