Radioactive exchange between two surfaces

Percentage Accurate: 85.2% → 91.4%

Time: 2.1s

Alternatives: 3

Speedup: 0.7×

• 61.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ {x}^{4} - {y}^{4} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (pow x 4.0) (pow y 4.0)))

C

double code(double x, double y) {
	return pow(x, 4.0) - pow(y, 4.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x ** 4.0d0) - (y ** 4.0d0)
end function

Java

public static double code(double x, double y) {
	return Math.pow(x, 4.0) - Math.pow(y, 4.0);
}

Python

def code(x, y):
	return math.pow(x, 4.0) - math.pow(y, 4.0)

Julia

function code(x, y)
	return Float64((x ^ 4.0) - (y ^ 4.0))
end

MATLAB

function tmp = code(x, y)
	tmp = (x ^ 4.0) - (y ^ 4.0);
end

Wolfram

code[x_, y_] := N[(N[Power[x, 4.0], $MachinePrecision] - N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision]

Initial Program: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ {x}^{4} - {y}^{4} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (pow x 4.0) (pow y 4.0)))

C

double code(double x, double y) {
	return pow(x, 4.0) - pow(y, 4.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x ** 4.0d0) - (y ** 4.0d0)
end function

Java

public static double code(double x, double y) {
	return Math.pow(x, 4.0) - Math.pow(y, 4.0);
}

Python

def code(x, y):
	return math.pow(x, 4.0) - math.pow(y, 4.0)

Julia

function code(x, y)
	return Float64((x ^ 4.0) - (y ^ 4.0))
end

MATLAB

function tmp = code(x, y)
	tmp = (x ^ 4.0) - (y ^ 4.0);
end

Wolfram

code[x_, y_] := N[(N[Power[x, 4.0], $MachinePrecision] - N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision]

Alternative 1: 91.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;{x}^{4} \leq 3.2 \cdot 10^{+234}:\\ \;\;\;\;{x}^{4} - {y}^{4}\\ \mathbf{else}:\\ \;\;\;\;{x}^{4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (pow x 4.0) 3.2e+234) (- (pow x 4.0) (pow y 4.0)) (pow x 4.0)))

C

double code(double x, double y) {
	double tmp;
	if (pow(x, 4.0) <= 3.2e+234) {
		tmp = pow(x, 4.0) - pow(y, 4.0);
	} else {
		tmp = pow(x, 4.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x ** 4.0d0) <= 3.2d+234) then
        tmp = (x ** 4.0d0) - (y ** 4.0d0)
    else
        tmp = x ** 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.pow(x, 4.0) <= 3.2e+234) {
		tmp = Math.pow(x, 4.0) - Math.pow(y, 4.0);
	} else {
		tmp = Math.pow(x, 4.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.pow(x, 4.0) <= 3.2e+234:
		tmp = math.pow(x, 4.0) - math.pow(y, 4.0)
	else:
		tmp = math.pow(x, 4.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x ^ 4.0) <= 3.2e+234)
		tmp = Float64((x ^ 4.0) - (y ^ 4.0));
	else
		tmp = x ^ 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x ^ 4.0) <= 3.2e+234)
		tmp = (x ^ 4.0) - (y ^ 4.0);
	else
		tmp = x ^ 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Power[x, 4.0], $MachinePrecision], 3.2e+234], N[(N[Power[x, 4.0], $MachinePrecision] - N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision], N[Power[x, 4.0], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (pow.f64 x 4) < 3.19999999999999992e234

   1. Initial program 100.0%

      \[{x}^{4} - {y}^{4} \]
   2. Add Preprocessing

   if 3.19999999999999992e234 < (pow.f64 x 4)

   1. Initial program 59.6%

      \[{x}^{4} - {y}^{4} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 81.8%

      \[\leadsto \color{blue}{{x}^{4}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 82.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.1 \cdot 10^{+35}:\\ \;\;\;\;{x}^{4}\\ \mathbf{elif}\;x \leq 5.9 \cdot 10^{-5}:\\ \;\;\;\;-1 \cdot {y}^{4}\\ \mathbf{else}:\\ \;\;\;\;{x}^{4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.1e+35)
   (pow x 4.0)
   (if (<= x 5.9e-5) (* -1.0 (pow y 4.0)) (pow x 4.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.1e+35) {
		tmp = pow(x, 4.0);
	} else if (x <= 5.9e-5) {
		tmp = -1.0 * pow(y, 4.0);
	} else {
		tmp = pow(x, 4.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-6.1d+35)) then
        tmp = x ** 4.0d0
    else if (x <= 5.9d-5) then
        tmp = (-1.0d0) * (y ** 4.0d0)
    else
        tmp = x ** 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -6.1e+35) {
		tmp = Math.pow(x, 4.0);
	} else if (x <= 5.9e-5) {
		tmp = -1.0 * Math.pow(y, 4.0);
	} else {
		tmp = Math.pow(x, 4.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.1e+35:
		tmp = math.pow(x, 4.0)
	elif x <= 5.9e-5:
		tmp = -1.0 * math.pow(y, 4.0)
	else:
		tmp = math.pow(x, 4.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.1e+35)
		tmp = x ^ 4.0;
	elseif (x <= 5.9e-5)
		tmp = Float64(-1.0 * (y ^ 4.0));
	else
		tmp = x ^ 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6.1e+35)
		tmp = x ^ 4.0;
	elseif (x <= 5.9e-5)
		tmp = -1.0 * (y ^ 4.0);
	else
		tmp = x ^ 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.1e+35], N[Power[x, 4.0], $MachinePrecision], If[LessEqual[x, 5.9e-5], N[(-1.0 * N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision], N[Power[x, 4.0], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.09999999999999977e35 or 5.8999999999999998e-5 < x

   1. Initial program 66.1%

      \[{x}^{4} - {y}^{4} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 78.8%

      \[\leadsto \color{blue}{{x}^{4}} \]

   if -6.09999999999999977e35 < x < 5.8999999999999998e-5

   1. Initial program 100.0%

      \[{x}^{4} - {y}^{4} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 91.1%

      \[\leadsto \color{blue}{-1 \cdot {y}^{4}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 57.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ {x}^{4} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (pow x 4.0))

C

double code(double x, double y) {
	return pow(x, 4.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x ** 4.0d0
end function

Java

public static double code(double x, double y) {
	return Math.pow(x, 4.0);
}

Python

def code(x, y):
	return math.pow(x, 4.0)

Julia

function code(x, y)
	return x ^ 4.0
end

MATLAB

function tmp = code(x, y)
	tmp = x ^ 4.0;
end

Wolfram

code[x_, y_] := N[Power[x, 4.0], $MachinePrecision]

Derivation

1. Initial program 84.4%

   \[{x}^{4} - {y}^{4} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 57.6%

   \[\leadsto \color{blue}{{x}^{4}} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024050 -o generate:simplify
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  :precision binary64
  (- (pow x 4.0) (pow y 4.0)))