Average Error: 0.0 → 0.0
Time: 8.8s
Precision: 64
$-1 \le x \le 1 \land -1 \le y \le 1$
$1 - \left(x \cdot x + y \cdot y\right)$
$1 - \left(\sqrt[3]{x \cdot x + y \cdot y} \cdot \sqrt[3]{x \cdot x + y \cdot y}\right) \cdot \sqrt[3]{x \cdot x + y \cdot y}$
1 - \left(x \cdot x + y \cdot y\right)
1 - \left(\sqrt[3]{x \cdot x + y \cdot y} \cdot \sqrt[3]{x \cdot x + y \cdot y}\right) \cdot \sqrt[3]{x \cdot x + y \cdot y}
double f(double x, double y) {
double r19764 = 1.0;
double r19765 = x;
double r19766 = r19765 * r19765;
double r19767 = y;
double r19768 = r19767 * r19767;
double r19769 = r19766 + r19768;
double r19770 = r19764 - r19769;
return r19770;
}


double f(double x, double y) {
double r19771 = 1.0;
double r19772 = x;
double r19773 = r19772 * r19772;
double r19774 = y;
double r19775 = r19774 * r19774;
double r19776 = r19773 + r19775;
double r19777 = cbrt(r19776);
double r19778 = r19777 * r19777;
double r19779 = r19778 * r19777;
double r19780 = r19771 - r19779;
return r19780;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.0

$1 - \left(x \cdot x + y \cdot y\right)$
2. Using strategy rm

$\leadsto 1 - \color{blue}{\left(\sqrt[3]{x \cdot x + y \cdot y} \cdot \sqrt[3]{x \cdot x + y \cdot y}\right) \cdot \sqrt[3]{x \cdot x + y \cdot y}}$
4. Final simplification0.0

$\leadsto 1 - \left(\sqrt[3]{x \cdot x + y \cdot y} \cdot \sqrt[3]{x \cdot x + y \cdot y}\right) \cdot \sqrt[3]{x \cdot x + y \cdot y}$

# Reproduce

herbie shell --seed 1
(FPCore (x y)
:name "1 - (x*x + y*y)"
:precision binary64
:pre (and (<= (- 1) x 1) (<= (- 1) y 1))
(- 1 (+ (* x x) (* y y))))