Average Error: 0.0 → 0.0
Time: 4.9s
Precision: 64
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[x \cdot \left(x \cdot x + x\right)\]
double f(double x) {
        double r15343455 = x;
        double r15343456 = r15343455 * r15343455;
        double r15343457 = r15343455 * r15343456;
        double r15343458 = r15343457 + r15343456;
        return r15343458;
}
↓
double f(double x) {
        double r15343459 = x;
        double r15343460 = r15343459 * r15343459;
        double r15343461 = r15343460 + r15343459;
        double r15343462 = r15343459 * r15343461;
        return r15343462;
}


x \cdot \left(x \cdot x\right) + x \cdot x
↓
x \cdot \left(x \cdot x + x\right)

Error

Bits error versus x

Target

Original0.0
Target0.0
Herbie0.0
\[\left(\left(1.0 + x\right) \cdot x\right) \cdot x\]

Derivation

  1. Initial program 0.0

    \[x \cdot \left(x \cdot x\right) + x \cdot x\]
  2. Using strategy rm

  3. Applied distribute-lft-out0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019102 
(FPCore (x)
  :name "Expression 3, p15"
  :pre (<= 0 x 2)

  :herbie-target
  (* (* (+ 1.0 x) x) x)

  (+ (* x (* x x)) (* x x)))