Average Error: 29.0 → 0.0
Time: 24.5s
Precision: 64
\[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -0.007903465556076343:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \mathbf{elif}\;x \le 0.00792720968856004:\\ \;\;\;\;\left(\left(\frac{-1}{3} \cdot \left(x \cdot x\right)\right) \cdot x + x\right) + {x}^{5} \cdot \frac{2}{15}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \end{array}\]
\frac{2}{1 + e^{-2 \cdot x}} - 1
↓
\begin{array}{l}
\mathbf{if}\;x \le -0.007903465556076343:\\
\;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\

\mathbf{elif}\;x \le 0.00792720968856004:\\
\;\;\;\;\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}{1 + e^{-2 \cdot x}} - 1\\

\end{array}
double f(double x, double __attribute__((unused)) y) {
        double r4072727 = 2.0;
        double r4072728 = 1.0;
        double r4072729 = -2.0;
        double r4072730 = x;
        double r4072731 = r4072729 * r4072730;
        double r4072732 = exp(r4072731);
        double r4072733 = r4072728 + r4072732;
        double r4072734 = r4072727 / r4072733;
        double r4072735 = r4072734 - r4072728;
        return r4072735;
}
↓
double f(double x, double __attribute__((unused)) y) {
        double r4072736 = x;
        double r4072737 = -0.007903465556076343;
        bool r4072738 = r4072736 <= r4072737;
        double r4072739 = 2.0;
        double r4072740 = 1.0;
        double r4072741 = -2.0;
        double r4072742 = r4072741 * r4072736;
        double r4072743 = exp(r4072742);
        double r4072744 = r4072740 + r4072743;
        double r4072745 = r4072739 / r4072744;
        double r4072746 = r4072745 - r4072740;
        double r4072747 = 0.00792720968856004;
        bool r4072748 = r4072736 <= r4072747;
        double r4072749 = -0.3333333333333333;
        double r4072750 = r4072736 * r4072736;
        double r4072751 = r4072749 * r4072750;
        double r4072752 = r4072751 * r4072736;
        double r4072753 = r4072752 + r4072736;
        double r4072754 = 5.0;
        double r4072755 = pow(r4072736, r4072754);
        double r4072756 = 0.13333333333333333;
        double r4072757 = r4072755 * r4072756;
        double r4072758 = r4072753 + r4072757;
        double r4072759 = r4072748 ? r4072758 : r4072746;
        double r4072760 = r4072738 ? r4072746 : r4072759;
        return r4072760;
}

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 < -0.007903465556076343 or 0.00792720968856004 < 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 -0.007903465556076343 < x < 0.00792720968856004

    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

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

  4. Final simplification0.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -0.007903465556076343:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \mathbf{elif}\;x \le 0.00792720968856004:\\ \;\;\;\;\left(\left(\frac{-1}{3} \cdot \left(x \cdot x\right)\right) \cdot x + x\right) + {x}^{5} \cdot \frac{2}{15}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \end{array}\]

Reproduce

herbie shell --seed 2019121 
(FPCore (x y)
  :name "Logistic function from Lakshay Garg"
  (- (/ 2 (+ 1 (exp (* -2 x)))) 1))