Average Error: 0.5 → 0.5
Time: 18.0s
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 r5037704 = 1.0;
        double r5037705 = x;
        double r5037706 = exp(r5037705);
        double r5037707 = r5037704 + r5037706;
        double r5037708 = log(r5037707);
        double r5037709 = y;
        double r5037710 = r5037705 * r5037709;
        double r5037711 = r5037708 - r5037710;
        return r5037711;
}
↓
double f(double x, double y) {
        double r5037712 = 1.0;
        double r5037713 = x;
        double r5037714 = exp(r5037713);
        double r5037715 = r5037712 + r5037714;
        double r5037716 = log(r5037715);
        double r5037717 = y;
        double r5037718 = r5037717 * r5037713;
        double r5037719 = r5037716 - r5037718;
        return r5037719;
}

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 2019130 
(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)))