Average Error: 0.5 → 0.5
Time: 15.9s
Precision: 64
\[\log \left(1 + e^{x}\right) - x \cdot y\]
↓
\[\log \left(1 + e^{x}\right) - x \cdot y\]
\log \left(1 + e^{x}\right) - x \cdot y
↓
\log \left(1 + e^{x}\right) - x \cdot y
double f(double x, double y) {
        double r146525 = 1.0;
        double r146526 = x;
        double r146527 = exp(r146526);
        double r146528 = r146525 + r146527;
        double r146529 = log(r146528);
        double r146530 = y;
        double r146531 = r146526 * r146530;
        double r146532 = r146529 - r146531;
        return r146532;
}
↓
double f(double x, double y) {
        double r146533 = 1.0;
        double r146534 = x;
        double r146535 = exp(r146534);
        double r146536 = r146533 + r146535;
        double r146537 = log(r146536);
        double r146538 = y;
        double r146539 = r146534 * r146538;
        double r146540 = r146537 - r146539;
        return r146540;
}

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. Final simplification0.5

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

Reproduce

herbie shell --seed 2019323 
(FPCore (x y)
  :name "Logistic regression 2"
  :precision binary64

  :herbie-target
  (if (<= x 0.0) (- (log (+ 1 (exp x))) (* x y)) (- (log (+ 1 (exp (- x)))) (* (- x) (- 1 y))))

  (- (log (+ 1 (exp x))) (* x y)))