\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]

↓

\[(4 \cdot \left((\left(b \cdot b\right) \cdot 3 + \left(a \cdot a\right))_* - a \cdot \left(a \cdot a\right)\right) + \left((\left((b \cdot b + \left(a \cdot a\right))_*\right) \cdot \left((b \cdot b + \left(a \cdot a\right))_*\right) + -1)_*\right))_*\]

double f(double a, double b) {
        double r51110659 = a;
        double r51110660 = r51110659 * r51110659;
        double r51110661 = b;
        double r51110662 = r51110661 * r51110661;
        double r51110663 = r51110660 + r51110662;
        double r51110664 = 2.0;
        double r51110665 = pow(r51110663, r51110664);
        double r51110666 = 4.0;
        double r51110667 = 1.0;
        double r51110668 = r51110667 - r51110659;
        double r51110669 = r51110660 * r51110668;
        double r51110670 = 3.0;
        double r51110671 = r51110670 + r51110659;
        double r51110672 = r51110662 * r51110671;
        double r51110673 = r51110669 + r51110672;
        double r51110674 = r51110666 * r51110673;
        double r51110675 = r51110665 + r51110674;
        double r51110676 = r51110675 - r51110667;
        return r51110676;
}

↓

double f(double a, double b) {
        double r51110677 = 4.0;
        double r51110678 = b;
        double r51110679 = r51110678 * r51110678;
        double r51110680 = 3.0;
        double r51110681 = a;
        double r51110682 = r51110681 * r51110681;
        double r51110683 = fma(r51110679, r51110680, r51110682);
        double r51110684 = r51110681 * r51110682;
        double r51110685 = r51110683 - r51110684;
        double r51110686 = fma(r51110678, r51110678, r51110682);
        double r51110687 = -1.0;
        double r51110688 = fma(r51110686, r51110686, r51110687);
        double r51110689 = fma(r51110677, r51110685, r51110688);
        return r51110689;
}

\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1

↓

(4 \cdot \left((\left(b \cdot b\right) \cdot 3 + \left(a \cdot a\right))_* - a \cdot \left(a \cdot a\right)\right) + \left((\left((b \cdot b + \left(a \cdot a\right))_*\right) \cdot \left((b \cdot b + \left(a \cdot a\right))_*\right) + -1)_*\right))_*

Derivation

Initial program 0.2
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
Simplified0.2
\[\leadsto \color{blue}{(4 \cdot \left((a \cdot \left(\left(1 - a\right) \cdot a\right) + \left(\left(a + 3\right) \cdot \left(b \cdot b\right)\right))_*\right) + \left((\left((b \cdot b + \left(a \cdot a\right))_*\right) \cdot \left((b \cdot b + \left(a \cdot a\right))_*\right) + -1)_*\right))_*}\]
Taylor expanded around 0 0.2
\[\leadsto (4 \cdot \color{blue}{\left(\left({a}^{2} + 3 \cdot {b}^{2}\right) - {a}^{3}\right)} + \left((\left((b \cdot b + \left(a \cdot a\right))_*\right) \cdot \left((b \cdot b + \left(a \cdot a\right))_*\right) + -1)_*\right))_*\]
Simplified0.2
\[\leadsto (4 \cdot \color{blue}{\left((\left(b \cdot b\right) \cdot 3 + \left(a \cdot a\right))_* - a \cdot \left(a \cdot a\right)\right)} + \left((\left((b \cdot b + \left(a \cdot a\right))_*\right) \cdot \left((b \cdot b + \left(a \cdot a\right))_*\right) + -1)_*\right))_*\]
Final simplification0.2
\[\leadsto (4 \cdot \left((\left(b \cdot b\right) \cdot 3 + \left(a \cdot a\right))_* - a \cdot \left(a \cdot a\right)\right) + \left((\left((b \cdot b + \left(a \cdot a\right))_*\right) \cdot \left((b \cdot b + \left(a \cdot a\right))_*\right) + -1)_*\right))_*\]

Error

Derivation

Reproduce