Radioactive exchange between two surfaces

Percentage Accurate: 86.1% → 92.4%

Time: 2.0s

Alternatives: 3

Speedup: 1.0×

• 61.3% 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: 86.1% 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: 92.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \begin{array}{l} \mathbf{if}\;x_m \leq 2.8 \cdot 10^{+82}:\\ \;\;\;\;{x_m}^{4} - {y}^{4}\\ \mathbf{elif}\;x_m \leq 1.3 \cdot 10^{+93}:\\ \;\;\;\;-{y}^{4}\\ \mathbf{else}:\\ \;\;\;\;{x_m}^{4}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m y)
 :precision binary64
 (if (<= x_m 2.8e+82)
   (- (pow x_m 4.0) (pow y 4.0))
   (if (<= x_m 1.3e+93) (- (pow y 4.0)) (pow x_m 4.0))))

C

x_m = fabs(x);
double code(double x_m, double y) {
	double tmp;
	if (x_m <= 2.8e+82) {
		tmp = pow(x_m, 4.0) - pow(y, 4.0);
	} else if (x_m <= 1.3e+93) {
		tmp = -pow(y, 4.0);
	} else {
		tmp = pow(x_m, 4.0);
	}
	return tmp;
}

Fortran

x_m = abs(x)
real(8) function code(x_m, y)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x_m <= 2.8d+82) then
        tmp = (x_m ** 4.0d0) - (y ** 4.0d0)
    else if (x_m <= 1.3d+93) then
        tmp = -(y ** 4.0d0)
    else
        tmp = x_m ** 4.0d0
    end if
    code = tmp
end function

Java

x_m = Math.abs(x);
public static double code(double x_m, double y) {
	double tmp;
	if (x_m <= 2.8e+82) {
		tmp = Math.pow(x_m, 4.0) - Math.pow(y, 4.0);
	} else if (x_m <= 1.3e+93) {
		tmp = -Math.pow(y, 4.0);
	} else {
		tmp = Math.pow(x_m, 4.0);
	}
	return tmp;
}

Python

x_m = math.fabs(x)
def code(x_m, y):
	tmp = 0
	if x_m <= 2.8e+82:
		tmp = math.pow(x_m, 4.0) - math.pow(y, 4.0)
	elif x_m <= 1.3e+93:
		tmp = -math.pow(y, 4.0)
	else:
		tmp = math.pow(x_m, 4.0)
	return tmp

Julia

x_m = abs(x)
function code(x_m, y)
	tmp = 0.0
	if (x_m <= 2.8e+82)
		tmp = Float64((x_m ^ 4.0) - (y ^ 4.0));
	elseif (x_m <= 1.3e+93)
		tmp = Float64(-(y ^ 4.0));
	else
		tmp = x_m ^ 4.0;
	end
	return tmp
end

MATLAB

x_m = abs(x);
function tmp_2 = code(x_m, y)
	tmp = 0.0;
	if (x_m <= 2.8e+82)
		tmp = (x_m ^ 4.0) - (y ^ 4.0);
	elseif (x_m <= 1.3e+93)
		tmp = -(y ^ 4.0);
	else
		tmp = x_m ^ 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y_] := If[LessEqual[x$95$m, 2.8e+82], N[(N[Power[x$95$m, 4.0], $MachinePrecision] - N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[x$95$m, 1.3e+93], (-N[Power[y, 4.0], $MachinePrecision]), N[Power[x$95$m, 4.0], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 2.8e82

   1. Initial program 92.1%

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

   if 2.8e82 < x < 1.3e93

   1. Initial program 25.0%

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

   3. Taylor expanded in x around 0 75.4%

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

      1. neg-mul-1 75.4%

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

   5. Simplified 75.4%

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

   if 1.3e93 < x

   1. Initial program 48.6%

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

   3. Taylor expanded in x around inf 78.4%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.8 \cdot 10^{+82}:\\ \;\;\;\;{x}^{4} - {y}^{4}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+93}:\\ \;\;\;\;-{y}^{4}\\ \mathbf{else}:\\ \;\;\;\;{x}^{4}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 81.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \begin{array}{l} \mathbf{if}\;{y}^{4} \leq 1.05 \cdot 10^{-28} \lor \neg \left({y}^{4} \leq 3.5 \cdot 10^{+246}\right) \land {y}^{4} \leq 4 \cdot 10^{+279}:\\ \;\;\;\;{x_m}^{4}\\ \mathbf{else}:\\ \;\;\;\;-{y}^{4}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m y)
 :precision binary64
 (if (or (<= (pow y 4.0) 1.05e-28)
         (and (not (<= (pow y 4.0) 3.5e+246)) (<= (pow y 4.0) 4e+279)))
   (pow x_m 4.0)
   (- (pow y 4.0))))

C

x_m = fabs(x);
double code(double x_m, double y) {
	double tmp;
	if ((pow(y, 4.0) <= 1.05e-28) || (!(pow(y, 4.0) <= 3.5e+246) && (pow(y, 4.0) <= 4e+279))) {
		tmp = pow(x_m, 4.0);
	} else {
		tmp = -pow(y, 4.0);
	}
	return tmp;
}

Fortran

x_m = abs(x)
real(8) function code(x_m, y)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8) :: tmp
    if (((y ** 4.0d0) <= 1.05d-28) .or. (.not. ((y ** 4.0d0) <= 3.5d+246)) .and. ((y ** 4.0d0) <= 4d+279)) then
        tmp = x_m ** 4.0d0
    else
        tmp = -(y ** 4.0d0)
    end if
    code = tmp
end function

Java

x_m = Math.abs(x);
public static double code(double x_m, double y) {
	double tmp;
	if ((Math.pow(y, 4.0) <= 1.05e-28) || (!(Math.pow(y, 4.0) <= 3.5e+246) && (Math.pow(y, 4.0) <= 4e+279))) {
		tmp = Math.pow(x_m, 4.0);
	} else {
		tmp = -Math.pow(y, 4.0);
	}
	return tmp;
}

Python

x_m = math.fabs(x)
def code(x_m, y):
	tmp = 0
	if (math.pow(y, 4.0) <= 1.05e-28) or (not (math.pow(y, 4.0) <= 3.5e+246) and (math.pow(y, 4.0) <= 4e+279)):
		tmp = math.pow(x_m, 4.0)
	else:
		tmp = -math.pow(y, 4.0)
	return tmp

Julia

x_m = abs(x)
function code(x_m, y)
	tmp = 0.0
	if (((y ^ 4.0) <= 1.05e-28) || (!((y ^ 4.0) <= 3.5e+246) && ((y ^ 4.0) <= 4e+279)))
		tmp = x_m ^ 4.0;
	else
		tmp = Float64(-(y ^ 4.0));
	end
	return tmp
end

MATLAB

x_m = abs(x);
function tmp_2 = code(x_m, y)
	tmp = 0.0;
	if (((y ^ 4.0) <= 1.05e-28) || (~(((y ^ 4.0) <= 3.5e+246)) && ((y ^ 4.0) <= 4e+279)))
		tmp = x_m ^ 4.0;
	else
		tmp = -(y ^ 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y_] := If[Or[LessEqual[N[Power[y, 4.0], $MachinePrecision], 1.05e-28], And[N[Not[LessEqual[N[Power[y, 4.0], $MachinePrecision], 3.5e+246]], $MachinePrecision], LessEqual[N[Power[y, 4.0], $MachinePrecision], 4e+279]]], N[Power[x$95$m, 4.0], $MachinePrecision], (-N[Power[y, 4.0], $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if (pow.f64 y 4) < 1.05000000000000003e-28 or 3.49999999999999975e246 < (pow.f64 y 4) < 4.00000000000000023e279

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 91.4%

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

   if 1.05000000000000003e-28 < (pow.f64 y 4) < 3.49999999999999975e246 or 4.00000000000000023e279 < (pow.f64 y 4)

   1. Initial program 68.5%

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

   3. Taylor expanded in x around 0 78.3%

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

      1. neg-mul-1 78.3%

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

   5. Simplified 78.3%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;{y}^{4} \leq 1.05 \cdot 10^{-28} \lor \neg \left({y}^{4} \leq 3.5 \cdot 10^{+246}\right) \land {y}^{4} \leq 4 \cdot 10^{+279}:\\ \;\;\;\;{x}^{4}\\ \mathbf{else}:\\ \;\;\;\;-{y}^{4}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 57.1% accurate, 2.0× speedup

Math

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

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m y) :precision binary64 (pow x_m 4.0))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y_] := N[Power[x$95$m, 4.0], $MachinePrecision]

Derivation

1. Initial program 84.8%

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

3. Taylor expanded in x around inf 58.1%

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

4. Final simplification 58.1%

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

Reproduce

herbie shell --seed 2024019 
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  :precision binary64
  (- (pow x 4.0) (pow y 4.0)))