Average Error: 0.0 → 0.0
Time: 8.8s
Precision: 64
\[2 \cdot \left(x \cdot x + x \cdot y\right)\]
↓
\[x \cdot \left(2 \cdot x\right) + y \cdot \left(2 \cdot x\right)\]
2 \cdot \left(x \cdot x + x \cdot y\right)
↓
x \cdot \left(2 \cdot x\right) + y \cdot \left(2 \cdot x\right)
double f(double x, double y) {
        double r411817 = 2.0;
        double r411818 = x;
        double r411819 = r411818 * r411818;
        double r411820 = y;
        double r411821 = r411818 * r411820;
        double r411822 = r411819 + r411821;
        double r411823 = r411817 * r411822;
        return r411823;
}
↓
double f(double x, double y) {
        double r411824 = x;
        double r411825 = 2.0;
        double r411826 = r411825 * r411824;
        double r411827 = r411824 * r411826;
        double r411828 = y;
        double r411829 = r411828 * r411826;
        double r411830 = r411827 + r411829;
        return r411830;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\left(x \cdot 2\right) \cdot \left(x + y\right)\]

Derivation

  1. Initial program 0.0

    \[2 \cdot \left(x \cdot x + x \cdot y\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(x \cdot \left(x + y\right)\right) \cdot 2}\]
  3. Using strategy rm

  4. Applied pow10.0

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

  5. Applied pow10.0

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

  6. Applied pow10.0

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

  7. Applied pow-prod-down0.0

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

  8. Applied pow-prod-down0.0

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

  9. Simplified0.0

    \[\leadsto {\color{blue}{\left(\left(2 \cdot x\right) \cdot \left(x + y\right)\right)}}^{1}\]
  10. Using strategy rm

  11. Applied distribute-lft-in0.0

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

  12. Simplified0.0

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

  13. Simplified0.0

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

  14. Final simplification0.0

    \[\leadsto x \cdot \left(2 \cdot x\right) + y \cdot \left(2 \cdot x\right)\]

Reproduce

herbie shell --seed 2019305 
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (* (* x 2) (+ x y))

  (* 2 (+ (* x x) (* x y))))