Average Error: 0.0 → 0.0
Time: 5.3s
Precision: 64
\[0.0 \lt e \lt 1\]
\[\sqrt{1 - e \cdot e}\]
\[\frac{\sqrt{1 \cdot 1 - {e}^{4}}}{\sqrt{1 + e \cdot e}}\]
\sqrt{1 - e \cdot e}
\frac{\sqrt{1 \cdot 1 - {e}^{4}}}{\sqrt{1 + e \cdot e}}
double f(double e) {
        double r895594 = 1.0;
        double r895595 = e;
        double r895596 = r895595 * r895595;
        double r895597 = r895594 - r895596;
        double r895598 = sqrt(r895597);
        return r895598;
}

double f(double e) {
        double r895599 = 1.0;
        double r895600 = r895599 * r895599;
        double r895601 = e;
        double r895602 = 4.0;
        double r895603 = pow(r895601, r895602);
        double r895604 = r895600 - r895603;
        double r895605 = sqrt(r895604);
        double r895606 = r895601 * r895601;
        double r895607 = r895599 + r895606;
        double r895608 = sqrt(r895607);
        double r895609 = r895605 / r895608;
        return r895609;
}

Error

Bits error versus e

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\sqrt{1 - e \cdot e}\]
  2. Using strategy rm
  3. Applied flip--0.0

    \[\leadsto \sqrt{\color{blue}{\frac{1 \cdot 1 - \left(e \cdot e\right) \cdot \left(e \cdot e\right)}{1 + e \cdot e}}}\]
  4. Applied sqrt-div0.0

    \[\leadsto \color{blue}{\frac{\sqrt{1 \cdot 1 - \left(e \cdot e\right) \cdot \left(e \cdot e\right)}}{\sqrt{1 + e \cdot e}}}\]
  5. Simplified0.0

    \[\leadsto \frac{\color{blue}{\sqrt{1 \cdot 1 - {e}^{4}}}}{\sqrt{1 + e \cdot e}}\]
  6. Final simplification0.0

    \[\leadsto \frac{\sqrt{1 \cdot 1 - {e}^{4}}}{\sqrt{1 + e \cdot e}}\]

Reproduce

herbie shell --seed 1 
(FPCore (e)
  :name "sqrt(1-e*e)"
  :precision binary64
  :pre (< 0.0 e 1)
  (sqrt (- 1 (* e e))))