Average Error: 0.6 → 0.6
Time: 18.2s
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 r4243565 = 1.0;
        double r4243566 = x;
        double r4243567 = exp(r4243566);
        double r4243568 = r4243565 + r4243567;
        double r4243569 = log(r4243568);
        double r4243570 = y;
        double r4243571 = r4243566 * r4243570;
        double r4243572 = r4243569 - r4243571;
        return r4243572;
}
↓
double f(double x, double y) {
        double r4243573 = 1.0;
        double r4243574 = x;
        double r4243575 = exp(r4243574);
        double r4243576 = r4243573 + r4243575;
        double r4243577 = log(r4243576);
        double r4243578 = r4243577 * r4243577;
        double r4243579 = r4243577 * r4243578;
        double r4243580 = cbrt(r4243579);
        double r4243581 = y;
        double r4243582 = r4243581 * r4243574;
        double r4243583 = r4243580 - r4243582;
        return r4243583;
}

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
Target0.0
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. Using strategy rm

  3. Applied add-cbrt-cube0.6

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

  4. Final simplification0.6

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

Reproduce

herbie shell --seed 2019129 
(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)))