Average Error: 0.0 → 0.0
Time: 6.6s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\frac{-2}{\frac{-1}{e^{x}} - e^{x}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\frac{-2}{\frac{-1}{e^{x}} - e^{x}}
double f(double x) {
        double r50153 = 2.0;
        double r50154 = x;
        double r50155 = exp(r50154);
        double r50156 = -r50154;
        double r50157 = exp(r50156);
        double r50158 = r50155 + r50157;
        double r50159 = r50153 / r50158;
        return r50159;
}
↓
double f(double x) {
        double r50160 = 2.0;
        double r50161 = -r50160;
        double r50162 = -1.0;
        double r50163 = x;
        double r50164 = exp(r50163);
        double r50165 = r50162 / r50164;
        double r50166 = r50165 - r50164;
        double r50167 = r50161 / r50166;
        return r50167;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{2}{e^{x} + e^{-x}}\]
  2. Using strategy rm

  3. Applied frac-2neg0.0

    \[\leadsto \color{blue}{\frac{-2}{-\left(e^{x} + e^{-x}\right)}}\]

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2.0 (+ (exp x) (exp (- x)))))