Average Error: 0.5 → 0.5
Time: 3.2s
Precision: 64
\[\log \left(1 + e^{x}\right) - x \cdot y\]
↓
\[\log \left(1 + e^{x}\right) - x \cdot y\]
\log \left(1 + e^{x}\right) - x \cdot y
↓
\log \left(1 + e^{x}\right) - x \cdot y
double f(double x, double y) {
        double r157923 = 1.0;
        double r157924 = x;
        double r157925 = exp(r157924);
        double r157926 = r157923 + r157925;
        double r157927 = log(r157926);
        double r157928 = y;
        double r157929 = r157924 * r157928;
        double r157930 = r157927 - r157929;
        return r157930;
}
↓
double f(double x, double y) {
        double r157931 = 1.0;
        double r157932 = x;
        double r157933 = exp(r157932);
        double r157934 = r157931 + r157933;
        double r157935 = log(r157934);
        double r157936 = y;
        double r157937 = r157932 * r157936;
        double r157938 = r157935 - r157937;
        return r157938;
}

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
\[\begin{array}{l} \mathbf{if}\;x \le 0.0:\\ \;\;\;\;\log \left(1 + e^{x}\right) - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\log \left(1 + e^{-x}\right) - \left(-x\right) \cdot \left(1 - y\right)\\ \end{array}\]

Derivation

  1. Initial program 0.5

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

  2. Final simplification0.5

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

Reproduce

herbie shell --seed 2020089 +o rules:numerics
(FPCore (x y)
  :name "Logistic regression 2"
  :precision binary64

  :herbie-target
  (if (<= x 0.0) (- (log (+ 1 (exp x))) (* x y)) (- (log (+ 1 (exp (- x)))) (* (- x) (- 1 y))))

  (- (log (+ 1 (exp x))) (* x y)))