Average Error: 0.5 → 0.5
Time: 32.2s
Precision: 64
\[\log \left(1 + e^{x}\right) - x \cdot y\]
↓
\[\log \left(e^{x} + 1\right) - y \cdot x\]
\log \left(1 + e^{x}\right) - x \cdot y
↓
\log \left(e^{x} + 1\right) - y \cdot x
double f(double x, double y) {
        double r4777535 = 1.0;
        double r4777536 = x;
        double r4777537 = exp(r4777536);
        double r4777538 = r4777535 + r4777537;
        double r4777539 = log(r4777538);
        double r4777540 = y;
        double r4777541 = r4777536 * r4777540;
        double r4777542 = r4777539 - r4777541;
        return r4777542;
}
↓
double f(double x, double y) {
        double r4777543 = x;
        double r4777544 = exp(r4777543);
        double r4777545 = 1.0;
        double r4777546 = r4777544 + r4777545;
        double r4777547 = log(r4777546);
        double r4777548 = y;
        double r4777549 = r4777548 * r4777543;
        double r4777550 = r4777547 - r4777549;
        return r4777550;
}

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. Taylor expanded around inf 0.5

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

  3. Final simplification0.5

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y)
  :name "Logistic regression 2"

  :herbie-target
  (if (<= x 0.0) (- (log (+ 1.0 (exp x))) (* x y)) (- (log (+ 1.0 (exp (- x)))) (* (- x) (- 1.0 y))))

  (- (log (+ 1.0 (exp x))) (* x y)))