Radioactive exchange between two surfaces

Percentage Accurate: 85.0% → 92.6%

Time: 3.0s

Alternatives: 4

Speedup: 0.5×

• 61.4% 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: 85.0% 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: 92.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;{x}^{4} - {y}^{4} \leq -5 \cdot 10^{-321}:\\ \;\;\;\;{y}^{4} \cdot \left(\frac{{x}^{4}}{{y}^{4}} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;{x}^{4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (- (pow x 4.0) (pow y 4.0)) -5e-321)
   (* (pow y 4.0) (+ (/ (pow x 4.0) (pow y 4.0)) -1.0))
   (pow x 4.0)))

C

double code(double x, double y) {
	double tmp;
	if ((pow(x, 4.0) - pow(y, 4.0)) <= -5e-321) {
		tmp = pow(y, 4.0) * ((pow(x, 4.0) / pow(y, 4.0)) + -1.0);
	} 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) - (y ** 4.0d0)) <= (-5d-321)) then
        tmp = (y ** 4.0d0) * (((x ** 4.0d0) / (y ** 4.0d0)) + (-1.0d0))
    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) - Math.pow(y, 4.0)) <= -5e-321) {
		tmp = Math.pow(y, 4.0) * ((Math.pow(x, 4.0) / Math.pow(y, 4.0)) + -1.0);
	} else {
		tmp = Math.pow(x, 4.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (math.pow(x, 4.0) - math.pow(y, 4.0)) <= -5e-321:
		tmp = math.pow(y, 4.0) * ((math.pow(x, 4.0) / math.pow(y, 4.0)) + -1.0)
	else:
		tmp = math.pow(x, 4.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64((x ^ 4.0) - (y ^ 4.0)) <= -5e-321)
		tmp = Float64((y ^ 4.0) * Float64(Float64((x ^ 4.0) / (y ^ 4.0)) + -1.0));
	else
		tmp = x ^ 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((x ^ 4.0) - (y ^ 4.0)) <= -5e-321)
		tmp = (y ^ 4.0) * (((x ^ 4.0) / (y ^ 4.0)) + -1.0);
	else
		tmp = x ^ 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[Power[x, 4.0], $MachinePrecision] - N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision], -5e-321], N[(N[Power[y, 4.0], $MachinePrecision] * N[(N[(N[Power[x, 4.0], $MachinePrecision] / N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[Power[x, 4.0], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) < -4.99994e-321

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{{y}^{4} \cdot \left(\frac{{x}^{4}}{{y}^{4}} - 1\right)} \]

   if -4.99994e-321 < (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))

   1. Initial program 83.0%

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

   3. Taylor expanded in x around inf 91.5%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;{x}^{4} - {y}^{4} \leq -5 \cdot 10^{-321}:\\ \;\;\;\;{y}^{4} \cdot \left(\frac{{x}^{4}}{{y}^{4}} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;{x}^{4}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {x}^{4} - {y}^{4}\\ \mathbf{if}\;t\_0 \leq \infty:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-{y}^{4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (pow x 4.0) (pow y 4.0))))
   (if (<= t_0 INFINITY) t_0 (- (pow y 4.0)))))

C

double code(double x, double y) {
	double t_0 = pow(x, 4.0) - pow(y, 4.0);
	double tmp;
	if (t_0 <= ((double) INFINITY)) {
		tmp = t_0;
	} else {
		tmp = -pow(y, 4.0);
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double t_0 = Math.pow(x, 4.0) - Math.pow(y, 4.0);
	double tmp;
	if (t_0 <= Double.POSITIVE_INFINITY) {
		tmp = t_0;
	} else {
		tmp = -Math.pow(y, 4.0);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.pow(x, 4.0) - math.pow(y, 4.0)
	tmp = 0
	if t_0 <= math.inf:
		tmp = t_0
	else:
		tmp = -math.pow(y, 4.0)
	return tmp

Julia

function code(x, y)
	t_0 = Float64((x ^ 4.0) - (y ^ 4.0))
	tmp = 0.0
	if (t_0 <= Inf)
		tmp = t_0;
	else
		tmp = Float64(-(y ^ 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x ^ 4.0) - (y ^ 4.0);
	tmp = 0.0;
	if (t_0 <= Inf)
		tmp = t_0;
	else
		tmp = -(y ^ 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Power[x, 4.0], $MachinePrecision] - N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, Infinity], t$95$0, (-N[Power[y, 4.0], $MachinePrecision])]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0 50.0%

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

      1. neg-mul-1 50.0%

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

   5. Simplified 50.0%

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

Alternative 3: 82.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;{x}^{4} \leq 1.06 \cdot 10^{+18}:\\ \;\;\;\;-{y}^{4}\\ \mathbf{else}:\\ \;\;\;\;{x}^{4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (pow x 4.0) 1.06e+18) (- (pow y 4.0)) (pow x 4.0)))

C

double code(double x, double y) {
	double tmp;
	if (pow(x, 4.0) <= 1.06e+18) {
		tmp = -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) <= 1.06d+18) then
        tmp = -(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) <= 1.06e+18) {
		tmp = -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) <= 1.06e+18:
		tmp = -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) <= 1.06e+18)
		tmp = Float64(-(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) <= 1.06e+18)
		tmp = -(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], 1.06e+18], (-N[Power[y, 4.0], $MachinePrecision]), N[Power[x, 4.0], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (pow.f64 x #s(literal 4 binary64)) < 1.06e18

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 91.6%

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

      1. neg-mul-1 91.6%

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

   5. Simplified 91.6%

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

   if 1.06e18 < (pow.f64 x #s(literal 4 binary64))

   1. Initial program 79.8%

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

   3. Taylor expanded in x around inf 79.1%

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

Alternative 4: 57.4% 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 89.8%

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

3. Taylor expanded in x around inf 55.9%

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

Reproduce

herbie shell --seed 2024100 
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  :precision binary64
  (- (pow x 4.0) (pow y 4.0)))