Data.Random.Distribution.Normal:normalTail from random-fu-0.2.6.2

Average Error: 0.0 → 0.0

Time: 1.5s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

(FPCore (x y) :precision binary64 (+ (+ (* x x) y) y))

↓

(FPCore (x y) :precision binary64 (+ (* x x) (+ y y)))

C

double code(double x, double y) {
	return ((x * x) + y) + y;
}

↓

double code(double x, double y) {
	return (x * x) + (y + y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * x) + y) + y
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * x) + (y + y)
end function

Java

public static double code(double x, double y) {
	return ((x * x) + y) + y;
}

↓

public static double code(double x, double y) {
	return (x * x) + (y + y);
}

Python

def code(x, y):
	return ((x * x) + y) + y

↓

def code(x, y):
	return (x * x) + (y + y)

Julia

function code(x, y)
	return Float64(Float64(Float64(x * x) + y) + y)
end

↓

function code(x, y)
	return Float64(Float64(x * x) + Float64(y + y))
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * x) + y) + y;
end

↓

function tmp = code(x, y)
	tmp = (x * x) + (y + y);
end

Wolfram

code[x_, y_] := N[(N[(N[(x * x), $MachinePrecision] + y), $MachinePrecision] + y), $MachinePrecision]

↓

code[x_, y_] := N[(N[(x * x), $MachinePrecision] + N[(y + y), $MachinePrecision]), $MachinePrecision]

Target

Original	0.0
Target	0.0
Herbie	0.0

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

Derivation

1. Initial program 0.0

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

2. Simplified 0.0

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

   [Start] 0.0	\[ \left(x \cdot x + y\right) + y \]
   rational_best-simplify-1 [=>] 0.0	\[ \color{blue}{y + \left(x \cdot x + y\right)} \]
   rational_best-simplify-1 [=>] 0.0	\[ y + \color{blue}{\left(y + x \cdot x\right)} \]
   rational_best-simplify-43 [=>] 0.0	\[ \color{blue}{x \cdot x + \left(y + y\right)} \]

3. Final simplification 0.0

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

Reproduce

herbie shell --seed 2023096 
(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))