Radioactive exchange between two surfaces

Percentage Accurate: 85.5% → 91.6%

Time: 14.7s

Alternatives: 4

Speedup: 0.7×

• 61.1% 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: 85.5% 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: 91.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;{y}^{4} \leq 6 \cdot 10^{+255}:\\ \;\;\;\;{x}^{4} - {y}^{4}\\ \mathbf{else}:\\ \;\;\;\;-{y}^{4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (pow y 4.0) 6e+255) (- (pow x 4.0) (pow y 4.0)) (- (pow y 4.0))))

C

double code(double x, double y) {
	double tmp;
	if (pow(y, 4.0) <= 6e+255) {
		tmp = pow(x, 4.0) - pow(y, 4.0);
	} else {
		tmp = -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) <= 6d+255) then
        tmp = (x ** 4.0d0) - (y ** 4.0d0)
    else
        tmp = -(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) <= 6e+255) {
		tmp = Math.pow(x, 4.0) - Math.pow(y, 4.0);
	} else {
		tmp = -Math.pow(y, 4.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.pow(y, 4.0) <= 6e+255:
		tmp = math.pow(x, 4.0) - math.pow(y, 4.0)
	else:
		tmp = -math.pow(y, 4.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y ^ 4.0) <= 6e+255)
		tmp = Float64((x ^ 4.0) - (y ^ 4.0));
	else
		tmp = Float64(-(y ^ 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y ^ 4.0) <= 6e+255)
		tmp = (x ^ 4.0) - (y ^ 4.0);
	else
		tmp = -(y ^ 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Power[y, 4.0], $MachinePrecision], 6e+255], N[(N[Power[x, 4.0], $MachinePrecision] - N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision], (-N[Power[y, 4.0], $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if (pow.f64 y #s(literal 4 binary64)) < 6.00000000000000035e255

   1. Initial program 100.0%

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

   if 6.00000000000000035e255 < (pow.f64 y #s(literal 4 binary64))

   1. Initial program 60.8%

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

   3. Taylor expanded in x around 0 81.4%

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

      1. neg-mul-1 81.4%

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

   5. Simplified 81.4%

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

Alternative 2: 80.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;{y}^{4} \leq 1.36 \cdot 10^{-210}:\\ \;\;\;\;{x}^{4}\\ \mathbf{else}:\\ \;\;\;\;-{y}^{4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (pow y 4.0) 1.36e-210) (pow x 4.0) (- (pow y 4.0))))

C

double code(double x, double y) {
	double tmp;
	if (pow(y, 4.0) <= 1.36e-210) {
		tmp = pow(x, 4.0);
	} else {
		tmp = -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) <= 1.36d-210) then
        tmp = x ** 4.0d0
    else
        tmp = -(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) <= 1.36e-210) {
		tmp = Math.pow(x, 4.0);
	} else {
		tmp = -Math.pow(y, 4.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.pow(y, 4.0) <= 1.36e-210:
		tmp = math.pow(x, 4.0)
	else:
		tmp = -math.pow(y, 4.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y ^ 4.0) <= 1.36e-210)
		tmp = x ^ 4.0;
	else
		tmp = Float64(-(y ^ 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y ^ 4.0) <= 1.36e-210)
		tmp = x ^ 4.0;
	else
		tmp = -(y ^ 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Power[y, 4.0], $MachinePrecision], 1.36e-210], N[Power[x, 4.0], $MachinePrecision], (-N[Power[y, 4.0], $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if (pow.f64 y #s(literal 4 binary64)) < 1.36e-210

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 96.8%

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

   if 1.36e-210 < (pow.f64 y #s(literal 4 binary64))

   1. Initial program 74.0%

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

   3. Taylor expanded in x around 0 72.7%

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

      1. neg-mul-1 72.7%

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

   5. Simplified 72.7%

      \[\leadsto \color{blue}{-{y}^{4}} \]
3. Recombined 2 regimes into one program.
4. 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 85.2%

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

3. Taylor expanded in x around inf 57.8%

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

Alternative 4: 15.1% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.0)

C

double code(double x, double y) {
	return 0.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.0d0
end function

Java

public static double code(double x, double y) {
	return 0.0;
}

Python

def code(x, y):
	return 0.0

Julia

function code(x, y)
	return 0.0
end

MATLAB

function tmp = code(x, y)
	tmp = 0.0;
end

Wolfram

code[x_, y_] := 0.0

Derivation

1. Initial program 85.2%

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

3. Taylor expanded in x around 0 59.7%

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

   1. neg-mul-1 59.7%

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

5. Simplified 59.7%

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

   1. add-sqr-sqrt 16.6%

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

   2. sqrt-unprod 28.2%

      \[\leadsto \color{blue}{\sqrt{\left(-{y}^{4}\right) \cdot \left(-{y}^{4}\right)}} \]

   3. sqr-neg 28.2%

      \[\leadsto \sqrt{\color{blue}{{y}^{4} \cdot {y}^{4}}} \]

   4. sqrt-unprod 24.5%

      \[\leadsto \color{blue}{\sqrt{{y}^{4}} \cdot \sqrt{{y}^{4}}} \]

   5. add-log-exp 30.1%

      \[\leadsto \color{blue}{\log \left(e^{\sqrt{{y}^{4}} \cdot \sqrt{{y}^{4}}}\right)} \]

   6. add-sqr-sqrt 30.1%

      \[\leadsto \log \left(e^{\color{blue}{{y}^{4}}}\right) \]

   7. add-sqr-sqrt 30.1%

      \[\leadsto \log \color{blue}{\left(\sqrt{e^{{y}^{4}}} \cdot \sqrt{e^{{y}^{4}}}\right)} \]

   8. sqrt-unprod 30.1%

      \[\leadsto \log \color{blue}{\left(\sqrt{e^{{y}^{4}} \cdot e^{{y}^{4}}}\right)} \]

   9. *-un-lft-identity 30.1%

      \[\leadsto \log \left(\sqrt{e^{{y}^{4}} \cdot e^{\color{blue}{1 \cdot {y}^{4}}}}\right) \]

   10. exp-prod 30.1%

       \[\leadsto \log \left(\sqrt{e^{{y}^{4}} \cdot \color{blue}{{\left(e^{1}\right)}^{\left({y}^{4}\right)}}}\right) \]

   11. add-sqr-sqrt 30.1%

       \[\leadsto \log \left(\sqrt{e^{{y}^{4}} \cdot {\left(e^{1}\right)}^{\color{blue}{\left(\sqrt{{y}^{4}} \cdot \sqrt{{y}^{4}}\right)}}}\right) \]

   12. sqrt-unprod 30.1%

       \[\leadsto \log \left(\sqrt{e^{{y}^{4}} \cdot {\left(e^{1}\right)}^{\color{blue}{\left(\sqrt{{y}^{4} \cdot {y}^{4}}\right)}}}\right) \]

   13. sqr-neg 30.1%

       \[\leadsto \log \left(\sqrt{e^{{y}^{4}} \cdot {\left(e^{1}\right)}^{\left(\sqrt{\color{blue}{\left(-{y}^{4}\right) \cdot \left(-{y}^{4}\right)}}\right)}}\right) \]

   14. sqrt-unprod 16.6%

       \[\leadsto \log \left(\sqrt{e^{{y}^{4}} \cdot {\left(e^{1}\right)}^{\color{blue}{\left(\sqrt{-{y}^{4}} \cdot \sqrt{-{y}^{4}}\right)}}}\right) \]

   15. add-sqr-sqrt 17.2%

       \[\leadsto \log \left(\sqrt{e^{{y}^{4}} \cdot {\left(e^{1}\right)}^{\color{blue}{\left(-{y}^{4}\right)}}}\right) \]

   16. exp-prod 17.2%

       \[\leadsto \log \left(\sqrt{e^{{y}^{4}} \cdot \color{blue}{e^{1 \cdot \left(-{y}^{4}\right)}}}\right) \]

   17. *-un-lft-identity 17.2%

       \[\leadsto \log \left(\sqrt{e^{{y}^{4}} \cdot e^{\color{blue}{-{y}^{4}}}}\right) \]

   18. exp-neg 17.2%

       \[\leadsto \log \left(\sqrt{e^{{y}^{4}} \cdot \color{blue}{\frac{1}{e^{{y}^{4}}}}}\right) \]

   19. rgt-mult-inverse 18.0%

       \[\leadsto \log \left(\sqrt{\color{blue}{1}}\right) \]

7. Applied egg-rr 18.0%

   \[\leadsto \color{blue}{0} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024143 
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  :precision binary64
  (- (pow x 4.0) (pow y 4.0)))