Average Error: 29.7 → 0.0
Time: 14.2s
Precision: 64
\[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -0.007072373127510205:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \mathbf{elif}\;x \le 0.006564839170329155:\\ \;\;\;\;\left(x - \frac{1}{3} \cdot \left(x \cdot \left(x \cdot x\right)\right)\right) + {x}^{5} \cdot \frac{2}{15}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \end{array}\]
\frac{2}{1 + e^{-2 \cdot x}} - 1
↓
\begin{array}{l}
\mathbf{if}\;x \le -0.007072373127510205:\\
\;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\

\mathbf{elif}\;x \le 0.006564839170329155:\\
\;\;\;\;\left(x - \frac{1}{3} \cdot \left(x \cdot \left(x \cdot x\right)\right)\right) + {x}^{5} \cdot \frac{2}{15}\\

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

\end{array}
double f(double x, double __attribute__((unused)) y) {
        double r1530474 = 2.0;
        double r1530475 = 1.0;
        double r1530476 = -2.0;
        double r1530477 = x;
        double r1530478 = r1530476 * r1530477;
        double r1530479 = exp(r1530478);
        double r1530480 = r1530475 + r1530479;
        double r1530481 = r1530474 / r1530480;
        double r1530482 = r1530481 - r1530475;
        return r1530482;
}
↓
double f(double x, double __attribute__((unused)) y) {
        double r1530483 = x;
        double r1530484 = -0.007072373127510205;
        bool r1530485 = r1530483 <= r1530484;
        double r1530486 = 2.0;
        double r1530487 = 1.0;
        double r1530488 = -2.0;
        double r1530489 = r1530488 * r1530483;
        double r1530490 = exp(r1530489);
        double r1530491 = r1530487 + r1530490;
        double r1530492 = r1530486 / r1530491;
        double r1530493 = r1530492 - r1530487;
        double r1530494 = 0.006564839170329155;
        bool r1530495 = r1530483 <= r1530494;
        double r1530496 = 0.3333333333333333;
        double r1530497 = r1530483 * r1530483;
        double r1530498 = r1530483 * r1530497;
        double r1530499 = r1530496 * r1530498;
        double r1530500 = r1530483 - r1530499;
        double r1530501 = 5.0;
        double r1530502 = pow(r1530483, r1530501);
        double r1530503 = 0.13333333333333333;
        double r1530504 = r1530502 * r1530503;
        double r1530505 = r1530500 + r1530504;
        double r1530506 = r1530495 ? r1530505 : r1530493;
        double r1530507 = r1530485 ? r1530493 : r1530506;
        return r1530507;
}

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 < -0.007072373127510205 or 0.006564839170329155 < x

    1. Initial program 0.0

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

    2. Taylor expanded around -inf 0.0

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

    if -0.007072373127510205 < x < 0.006564839170329155

    1. Initial program 58.9

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

    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

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

  4. Final simplification0.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -0.007072373127510205:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \mathbf{elif}\;x \le 0.006564839170329155:\\ \;\;\;\;\left(x - \frac{1}{3} \cdot \left(x \cdot \left(x \cdot x\right)\right)\right) + {x}^{5} \cdot \frac{2}{15}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \end{array}\]

Reproduce

herbie shell --seed 2019134 
(FPCore (x y)
  :name "Logistic function from Lakshay Garg"
  (- (/ 2 (+ 1 (exp (* -2 x)))) 1))