Average Error: 0.0 → 0.0
Time: 3.6s
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 r39641965 = x;
        double r39641966 = r39641965 * r39641965;
        double r39641967 = y;
        double r39641968 = r39641966 + r39641967;
        double r39641969 = r39641968 + r39641967;
        return r39641969;
}
↓
double f(double x, double y) {
        double r39641970 = x;
        double r39641971 = r39641970 * r39641970;
        double r39641972 = y;
        double r39641973 = r39641972 + r39641972;
        double r39641974 = r39641971 + r39641973;
        return r39641974;
}

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 2019170 +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))