Average Error: 0.5 → 0.5
Time: 16.8s
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 r5859868 = 1.0;
        double r5859869 = x;
        double r5859870 = exp(r5859869);
        double r5859871 = r5859868 + r5859870;
        double r5859872 = log(r5859871);
        double r5859873 = y;
        double r5859874 = r5859869 * r5859873;
        double r5859875 = r5859872 - r5859874;
        return r5859875;
}
↓
double f(double x, double y) {
        double r5859876 = 1.0;
        double r5859877 = x;
        double r5859878 = exp(r5859877);
        double r5859879 = r5859876 + r5859878;
        double r5859880 = log(r5859879);
        double r5859881 = y;
        double r5859882 = r5859881 * r5859877;
        double r5859883 = r5859880 - r5859882;
        return r5859883;
}

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
Target0.0
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 2019141 
(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)))