Average Error: 0.5 → 0.5
Time: 14.2s
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 r4765685 = 1.0;
        double r4765686 = x;
        double r4765687 = exp(r4765686);
        double r4765688 = r4765685 + r4765687;
        double r4765689 = log(r4765688);
        double r4765690 = y;
        double r4765691 = r4765686 * r4765690;
        double r4765692 = r4765689 - r4765691;
        return r4765692;
}
↓
double f(double x, double y) {
        double r4765693 = 1.0;
        double r4765694 = x;
        double r4765695 = exp(r4765694);
        double r4765696 = r4765693 + r4765695;
        double r4765697 = log(r4765696);
        double r4765698 = y;
        double r4765699 = r4765698 * r4765694;
        double r4765700 = r4765697 - r4765699;
        return r4765700;
}

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

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(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)))