Average Error: 0.6 → 0.6
Time: 4.2s
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 r168248 = 1.0;
        double r168249 = x;
        double r168250 = exp(r168249);
        double r168251 = r168248 + r168250;
        double r168252 = log(r168251);
        double r168253 = y;
        double r168254 = r168249 * r168253;
        double r168255 = r168252 - r168254;
        return r168255;
}
↓
double f(double x, double y) {
        double r168256 = 1.0;
        double r168257 = x;
        double r168258 = exp(r168257);
        double r168259 = r168256 + r168258;
        double r168260 = log(r168259);
        double r168261 = y;
        double r168262 = r168257 * r168261;
        double r168263 = r168260 - r168262;
        return r168263;
}

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
Target0.1
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 2020059 +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)))