Average Error: 0.0 → 0.0
Time: 14.8s
Precision: 64
\[0.0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[\sqrt{{x}^{3} + x \cdot x} \cdot \sqrt{{x}^{3} + x \cdot x}\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
\sqrt{{x}^{3} + x \cdot x} \cdot \sqrt{{x}^{3} + x \cdot x}
double f(double x) {
        double r83882 = x;
        double r83883 = r83882 * r83882;
        double r83884 = r83882 * r83883;
        double r83885 = r83884 + r83883;
        return r83885;
}
↓
double f(double x) {
        double r83886 = x;
        double r83887 = 3.0;
        double r83888 = pow(r83886, r83887);
        double r83889 = r83886 * r83886;
        double r83890 = r83888 + r83889;
        double r83891 = sqrt(r83890);
        double r83892 = r83891 * r83891;
        return r83892;
}

Error

Bits error versus x

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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. Simplified0.0

    \[\leadsto \color{blue}{{x}^{3} + x \cdot x}\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt0.0

    \[\leadsto \color{blue}{\sqrt{{x}^{3} + x \cdot x} \cdot \sqrt{{x}^{3} + x \cdot x}}\]

  5. Final simplification0.0

    \[\leadsto \sqrt{{x}^{3} + x \cdot x} \cdot \sqrt{{x}^{3} + x \cdot x}\]

Reproduce

herbie shell --seed 2019208 
(FPCore (x)
  :name "Expression 3, p15"
  :precision binary64
  :pre (<= 0.0 x 2)

  :herbie-target
  (* (* (+ 1 x) x) x)

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