Average Error: 0.0 → 0.1
Time: 35.3s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\sqrt[3]{\left(\frac{2}{e^{x} + e^{-x}} \cdot \frac{2}{e^{x} + e^{-x}}\right) \cdot \frac{2}{e^{x} + e^{-x}}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\sqrt[3]{\left(\frac{2}{e^{x} + e^{-x}} \cdot \frac{2}{e^{x} + e^{-x}}\right) \cdot \frac{2}{e^{x} + e^{-x}}}
double f(double x) {
        double r6860990 = 2.0;
        double r6860991 = x;
        double r6860992 = exp(r6860991);
        double r6860993 = -r6860991;
        double r6860994 = exp(r6860993);
        double r6860995 = r6860992 + r6860994;
        double r6860996 = r6860990 / r6860995;
        return r6860996;
}
↓
double f(double x) {
        double r6860997 = 2.0;
        double r6860998 = x;
        double r6860999 = exp(r6860998);
        double r6861000 = -r6860998;
        double r6861001 = exp(r6861000);
        double r6861002 = r6860999 + r6861001;
        double r6861003 = r6860997 / r6861002;
        double r6861004 = r6861003 * r6861003;
        double r6861005 = r6861004 * r6861003;
        double r6861006 = cbrt(r6861005);
        return r6861006;
}

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-cbrt-cube0.1

    \[\leadsto \color{blue}{\sqrt[3]{\left(\frac{2}{e^{x} + e^{-x}} \cdot \frac{2}{e^{x} + e^{-x}}\right) \cdot \frac{2}{e^{x} + e^{-x}}}}\]

  4. Final simplification0.1

    \[\leadsto \sqrt[3]{\left(\frac{2}{e^{x} + e^{-x}} \cdot \frac{2}{e^{x} + e^{-x}}\right) \cdot \frac{2}{e^{x} + e^{-x}}}\]

Reproduce

herbie shell --seed 2019112 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))