Average Error: 0.0 → 0.0
Time: 8.5s
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 r66202 = x;
        double r66203 = r66202 * r66202;
        double r66204 = r66202 * r66203;
        double r66205 = r66204 + r66203;
        return r66205;
}
↓
double f(double x) {
        double r66206 = x;
        double r66207 = sqrt(r66206);
        double r66208 = r66206 * r66207;
        double r66209 = r66208 * r66208;
        double r66210 = r66206 * r66206;
        double r66211 = r66209 + r66210;
        return r66211;
}

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 2019194 
(FPCore (x)
  :name "Expression 3, p15"
  :pre (<= 0.0 x 2.0)

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

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