Average Error: 0.0 → 0.0
Time: 1.5s
Precision: binary64
\[0.0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[{x}^{\frac{3}{2}} \cdot {x}^{\frac{3}{2}} + x \cdot x\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
{x}^{\frac{3}{2}} \cdot {x}^{\frac{3}{2}} + x \cdot x
double code(double x) {
	return ((double) (((double) (x * ((double) (x * x)))) + ((double) (x * x))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) pow(x, 1.5)) * ((double) pow(x, 1.5)))) + ((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-sqr-sqrt0.0

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

  4. Applied unswap-sqr0.0

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

  5. Simplified0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020161 
(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)))