Average Error: 0.0 → 0.0
Time: 10.3s
Precision: 64
\[0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[x \cdot x + \left(\left(x \cdot x\right) \cdot \sqrt{x}\right) \cdot \sqrt{x}\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
x \cdot x + \left(\left(x \cdot x\right) \cdot \sqrt{x}\right) \cdot \sqrt{x}
double f(double x) {
        double r4440351 = x;
        double r4440352 = r4440351 * r4440351;
        double r4440353 = r4440351 * r4440352;
        double r4440354 = r4440353 + r4440352;
        return r4440354;
}
↓
double f(double x) {
        double r4440355 = x;
        double r4440356 = r4440355 * r4440355;
        double r4440357 = sqrt(r4440355);
        double r4440358 = r4440356 * r4440357;
        double r4440359 = r4440358 * r4440357;
        double r4440360 = r4440356 + r4440359;
        return r4440360;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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 add-sqr-sqrt0.0

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

  4. Applied associate-*l*0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x)
  :name "Expression 3, p15"
  :pre (<= 0 x 2)

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

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