Average Error: 0.0 → 0.0
Time: 5.2s
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 r31724025 = x;
        double r31724026 = r31724025 * r31724025;
        double r31724027 = y;
        double r31724028 = r31724026 + r31724027;
        double r31724029 = r31724028 + r31724027;
        return r31724029;
}
↓
double f(double x, double y) {
        double r31724030 = x;
        double r31724031 = r31724030 * r31724030;
        double r31724032 = y;
        double r31724033 = r31724032 + r31724032;
        double r31724034 = r31724031 + r31724033;
        return r31724034;
}

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 2019179 +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))