Average Error: 0.5 → 0.5
Time: 4.9s
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 r161312 = 1.0;
        double r161313 = x;
        double r161314 = exp(r161313);
        double r161315 = r161312 + r161314;
        double r161316 = log(r161315);
        double r161317 = y;
        double r161318 = r161313 * r161317;
        double r161319 = r161316 - r161318;
        return r161319;
}
↓
double f(double x, double y) {
        double r161320 = 1.0;
        double r161321 = x;
        double r161322 = exp(r161321);
        double r161323 = r161320 + r161322;
        double r161324 = log(r161323);
        double r161325 = y;
        double r161326 = r161321 * r161325;
        double r161327 = r161324 - r161326;
        return r161327;
}

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 2020020 +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)))