Average Error: 0.0 → 0.0
Time: 1.9s
Precision: 64
\[0.0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[\frac{x + {x}^{4}}{x \cdot x + \left(1 - x \cdot 1\right)} \cdot x\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
\frac{x + {x}^{4}}{x \cdot x + \left(1 - x \cdot 1\right)} \cdot x
double code(double x) {
	return ((double) (((double) (x * ((double) (x * x)))) + ((double) (x * x))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) (x + ((double) pow(x, 4.0)))) / ((double) (((double) (x * x)) + ((double) (1.0 - ((double) (x * 1.0)))))))) * 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. Simplified0.0

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

  4. Applied distribute-lft1-in0.0

    \[\leadsto x \cdot \color{blue}{\left(\left(x + 1\right) \cdot x\right)}\]

  5. Applied associate-*r*0.0

    \[\leadsto \color{blue}{\left(x \cdot \left(x + 1\right)\right) \cdot x}\]
  6. Using strategy rm

  7. Applied flip3-+0.0

    \[\leadsto \left(x \cdot \color{blue}{\frac{{x}^{3} + {1}^{3}}{x \cdot x + \left(1 \cdot 1 - x \cdot 1\right)}}\right) \cdot x\]

  8. Applied associate-*r/0.0

    \[\leadsto \color{blue}{\frac{x \cdot \left({x}^{3} + {1}^{3}\right)}{x \cdot x + \left(1 \cdot 1 - x \cdot 1\right)}} \cdot x\]

  9. Simplified0.0

    \[\leadsto \frac{\color{blue}{x + {x}^{4}}}{x \cdot x + \left(1 \cdot 1 - x \cdot 1\right)} \cdot x\]

  10. Final simplification0.0

    \[\leadsto \frac{x + {x}^{4}}{x \cdot x + \left(1 - x \cdot 1\right)} \cdot x\]

Reproduce

herbie shell --seed 2020114 
(FPCore (x)
  :name "Expression 3, p15"
  :precision binary64
  :pre (<= 0.0 x 2)

  :herbie-target
  (* (* (+ 1 x) x) x)

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