Average Error: 0.0 → 0.0
Time: 5.1s
Precision: 64
\[\left(x \cdot x + y\right) + y\]
↓
\[x \cdot x + \left(y + y\right)\]
\left(x \cdot x + y\right) + y
↓
x \cdot x + \left(y + y\right)
double f(double x, double y) {
        double r31673469 = x;
        double r31673470 = r31673469 * r31673469;
        double r31673471 = y;
        double r31673472 = r31673470 + r31673471;
        double r31673473 = r31673472 + r31673471;
        return r31673473;
}
↓
double f(double x, double y) {
        double r31673474 = x;
        double r31673475 = r31673474 * r31673474;
        double r31673476 = y;
        double r31673477 = r31673476 + r31673476;
        double r31673478 = r31673475 + r31673477;
        return r31673478;
}

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

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  4. Applied fma-udef0.0

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

  5. Applied associate-+l+0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalTail from random-fu-0.2.6.2"

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

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