Average Error: 30.2 → 0
Time: 7.5s
Precision: 64
$\sqrt{{x}^{2}}$
$\left|{x}^{\left(\frac{2}{2}\right)}\right|$
\sqrt{{x}^{2}}
\left|{x}^{\left(\frac{2}{2}\right)}\right|
double f(double x) {
double r1858567 = x;
double r1858568 = 2.0;
double r1858569 = pow(r1858567, r1858568);
double r1858570 = sqrt(r1858569);
return r1858570;
}


double f(double x) {
double r1858571 = x;
double r1858572 = 2.0;
double r1858573 = 2.0;
double r1858574 = r1858572 / r1858573;
double r1858575 = pow(r1858571, r1858574);
double r1858576 = fabs(r1858575);
return r1858576;
}



# Try it out

Results

 In Out
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# Derivation

1. Initial program 30.2

$\sqrt{{x}^{2}}$
2. Using strategy rm
3. Applied sqr-pow30.2

$\leadsto \sqrt{\color{blue}{{x}^{\left(\frac{2}{2}\right)} \cdot {x}^{\left(\frac{2}{2}\right)}}}$
4. Applied rem-sqrt-square0

$\leadsto \color{blue}{\left|{x}^{\left(\frac{2}{2}\right)}\right|}$
5. Final simplification0

$\leadsto \left|{x}^{\left(\frac{2}{2}\right)}\right|$

# Reproduce

herbie shell --seed 1
(FPCore (x)
:name "sqrt(x^2)"
:precision binary64
(sqrt (pow x 2)))