Average Error: 0.7 → 0.0
Time: 10.0s
Precision: 64
\[e^{x + 1} - e^{2 \cdot x}\]
\[\left(\sqrt{e^{x + 1}} + \sqrt{e^{2 \cdot x}}\right) \cdot \left(\sqrt{e^{x + 1}} - \sqrt{e^{2 \cdot x}}\right)\]
e^{x + 1} - e^{2 \cdot x}
\left(\sqrt{e^{x + 1}} + \sqrt{e^{2 \cdot x}}\right) \cdot \left(\sqrt{e^{x + 1}} - \sqrt{e^{2 \cdot x}}\right)
double f(double x) {
        double r1622768 = x;
        double r1622769 = 1.0;
        double r1622770 = r1622768 + r1622769;
        double r1622771 = exp(r1622770);
        double r1622772 = 2.0;
        double r1622773 = r1622772 * r1622768;
        double r1622774 = exp(r1622773);
        double r1622775 = r1622771 - r1622774;
        return r1622775;
}

double f(double x) {
        double r1622776 = x;
        double r1622777 = 1.0;
        double r1622778 = r1622776 + r1622777;
        double r1622779 = exp(r1622778);
        double r1622780 = sqrt(r1622779);
        double r1622781 = 2.0;
        double r1622782 = r1622781 * r1622776;
        double r1622783 = exp(r1622782);
        double r1622784 = sqrt(r1622783);
        double r1622785 = r1622780 + r1622784;
        double r1622786 = r1622780 - r1622784;
        double r1622787 = r1622785 * r1622786;
        return r1622787;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.7

    \[e^{x + 1} - e^{2 \cdot x}\]
  2. Using strategy rm
  3. Applied add-sqr-sqrt0.7

    \[\leadsto e^{x + 1} - \color{blue}{\sqrt{e^{2 \cdot x}} \cdot \sqrt{e^{2 \cdot x}}}\]
  4. Applied add-sqr-sqrt0.7

    \[\leadsto \color{blue}{\sqrt{e^{x + 1}} \cdot \sqrt{e^{x + 1}}} - \sqrt{e^{2 \cdot x}} \cdot \sqrt{e^{2 \cdot x}}\]
  5. Applied difference-of-squares0.0

    \[\leadsto \color{blue}{\left(\sqrt{e^{x + 1}} + \sqrt{e^{2 \cdot x}}\right) \cdot \left(\sqrt{e^{x + 1}} - \sqrt{e^{2 \cdot x}}\right)}\]
  6. Final simplification0.0

    \[\leadsto \left(\sqrt{e^{x + 1}} + \sqrt{e^{2 \cdot x}}\right) \cdot \left(\sqrt{e^{x + 1}} - \sqrt{e^{2 \cdot x}}\right)\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "exp(x+1)-exp(2*x)"
  :precision binary64
  (- (exp (+ x 1)) (exp (* 2 x))))