Average Error: 0.3 → 0.3
Time: 8.7s
Precision: 64
$\frac{1}{\sqrt{x}}$
$\sqrt{\frac{\frac{1}{\sqrt{x}} \cdot 1}{\sqrt{x}}}$
\frac{1}{\sqrt{x}}
\sqrt{\frac{\frac{1}{\sqrt{x}} \cdot 1}{\sqrt{x}}}
double f(double x) {
double r245583 = 1.0;
double r245584 = x;
double r245585 = sqrt(r245584);
double r245586 = r245583 / r245585;
return r245586;
}


double f(double x) {
double r245587 = 1.0;
double r245588 = x;
double r245589 = sqrt(r245588);
double r245590 = r245587 / r245589;
double r245591 = r245590 * r245587;
double r245592 = r245591 / r245589;
double r245593 = sqrt(r245592);
return r245593;
}



# Try it out

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# Derivation

1. Initial program 0.3

$\frac{1}{\sqrt{x}}$
2. Using strategy rm
3. Applied add-sqr-sqrt0.6

$\leadsto \color{blue}{\sqrt{\frac{1}{\sqrt{x}}} \cdot \sqrt{\frac{1}{\sqrt{x}}}}$
4. Using strategy rm
5. Applied sqrt-unprod0.3

$\leadsto \color{blue}{\sqrt{\frac{1}{\sqrt{x}} \cdot \frac{1}{\sqrt{x}}}}$
6. Simplified0.3

$\leadsto \sqrt{\color{blue}{\frac{\frac{1}{\sqrt{x}} \cdot 1}{\sqrt{x}}}}$
7. Final simplification0.3

$\leadsto \sqrt{\frac{\frac{1}{\sqrt{x}} \cdot 1}{\sqrt{x}}}$

# Reproduce

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