Average Error: 0.2 → 0.2
Time: 13.9s
Precision: 64
$\left(\left(x \cdot x - 7 \cdot x\right) \cdot x + 28 \cdot x\right) \cdot x$
$\left(28 \cdot {x}^{2} + {x}^{4}\right) - 7 \cdot {x}^{3}$
\left(\left(x \cdot x - 7 \cdot x\right) \cdot x + 28 \cdot x\right) \cdot x
\left(28 \cdot {x}^{2} + {x}^{4}\right) - 7 \cdot {x}^{3}
double f(double x) {
double r145345 = x;
double r145346 = r145345 * r145345;
double r145347 = 7.0;
double r145348 = r145347 * r145345;
double r145349 = r145346 - r145348;
double r145350 = r145349 * r145345;
double r145351 = 28.0;
double r145352 = r145351 * r145345;
double r145353 = r145350 + r145352;
double r145354 = r145353 * r145345;
return r145354;
}

double f(double x) {
double r145355 = 28.0;
double r145356 = x;
double r145357 = 2.0;
double r145358 = pow(r145356, r145357);
double r145359 = r145355 * r145358;
double r145360 = 4.0;
double r145361 = pow(r145356, r145360);
double r145362 = r145359 + r145361;
double r145363 = 7.0;
double r145364 = 3.0;
double r145365 = pow(r145356, r145364);
double r145366 = r145363 * r145365;
double r145367 = r145362 - r145366;
return r145367;
}

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.2

$\left(\left(x \cdot x - 7 \cdot x\right) \cdot x + 28 \cdot x\right) \cdot x$
2. Taylor expanded around 0 0.2

$\leadsto \color{blue}{\left(28 \cdot {x}^{2} + {x}^{4}\right) - 7 \cdot {x}^{3}}$
3. Final simplification0.2

$\leadsto \left(28 \cdot {x}^{2} + {x}^{4}\right) - 7 \cdot {x}^{3}$

# Reproduce

herbie shell --seed 1
(FPCore (x)
:name "((x*x - 7*x)*x + 28 * x)*x"
:precision binary64
(* (+ (* (- (* x x) (* 7 x)) x) (* 28 x)) x))