Average Error: 0.0 → 0.0
Time: 1.5s
Precision: 64
\[0.0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[\sqrt[3]{{\left({x}^{3}\right)}^{3}} + x \cdot x\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
\sqrt[3]{{\left({x}^{3}\right)}^{3}} + x \cdot x
double code(double x) {
	return ((double) (((double) (x * ((double) (x * x)))) + ((double) (x * x))));
}
↓
double code(double x) {
	return ((double) (((double) cbrt(((double) pow(((double) pow(x, 3.0)), 3.0)))) + ((double) (x * x))));
}

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-cbrt-cube0.0

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

  4. Applied add-cbrt-cube0.0

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

  5. Applied cbrt-unprod0.0

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

  6. Applied add-cbrt-cube0.0

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

  7. Applied cbrt-unprod0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020130 
(FPCore (x)
  :name "Expression 3, p15"
  :precision binary64
  :pre (<= 0.0 x 2.0)

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

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