Average Error: 0.0 → 0.0
Time: 9.2s
Precision: 64
\[0.0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[\left(x \cdot \sqrt{x}\right) \cdot \left(x \cdot \sqrt{x}\right) + x \cdot x\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
\left(x \cdot \sqrt{x}\right) \cdot \left(x \cdot \sqrt{x}\right) + x \cdot x
double f(double x) {
        double r89778 = x;
        double r89779 = r89778 * r89778;
        double r89780 = r89778 * r89779;
        double r89781 = r89780 + r89779;
        return r89781;
}
↓
double f(double x) {
        double r89782 = x;
        double r89783 = sqrt(r89782);
        double r89784 = r89782 * r89783;
        double r89785 = r89784 * r89784;
        double r89786 = r89782 * r89782;
        double r89787 = r89785 + r89786;
        return r89787;
}

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

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 unswap-sqr0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019195 
(FPCore (x)
  :name "Expression 3, p15"
  :pre (<= 0.0 x 2.0)

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

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