Average Error: 0.4 → 0.4
Time: 50.8s
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 r22607296 = 1.0;
        double r22607297 = x;
        double r22607298 = exp(r22607297);
        double r22607299 = r22607296 + r22607298;
        double r22607300 = log(r22607299);
        double r22607301 = y;
        double r22607302 = r22607297 * r22607301;
        double r22607303 = r22607300 - r22607302;
        return r22607303;
}
↓
double f(double x, double y) {
        double r22607304 = 1.0;
        double r22607305 = x;
        double r22607306 = exp(r22607305);
        double r22607307 = r22607304 + r22607306;
        double r22607308 = log(r22607307);
        double r22607309 = y;
        double r22607310 = r22607309 * r22607305;
        double r22607311 = r22607308 - r22607310;
        return r22607311;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.4
Target0.1
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;x \le 0:\\ \;\;\;\;\log \left(1 + e^{x}\right) - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\log \left(1 + e^{-x}\right) - \left(-x\right) \cdot \left(1 - y\right)\\ \end{array}\]

Derivation

  1. Initial program 0.4

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

  2. Final simplification0.4

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

Reproduce

herbie shell --seed 2019104 
(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)))