Average Error: 30.0 → 0.0
Time: 45.8s
Precision: 64
\[\frac{2}{1 + e^{-2 \cdot x}} - 1\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -0.007294245055471922:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \mathbf{elif}\;x \le 0.008176101527675436:\\ \;\;\;\;\left(\left(\frac{-1}{3} \cdot \left(x \cdot x\right)\right) \cdot x + x\right) + {x}^{5} \cdot \frac{2}{15}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \end{array}\]
\frac{2}{1 + e^{-2 \cdot x}} - 1
↓
\begin{array}{l}
\mathbf{if}\;x \le -0.007294245055471922:\\
\;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\

\mathbf{elif}\;x \le 0.008176101527675436:\\
\;\;\;\;\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 r8092388 = 2.0;
        double r8092389 = 1.0;
        double r8092390 = -2.0;
        double r8092391 = x;
        double r8092392 = r8092390 * r8092391;
        double r8092393 = exp(r8092392);
        double r8092394 = r8092389 + r8092393;
        double r8092395 = r8092388 / r8092394;
        double r8092396 = r8092395 - r8092389;
        return r8092396;
}
↓
double f(double x, double __attribute__((unused)) y) {
        double r8092397 = x;
        double r8092398 = -0.007294245055471922;
        bool r8092399 = r8092397 <= r8092398;
        double r8092400 = 2.0;
        double r8092401 = 1.0;
        double r8092402 = -2.0;
        double r8092403 = r8092402 * r8092397;
        double r8092404 = exp(r8092403);
        double r8092405 = r8092401 + r8092404;
        double r8092406 = r8092400 / r8092405;
        double r8092407 = r8092406 - r8092401;
        double r8092408 = 0.008176101527675436;
        bool r8092409 = r8092397 <= r8092408;
        double r8092410 = -0.3333333333333333;
        double r8092411 = r8092397 * r8092397;
        double r8092412 = r8092410 * r8092411;
        double r8092413 = r8092412 * r8092397;
        double r8092414 = r8092413 + r8092397;
        double r8092415 = 5.0;
        double r8092416 = pow(r8092397, r8092415);
        double r8092417 = 0.13333333333333333;
        double r8092418 = r8092416 * r8092417;
        double r8092419 = r8092414 + r8092418;
        double r8092420 = r8092409 ? r8092419 : r8092407;
        double r8092421 = r8092399 ? r8092407 : r8092420;
        return r8092421;
}

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 < -0.007294245055471922 or 0.008176101527675436 < 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 -0.007294245055471922 < x < 0.008176101527675436

    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

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -0.007294245055471922:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \mathbf{elif}\;x \le 0.008176101527675436:\\ \;\;\;\;\left(\left(\frac{-1}{3} \cdot \left(x \cdot x\right)\right) \cdot x + x\right) + {x}^{5} \cdot \frac{2}{15}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{1 + e^{-2 \cdot x}} - 1\\ \end{array}\]

Reproduce

herbie shell --seed 2019112 
(FPCore (x y)
  :name "Logistic function from Lakshay Garg"
  (- (/ 2 (+ 1 (exp (* -2 x)))) 1))