Average Error: 0.0 → 0.0
Time: 7.5s
Precision: 64
\[x + x \cdot x\]
↓
\[\left(1 + x\right) \cdot x\]
x + x \cdot x
↓
\left(1 + x\right) \cdot x
double f(double x) {
        double r114650 = x;
        double r114651 = r114650 * r114650;
        double r114652 = r114650 + r114651;
        return r114652;
}
↓
double f(double x) {
        double r114653 = 1.0;
        double r114654 = x;
        double r114655 = r114653 + r114654;
        double r114656 = r114655 * r114654;
        return r114656;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x + x \cdot x\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{{x}^{2} + x}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{\left(1 + x\right) \cdot x}\]

  4. Final simplification0.0

    \[\leadsto \left(1 + x\right) \cdot x\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x)
  :name "Main:bigenough1 from B"
  :precision binary64
  (+ x (* x x)))