Average Error: 0.5 → 0.5
Time: 12.9s
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 r6131803 = 1.0;
        double r6131804 = x;
        double r6131805 = exp(r6131804);
        double r6131806 = r6131803 + r6131805;
        double r6131807 = log(r6131806);
        double r6131808 = y;
        double r6131809 = r6131804 * r6131808;
        double r6131810 = r6131807 - r6131809;
        return r6131810;
}
↓
double f(double x, double y) {
        double r6131811 = 1.0;
        double r6131812 = x;
        double r6131813 = exp(r6131812);
        double r6131814 = r6131811 + r6131813;
        double r6131815 = log(r6131814);
        double r6131816 = r6131815 * r6131815;
        double r6131817 = r6131815 * r6131816;
        double r6131818 = cbrt(r6131817);
        double r6131819 = y;
        double r6131820 = r6131819 * r6131812;
        double r6131821 = r6131818 - r6131820;
        return r6131821;
}

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)))