Average Error: 0.5 → 0.5
Time: 48.6s
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 r17324863 = 1.0;
        double r17324864 = x;
        double r17324865 = exp(r17324864);
        double r17324866 = r17324863 + r17324865;
        double r17324867 = log(r17324866);
        double r17324868 = y;
        double r17324869 = r17324864 * r17324868;
        double r17324870 = r17324867 - r17324869;
        return r17324870;
}
↓
double f(double x, double y) {
        double r17324871 = 1.0;
        double r17324872 = x;
        double r17324873 = exp(r17324872);
        double r17324874 = r17324871 + r17324873;
        double r17324875 = log(r17324874);
        double r17324876 = y;
        double r17324877 = r17324876 * r17324872;
        double r17324878 = r17324875 - r17324877;
        return r17324878;
}

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 2019112 
(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)))