Average Error: 0.0 → 0.0
Time: 2.5s
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 r63083 = 2.0;
        double r63084 = x;
        double r63085 = exp(r63084);
        double r63086 = -r63084;
        double r63087 = exp(r63086);
        double r63088 = r63085 + r63087;
        double r63089 = r63083 / r63088;
        return r63089;
}
↓
double f(double x) {
        double r63090 = 2.0;
        double r63091 = x;
        double r63092 = exp(r63091);
        double r63093 = -r63091;
        double r63094 = exp(r63093);
        double r63095 = r63092 + r63094;
        double r63096 = r63090 / r63095;
        double r63097 = sqrt(r63096);
        double r63098 = r63097 * r63097;
        return r63098;
}

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)))))