Radioactive exchange between two surfaces

Percentage Accurate: 86.0% → 86.0%

Time: 2.7s

Alternatives: 3

Speedup: 0.7×

• 60.7% 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: 86.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;{y}^{4} \leq \infty:\\ \;\;\;\;{x}^{4} - {y}^{4}\\ \mathbf{else}:\\ \;\;\;\;-{y}^{4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (pow y 4.0) INFINITY) (- (pow x 4.0) (pow y 4.0)) (- (pow y 4.0))))

C

double code(double x, double y) {
	double tmp;
	if (pow(y, 4.0) <= ((double) INFINITY)) {
		tmp = pow(x, 4.0) - pow(y, 4.0);
	} else {
		tmp = -pow(y, 4.0);
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.pow(y, 4.0) <= Double.POSITIVE_INFINITY) {
		tmp = Math.pow(x, 4.0) - Math.pow(y, 4.0);
	} else {
		tmp = -Math.pow(y, 4.0);
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y ^ 4.0) <= Inf)
		tmp = (x ^ 4.0) - (y ^ 4.0);
	else
		tmp = -(y ^ 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (pow.f64 y #s(literal 4 binary64)) < +inf.0

   1. Initial program 88.3%

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

   if +inf.0 < (pow.f64 y #s(literal 4 binary64))

   1. Initial program 88.3%

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

   3. Taylor expanded in x around 0 57.1%

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

      1. neg-mul-1 57.1%

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

   5. Simplified 57.1%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;{y}^{4} \leq \infty:\\ \;\;\;\;{x}^{4} - {y}^{4}\\ \mathbf{else}:\\ \;\;\;\;-{y}^{4}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 81.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+17} \lor \neg \left(x \leq 3 \cdot 10^{-66}\right):\\ \;\;\;\;{x}^{4}\\ \mathbf{else}:\\ \;\;\;\;-{y}^{4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.2e+17) (not (<= x 3e-66))) (pow x 4.0) (- (pow y 4.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.2e+17) || !(x <= 3e-66)) {
		tmp = pow(x, 4.0);
	} else {
		tmp = -pow(y, 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 <= (-2.2d+17)) .or. (.not. (x <= 3d-66))) then
        tmp = x ** 4.0d0
    else
        tmp = -(y ** 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -2.2e+17) || !(x <= 3e-66)) {
		tmp = Math.pow(x, 4.0);
	} else {
		tmp = -Math.pow(y, 4.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.2e+17) or not (x <= 3e-66):
		tmp = math.pow(x, 4.0)
	else:
		tmp = -math.pow(y, 4.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.2e+17) || !(x <= 3e-66))
		tmp = x ^ 4.0;
	else
		tmp = Float64(-(y ^ 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2.2e+17) || ~((x <= 3e-66)))
		tmp = x ^ 4.0;
	else
		tmp = -(y ^ 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.2e+17], N[Not[LessEqual[x, 3e-66]], $MachinePrecision]], N[Power[x, 4.0], $MachinePrecision], (-N[Power[y, 4.0], $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if x < -2.2e17 or 3.0000000000000002e-66 < x

   1. Initial program 78.1%

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

   3. Taylor expanded in x around inf 79.6%

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

   if -2.2e17 < x < 3.0000000000000002e-66

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 97.9%

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

      1. neg-mul-1 97.9%

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

   5. Simplified 97.9%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+17} \lor \neg \left(x \leq 3 \cdot 10^{-66}\right):\\ \;\;\;\;{x}^{4}\\ \mathbf{else}:\\ \;\;\;\;-{y}^{4}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 57.6% 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 88.3%

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

3. Taylor expanded in x around inf 57.3%

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

4. Final simplification 57.3%

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

Reproduce

herbie shell --seed 2024072 
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  :precision binary64
  (- (pow x 4.0) (pow y 4.0)))