Average Error: 0.5 → 0.5
Time: 16.1s
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 r2755638 = 1.0;
        double r2755639 = x;
        double r2755640 = exp(r2755639);
        double r2755641 = r2755638 + r2755640;
        double r2755642 = log(r2755641);
        double r2755643 = y;
        double r2755644 = r2755639 * r2755643;
        double r2755645 = r2755642 - r2755644;
        return r2755645;
}
↓
double f(double x, double y) {
        double r2755646 = 1.0;
        double r2755647 = x;
        double r2755648 = exp(r2755647);
        double r2755649 = r2755646 + r2755648;
        double r2755650 = log(r2755649);
        double r2755651 = y;
        double r2755652 = r2755651 * r2755647;
        double r2755653 = r2755650 - r2755652;
        return r2755653;
}

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

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 2019155 
(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)))