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;
}



# Try it out

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 In Out
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))))