Average Error: 0.6 → 0.6
Time: 4.0s
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 r153339 = 1.0;
        double r153340 = x;
        double r153341 = exp(r153340);
        double r153342 = r153339 + r153341;
        double r153343 = log(r153342);
        double r153344 = y;
        double r153345 = r153340 * r153344;
        double r153346 = r153343 - r153345;
        return r153346;
}
↓
double f(double x, double y) {
        double r153347 = 1.0;
        double r153348 = x;
        double r153349 = exp(r153348);
        double r153350 = r153347 + r153349;
        double r153351 = log(r153350);
        double r153352 = y;
        double r153353 = r153348 * r153352;
        double r153354 = r153351 - r153353;
        return r153354;
}

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 2020083 
(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)))