Radioactive exchange between two surfaces

Percentage Accurate: 85.7% → 85.7%

Time: 3.5s

Alternatives: 3

Speedup: 0.7×

• 60.9% 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: 85.7% 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: 85.7% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (pow x 4.0) INFINITY) (- (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) <= ((double) INFINITY)) {
		tmp = pow(x, 4.0) - pow(y, 4.0);
	} else {
		tmp = pow(x, 4.0);
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.pow(x, 4.0) <= Double.POSITIVE_INFINITY) {
		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) <= math.inf:
		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) <= Inf)
		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) <= Inf)
		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], Infinity], 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)) < +inf.0

   1. Initial program 83.6%

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

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

   1. Initial program 83.6%

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

   3. Taylor expanded in x around inf

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

      1. pow-lowering-pow.f64 54.5%

         \[\leadsto \mathsf{pow.f64}\left(x, \color{blue}{4}\right) \]

   5. Simplified 54.5%

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

Alternative 2: 82.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;{y}^{4} \leq 5.5 \cdot 10^{+62}:\\ \;\;\;\;{x}^{4}\\ \mathbf{else}:\\ \;\;\;\;0 - {y}^{4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (pow y 4.0) 5.5e+62) (pow x 4.0) (- 0.0 (pow y 4.0))))

C

double code(double x, double y) {
	double tmp;
	if (pow(y, 4.0) <= 5.5e+62) {
		tmp = pow(x, 4.0);
	} else {
		tmp = 0.0 - pow(y, 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 ((y ** 4.0d0) <= 5.5d+62) then
        tmp = x ** 4.0d0
    else
        tmp = 0.0d0 - (y ** 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.pow(y, 4.0) <= 5.5e+62) {
		tmp = Math.pow(x, 4.0);
	} else {
		tmp = 0.0 - Math.pow(y, 4.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.pow(y, 4.0) <= 5.5e+62:
		tmp = math.pow(x, 4.0)
	else:
		tmp = 0.0 - math.pow(y, 4.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y ^ 4.0) <= 5.5e+62)
		tmp = x ^ 4.0;
	else
		tmp = Float64(0.0 - (y ^ 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y ^ 4.0) <= 5.5e+62)
		tmp = x ^ 4.0;
	else
		tmp = 0.0 - (y ^ 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Power[y, 4.0], $MachinePrecision], 5.5e+62], N[Power[x, 4.0], $MachinePrecision], N[(0.0 - N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (pow.f64 y #s(literal 4 binary64)) < 5.4999999999999997e62

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. pow-lowering-pow.f64 87.9%

         \[\leadsto \mathsf{pow.f64}\left(x, \color{blue}{4}\right) \]

   5. Simplified 87.9%

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

   if 5.4999999999999997e62 < (pow.f64 y #s(literal 4 binary64))

   1. Initial program 67.4%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left({y}^{4}\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{{y}^{4}} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left({y}^{4}\right)}\right) \]

      4. pow-lowering-pow.f64 78.6%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{pow.f64}\left(y, \color{blue}{4}\right)\right) \]

   5. Simplified 78.6%

      \[\leadsto \color{blue}{0 - {y}^{4}} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left({y}^{4}\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left({y}^{4}\right)\right) \]

      3. rem-exp-log N/A

         \[\leadsto \mathsf{neg.f64}\left(\left({\left(e^{\log y}\right)}^{4}\right)\right) \]

      4. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{pow.f64}\left(\left(e^{\log y}\right), 4\right)\right) \]

      5. rem-exp-log 78.6%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{pow.f64}\left(y, 4\right)\right) \]

   7. Applied egg-rr 78.6%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;{y}^{4} \leq 5.5 \cdot 10^{+62}:\\ \;\;\;\;{x}^{4}\\ \mathbf{else}:\\ \;\;\;\;0 - {y}^{4}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 57.1% 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 83.6%

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

3. Taylor expanded in x around inf

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

   1. pow-lowering-pow.f64 54.5%

      \[\leadsto \mathsf{pow.f64}\left(x, \color{blue}{4}\right) \]

5. Simplified 54.5%

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

Reproduce

herbie shell --seed 2024164 
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  :precision binary64
  (- (pow x 4.0) (pow y 4.0)))