Average Error: 0.5 → 0.5
Time: 5.2s
Precision: 64
\[\log \left(1 + e^{x}\right) - x \cdot y\]
↓
\[\log \left(1 + e^{x}\right) - x \cdot y\]
\log \left(1 + e^{x}\right) - x \cdot y
↓
\log \left(1 + e^{x}\right) - x \cdot y
double f(double x, double y) {
        double r130199 = 1.0;
        double r130200 = x;
        double r130201 = exp(r130200);
        double r130202 = r130199 + r130201;
        double r130203 = log(r130202);
        double r130204 = y;
        double r130205 = r130200 * r130204;
        double r130206 = r130203 - r130205;
        return r130206;
}
↓
double f(double x, double y) {
        double r130207 = 1.0;
        double r130208 = x;
        double r130209 = exp(r130208);
        double r130210 = r130207 + r130209;
        double r130211 = log(r130210);
        double r130212 = y;
        double r130213 = r130208 * r130212;
        double r130214 = r130211 - r130213;
        return r130214;
}

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

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

Reproduce

herbie shell --seed 2020065 
(FPCore (x y)
  :name "Logistic regression 2"
  :precision binary64

  :herbie-target
  (if (<= x 0.0) (- (log (+ 1 (exp x))) (* x y)) (- (log (+ 1 (exp (- x)))) (* (- x) (- 1 y))))

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