Average Error: 0.0 → 0.0
Time: 18.5s
Precision: 64
\[0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[x \cdot x + \left(\left(x \cdot x\right) \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\]
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 r2301358 = x;
        double r2301359 = r2301358 * r2301358;
        double r2301360 = r2301358 * r2301359;
        double r2301361 = r2301360 + r2301359;
        return r2301361;
}
↓
double f(double x) {
        double r2301362 = x;
        double r2301363 = r2301362 * r2301362;
        double r2301364 = cbrt(r2301362);
        double r2301365 = r2301363 * r2301364;
        double r2301366 = r2301364 * r2301364;
        double r2301367 = r2301365 * r2301366;
        double r2301368 = r2301363 + r2301367;
        return r2301368;
}

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-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 2019133 
(FPCore (x)
  :name "Expression 3, p15"
  :pre (<= 0 x 2)

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

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