Average Error: 29.4 → 0.0
Time: 24.9s
Precision: 64
\[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -0.008132844190967993:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \mathbf{elif}\;x \le 0.006948963129088722:\\ \;\;\;\;\left(\left(x \cdot x\right) \cdot \left(x \cdot \frac{-1}{3}\right) + x\right) + {x}^{5} \cdot \frac{2}{15}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \end{array}\]
\frac{2}{1 + e^{-2 \cdot x}} - 1
↓
\begin{array}{l}
\mathbf{if}\;x \le -0.008132844190967993:\\
\;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\

\mathbf{elif}\;x \le 0.006948963129088722:\\
\;\;\;\;\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}{1 + e^{-2 \cdot x}} - 1\\

\end{array}
double f(double x, double __attribute__((unused)) y) {
        double r3368547 = 2.0;
        double r3368548 = 1.0;
        double r3368549 = -2.0;
        double r3368550 = x;
        double r3368551 = r3368549 * r3368550;
        double r3368552 = exp(r3368551);
        double r3368553 = r3368548 + r3368552;
        double r3368554 = r3368547 / r3368553;
        double r3368555 = r3368554 - r3368548;
        return r3368555;
}
↓
double f(double x, double __attribute__((unused)) y) {
        double r3368556 = x;
        double r3368557 = -0.008132844190967993;
        bool r3368558 = r3368556 <= r3368557;
        double r3368559 = 2.0;
        double r3368560 = 1.0;
        double r3368561 = -2.0;
        double r3368562 = r3368561 * r3368556;
        double r3368563 = exp(r3368562);
        double r3368564 = r3368560 + r3368563;
        double r3368565 = r3368559 / r3368564;
        double r3368566 = r3368565 - r3368560;
        double r3368567 = 0.006948963129088722;
        bool r3368568 = r3368556 <= r3368567;
        double r3368569 = r3368556 * r3368556;
        double r3368570 = -0.3333333333333333;
        double r3368571 = r3368556 * r3368570;
        double r3368572 = r3368569 * r3368571;
        double r3368573 = r3368572 + r3368556;
        double r3368574 = 5.0;
        double r3368575 = pow(r3368556, r3368574);
        double r3368576 = 0.13333333333333333;
        double r3368577 = r3368575 * r3368576;
        double r3368578 = r3368573 + r3368577;
        double r3368579 = r3368568 ? r3368578 : r3368566;
        double r3368580 = r3368558 ? r3368566 : r3368579;
        return r3368580;
}

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 < -0.008132844190967993 or 0.006948963129088722 < x

    1. Initial program 0.0

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

    2. Taylor expanded around inf 0.0

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

    if -0.008132844190967993 < x < 0.006948963129088722

    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

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

  4. Final simplification0.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -0.008132844190967993:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \mathbf{elif}\;x \le 0.006948963129088722:\\ \;\;\;\;\left(\left(x \cdot x\right) \cdot \left(x \cdot \frac{-1}{3}\right) + x\right) + {x}^{5} \cdot \frac{2}{15}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \end{array}\]

Reproduce

herbie shell --seed 2019124 
(FPCore (x y)
  :name "Logistic function from Lakshay Garg"
  (- (/ 2 (+ 1 (exp (* -2 x)))) 1))