Average Error: 0.0 → 0.0
Time: 2.5s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\frac{\sqrt{2}}{\frac{\frac{e^{x} + e^{-x}}{\sqrt{\sqrt{2}}}}{\sqrt{\sqrt{2}}}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\frac{\sqrt{2}}{\frac{\frac{e^{x} + e^{-x}}{\sqrt{\sqrt{2}}}}{\sqrt{\sqrt{2}}}}
double f(double x) {
        double r58605 = 2.0;
        double r58606 = x;
        double r58607 = exp(r58606);
        double r58608 = -r58606;
        double r58609 = exp(r58608);
        double r58610 = r58607 + r58609;
        double r58611 = r58605 / r58610;
        return r58611;
}
↓
double f(double x) {
        double r58612 = 2.0;
        double r58613 = sqrt(r58612);
        double r58614 = x;
        double r58615 = exp(r58614);
        double r58616 = -r58614;
        double r58617 = exp(r58616);
        double r58618 = r58615 + r58617;
        double r58619 = sqrt(r58613);
        double r58620 = r58618 / r58619;
        double r58621 = r58620 / r58619;
        double r58622 = r58613 / r58621;
        return r58622;
}

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-sqrt0.5

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

  4. Applied associate-/l*0.5

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

  6. Applied add-sqr-sqrt0.5

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

  7. Applied sqrt-prod0.0

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

  8. Applied associate-/r*0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019362 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2 (+ (exp x) (exp (- x)))))