Average Error: 0.6 → 0.0
Time: 8.8s
Precision: 64
\[e^{x + 1} - e^{x}\]
\[\left(\sqrt{e^{x}} \cdot \sqrt{e^{1}} - \sqrt{e^{x}}\right) \cdot \left(\sqrt{e^{x}} + \sqrt{e^{x + 1}}\right)\]
e^{x + 1} - e^{x}
\left(\sqrt{e^{x}} \cdot \sqrt{e^{1}} - \sqrt{e^{x}}\right) \cdot \left(\sqrt{e^{x}} + \sqrt{e^{x + 1}}\right)
double f(double x) {
        double r7748974 = x;
        double r7748975 = 1.0;
        double r7748976 = r7748974 + r7748975;
        double r7748977 = exp(r7748976);
        double r7748978 = exp(r7748974);
        double r7748979 = r7748977 - r7748978;
        return r7748979;
}

double f(double x) {
        double r7748980 = x;
        double r7748981 = exp(r7748980);
        double r7748982 = sqrt(r7748981);
        double r7748983 = 1.0;
        double r7748984 = exp(r7748983);
        double r7748985 = sqrt(r7748984);
        double r7748986 = r7748982 * r7748985;
        double r7748987 = r7748986 - r7748982;
        double r7748988 = r7748980 + r7748983;
        double r7748989 = exp(r7748988);
        double r7748990 = sqrt(r7748989);
        double r7748991 = r7748982 + r7748990;
        double r7748992 = r7748987 * r7748991;
        return r7748992;
}

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

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

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

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

    \[\leadsto \color{blue}{\left(\sqrt{e^{x + 1}} + \sqrt{e^{x}}\right) \cdot \left(\sqrt{e^{x + 1}} - \sqrt{e^{x}}\right)}\]
  6. Using strategy rm
  7. Applied exp-sum0.0

    \[\leadsto \left(\sqrt{e^{x + 1}} + \sqrt{e^{x}}\right) \cdot \left(\sqrt{\color{blue}{e^{x} \cdot e^{1}}} - \sqrt{e^{x}}\right)\]
  8. Applied sqrt-prod0.0

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

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

Reproduce

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