Average Error: 0.0 → 0.0
Time: 3.4s
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 r76654 = 2.0;
        double r76655 = x;
        double r76656 = exp(r76655);
        double r76657 = -r76655;
        double r76658 = exp(r76657);
        double r76659 = r76656 + r76658;
        double r76660 = r76654 / r76659;
        return r76660;
}
↓
double f(double x) {
        double r76661 = 2.0;
        double r76662 = x;
        double r76663 = exp(r76662);
        double r76664 = -r76662;
        double r76665 = exp(r76664);
        double r76666 = r76663 + r76665;
        double r76667 = r76661 / r76666;
        double r76668 = sqrt(r76667);
        double r76669 = r76668 * r76668;
        return r76669;
}

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 2019318 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2 (+ (exp x) (exp (- x)))))