Average Error: 0.5 → 0.5
Time: 18.2s
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 r6066931 = 1.0;
        double r6066932 = x;
        double r6066933 = exp(r6066932);
        double r6066934 = r6066931 + r6066933;
        double r6066935 = log(r6066934);
        double r6066936 = y;
        double r6066937 = r6066932 * r6066936;
        double r6066938 = r6066935 - r6066937;
        return r6066938;
}
↓
double f(double x, double y) {
        double r6066939 = 1.0;
        double r6066940 = x;
        double r6066941 = exp(r6066940);
        double r6066942 = r6066939 + r6066941;
        double r6066943 = log(r6066942);
        double r6066944 = y;
        double r6066945 = r6066944 * r6066940;
        double r6066946 = r6066943 - r6066945;
        return r6066946;
}

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)))