Radioactive exchange between two surfaces

Percentage Accurate: 86.1% → 92.7%

Time: 2.2s

Alternatives: 3

Speedup: 0.7×

• 61.9% 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: 92.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;{x}^{4} \leq 2.8 \cdot 10^{+297}:\\ \;\;\;\;{x}^{4} - {y}^{4}\\ \mathbf{else}:\\ \;\;\;\;{x}^{4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (pow x 4.0) 2.8e+297) (- (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) <= 2.8e+297) {
		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) <= 2.8d+297) 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) <= 2.8e+297) {
		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) <= 2.8e+297:
		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) <= 2.8e+297)
		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) <= 2.8e+297)
		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], 2.8e+297], 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)) < 2.8000000000000002e297

   1. Initial program 100.0%

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

   if 2.8000000000000002e297 < (pow.f64 x #s(literal 4 binary64))

   1. Initial program 65.5%

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

   3. Taylor expanded in x around inf 87.1%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;{x}^{4} \leq 2.8 \cdot 10^{+297}:\\ \;\;\;\;{x}^{4} - {y}^{4}\\ \mathbf{else}:\\ \;\;\;\;{x}^{4}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 81.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;{x}^{4} \leq 7.8 \cdot 10^{-234} \lor \neg \left({x}^{4} \leq 1.4 \cdot 10^{-142}\right) \land \left({x}^{4} \leq 3.4 \cdot 10^{-86} \lor \neg \left({x}^{4} \leq 2.35 \cdot 10^{-14}\right) \land {x}^{4} \leq 3.3 \cdot 10^{+142}\right):\\ \;\;\;\;-{y}^{4}\\ \mathbf{else}:\\ \;\;\;\;{x}^{4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= (pow x 4.0) 7.8e-234)
         (and (not (<= (pow x 4.0) 1.4e-142))
              (or (<= (pow x 4.0) 3.4e-86)
                  (and (not (<= (pow x 4.0) 2.35e-14))
                       (<= (pow x 4.0) 3.3e+142)))))
   (- (pow y 4.0))
   (pow x 4.0)))

C

double code(double x, double y) {
	double tmp;
	if ((pow(x, 4.0) <= 7.8e-234) || (!(pow(x, 4.0) <= 1.4e-142) && ((pow(x, 4.0) <= 3.4e-86) || (!(pow(x, 4.0) <= 2.35e-14) && (pow(x, 4.0) <= 3.3e+142))))) {
		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) <= 7.8d-234) .or. (.not. ((x ** 4.0d0) <= 1.4d-142)) .and. ((x ** 4.0d0) <= 3.4d-86) .or. (.not. ((x ** 4.0d0) <= 2.35d-14)) .and. ((x ** 4.0d0) <= 3.3d+142)) 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) <= 7.8e-234) || (!(Math.pow(x, 4.0) <= 1.4e-142) && ((Math.pow(x, 4.0) <= 3.4e-86) || (!(Math.pow(x, 4.0) <= 2.35e-14) && (Math.pow(x, 4.0) <= 3.3e+142))))) {
		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) <= 7.8e-234) or (not (math.pow(x, 4.0) <= 1.4e-142) and ((math.pow(x, 4.0) <= 3.4e-86) or (not (math.pow(x, 4.0) <= 2.35e-14) and (math.pow(x, 4.0) <= 3.3e+142)))):
		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) <= 7.8e-234) || (!((x ^ 4.0) <= 1.4e-142) && (((x ^ 4.0) <= 3.4e-86) || (!((x ^ 4.0) <= 2.35e-14) && ((x ^ 4.0) <= 3.3e+142)))))
		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) <= 7.8e-234) || (~(((x ^ 4.0) <= 1.4e-142)) && (((x ^ 4.0) <= 3.4e-86) || (~(((x ^ 4.0) <= 2.35e-14)) && ((x ^ 4.0) <= 3.3e+142)))))
		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], 7.8e-234], And[N[Not[LessEqual[N[Power[x, 4.0], $MachinePrecision], 1.4e-142]], $MachinePrecision], Or[LessEqual[N[Power[x, 4.0], $MachinePrecision], 3.4e-86], And[N[Not[LessEqual[N[Power[x, 4.0], $MachinePrecision], 2.35e-14]], $MachinePrecision], LessEqual[N[Power[x, 4.0], $MachinePrecision], 3.3e+142]]]]], (-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)) < 7.8000000000000002e-234 or 1.40000000000000002e-142 < (pow.f64 x #s(literal 4 binary64)) < 3.4e-86 or 2.3500000000000001e-14 < (pow.f64 x #s(literal 4 binary64)) < 3.3000000000000002e142

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 95.2%

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

      1. neg-mul-1 95.2%

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

   5. Simplified 95.2%

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

   if 7.8000000000000002e-234 < (pow.f64 x #s(literal 4 binary64)) < 1.40000000000000002e-142 or 3.4e-86 < (pow.f64 x #s(literal 4 binary64)) < 2.3500000000000001e-14 or 3.3000000000000002e142 < (pow.f64 x #s(literal 4 binary64))

   1. Initial program 74.4%

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

   3. Taylor expanded in x around inf 82.9%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;{x}^{4} \leq 7.8 \cdot 10^{-234} \lor \neg \left({x}^{4} \leq 1.4 \cdot 10^{-142}\right) \land \left({x}^{4} \leq 3.4 \cdot 10^{-86} \lor \neg \left({x}^{4} \leq 2.35 \cdot 10^{-14}\right) \land {x}^{4} \leq 3.3 \cdot 10^{+142}\right):\\ \;\;\;\;-{y}^{4}\\ \mathbf{else}:\\ \;\;\;\;{x}^{4}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 57.5% 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 84.4%

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

3. Taylor expanded in x around inf 63.2%

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

4. Final simplification 63.2%

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

Reproduce

herbie shell --seed 2024079 
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  :precision binary64
  (- (pow x 4.0) (pow y 4.0)))