Average Error: 0.0 → 0.0
Time: 13.1s
Precision: 64
$a \cdot a - b \cdot b$
$\left(a + b\right) \cdot \left(a - b\right)$
a \cdot a - b \cdot b
\left(a + b\right) \cdot \left(a - b\right)
double f(double a, double b) {
double r16533553 = a;
double r16533554 = r16533553 * r16533553;
double r16533555 = b;
double r16533556 = r16533555 * r16533555;
double r16533557 = r16533554 - r16533556;
return r16533557;
}


double f(double a, double b) {
double r16533558 = a;
double r16533559 = b;
double r16533560 = r16533558 + r16533559;
double r16533561 = r16533558 - r16533559;
double r16533562 = r16533560 * r16533561;
return r16533562;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.0

$a \cdot a - b \cdot b$
2. Taylor expanded around 0 0.0

$\leadsto \color{blue}{{a}^{2} - {b}^{2}}$
3. Simplified0.0

$\leadsto \color{blue}{\left(a + b\right) \cdot \left(a - b\right)}$
4. Final simplification0.0

$\leadsto \left(a + b\right) \cdot \left(a - b\right)$

# Reproduce

herbie shell --seed 1
(FPCore (a b)
:name "a*a - b*b"
(- (* a a) (* b b)))