Average Error: 0.0 → 0.0
Time: 17.6s
Precision: 64
\[0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[\sqrt[3]{\sqrt{x \cdot \left(x \cdot x\right)} \cdot \sqrt{x \cdot \left(x \cdot x\right)}} \cdot \left(\sqrt[3]{\sqrt{x \cdot \left(x \cdot x\right)} \cdot \sqrt{x \cdot \left(x \cdot x\right)}} \cdot \sqrt[3]{\sqrt{x \cdot \left(x \cdot x\right)} \cdot \sqrt{x \cdot \left(x \cdot x\right)}}\right) + x \cdot x\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
\sqrt[3]{\sqrt{x \cdot \left(x \cdot x\right)} \cdot \sqrt{x \cdot \left(x \cdot x\right)}} \cdot \left(\sqrt[3]{\sqrt{x \cdot \left(x \cdot x\right)} \cdot \sqrt{x \cdot \left(x \cdot x\right)}} \cdot \sqrt[3]{\sqrt{x \cdot \left(x \cdot x\right)} \cdot \sqrt{x \cdot \left(x \cdot x\right)}}\right) + x \cdot x
double f(double x) {
        double r14956590 = x;
        double r14956591 = r14956590 * r14956590;
        double r14956592 = r14956590 * r14956591;
        double r14956593 = r14956592 + r14956591;
        return r14956593;
}
↓
double f(double x) {
        double r14956594 = x;
        double r14956595 = r14956594 * r14956594;
        double r14956596 = r14956594 * r14956595;
        double r14956597 = sqrt(r14956596);
        double r14956598 = r14956597 * r14956597;
        double r14956599 = cbrt(r14956598);
        double r14956600 = r14956599 * r14956599;
        double r14956601 = r14956599 * r14956600;
        double r14956602 = r14956601 + r14956595;
        return r14956602;
}

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

    \[\leadsto \color{blue}{\sqrt{x \cdot \left(x \cdot x\right)} \cdot \sqrt{x \cdot \left(x \cdot x\right)}} + x \cdot x\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019120 
(FPCore (x)
  :name "Expression 3, p15"
  :pre (<= 0 x 2)

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

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