Average Error: 0.0 → 0.0
Time: 2.1s
Precision: 64
\[0.0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[\left|{x}^{\frac{3}{2}}\right| \cdot \left|{x}^{\frac{3}{2}}\right| + x \cdot x\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
\left|{x}^{\frac{3}{2}}\right| \cdot \left|{x}^{\frac{3}{2}}\right| + x \cdot x
double f(double x) {
        double r104157 = x;
        double r104158 = r104157 * r104157;
        double r104159 = r104157 * r104158;
        double r104160 = r104159 + r104158;
        return r104160;
}
↓
double f(double x) {
        double r104161 = x;
        double r104162 = 1.5;
        double r104163 = pow(r104161, r104162);
        double r104164 = fabs(r104163);
        double r104165 = r104164 * r104164;
        double r104166 = r104161 * r104161;
        double r104167 = r104165 + r104166;
        return r104167;
}

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

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

  4. Simplified0.0

    \[\leadsto \color{blue}{\left|{x}^{\frac{3}{2}}\right|} \cdot \sqrt{x \cdot \left(x \cdot x\right)} + x \cdot x\]

  5. Simplified0.0

    \[\leadsto \left|{x}^{\frac{3}{2}}\right| \cdot \color{blue}{\left|{x}^{\frac{3}{2}}\right|} + x \cdot x\]

  6. Final simplification0.0

    \[\leadsto \left|{x}^{\frac{3}{2}}\right| \cdot \left|{x}^{\frac{3}{2}}\right| + x \cdot x\]

Reproduce

herbie shell --seed 2020036 
(FPCore (x)
  :name "Expression 3, p15"
  :precision binary64
  :pre (<= 0.0 x 2)

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

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