Radioactive exchange between two surfaces

Percentage Accurate: 85.7% → 85.7%

Time: 1.6s

Alternatives: 3

Speedup: 0.7×

• 60.2% 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: 85.7% 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: 85.7% 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 4) < +inf.0

   1. Initial program 87.5%

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

   if +inf.0 < (pow.f64 y 4)

   1. Initial program 87.5%

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

   2. Taylor expanded in x around 0 61.1%

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

      1. neg-mul-1 61.1%

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

   4. Simplified 61.1%

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

4. Final simplification 87.5%

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

Alternative 2: 68.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.55 \cdot 10^{-47} \lor \neg \left(y \leq 410000000000\right) \land y \leq 4.7 \cdot 10^{+87}:\\ \;\;\;\;{x}^{4}\\ \mathbf{else}:\\ \;\;\;\;-{y}^{4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y 1.55e-47) (and (not (<= y 410000000000.0)) (<= y 4.7e+87)))
   (pow x 4.0)
   (- (pow y 4.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= 1.55e-47) || (!(y <= 410000000000.0) && (y <= 4.7e+87))) {
		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 ((y <= 1.55d-47) .or. (.not. (y <= 410000000000.0d0)) .and. (y <= 4.7d+87)) 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 ((y <= 1.55e-47) || (!(y <= 410000000000.0) && (y <= 4.7e+87))) {
		tmp = Math.pow(x, 4.0);
	} else {
		tmp = -Math.pow(y, 4.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= 1.55e-47) or (not (y <= 410000000000.0) and (y <= 4.7e+87)):
		tmp = math.pow(x, 4.0)
	else:
		tmp = -math.pow(y, 4.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= 1.55e-47) || (!(y <= 410000000000.0) && (y <= 4.7e+87)))
		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 ((y <= 1.55e-47) || (~((y <= 410000000000.0)) && (y <= 4.7e+87)))
		tmp = x ^ 4.0;
	else
		tmp = -(y ^ 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, 1.55e-47], And[N[Not[LessEqual[y, 410000000000.0]], $MachinePrecision], LessEqual[y, 4.7e+87]]], N[Power[x, 4.0], $MachinePrecision], (-N[Power[y, 4.0], $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if y < 1.5499999999999999e-47 or 4.1e11 < y < 4.7000000000000004e87

   1. Initial program 89.3%

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

   2. Taylor expanded in x around inf 67.8%

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

   if 1.5499999999999999e-47 < y < 4.1e11 or 4.7000000000000004e87 < y

   1. Initial program 80.4%

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

   2. Taylor expanded in x around 0 90.2%

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

      1. neg-mul-1 90.2%

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

   4. Simplified 90.2%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.55 \cdot 10^{-47} \lor \neg \left(y \leq 410000000000\right) \land y \leq 4.7 \cdot 10^{+87}:\\ \;\;\;\;{x}^{4}\\ \mathbf{else}:\\ \;\;\;\;-{y}^{4}\\ \end{array} \]

Alternative 3: 58.1% 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 87.5%

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

2. Taylor expanded in x around inf 56.5%

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

3. Final simplification 56.5%

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

Reproduce

herbie shell --seed 2023333 
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  :precision binary64
  (- (pow x 4.0) (pow y 4.0)))