Average Error: 0.5 → 0.5
Time: 15.5s
Precision: 64
\[\log \left(1 + e^{x}\right) - x \cdot y\]
↓
\[\sqrt[3]{\log \left(1 + e^{x}\right) \cdot \left(\log \left(1 + e^{x}\right) \cdot \log \left(1 + e^{x}\right)\right)} - y \cdot x\]
\log \left(1 + e^{x}\right) - x \cdot y
↓
\sqrt[3]{\log \left(1 + e^{x}\right) \cdot \left(\log \left(1 + e^{x}\right) \cdot \log \left(1 + e^{x}\right)\right)} - y \cdot x
double f(double x, double y) {
        double r6431646 = 1.0;
        double r6431647 = x;
        double r6431648 = exp(r6431647);
        double r6431649 = r6431646 + r6431648;
        double r6431650 = log(r6431649);
        double r6431651 = y;
        double r6431652 = r6431647 * r6431651;
        double r6431653 = r6431650 - r6431652;
        return r6431653;
}
↓
double f(double x, double y) {
        double r6431654 = 1.0;
        double r6431655 = x;
        double r6431656 = exp(r6431655);
        double r6431657 = r6431654 + r6431656;
        double r6431658 = log(r6431657);
        double r6431659 = r6431658 * r6431658;
        double r6431660 = r6431658 * r6431659;
        double r6431661 = cbrt(r6431660);
        double r6431662 = y;
        double r6431663 = r6431662 * r6431655;
        double r6431664 = r6431661 - r6431663;
        return r6431664;
}

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. Using strategy rm

  3. Applied add-cbrt-cube0.5

    \[\leadsto \color{blue}{\sqrt[3]{\left(\log \left(1 + e^{x}\right) \cdot \log \left(1 + e^{x}\right)\right) \cdot \log \left(1 + e^{x}\right)}} - x \cdot y\]

  4. Final simplification0.5

    \[\leadsto \sqrt[3]{\log \left(1 + e^{x}\right) \cdot \left(\log \left(1 + e^{x}\right) \cdot \log \left(1 + e^{x}\right)\right)} - y \cdot x\]

Reproduce

herbie shell --seed 2019172 
(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)))