Average Error: 0.5 → 0.5
Time: 17.4s
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 r5413015 = 1.0;
        double r5413016 = x;
        double r5413017 = exp(r5413016);
        double r5413018 = r5413015 + r5413017;
        double r5413019 = log(r5413018);
        double r5413020 = y;
        double r5413021 = r5413016 * r5413020;
        double r5413022 = r5413019 - r5413021;
        return r5413022;
}
↓
double f(double x, double y) {
        double r5413023 = 1.0;
        double r5413024 = x;
        double r5413025 = exp(r5413024);
        double r5413026 = r5413023 + r5413025;
        double r5413027 = log(r5413026);
        double r5413028 = y;
        double r5413029 = r5413028 * r5413024;
        double r5413030 = r5413027 - r5413029;
        return r5413030;
}

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
Target0.0
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 2019142 
(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)))