Average Error: 0.0 → 0.0
Time: 1.3s
Precision: binary64
\[\left(x \cdot x + y\right) + y\]
↓
\[\left(y + y\right) + x \cdot x\]
\left(x \cdot x + y\right) + y
↓
\left(y + y\right) + x \cdot x
(FPCore (x y) :precision binary64 (+ (+ (* x x) y) y))
↓
(FPCore (x y) :precision binary64 (+ (+ y y) (* x x)))
double code(double x, double y) {
	return ((x * x) + y) + y;
}
↓
double code(double x, double y) {
	return (y + y) + (x * x);
}

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. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{{x}^{2} + 2 \cdot y}\]

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2021044 
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalTail from random-fu-0.2.6.2"
  :precision binary64

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

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