Average Error: 0.0 → 0.0
Time: 1.2m
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\frac{\frac{\frac{2}{\sqrt{\sqrt{e^{x} + e^{-x}}}}}{\sqrt{\sqrt{e^{x} + e^{-x}}}}}{\sqrt{e^{x} + e^{-x}}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\frac{\frac{\frac{2}{\sqrt{\sqrt{e^{x} + e^{-x}}}}}{\sqrt{\sqrt{e^{x} + e^{-x}}}}}{\sqrt{e^{x} + e^{-x}}}
double f(double x) {
        double r2707703 = 2.0;
        double r2707704 = x;
        double r2707705 = exp(r2707704);
        double r2707706 = -r2707704;
        double r2707707 = exp(r2707706);
        double r2707708 = r2707705 + r2707707;
        double r2707709 = r2707703 / r2707708;
        return r2707709;
}
↓
double f(double x) {
        double r2707710 = 2.0;
        double r2707711 = x;
        double r2707712 = exp(r2707711);
        double r2707713 = -r2707711;
        double r2707714 = exp(r2707713);
        double r2707715 = r2707712 + r2707714;
        double r2707716 = sqrt(r2707715);
        double r2707717 = sqrt(r2707716);
        double r2707718 = r2707710 / r2707717;
        double r2707719 = r2707718 / r2707717;
        double r2707720 = r2707719 / r2707716;
        return r2707720;
}

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-sqrt0.8

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

  4. Applied associate-/r*0.5

    \[\leadsto \color{blue}{\frac{\frac{2}{\sqrt{e^{x} + e^{-x}}}}{\sqrt{e^{x} + e^{-x}}}}\]
  5. Using strategy rm

  6. Applied add-sqr-sqrt0.0

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

  7. Applied associate-/r*0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019141 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))