Average Error: 0.5 → 0.5
Time: 10.1s
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 r3996321 = 1.0;
        double r3996322 = x;
        double r3996323 = exp(r3996322);
        double r3996324 = r3996321 + r3996323;
        double r3996325 = log(r3996324);
        double r3996326 = y;
        double r3996327 = r3996322 * r3996326;
        double r3996328 = r3996325 - r3996327;
        return r3996328;
}
↓
double f(double x, double y) {
        double r3996329 = 1.0;
        double r3996330 = x;
        double r3996331 = exp(r3996330);
        double r3996332 = r3996329 + r3996331;
        double r3996333 = log(r3996332);
        double r3996334 = y;
        double r3996335 = r3996334 * r3996330;
        double r3996336 = r3996333 - r3996335;
        return r3996336;
}

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
\[\begin{array}{l} \mathbf{if}\;x \le 0:\\ \;\;\;\;\log \left(1 + e^{x}\right) - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\log \left(1 + e^{-x}\right) - \left(-x\right) \cdot \left(1 - y\right)\\ \end{array}\]

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 2019152 
(FPCore (x y)
  :name "Logistic regression 2"

  :herbie-target
  (if (<= x 0) (- (log (+ 1 (exp x))) (* x y)) (- (log (+ 1 (exp (- x)))) (* (- x) (- 1 y))))

  (- (log (+ 1 (exp x))) (* x y)))