Average Error: 0.0 → 0.0
Time: 2.4s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\sqrt{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt{\frac{2}{e^{x} + e^{-x}}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\sqrt{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt{\frac{2}{e^{x} + e^{-x}}}
double f(double x) {
        double r34121 = 2.0;
        double r34122 = x;
        double r34123 = exp(r34122);
        double r34124 = -r34122;
        double r34125 = exp(r34124);
        double r34126 = r34123 + r34125;
        double r34127 = r34121 / r34126;
        return r34127;
}
↓
double f(double x) {
        double r34128 = 2.0;
        double r34129 = x;
        double r34130 = exp(r34129);
        double r34131 = -r34129;
        double r34132 = exp(r34131);
        double r34133 = r34130 + r34132;
        double r34134 = r34128 / r34133;
        double r34135 = sqrt(r34134);
        double r34136 = r34135 * r34135;
        return r34136;
}

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 add-sqr-sqrt0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019353 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2 (+ (exp x) (exp (- x)))))