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

Average Error: 0.0 → 0.0

Time: 1.0min

Precision: binary64

Cost: 13312

Math

\[e^{\left(x \cdot y\right) \cdot y} \]

↓

\[{\left(e^{-9}\right)}^{\left(\left(y \cdot \left(x \cdot y\right)\right) \cdot -0.1111111111111111\right)} \]

FPCore

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

↓

(FPCore (x y)
 :precision binary64
 (pow (exp -9.0) (* (* y (* x y)) -0.1111111111111111)))

C

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

↓

double code(double x, double y) {
	return pow(exp(-9.0), ((y * (x * y)) * -0.1111111111111111));
}

Fortran

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

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = exp((-9.0d0)) ** ((y * (x * y)) * (-0.1111111111111111d0))
end function

Java

public static double code(double x, double y) {
	return Math.exp(((x * y) * y));
}

↓

public static double code(double x, double y) {
	return Math.pow(Math.exp(-9.0), ((y * (x * y)) * -0.1111111111111111));
}

Python

def code(x, y):
	return math.exp(((x * y) * y))

↓

def code(x, y):
	return math.pow(math.exp(-9.0), ((y * (x * y)) * -0.1111111111111111))

Julia

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

↓

function code(x, y)
	return exp(-9.0) ^ Float64(Float64(y * Float64(x * y)) * -0.1111111111111111)
end

MATLAB

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

↓

function tmp = code(x, y)
	tmp = exp(-9.0) ^ ((y * (x * y)) * -0.1111111111111111);
end

Wolfram

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

↓

code[x_, y_] := N[Power[N[Exp[-9.0], $MachinePrecision], N[(N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision] * -0.1111111111111111), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 0.0

   \[e^{\left(x \cdot y\right) \cdot y} \]

2. Applied egg-rr 0.0

   \[\leadsto e^{\color{blue}{\left(y \cdot \left(x \cdot y\right) + 9\right) - 9}} \]

3. Applied egg-rr 0.7

   \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, x \cdot y, 9\right)} \cdot e^{-9}} \]

4. Applied egg-rr 0.7

   \[\leadsto e^{\color{blue}{y \cdot \left(x \cdot y\right) - -9}} \cdot e^{-9} \]

5. Applied egg-rr 0.0

   \[\leadsto \color{blue}{{\left(e^{-9}\right)}^{\left(\left(y \cdot \left(x \cdot y\right)\right) \cdot -0.1111111111111111\right)}} \]

Alternatives

Alternative 1
Error	0.0
Cost	6720

\[e^{\left(x \cdot y\right) \cdot y} \]

Alternative 2
Error	21.1
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023033 
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  :precision binary64
  (exp (* (* x y) y)))