Average Error: 0.5 → 0.5
Time: 10.7s
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 r3887776 = 1.0;
        double r3887777 = x;
        double r3887778 = exp(r3887777);
        double r3887779 = r3887776 + r3887778;
        double r3887780 = log(r3887779);
        double r3887781 = y;
        double r3887782 = r3887777 * r3887781;
        double r3887783 = r3887780 - r3887782;
        return r3887783;
}
↓
double f(double x, double y) {
        double r3887784 = 1.0;
        double r3887785 = x;
        double r3887786 = exp(r3887785);
        double r3887787 = r3887784 + r3887786;
        double r3887788 = log(r3887787);
        double r3887789 = y;
        double r3887790 = r3887789 * r3887785;
        double r3887791 = r3887788 - r3887790;
        return r3887791;
}

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 2019135 
(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)))