Average Error: 0.0 → 0.0
Time: 14.1s
Precision: 64
\[0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[\left(x \cdot \sqrt{x}\right) \cdot \left(x \cdot \sqrt{x}\right) + x \cdot x\]
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 r16651743 = x;
        double r16651744 = r16651743 * r16651743;
        double r16651745 = r16651743 * r16651744;
        double r16651746 = r16651745 + r16651744;
        return r16651746;
}
↓
double f(double x) {
        double r16651747 = x;
        double r16651748 = sqrt(r16651747);
        double r16651749 = r16651747 * r16651748;
        double r16651750 = r16651749 * r16651749;
        double r16651751 = r16651747 * r16651747;
        double r16651752 = r16651750 + r16651751;
        return r16651752;
}

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 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 2019120 +o rules:numerics
(FPCore (x)
  :name "Expression 3, p15"
  :pre (<= 0 x 2)

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

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