Average Error: 0.5 → 0.5
Time: 4.6s
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 r137820 = 1.0;
        double r137821 = x;
        double r137822 = exp(r137821);
        double r137823 = r137820 + r137822;
        double r137824 = log(r137823);
        double r137825 = y;
        double r137826 = r137821 * r137825;
        double r137827 = r137824 - r137826;
        return r137827;
}
↓
double f(double x, double y) {
        double r137828 = 1.0;
        double r137829 = x;
        double r137830 = exp(r137829);
        double r137831 = r137828 + r137830;
        double r137832 = log(r137831);
        double r137833 = y;
        double r137834 = r137829 * r137833;
        double r137835 = r137832 - r137834;
        return r137835;
}

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 2020057 
(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)))