Average Error: 0.0 → 0.0
Time: 1.5s
Precision: 64
\[0.0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[\frac{{x}^{2} + {x}^{5}}{x \cdot x + \left(1 - x \cdot 1\right)}\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
\frac{{x}^{2} + {x}^{5}}{x \cdot x + \left(1 - x \cdot 1\right)}
double f(double x) {
        double r90362 = x;
        double r90363 = r90362 * r90362;
        double r90364 = r90362 * r90363;
        double r90365 = r90364 + r90363;
        return r90365;
}
↓
double f(double x) {
        double r90366 = x;
        double r90367 = 2.0;
        double r90368 = pow(r90366, r90367);
        double r90369 = 5.0;
        double r90370 = pow(r90366, r90369);
        double r90371 = r90368 + r90370;
        double r90372 = r90366 * r90366;
        double r90373 = 1.0;
        double r90374 = r90366 * r90373;
        double r90375 = r90373 - r90374;
        double r90376 = r90372 + r90375;
        double r90377 = r90371 / r90376;
        return r90377;
}

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 distribute-lft1-in0.0

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

  5. Applied flip3-+0.0

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

  6. Applied associate-*l/0.0

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

  7. Simplified0.0

    \[\leadsto \frac{\color{blue}{{x}^{2} + {x}^{5}}}{x \cdot x + \left(1 \cdot 1 - x \cdot 1\right)}\]

  8. Final simplification0.0

    \[\leadsto \frac{{x}^{2} + {x}^{5}}{x \cdot x + \left(1 - x \cdot 1\right)}\]

Reproduce

herbie shell --seed 2020018 
(FPCore (x)
  :name "Expression 3, p15"
  :precision binary64
  :pre (<= 0.0 x 2)

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

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