Average Error: 29.4 → 0.0
Time: 23.7s
Precision: 64
\[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -0.007333471846547681:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \mathbf{elif}\;x \le 0.006247673021062525:\\ \;\;\;\;\left(\left(\frac{-1}{3} \cdot \left(x \cdot x\right)\right) \cdot x + x\right) + {x}^{5} \cdot \frac{2}{15}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \end{array}\]
\frac{2}{1 + e^{-2 \cdot x}} - 1
↓
\begin{array}{l}
\mathbf{if}\;x \le -0.007333471846547681:\\
\;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\

\mathbf{elif}\;x \le 0.006247673021062525:\\
\;\;\;\;\left(\left(\frac{-1}{3} \cdot \left(x \cdot x\right)\right) \cdot x + 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 r7153242 = 2.0;
        double r7153243 = 1.0;
        double r7153244 = -2.0;
        double r7153245 = x;
        double r7153246 = r7153244 * r7153245;
        double r7153247 = exp(r7153246);
        double r7153248 = r7153243 + r7153247;
        double r7153249 = r7153242 / r7153248;
        double r7153250 = r7153249 - r7153243;
        return r7153250;
}
↓
double f(double x, double __attribute__((unused)) y) {
        double r7153251 = x;
        double r7153252 = -0.007333471846547681;
        bool r7153253 = r7153251 <= r7153252;
        double r7153254 = 2.0;
        double r7153255 = -2.0;
        double r7153256 = r7153255 * r7153251;
        double r7153257 = exp(r7153256);
        double r7153258 = 1.0;
        double r7153259 = r7153257 + r7153258;
        double r7153260 = r7153254 / r7153259;
        double r7153261 = r7153260 - r7153258;
        double r7153262 = 0.006247673021062525;
        bool r7153263 = r7153251 <= r7153262;
        double r7153264 = -0.3333333333333333;
        double r7153265 = r7153251 * r7153251;
        double r7153266 = r7153264 * r7153265;
        double r7153267 = r7153266 * r7153251;
        double r7153268 = r7153267 + r7153251;
        double r7153269 = 5.0;
        double r7153270 = pow(r7153251, r7153269);
        double r7153271 = 0.13333333333333333;
        double r7153272 = r7153270 * r7153271;
        double r7153273 = r7153268 + r7153272;
        double r7153274 = r7153263 ? r7153273 : r7153261;
        double r7153275 = r7153253 ? r7153261 : r7153274;
        return r7153275;
}

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 < -0.007333471846547681 or 0.006247673021062525 < 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 -0.007333471846547681 < x < 0.006247673021062525

    1. Initial program 59.1

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

    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

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

  4. Final simplification0.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -0.007333471846547681:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \mathbf{elif}\;x \le 0.006247673021062525:\\ \;\;\;\;\left(\left(\frac{-1}{3} \cdot \left(x \cdot x\right)\right) \cdot x + x\right) + {x}^{5} \cdot \frac{2}{15}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{e^{-2 \cdot x} + 1} - 1\\ \end{array}\]

Reproduce

herbie shell --seed 2019104 
(FPCore (x y)
  :name "Logistic function from Lakshay Garg"
  (- (/ 2 (+ 1 (exp (* -2 x)))) 1))