Average Error: 0.4 → 0.4
Time: 9.6s
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 r115659 = 1.0;
        double r115660 = x;
        double r115661 = exp(r115660);
        double r115662 = r115659 + r115661;
        double r115663 = log(r115662);
        double r115664 = y;
        double r115665 = r115660 * r115664;
        double r115666 = r115663 - r115665;
        return r115666;
}
↓
double f(double x, double y) {
        double r115667 = 1.0;
        double r115668 = x;
        double r115669 = exp(r115668);
        double r115670 = r115667 + r115669;
        double r115671 = log(r115670);
        double r115672 = y;
        double r115673 = r115668 * r115672;
        double r115674 = r115671 - r115673;
        return r115674;
}

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
Target0.0
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;x \le 0.0:\\ \;\;\;\;\log \left(1 + e^{x}\right) - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\log \left(1 + e^{-x}\right) - \left(-x\right) \cdot \left(1 - y\right)\\ \end{array}\]

Derivation

  1. Initial program 0.4

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

  2. Final simplification0.4

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

Reproduce

herbie shell --seed 2019291 
(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)))