Average Error: 0.6 → 0.6
Time: 7.2s
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 r187546 = 1.0;
        double r187547 = x;
        double r187548 = exp(r187547);
        double r187549 = r187546 + r187548;
        double r187550 = log(r187549);
        double r187551 = y;
        double r187552 = r187547 * r187551;
        double r187553 = r187550 - r187552;
        return r187553;
}
↓
double f(double x, double y) {
        double r187554 = 1.0;
        double r187555 = x;
        double r187556 = exp(r187555);
        double r187557 = r187554 + r187556;
        double r187558 = log(r187557);
        double r187559 = y;
        double r187560 = r187555 * r187559;
        double r187561 = r187558 - r187560;
        return r187561;
}

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 2019322 
(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)))