Average Error: 0.0 → 0.0
Time: 15.5s
Precision: 64
\[\frac{\sqrt{x} + e^{x}}{\cos x}\]
\[\frac{e^{\log \left(\sqrt{x} + e^{x}\right)}}{\cos x}\]
\frac{\sqrt{x} + e^{x}}{\cos x}
\frac{e^{\log \left(\sqrt{x} + e^{x}\right)}}{\cos x}
double f(double x) {
        double r866017 = x;
        double r866018 = sqrt(r866017);
        double r866019 = exp(r866017);
        double r866020 = r866018 + r866019;
        double r866021 = cos(r866017);
        double r866022 = r866020 / r866021;
        return r866022;
}

double f(double x) {
        double r866023 = x;
        double r866024 = sqrt(r866023);
        double r866025 = exp(r866023);
        double r866026 = r866024 + r866025;
        double r866027 = log(r866026);
        double r866028 = exp(r866027);
        double r866029 = cos(r866023);
        double r866030 = r866028 / r866029;
        return r866030;
}

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

    \[\frac{\sqrt{x} + e^{x}}{\cos x}\]
  2. Using strategy rm
  3. Applied add-exp-log0.0

    \[\leadsto \frac{\color{blue}{e^{\log \left(\sqrt{x} + e^{x}\right)}}}{\cos x}\]
  4. Final simplification0.0

    \[\leadsto \frac{e^{\log \left(\sqrt{x} + e^{x}\right)}}{\cos x}\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "(sqrt(x)+exp(x))/cos(x)"
  :precision binary64
  (/ (+ (sqrt x) (exp x)) (cos x)))