Average Error: 29.4 → 0.0
Time: 47.2s
Precision: 64
\[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -0.006917970556878751:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \mathbf{elif}\;x \le 0.007657697468686109:\\ \;\;\;\;\left(\left(x \cdot x\right) \cdot \left(x \cdot \frac{-1}{3}\right) + x\right) + {x}^{5} \cdot \frac{2}{15}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \end{array}\]
\frac{2}{1 + e^{-2 \cdot x}} - 1
↓
\begin{array}{l}
\mathbf{if}\;x \le -0.006917970556878751:\\
\;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\

\mathbf{elif}\;x \le 0.007657697468686109:\\
\;\;\;\;\left(\left(x \cdot x\right) \cdot \left(x \cdot \frac{-1}{3}\right) + x\right) + {x}^{5} \cdot \frac{2}{15}\\

\mathbf{else}:\\
\;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\

\end{array}
double f(double x, double __attribute__((unused)) y) {
        double r10031253 = 2.0;
        double r10031254 = 1.0;
        double r10031255 = -2.0;
        double r10031256 = x;
        double r10031257 = r10031255 * r10031256;
        double r10031258 = exp(r10031257);
        double r10031259 = r10031254 + r10031258;
        double r10031260 = r10031253 / r10031259;
        double r10031261 = r10031260 - r10031254;
        return r10031261;
}
↓
double f(double x, double __attribute__((unused)) y) {
        double r10031262 = x;
        double r10031263 = -0.006917970556878751;
        bool r10031264 = r10031262 <= r10031263;
        double r10031265 = 2.0;
        double r10031266 = -2.0;
        double r10031267 = r10031266 * r10031262;
        double r10031268 = exp(r10031267);
        double r10031269 = 1.0;
        double r10031270 = r10031268 + r10031269;
        double r10031271 = r10031265 / r10031270;
        double r10031272 = r10031271 - r10031269;
        double r10031273 = 0.007657697468686109;
        bool r10031274 = r10031262 <= r10031273;
        double r10031275 = r10031262 * r10031262;
        double r10031276 = -0.3333333333333333;
        double r10031277 = r10031262 * r10031276;
        double r10031278 = r10031275 * r10031277;
        double r10031279 = r10031278 + r10031262;
        double r10031280 = 5.0;
        double r10031281 = pow(r10031262, r10031280);
        double r10031282 = 0.13333333333333333;
        double r10031283 = r10031281 * r10031282;
        double r10031284 = r10031279 + r10031283;
        double r10031285 = r10031274 ? r10031284 : r10031272;
        double r10031286 = r10031264 ? r10031272 : r10031285;
        return r10031286;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if x < -0.006917970556878751 or 0.007657697468686109 < x

    1. Initial program 0.0

      \[\frac{2}{1 + e^{-2 \cdot x}} - 1\]

    2. Taylor expanded around -inf 0.0

      \[\leadsto \color{blue}{2 \cdot \frac{1}{e^{-2 \cdot x} + 1} - 1}\]

    3. Simplified0.0

      \[\leadsto \color{blue}{\frac{2}{1 + e^{-2 \cdot x}} - 1}\]

    if -0.006917970556878751 < x < 0.007657697468686109

    1. Initial program 59.0

      \[\frac{2}{1 + e^{-2 \cdot x}} - 1\]

    2. Taylor expanded around 0 0.0

      \[\leadsto \color{blue}{\left(x + \frac{2}{15} \cdot {x}^{5}\right) - \frac{1}{3} \cdot {x}^{3}}\]

    3. Simplified0.0

      \[\leadsto \color{blue}{\left(\left(x \cdot x\right) \cdot \left(x \cdot \frac{-1}{3}\right) + x\right) + {x}^{5} \cdot \frac{2}{15}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -0.006917970556878751:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \mathbf{elif}\;x \le 0.007657697468686109:\\ \;\;\;\;\left(\left(x \cdot x\right) \cdot \left(x \cdot \frac{-1}{3}\right) + x\right) + {x}^{5} \cdot \frac{2}{15}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \end{array}\]

Reproduce

herbie shell --seed 2019125 
(FPCore (x y)
  :name "Logistic function from Lakshay Garg"
  (- (/ 2 (+ 1 (exp (* -2 x)))) 1))