Average Error: 0.0 → 0.0
Time: 7.4s
Precision: 64
\[x + x \cdot x\]
↓
\[x \cdot \left(x + 1\right)\]
x + x \cdot x
↓
x \cdot \left(x + 1\right)
double f(double x) {
        double r110378 = x;
        double r110379 = r110378 * r110378;
        double r110380 = r110378 + r110379;
        return r110380;
}
↓
double f(double x) {
        double r110381 = x;
        double r110382 = 1.0;
        double r110383 = r110381 + r110382;
        double r110384 = r110381 * r110383;
        return r110384;
}

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. Using strategy rm

  3. Applied *-un-lft-identity0.0

    \[\leadsto \color{blue}{1 \cdot x} + x \cdot x\]

  4. Applied distribute-rgt-out0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

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