Radioactive exchange between two surfaces

Percentage Accurate: 85.7% → 93.0%

Time: 2.7s

Alternatives: 3

Speedup: 0.7×

• 61.8% 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: 93.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;{x}^{4} \leq 10^{+307}:\\ \;\;\;\;{x}^{4} - {y}^{4}\\ \mathbf{else}:\\ \;\;\;\;{x}^{4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (pow x 4.0) 1e+307) (- (pow x 4.0) (pow y 4.0)) (pow x 4.0)))

C

double code(double x, double y) {
	double tmp;
	if (pow(x, 4.0) <= 1e+307) {
		tmp = pow(x, 4.0) - 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) <= 1d+307) then
        tmp = (x ** 4.0d0) - (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) <= 1e+307) {
		tmp = Math.pow(x, 4.0) - 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) <= 1e+307:
		tmp = math.pow(x, 4.0) - 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) <= 1e+307)
		tmp = Float64((x ^ 4.0) - (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) <= 1e+307)
		tmp = (x ^ 4.0) - (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], 1e+307], N[(N[Power[x, 4.0], $MachinePrecision] - N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision], N[Power[x, 4.0], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (pow.f64 x #s(literal 4 binary64)) < 9.99999999999999986e306

   1. Initial program 100.0%

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

   if 9.99999999999999986e306 < (pow.f64 x #s(literal 4 binary64))

   1. Initial program 64.4%

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

   3. Taylor expanded in x around inf 83.2%

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

Alternative 2: 81.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;{x}^{4} \leq 4 \cdot 10^{-143} \lor \neg \left({x}^{4} \leq 2 \cdot 10^{+122}\right) \land {x}^{4} \leq 5 \cdot 10^{+207}:\\ \;\;\;\;-{y}^{4}\\ \mathbf{else}:\\ \;\;\;\;{x}^{4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= (pow x 4.0) 4e-143)
         (and (not (<= (pow x 4.0) 2e+122)) (<= (pow x 4.0) 5e+207)))
   (- (pow y 4.0))
   (pow x 4.0)))

C

double code(double x, double y) {
	double tmp;
	if ((pow(x, 4.0) <= 4e-143) || (!(pow(x, 4.0) <= 2e+122) && (pow(x, 4.0) <= 5e+207))) {
		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) <= 4d-143) .or. (.not. ((x ** 4.0d0) <= 2d+122)) .and. ((x ** 4.0d0) <= 5d+207)) 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) <= 4e-143) || (!(Math.pow(x, 4.0) <= 2e+122) && (Math.pow(x, 4.0) <= 5e+207))) {
		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) <= 4e-143) or (not (math.pow(x, 4.0) <= 2e+122) and (math.pow(x, 4.0) <= 5e+207)):
		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) <= 4e-143) || (!((x ^ 4.0) <= 2e+122) && ((x ^ 4.0) <= 5e+207)))
		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) <= 4e-143) || (~(((x ^ 4.0) <= 2e+122)) && ((x ^ 4.0) <= 5e+207)))
		tmp = -(y ^ 4.0);
	else
		tmp = x ^ 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[N[Power[x, 4.0], $MachinePrecision], 4e-143], And[N[Not[LessEqual[N[Power[x, 4.0], $MachinePrecision], 2e+122]], $MachinePrecision], LessEqual[N[Power[x, 4.0], $MachinePrecision], 5e+207]]], (-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)) < 3.9999999999999998e-143 or 2.00000000000000003e122 < (pow.f64 x #s(literal 4 binary64)) < 4.9999999999999999e207

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 95.6%

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

      1. neg-mul-1 95.6%

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

   5. Simplified 95.6%

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

   if 3.9999999999999998e-143 < (pow.f64 x #s(literal 4 binary64)) < 2.00000000000000003e122 or 4.9999999999999999e207 < (pow.f64 x #s(literal 4 binary64))

   1. Initial program 72.7%

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

   3. Taylor expanded in x around inf 81.1%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;{x}^{4} \leq 4 \cdot 10^{-143} \lor \neg \left({x}^{4} \leq 2 \cdot 10^{+122}\right) \land {x}^{4} \leq 5 \cdot 10^{+207}:\\ \;\;\;\;-{y}^{4}\\ \mathbf{else}:\\ \;\;\;\;{x}^{4}\\ \end{array} \]
5. Add Preprocessing

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 85.9%

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

3. Taylor expanded in x around inf 60.5%

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

Reproduce

herbie shell --seed 2024110 
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  :precision binary64
  (- (pow x 4.0) (pow y 4.0)))