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;
}



# Try it out

Results

 In Out
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))))