Average Error: 0.1 → 0.1
Time: 8.1s
Precision: 64
\[e^{\sqrt{x}}\]
\[{e}^{\left(\sqrt{x}\right)}\]
e^{\sqrt{x}}
{e}^{\left(\sqrt{x}\right)}
double f(double x) {
        double r1074934 = x;
        double r1074935 = sqrt(r1074934);
        double r1074936 = exp(r1074935);
        return r1074936;
}

double f(double x) {
        double r1074937 = exp(1.0);
        double r1074938 = x;
        double r1074939 = sqrt(r1074938);
        double r1074940 = pow(r1074937, r1074939);
        return r1074940;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[e^{\sqrt{x}}\]
  2. Using strategy rm
  3. Applied *-un-lft-identity0.1

    \[\leadsto e^{\sqrt{\color{blue}{1 \cdot x}}}\]
  4. Applied sqrt-prod0.1

    \[\leadsto e^{\color{blue}{\sqrt{1} \cdot \sqrt{x}}}\]
  5. Applied exp-prod0.1

    \[\leadsto \color{blue}{{\left(e^{\sqrt{1}}\right)}^{\left(\sqrt{x}\right)}}\]
  6. Simplified0.1

    \[\leadsto {\color{blue}{e}}^{\left(\sqrt{x}\right)}\]
  7. Final simplification0.1

    \[\leadsto {e}^{\left(\sqrt{x}\right)}\]

Reproduce

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