Average Error: 0.6 → 0.6
Time: 44.9s
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 r25076761 = 1.0;
        double r25076762 = x;
        double r25076763 = exp(r25076762);
        double r25076764 = r25076761 + r25076763;
        double r25076765 = log(r25076764);
        double r25076766 = y;
        double r25076767 = r25076762 * r25076766;
        double r25076768 = r25076765 - r25076767;
        return r25076768;
}
↓
double f(double x, double y) {
        double r25076769 = 1.0;
        double r25076770 = x;
        double r25076771 = exp(r25076770);
        double r25076772 = r25076769 + r25076771;
        double r25076773 = log(r25076772);
        double r25076774 = y;
        double r25076775 = r25076774 * r25076770;
        double r25076776 = r25076773 - r25076775;
        return r25076776;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.6
Target0.1
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;x \le 0:\\ \;\;\;\;\log \left(1 + e^{x}\right) - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\log \left(1 + e^{-x}\right) - \left(-x\right) \cdot \left(1 - y\right)\\ \end{array}\]

Derivation

  1. Initial program 0.6

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

  2. Final simplification0.6

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

Reproduce

herbie shell --seed 2019124 
(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)))