Average Error: 0.5 → 0.5
Time: 15.3s
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 r5411559 = 1.0;
        double r5411560 = x;
        double r5411561 = exp(r5411560);
        double r5411562 = r5411559 + r5411561;
        double r5411563 = log(r5411562);
        double r5411564 = y;
        double r5411565 = r5411560 * r5411564;
        double r5411566 = r5411563 - r5411565;
        return r5411566;
}
↓
double f(double x, double y) {
        double r5411567 = 1.0;
        double r5411568 = x;
        double r5411569 = exp(r5411568);
        double r5411570 = r5411567 + r5411569;
        double r5411571 = log(r5411570);
        double r5411572 = y;
        double r5411573 = r5411572 * r5411568;
        double r5411574 = r5411571 - r5411573;
        return r5411574;
}

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 +o rules:numerics
(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)))