Average Error: 0.5 → 0.5
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 r184400 = 1.0;
        double r184401 = x;
        double r184402 = exp(r184401);
        double r184403 = r184400 + r184402;
        double r184404 = log(r184403);
        double r184405 = y;
        double r184406 = r184401 * r184405;
        double r184407 = r184404 - r184406;
        return r184407;
}
↓
double f(double x, double y) {
        double r184408 = 1.0;
        double r184409 = x;
        double r184410 = exp(r184409);
        double r184411 = r184408 + r184410;
        double r184412 = log(r184411);
        double r184413 = y;
        double r184414 = r184409 * r184413;
        double r184415 = r184412 - r184414;
        return r184415;
}

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
Target0.0
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 2020049 
(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)))