Radioactive exchange between two surfaces

Percentage Accurate: 86.0% → 90.9%

Time: 3.6s

Alternatives: 3

Speedup: 1.0×

• 61.2% 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: 86.0% 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: 90.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} x = |x|\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 1.5 \cdot 10^{+97}:\\ \;\;\;\;{x}^{4} - {y}^{4}\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{+131}:\\ \;\;\;\;-{y}^{4}\\ \mathbf{else}:\\ \;\;\;\;{x}^{4}\\ \end{array} \end{array} \]

FPCore

NOTE: x should be positive before calling this function
(FPCore (x y)
 :precision binary64
 (if (<= x 1.5e+97)
   (- (pow x 4.0) (pow y 4.0))
   (if (<= x 5.7e+131) (- (pow y 4.0)) (pow x 4.0))))

C

x = abs(x);
double code(double x, double y) {
	double tmp;
	if (x <= 1.5e+97) {
		tmp = pow(x, 4.0) - pow(y, 4.0);
	} else if (x <= 5.7e+131) {
		tmp = -pow(y, 4.0);
	} else {
		tmp = pow(x, 4.0);
	}
	return tmp;
}

Fortran

NOTE: x should be positive before calling this function
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 1.5d+97) then
        tmp = (x ** 4.0d0) - (y ** 4.0d0)
    else if (x <= 5.7d+131) then
        tmp = -(y ** 4.0d0)
    else
        tmp = x ** 4.0d0
    end if
    code = tmp
end function

Java

x = Math.abs(x);
public static double code(double x, double y) {
	double tmp;
	if (x <= 1.5e+97) {
		tmp = Math.pow(x, 4.0) - Math.pow(y, 4.0);
	} else if (x <= 5.7e+131) {
		tmp = -Math.pow(y, 4.0);
	} else {
		tmp = Math.pow(x, 4.0);
	}
	return tmp;
}

Python

x = abs(x)
def code(x, y):
	tmp = 0
	if x <= 1.5e+97:
		tmp = math.pow(x, 4.0) - math.pow(y, 4.0)
	elif x <= 5.7e+131:
		tmp = -math.pow(y, 4.0)
	else:
		tmp = math.pow(x, 4.0)
	return tmp

Julia

x = abs(x)
function code(x, y)
	tmp = 0.0
	if (x <= 1.5e+97)
		tmp = Float64((x ^ 4.0) - (y ^ 4.0));
	elseif (x <= 5.7e+131)
		tmp = Float64(-(y ^ 4.0));
	else
		tmp = x ^ 4.0;
	end
	return tmp
end

MATLAB

x = abs(x)
function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 1.5e+97)
		tmp = (x ^ 4.0) - (y ^ 4.0);
	elseif (x <= 5.7e+131)
		tmp = -(y ^ 4.0);
	else
		tmp = x ^ 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x should be positive before calling this function
code[x_, y_] := If[LessEqual[x, 1.5e+97], N[(N[Power[x, 4.0], $MachinePrecision] - N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.7e+131], (-N[Power[y, 4.0], $MachinePrecision]), N[Power[x, 4.0], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 1.4999999999999999e97

   1. Initial program 89.6%

      \[{x}^{4} - {y}^{4} \]

   if 1.4999999999999999e97 < x < 5.7e131

   1. Initial program 50.0%

      \[{x}^{4} - {y}^{4} \]

   2. Taylor expanded in x around 0 50.8%

      \[\leadsto \color{blue}{-1 \cdot {y}^{4}} \]
   3. Step-by-step derivation

      1. mul-1-neg 50.8%

         \[\leadsto \color{blue}{-{y}^{4}} \]

   4. Simplified 50.8%

      \[\leadsto \color{blue}{-{y}^{4}} \]

   if 5.7e131 < x

   1. Initial program 62.7%

      \[{x}^{4} - {y}^{4} \]

   2. Taylor expanded in x around inf 82.4%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.5 \cdot 10^{+97}:\\ \;\;\;\;{x}^{4} - {y}^{4}\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{+131}:\\ \;\;\;\;-{y}^{4}\\ \mathbf{else}:\\ \;\;\;\;{x}^{4}\\ \end{array} \]

Alternative 2: 81.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} x = |x|\\ \\ \begin{array}{l} \mathbf{if}\;{x}^{4} \leq 4.4 \cdot 10^{+285}:\\ \;\;\;\;-{y}^{4}\\ \mathbf{else}:\\ \;\;\;\;{x}^{4}\\ \end{array} \end{array} \]

FPCore

NOTE: x should be positive before calling this function
(FPCore (x y)
 :precision binary64
 (if (<= (pow x 4.0) 4.4e+285) (- (pow y 4.0)) (pow x 4.0)))

C

x = abs(x);
double code(double x, double y) {
	double tmp;
	if (pow(x, 4.0) <= 4.4e+285) {
		tmp = -pow(y, 4.0);
	} else {
		tmp = pow(x, 4.0);
	}
	return tmp;
}

Fortran

NOTE: x should be positive before calling this function
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x ** 4.0d0) <= 4.4d+285) then
        tmp = -(y ** 4.0d0)
    else
        tmp = x ** 4.0d0
    end if
    code = tmp
end function

Java

x = Math.abs(x);
public static double code(double x, double y) {
	double tmp;
	if (Math.pow(x, 4.0) <= 4.4e+285) {
		tmp = -Math.pow(y, 4.0);
	} else {
		tmp = Math.pow(x, 4.0);
	}
	return tmp;
}

Python

x = abs(x)
def code(x, y):
	tmp = 0
	if math.pow(x, 4.0) <= 4.4e+285:
		tmp = -math.pow(y, 4.0)
	else:
		tmp = math.pow(x, 4.0)
	return tmp

Julia

x = abs(x)
function code(x, y)
	tmp = 0.0
	if ((x ^ 4.0) <= 4.4e+285)
		tmp = Float64(-(y ^ 4.0));
	else
		tmp = x ^ 4.0;
	end
	return tmp
end

MATLAB

x = abs(x)
function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x ^ 4.0) <= 4.4e+285)
		tmp = -(y ^ 4.0);
	else
		tmp = x ^ 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x should be positive before calling this function
code[x_, y_] := If[LessEqual[N[Power[x, 4.0], $MachinePrecision], 4.4e+285], (-N[Power[y, 4.0], $MachinePrecision]), N[Power[x, 4.0], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (pow.f64 x 4) < 4.4e285

   1. Initial program 100.0%

      \[{x}^{4} - {y}^{4} \]

   2. Taylor expanded in x around 0 90.1%

      \[\leadsto \color{blue}{-1 \cdot {y}^{4}} \]
   3. Step-by-step derivation

      1. mul-1-neg 90.1%

         \[\leadsto \color{blue}{-{y}^{4}} \]

   4. Simplified 90.1%

      \[\leadsto \color{blue}{-{y}^{4}} \]

   if 4.4e285 < (pow.f64 x 4)

   1. Initial program 59.6%

      \[{x}^{4} - {y}^{4} \]

   2. Taylor expanded in x around inf 79.8%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;{x}^{4} \leq 4.4 \cdot 10^{+285}:\\ \;\;\;\;-{y}^{4}\\ \mathbf{else}:\\ \;\;\;\;{x}^{4}\\ \end{array} \]

Alternative 3: 58.1% accurate, 2.0× speedup

Math

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

FPCore

NOTE: x should be positive before calling this function
(FPCore (x y) :precision binary64 (pow x 4.0))

C

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

Fortran

NOTE: x should be positive before calling this function
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x ** 4.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x should be positive before calling this function
code[x_, y_] := N[Power[x, 4.0], $MachinePrecision]

Derivation

1. Initial program 83.6%

   \[{x}^{4} - {y}^{4} \]

2. Taylor expanded in x around inf 52.5%

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

3. Final simplification 52.5%

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

Reproduce

herbie shell --seed 2023301 
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  :precision binary64
  (- (pow x 4.0) (pow y 4.0)))