Radioactive exchange between two surfaces

Percentage Accurate: 85.2% → 89.6%

Time: 3.2s

Alternatives: 3

Speedup: 1.0×

• 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: 85.2% 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: 89.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \begin{array}{l} \mathbf{if}\;x\_m \leq 1.9 \cdot 10^{+103}:\\ \;\;\;\;{x\_m}^{4} - {y}^{4}\\ \mathbf{elif}\;x\_m \leq 10^{+141}:\\ \;\;\;\;-{y}^{4}\\ \mathbf{else}:\\ \;\;\;\;{x\_m}^{4}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m y)
 :precision binary64
 (if (<= x_m 1.9e+103)
   (- (pow x_m 4.0) (pow y 4.0))
   (if (<= x_m 1e+141) (- (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 <= 1.9e+103) {
		tmp = pow(x_m, 4.0) - pow(y, 4.0);
	} else if (x_m <= 1e+141) {
		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 <= 1.9d+103) then
        tmp = (x_m ** 4.0d0) - (y ** 4.0d0)
    else if (x_m <= 1d+141) 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 <= 1.9e+103) {
		tmp = Math.pow(x_m, 4.0) - Math.pow(y, 4.0);
	} else if (x_m <= 1e+141) {
		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 <= 1.9e+103:
		tmp = math.pow(x_m, 4.0) - math.pow(y, 4.0)
	elif x_m <= 1e+141:
		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 <= 1.9e+103)
		tmp = Float64((x_m ^ 4.0) - (y ^ 4.0));
	elseif (x_m <= 1e+141)
		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 <= 1.9e+103)
		tmp = (x_m ^ 4.0) - (y ^ 4.0);
	elseif (x_m <= 1e+141)
		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, 1.9e+103], N[(N[Power[x$95$m, 4.0], $MachinePrecision] - N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[x$95$m, 1e+141], (-N[Power[y, 4.0], $MachinePrecision]), N[Power[x$95$m, 4.0], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 1.8999999999999998e103

   1. Initial program 90.2%

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

   if 1.8999999999999998e103 < x < 1.00000000000000002e141

   1. Initial program 40.0%

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

   3. Taylor expanded in x around 0 60.6%

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

      1. neg-mul-1 60.6%

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

   5. Simplified 60.6%

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

   if 1.00000000000000002e141 < x

   1. Initial program 56.8%

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

   3. Taylor expanded in x around inf 83.8%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.9 \cdot 10^{+103}:\\ \;\;\;\;{x}^{4} - {y}^{4}\\ \mathbf{elif}\;x \leq 10^{+141}:\\ \;\;\;\;-{y}^{4}\\ \mathbf{else}:\\ \;\;\;\;{x}^{4}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 82.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \begin{array}{l} \mathbf{if}\;{x\_m}^{4} \leq 6.2 \cdot 10^{-52} \lor \neg \left({x\_m}^{4} \leq 1.7 \cdot 10^{+33}\right) \land {x\_m}^{4} \leq 5.1 \cdot 10^{+135}:\\ \;\;\;\;-{y}^{4}\\ \mathbf{else}:\\ \;\;\;\;{x\_m}^{4}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m y)
 :precision binary64
 (if (or (<= (pow x_m 4.0) 6.2e-52)
         (and (not (<= (pow x_m 4.0) 1.7e+33)) (<= (pow x_m 4.0) 5.1e+135)))
   (- (pow y 4.0))
   (pow x_m 4.0)))

C

x_m = fabs(x);
double code(double x_m, double y) {
	double tmp;
	if ((pow(x_m, 4.0) <= 6.2e-52) || (!(pow(x_m, 4.0) <= 1.7e+33) && (pow(x_m, 4.0) <= 5.1e+135))) {
		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 ** 4.0d0) <= 6.2d-52) .or. (.not. ((x_m ** 4.0d0) <= 1.7d+33)) .and. ((x_m ** 4.0d0) <= 5.1d+135)) 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 ((Math.pow(x_m, 4.0) <= 6.2e-52) || (!(Math.pow(x_m, 4.0) <= 1.7e+33) && (Math.pow(x_m, 4.0) <= 5.1e+135))) {
		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 (math.pow(x_m, 4.0) <= 6.2e-52) or (not (math.pow(x_m, 4.0) <= 1.7e+33) and (math.pow(x_m, 4.0) <= 5.1e+135)):
		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 ^ 4.0) <= 6.2e-52) || (!((x_m ^ 4.0) <= 1.7e+33) && ((x_m ^ 4.0) <= 5.1e+135)))
		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 ^ 4.0) <= 6.2e-52) || (~(((x_m ^ 4.0) <= 1.7e+33)) && ((x_m ^ 4.0) <= 5.1e+135)))
		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[Or[LessEqual[N[Power[x$95$m, 4.0], $MachinePrecision], 6.2e-52], And[N[Not[LessEqual[N[Power[x$95$m, 4.0], $MachinePrecision], 1.7e+33]], $MachinePrecision], LessEqual[N[Power[x$95$m, 4.0], $MachinePrecision], 5.1e+135]]], (-N[Power[y, 4.0], $MachinePrecision]), N[Power[x$95$m, 4.0], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (pow.f64 x 4) < 6.1999999999999998e-52 or 1.7e33 < (pow.f64 x 4) < 5.09999999999999982e135

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 90.5%

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

      1. neg-mul-1 90.5%

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

   5. Simplified 90.5%

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

   if 6.1999999999999998e-52 < (pow.f64 x 4) < 1.7e33 or 5.09999999999999982e135 < (pow.f64 x 4)

   1. Initial program 65.2%

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

   3. Taylor expanded in x around inf 80.0%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;{x}^{4} \leq 6.2 \cdot 10^{-52} \lor \neg \left({x}^{4} \leq 1.7 \cdot 10^{+33}\right) \land {x}^{4} \leq 5.1 \cdot 10^{+135}:\\ \;\;\;\;-{y}^{4}\\ \mathbf{else}:\\ \;\;\;\;{x}^{4}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 57.8% 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 84.4%

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

3. Taylor expanded in x around inf 57.6%

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

4. Final simplification 57.6%

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

Reproduce

herbie shell --seed 2024050 
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  :precision binary64
  (- (pow x 4.0) (pow y 4.0)))