Average Error: 14.5 → 14.2
Time: 10.2s
Precision: 64
\[\frac{x \cdot x}{\sqrt{\left(x \cdot x\right) \cdot x + 1}}\]
\[x \cdot \frac{x}{\sqrt{1 + {x}^{3}}}\]
\frac{x \cdot x}{\sqrt{\left(x \cdot x\right) \cdot x + 1}}
x \cdot \frac{x}{\sqrt{1 + {x}^{3}}}
double f(double x) {
        double r39582 = x;
        double r39583 = r39582 * r39582;
        double r39584 = r39583 * r39582;
        double r39585 = 1.0;
        double r39586 = r39584 + r39585;
        double r39587 = sqrt(r39586);
        double r39588 = r39583 / r39587;
        return r39588;
}

double f(double x) {
        double r39589 = x;
        double r39590 = 1.0;
        double r39591 = 3.0;
        double r39592 = pow(r39589, r39591);
        double r39593 = r39590 + r39592;
        double r39594 = sqrt(r39593);
        double r39595 = r39589 / r39594;
        double r39596 = r39589 * r39595;
        return r39596;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.5

    \[\frac{x \cdot x}{\sqrt{\left(x \cdot x\right) \cdot x + 1}}\]
  2. Using strategy rm
  3. Applied *-un-lft-identity14.5

    \[\leadsto \frac{x \cdot x}{\sqrt{\color{blue}{1 \cdot \left(\left(x \cdot x\right) \cdot x + 1\right)}}}\]
  4. Applied sqrt-prod14.5

    \[\leadsto \frac{x \cdot x}{\color{blue}{\sqrt{1} \cdot \sqrt{\left(x \cdot x\right) \cdot x + 1}}}\]
  5. Applied times-frac14.2

    \[\leadsto \color{blue}{\frac{x}{\sqrt{1}} \cdot \frac{x}{\sqrt{\left(x \cdot x\right) \cdot x + 1}}}\]
  6. Simplified14.2

    \[\leadsto \color{blue}{x} \cdot \frac{x}{\sqrt{\left(x \cdot x\right) \cdot x + 1}}\]
  7. Simplified14.2

    \[\leadsto x \cdot \color{blue}{\frac{x}{\sqrt{1 + {x}^{3}}}}\]
  8. Final simplification14.2

    \[\leadsto x \cdot \frac{x}{\sqrt{1 + {x}^{3}}}\]

Reproduce

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