Average Error: 0.0 → 0.0
Time: 9.1s
Precision: 64
\[0.0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[x \cdot x + \left(\left(x \cdot x\right) \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
x \cdot x + \left(\left(x \cdot x\right) \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)
double f(double x) {
        double r88485 = x;
        double r88486 = r88485 * r88485;
        double r88487 = r88485 * r88486;
        double r88488 = r88487 + r88486;
        return r88488;
}
↓
double f(double x) {
        double r88489 = x;
        double r88490 = r88489 * r88489;
        double r88491 = cbrt(r88489);
        double r88492 = r88490 * r88491;
        double r88493 = r88491 * r88491;
        double r88494 = r88492 * r88493;
        double r88495 = r88490 + r88494;
        return r88495;
}

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-cube-cbrt0.0

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

  4. Applied associate-*l*0.0

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

  5. Final simplification0.0

    \[\leadsto x \cdot x + \left(\left(x \cdot x\right) \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\]

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)))