Average Error: 0.5 → 0.5
Time: 17.0s
Precision: 64
\[\log \left(1 + e^{x}\right) - x \cdot y\]
↓
\[\log \left(1 + e^{x}\right) - y \cdot x\]
\log \left(1 + e^{x}\right) - x \cdot y
↓
\log \left(1 + e^{x}\right) - y \cdot x
double f(double x, double y) {
        double r4735018 = 1.0;
        double r4735019 = x;
        double r4735020 = exp(r4735019);
        double r4735021 = r4735018 + r4735020;
        double r4735022 = log(r4735021);
        double r4735023 = y;
        double r4735024 = r4735019 * r4735023;
        double r4735025 = r4735022 - r4735024;
        return r4735025;
}
↓
double f(double x, double y) {
        double r4735026 = 1.0;
        double r4735027 = x;
        double r4735028 = exp(r4735027);
        double r4735029 = r4735026 + r4735028;
        double r4735030 = log(r4735029);
        double r4735031 = y;
        double r4735032 = r4735031 * r4735027;
        double r4735033 = r4735030 - r4735032;
        return r4735033;
}

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

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

Reproduce

herbie shell --seed 2019171 
(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)))