Average Error: 0.6 → 0.4
Time: 7.6s
Precision: 64
\[e^{x} - e^{1}\]
\[\left(\sqrt{e^{1}} + \sqrt{e^{x}}\right) \cdot \left(\sqrt{e^{x}} - \sqrt{e^{1}}\right)\]
e^{x} - e^{1}
\left(\sqrt{e^{1}} + \sqrt{e^{x}}\right) \cdot \left(\sqrt{e^{x}} - \sqrt{e^{1}}\right)
double f(double x) {
        double r45976612 = x;
        double r45976613 = exp(r45976612);
        double r45976614 = 1.0;
        double r45976615 = exp(r45976614);
        double r45976616 = r45976613 - r45976615;
        return r45976616;
}

double f(double x) {
        double r45976617 = 1.0;
        double r45976618 = exp(r45976617);
        double r45976619 = sqrt(r45976618);
        double r45976620 = x;
        double r45976621 = exp(r45976620);
        double r45976622 = sqrt(r45976621);
        double r45976623 = r45976619 + r45976622;
        double r45976624 = r45976622 - r45976619;
        double r45976625 = r45976623 * r45976624;
        return r45976625;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.6

    \[e^{x} - e^{1}\]
  2. Using strategy rm
  3. Applied add-sqr-sqrt1.0

    \[\leadsto e^{x} - \color{blue}{\sqrt{e^{1}} \cdot \sqrt{e^{1}}}\]
  4. Applied add-sqr-sqrt1.0

    \[\leadsto \color{blue}{\sqrt{e^{x}} \cdot \sqrt{e^{x}}} - \sqrt{e^{1}} \cdot \sqrt{e^{1}}\]
  5. Applied difference-of-squares0.4

    \[\leadsto \color{blue}{\left(\sqrt{e^{x}} + \sqrt{e^{1}}\right) \cdot \left(\sqrt{e^{x}} - \sqrt{e^{1}}\right)}\]
  6. Final simplification0.4

    \[\leadsto \left(\sqrt{e^{1}} + \sqrt{e^{x}}\right) \cdot \left(\sqrt{e^{x}} - \sqrt{e^{1}}\right)\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "exp(x)-exp(1)"
  (- (exp x) (exp 1.0)))