Average Error: 0.6 → 0.6
Time: 3.3s
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 r189416 = 1.0;
        double r189417 = x;
        double r189418 = exp(r189417);
        double r189419 = r189416 + r189418;
        double r189420 = log(r189419);
        double r189421 = y;
        double r189422 = r189417 * r189421;
        double r189423 = r189420 - r189422;
        return r189423;
}
↓
double f(double x, double y) {
        double r189424 = 1.0;
        double r189425 = x;
        double r189426 = exp(r189425);
        double r189427 = r189424 + r189426;
        double r189428 = log(r189427);
        double r189429 = y;
        double r189430 = r189425 * r189429;
        double r189431 = r189428 - r189430;
        return r189431;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.6
Target0.0
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;x \le 0.0:\\ \;\;\;\;\log \left(1 + e^{x}\right) - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\log \left(1 + e^{-x}\right) - \left(-x\right) \cdot \left(1 - y\right)\\ \end{array}\]

Derivation

  1. Initial program 0.6

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

  2. Final simplification0.6

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

Reproduce

herbie shell --seed 2020027 
(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)))