Average Error: 0.6 → 0.6
Time: 3.6s
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 r160498 = 1.0;
        double r160499 = x;
        double r160500 = exp(r160499);
        double r160501 = r160498 + r160500;
        double r160502 = log(r160501);
        double r160503 = y;
        double r160504 = r160499 * r160503;
        double r160505 = r160502 - r160504;
        return r160505;
}
↓
double f(double x, double y) {
        double r160506 = 1.0;
        double r160507 = x;
        double r160508 = exp(r160507);
        double r160509 = r160506 + r160508;
        double r160510 = log(r160509);
        double r160511 = y;
        double r160512 = r160507 * r160511;
        double r160513 = r160510 - r160512;
        return r160513;
}

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
Target0.1
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;x \le 0.0:\\ \;\;\;\;\log \left(1 + e^{x}\right) - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\log \left(1 + e^{-x}\right) - \left(-x\right) \cdot \left(1 - y\right)\\ \end{array}\]

Derivation

  1. Initial program 0.6

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

  2. Final simplification0.6

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

Reproduce

herbie shell --seed 2020083 +o rules:numerics
(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)))