Radioactive exchange between two surfaces

Percentage Accurate: 85.5% → 94.7%

Time: 4.0s

Alternatives: 5

Speedup: 12.0×

• 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: 85.5% 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: 94.7% accurate, 12.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot x + y \cdot y\\ \mathbf{if}\;x \leq 5.8 \cdot 10^{+145}:\\ \;\;\;\;t_0 \cdot \left(x \cdot x - y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (* x x) (* y y))))
   (if (<= x 5.8e+145) (* t_0 (- (* x x) (* y y))) (* (* x x) t_0))))

C

double code(double x, double y) {
	double t_0 = (x * x) + (y * y);
	double tmp;
	if (x <= 5.8e+145) {
		tmp = t_0 * ((x * x) - (y * y));
	} else {
		tmp = (x * x) * t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * x) + (y * y)
    if (x <= 5.8d+145) then
        tmp = t_0 * ((x * x) - (y * y))
    else
        tmp = (x * x) * t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x * x) + (y * y);
	double tmp;
	if (x <= 5.8e+145) {
		tmp = t_0 * ((x * x) - (y * y));
	} else {
		tmp = (x * x) * t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x * x) + (y * y)
	tmp = 0
	if x <= 5.8e+145:
		tmp = t_0 * ((x * x) - (y * y))
	else:
		tmp = (x * x) * t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x * x) + Float64(y * y))
	tmp = 0.0
	if (x <= 5.8e+145)
		tmp = Float64(t_0 * Float64(Float64(x * x) - Float64(y * y)));
	else
		tmp = Float64(Float64(x * x) * t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x * x) + (y * y);
	tmp = 0.0;
	if (x <= 5.8e+145)
		tmp = t_0 * ((x * x) - (y * y));
	else
		tmp = (x * x) * t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x * x), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 5.8e+145], N[(t$95$0 * N[(N[(x * x), $MachinePrecision] - N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * x), $MachinePrecision] * t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 5.8000000000000001e145

   1. Initial program 90.3%

      \[{x}^{4} - {y}^{4} \]
   2. Step-by-step derivation

      1. sqr-pow 90.1%

         \[\leadsto \color{blue}{{x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)}} - {y}^{4} \]

      2. sqr-pow 90.0%

         \[\leadsto {x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)} - \color{blue}{{y}^{\left(\frac{4}{2}\right)} \cdot {y}^{\left(\frac{4}{2}\right)}} \]

      3. difference-of-squares 98.3%

         \[\leadsto \color{blue}{\left({x}^{\left(\frac{4}{2}\right)} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right)} \]

      4. metadata-eval 98.3%

         \[\leadsto \left({x}^{\color{blue}{2}} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      5. pow2 98.3%

         \[\leadsto \left(\color{blue}{x \cdot x} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      6. metadata-eval 98.3%

         \[\leadsto \left(x \cdot x + {y}^{\color{blue}{2}}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      7. pow2 98.3%

         \[\leadsto \left(x \cdot x + \color{blue}{y \cdot y}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      8. metadata-eval 98.3%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left({x}^{\color{blue}{2}} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      9. pow2 98.3%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(\color{blue}{x \cdot x} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      10. metadata-eval 98.3%

          \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - {y}^{\color{blue}{2}}\right) \]

      11. pow2 98.3%

          \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - \color{blue}{y \cdot y}\right) \]

   3. Applied egg-rr 98.3%

      \[\leadsto \color{blue}{\left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - y \cdot y\right)} \]

   if 5.8000000000000001e145 < x

   1. Initial program 65.0%

      \[{x}^{4} - {y}^{4} \]
   2. Step-by-step derivation

      1. sqr-pow 65.0%

         \[\leadsto \color{blue}{{x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)}} - {y}^{4} \]

      2. sqr-pow 65.0%

         \[\leadsto {x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)} - \color{blue}{{y}^{\left(\frac{4}{2}\right)} \cdot {y}^{\left(\frac{4}{2}\right)}} \]

      3. difference-of-squares 75.0%

         \[\leadsto \color{blue}{\left({x}^{\left(\frac{4}{2}\right)} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right)} \]

      4. metadata-eval 75.0%

         \[\leadsto \left({x}^{\color{blue}{2}} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      5. pow2 75.0%

         \[\leadsto \left(\color{blue}{x \cdot x} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      6. metadata-eval 75.0%

         \[\leadsto \left(x \cdot x + {y}^{\color{blue}{2}}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      7. pow2 75.0%

         \[\leadsto \left(x \cdot x + \color{blue}{y \cdot y}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      8. metadata-eval 75.0%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left({x}^{\color{blue}{2}} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      9. pow2 75.0%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(\color{blue}{x \cdot x} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      10. metadata-eval 75.0%

          \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - {y}^{\color{blue}{2}}\right) \]

      11. pow2 75.0%

          \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - \color{blue}{y \cdot y}\right) \]

   3. Applied egg-rr 75.0%

      \[\leadsto \color{blue}{\left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - y \cdot y\right)} \]

   4. Taylor expanded in x around inf 87.5%

      \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{{x}^{2}} \]
   5. Step-by-step derivation

      1. unpow2 87.5%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(x \cdot x\right)} \]

   6. Simplified 87.5%

      \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(x \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5.8 \cdot 10^{+145}:\\ \;\;\;\;\left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(x \cdot x + y \cdot y\right)\\ \end{array} \]

Alternative 2: 79.3% accurate, 12.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+109} \lor \neg \left(y \leq 1.05 \cdot 10^{-57}\right):\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(y \cdot \left(-y\right) - x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(x \cdot x + y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.95e+109) (not (<= y 1.05e-57)))
   (* (* y y) (- (* y (- y)) (* x x)))
   (* (* x x) (+ (* x x) (* y y)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.95e+109) || !(y <= 1.05e-57)) {
		tmp = (y * y) * ((y * -y) - (x * x));
	} else {
		tmp = (x * x) * ((x * x) + (y * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.95d+109)) .or. (.not. (y <= 1.05d-57))) then
        tmp = (y * y) * ((y * -y) - (x * x))
    else
        tmp = (x * x) * ((x * x) + (y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.95e+109) || !(y <= 1.05e-57)) {
		tmp = (y * y) * ((y * -y) - (x * x));
	} else {
		tmp = (x * x) * ((x * x) + (y * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.95e+109) or not (y <= 1.05e-57):
		tmp = (y * y) * ((y * -y) - (x * x))
	else:
		tmp = (x * x) * ((x * x) + (y * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.95e+109) || !(y <= 1.05e-57))
		tmp = Float64(Float64(y * y) * Float64(Float64(y * Float64(-y)) - Float64(x * x)));
	else
		tmp = Float64(Float64(x * x) * Float64(Float64(x * x) + Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.95e+109) || ~((y <= 1.05e-57)))
		tmp = (y * y) * ((y * -y) - (x * x));
	else
		tmp = (x * x) * ((x * x) + (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.95e+109], N[Not[LessEqual[y, 1.05e-57]], $MachinePrecision]], N[(N[(y * y), $MachinePrecision] * N[(N[(y * (-y)), $MachinePrecision] - N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * x), $MachinePrecision] * N[(N[(x * x), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.95000000000000008e109 or 1.05e-57 < y

   1. Initial program 75.0%

      \[{x}^{4} - {y}^{4} \]
   2. Step-by-step derivation

      1. sqr-pow 75.0%

         \[\leadsto \color{blue}{{x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)}} - {y}^{4} \]

      2. sqr-pow 74.9%

         \[\leadsto {x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)} - \color{blue}{{y}^{\left(\frac{4}{2}\right)} \cdot {y}^{\left(\frac{4}{2}\right)}} \]

      3. difference-of-squares 88.7%

         \[\leadsto \color{blue}{\left({x}^{\left(\frac{4}{2}\right)} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right)} \]

      4. metadata-eval 88.7%

         \[\leadsto \left({x}^{\color{blue}{2}} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      5. pow2 88.7%

         \[\leadsto \left(\color{blue}{x \cdot x} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      6. metadata-eval 88.7%

         \[\leadsto \left(x \cdot x + {y}^{\color{blue}{2}}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      7. pow2 88.7%

         \[\leadsto \left(x \cdot x + \color{blue}{y \cdot y}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      8. metadata-eval 88.7%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left({x}^{\color{blue}{2}} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      9. pow2 88.7%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(\color{blue}{x \cdot x} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      10. metadata-eval 88.7%

          \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - {y}^{\color{blue}{2}}\right) \]

      11. pow2 88.7%

          \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - \color{blue}{y \cdot y}\right) \]

   3. Applied egg-rr 88.7%

      \[\leadsto \color{blue}{\left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - y \cdot y\right)} \]

   4. Taylor expanded in x around 0 84.4%

      \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(-1 \cdot {y}^{2}\right)} \]
   5. Step-by-step derivation

      1. unpow2 84.4%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(-1 \cdot \color{blue}{\left(y \cdot y\right)}\right) \]

      2. mul-1-neg 84.4%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(-y \cdot y\right)} \]

      3. distribute-rgt-neg-out 84.4%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(y \cdot \left(-y\right)\right)} \]

   6. Simplified 84.4%

      \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(y \cdot \left(-y\right)\right)} \]

   if -1.95000000000000008e109 < y < 1.05e-57

   1. Initial program 95.7%

      \[{x}^{4} - {y}^{4} \]
   2. Step-by-step derivation

      1. sqr-pow 95.5%

         \[\leadsto \color{blue}{{x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)}} - {y}^{4} \]

      2. sqr-pow 95.4%

         \[\leadsto {x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)} - \color{blue}{{y}^{\left(\frac{4}{2}\right)} \cdot {y}^{\left(\frac{4}{2}\right)}} \]

      3. difference-of-squares 99.7%

         \[\leadsto \color{blue}{\left({x}^{\left(\frac{4}{2}\right)} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right)} \]

      4. metadata-eval 99.7%

         \[\leadsto \left({x}^{\color{blue}{2}} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      5. pow2 99.7%

         \[\leadsto \left(\color{blue}{x \cdot x} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \left(x \cdot x + {y}^{\color{blue}{2}}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      7. pow2 99.7%

         \[\leadsto \left(x \cdot x + \color{blue}{y \cdot y}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      8. metadata-eval 99.7%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left({x}^{\color{blue}{2}} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      9. pow2 99.7%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(\color{blue}{x \cdot x} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      10. metadata-eval 99.7%

          \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - {y}^{\color{blue}{2}}\right) \]

      11. pow2 99.7%

          \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - \color{blue}{y \cdot y}\right) \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - y \cdot y\right)} \]

   4. Taylor expanded in x around inf 88.6%

      \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{{x}^{2}} \]
   5. Step-by-step derivation

      1. unpow2 88.6%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(x \cdot x\right)} \]

   6. Simplified 88.6%

      \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(x \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+109} \lor \neg \left(y \leq 1.05 \cdot 10^{-57}\right):\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(y \cdot \left(-y\right) - x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(x \cdot x + y \cdot y\right)\\ \end{array} \]

Alternative 3: 69.0% accurate, 13.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+110} \lor \neg \left(y \leq 1.22 \cdot 10^{+126}\right):\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(y \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(x \cdot x + y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3.1e+110) (not (<= y 1.22e+126)))
   (* (* x x) (* y (- y)))
   (* (* x x) (+ (* x x) (* y y)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3.1e+110) || !(y <= 1.22e+126)) {
		tmp = (x * x) * (y * -y);
	} else {
		tmp = (x * x) * ((x * x) + (y * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-3.1d+110)) .or. (.not. (y <= 1.22d+126))) then
        tmp = (x * x) * (y * -y)
    else
        tmp = (x * x) * ((x * x) + (y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -3.1e+110) || !(y <= 1.22e+126)) {
		tmp = (x * x) * (y * -y);
	} else {
		tmp = (x * x) * ((x * x) + (y * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3.1e+110) or not (y <= 1.22e+126):
		tmp = (x * x) * (y * -y)
	else:
		tmp = (x * x) * ((x * x) + (y * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3.1e+110) || !(y <= 1.22e+126))
		tmp = Float64(Float64(x * x) * Float64(y * Float64(-y)));
	else
		tmp = Float64(Float64(x * x) * Float64(Float64(x * x) + Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -3.1e+110) || ~((y <= 1.22e+126)))
		tmp = (x * x) * (y * -y);
	else
		tmp = (x * x) * ((x * x) + (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3.1e+110], N[Not[LessEqual[y, 1.22e+126]], $MachinePrecision]], N[(N[(x * x), $MachinePrecision] * N[(y * (-y)), $MachinePrecision]), $MachinePrecision], N[(N[(x * x), $MachinePrecision] * N[(N[(x * x), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.10000000000000017e110 or 1.21999999999999995e126 < y

   1. Initial program 68.8%

      \[{x}^{4} - {y}^{4} \]
   2. Step-by-step derivation

      1. sqr-pow 68.8%

         \[\leadsto \color{blue}{{x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)}} - {y}^{4} \]

      2. sqr-pow 68.8%

         \[\leadsto {x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)} - \color{blue}{{y}^{\left(\frac{4}{2}\right)} \cdot {y}^{\left(\frac{4}{2}\right)}} \]

      3. difference-of-squares 83.8%

         \[\leadsto \color{blue}{\left({x}^{\left(\frac{4}{2}\right)} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right)} \]

      4. metadata-eval 83.8%

         \[\leadsto \left({x}^{\color{blue}{2}} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      5. pow2 83.8%

         \[\leadsto \left(\color{blue}{x \cdot x} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      6. metadata-eval 83.8%

         \[\leadsto \left(x \cdot x + {y}^{\color{blue}{2}}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      7. pow2 83.8%

         \[\leadsto \left(x \cdot x + \color{blue}{y \cdot y}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      8. metadata-eval 83.8%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left({x}^{\color{blue}{2}} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      9. pow2 83.8%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(\color{blue}{x \cdot x} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      10. metadata-eval 83.8%

          \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - {y}^{\color{blue}{2}}\right) \]

      11. pow2 83.8%

          \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - \color{blue}{y \cdot y}\right) \]

   3. Applied egg-rr 83.8%

      \[\leadsto \color{blue}{\left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - y \cdot y\right)} \]

   4. Taylor expanded in x around 0 90.0%

      \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(-1 \cdot {y}^{2}\right)} \]
   5. Step-by-step derivation

      1. unpow2 90.0%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(-1 \cdot \color{blue}{\left(y \cdot y\right)}\right) \]

      2. mul-1-neg 90.0%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(-y \cdot y\right)} \]

      3. distribute-rgt-neg-out 90.0%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(y \cdot \left(-y\right)\right)} \]

   6. Simplified 90.0%

      \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(y \cdot \left(-y\right)\right)} \]

   7. Taylor expanded in x around inf 61.7%

      \[\leadsto \color{blue}{-1 \cdot \left({y}^{2} \cdot {x}^{2}\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 61.7%

         \[\leadsto \color{blue}{-{y}^{2} \cdot {x}^{2}} \]

      2. unpow2 61.7%

         \[\leadsto -\color{blue}{\left(y \cdot y\right)} \cdot {x}^{2} \]

      3. unpow2 61.7%

         \[\leadsto -\left(y \cdot y\right) \cdot \color{blue}{\left(x \cdot x\right)} \]

      4. *-commutative 61.7%

         \[\leadsto -\color{blue}{\left(x \cdot x\right) \cdot \left(y \cdot y\right)} \]

   9. Simplified 61.7%

      \[\leadsto \color{blue}{-\left(x \cdot x\right) \cdot \left(y \cdot y\right)} \]

   if -3.10000000000000017e110 < y < 1.21999999999999995e126

   1. Initial program 94.3%

      \[{x}^{4} - {y}^{4} \]
   2. Step-by-step derivation

      1. sqr-pow 94.1%

         \[\leadsto \color{blue}{{x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)}} - {y}^{4} \]

      2. sqr-pow 94.0%

         \[\leadsto {x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)} - \color{blue}{{y}^{\left(\frac{4}{2}\right)} \cdot {y}^{\left(\frac{4}{2}\right)}} \]

      3. difference-of-squares 99.7%

         \[\leadsto \color{blue}{\left({x}^{\left(\frac{4}{2}\right)} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right)} \]

      4. metadata-eval 99.7%

         \[\leadsto \left({x}^{\color{blue}{2}} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      5. pow2 99.7%

         \[\leadsto \left(\color{blue}{x \cdot x} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \left(x \cdot x + {y}^{\color{blue}{2}}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      7. pow2 99.7%

         \[\leadsto \left(x \cdot x + \color{blue}{y \cdot y}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      8. metadata-eval 99.7%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left({x}^{\color{blue}{2}} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      9. pow2 99.7%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(\color{blue}{x \cdot x} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      10. metadata-eval 99.7%

          \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - {y}^{\color{blue}{2}}\right) \]

      11. pow2 99.7%

          \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - \color{blue}{y \cdot y}\right) \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - y \cdot y\right)} \]

   4. Taylor expanded in x around inf 76.5%

      \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{{x}^{2}} \]
   5. Step-by-step derivation

      1. unpow2 76.5%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(x \cdot x\right)} \]

   6. Simplified 76.5%

      \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(x \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+110} \lor \neg \left(y \leq 1.22 \cdot 10^{+126}\right):\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(y \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(x \cdot x + y \cdot y\right)\\ \end{array} \]

Alternative 4: 44.6% accurate, 16.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+109} \lor \neg \left(y \leq 1.25 \cdot 10^{+126}\right):\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(y \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4.8e+109) (not (<= y 1.25e+126)))
   (* (* x x) (* y (- y)))
   (* (* x x) (* y y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4.8e+109) || !(y <= 1.25e+126)) {
		tmp = (x * x) * (y * -y);
	} else {
		tmp = (x * x) * (y * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-4.8d+109)) .or. (.not. (y <= 1.25d+126))) then
        tmp = (x * x) * (y * -y)
    else
        tmp = (x * x) * (y * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -4.8e+109) || !(y <= 1.25e+126)) {
		tmp = (x * x) * (y * -y);
	} else {
		tmp = (x * x) * (y * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4.8e+109) or not (y <= 1.25e+126):
		tmp = (x * x) * (y * -y)
	else:
		tmp = (x * x) * (y * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4.8e+109) || !(y <= 1.25e+126))
		tmp = Float64(Float64(x * x) * Float64(y * Float64(-y)));
	else
		tmp = Float64(Float64(x * x) * Float64(y * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -4.8e+109) || ~((y <= 1.25e+126)))
		tmp = (x * x) * (y * -y);
	else
		tmp = (x * x) * (y * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4.8e+109], N[Not[LessEqual[y, 1.25e+126]], $MachinePrecision]], N[(N[(x * x), $MachinePrecision] * N[(y * (-y)), $MachinePrecision]), $MachinePrecision], N[(N[(x * x), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.79999999999999975e109 or 1.24999999999999994e126 < y

   1. Initial program 68.8%

      \[{x}^{4} - {y}^{4} \]
   2. Step-by-step derivation

      1. sqr-pow 68.8%

         \[\leadsto \color{blue}{{x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)}} - {y}^{4} \]

      2. sqr-pow 68.8%

         \[\leadsto {x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)} - \color{blue}{{y}^{\left(\frac{4}{2}\right)} \cdot {y}^{\left(\frac{4}{2}\right)}} \]

      3. difference-of-squares 83.8%

         \[\leadsto \color{blue}{\left({x}^{\left(\frac{4}{2}\right)} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right)} \]

      4. metadata-eval 83.8%

         \[\leadsto \left({x}^{\color{blue}{2}} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      5. pow2 83.8%

         \[\leadsto \left(\color{blue}{x \cdot x} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      6. metadata-eval 83.8%

         \[\leadsto \left(x \cdot x + {y}^{\color{blue}{2}}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      7. pow2 83.8%

         \[\leadsto \left(x \cdot x + \color{blue}{y \cdot y}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      8. metadata-eval 83.8%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left({x}^{\color{blue}{2}} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      9. pow2 83.8%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(\color{blue}{x \cdot x} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      10. metadata-eval 83.8%

          \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - {y}^{\color{blue}{2}}\right) \]

      11. pow2 83.8%

          \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - \color{blue}{y \cdot y}\right) \]

   3. Applied egg-rr 83.8%

      \[\leadsto \color{blue}{\left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - y \cdot y\right)} \]

   4. Taylor expanded in x around 0 90.0%

      \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(-1 \cdot {y}^{2}\right)} \]
   5. Step-by-step derivation

      1. unpow2 90.0%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(-1 \cdot \color{blue}{\left(y \cdot y\right)}\right) \]

      2. mul-1-neg 90.0%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(-y \cdot y\right)} \]

      3. distribute-rgt-neg-out 90.0%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(y \cdot \left(-y\right)\right)} \]

   6. Simplified 90.0%

      \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(y \cdot \left(-y\right)\right)} \]

   7. Taylor expanded in x around inf 61.7%

      \[\leadsto \color{blue}{-1 \cdot \left({y}^{2} \cdot {x}^{2}\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 61.7%

         \[\leadsto \color{blue}{-{y}^{2} \cdot {x}^{2}} \]

      2. unpow2 61.7%

         \[\leadsto -\color{blue}{\left(y \cdot y\right)} \cdot {x}^{2} \]

      3. unpow2 61.7%

         \[\leadsto -\left(y \cdot y\right) \cdot \color{blue}{\left(x \cdot x\right)} \]

      4. *-commutative 61.7%

         \[\leadsto -\color{blue}{\left(x \cdot x\right) \cdot \left(y \cdot y\right)} \]

   9. Simplified 61.7%

      \[\leadsto \color{blue}{-\left(x \cdot x\right) \cdot \left(y \cdot y\right)} \]

   if -4.79999999999999975e109 < y < 1.24999999999999994e126

   1. Initial program 94.3%

      \[{x}^{4} - {y}^{4} \]
   2. Step-by-step derivation

      1. sqr-pow 94.1%

         \[\leadsto \color{blue}{{x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)}} - {y}^{4} \]

      2. sqr-pow 94.0%

         \[\leadsto {x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)} - \color{blue}{{y}^{\left(\frac{4}{2}\right)} \cdot {y}^{\left(\frac{4}{2}\right)}} \]

      3. difference-of-squares 99.7%

         \[\leadsto \color{blue}{\left({x}^{\left(\frac{4}{2}\right)} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right)} \]

      4. metadata-eval 99.7%

         \[\leadsto \left({x}^{\color{blue}{2}} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      5. pow2 99.7%

         \[\leadsto \left(\color{blue}{x \cdot x} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \left(x \cdot x + {y}^{\color{blue}{2}}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      7. pow2 99.7%

         \[\leadsto \left(x \cdot x + \color{blue}{y \cdot y}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      8. metadata-eval 99.7%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left({x}^{\color{blue}{2}} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      9. pow2 99.7%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(\color{blue}{x \cdot x} - {y}^{\left(\frac{4}{2}\right)}\right) \]

      10. metadata-eval 99.7%

          \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - {y}^{\color{blue}{2}}\right) \]

      11. pow2 99.7%

          \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - \color{blue}{y \cdot y}\right) \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - y \cdot y\right)} \]

   4. Taylor expanded in x around inf 76.5%

      \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{{x}^{2}} \]
   5. Step-by-step derivation

      1. unpow2 76.5%

         \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(x \cdot x\right)} \]

   6. Simplified 76.5%

      \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(x \cdot x\right)} \]

   7. Taylor expanded in x around 0 34.5%

      \[\leadsto \color{blue}{{y}^{2} \cdot {x}^{2}} \]
   8. Step-by-step derivation

      1. unpow2 34.5%

         \[\leadsto \color{blue}{\left(y \cdot y\right)} \cdot {x}^{2} \]

      2. unpow2 34.5%

         \[\leadsto \left(y \cdot y\right) \cdot \color{blue}{\left(x \cdot x\right)} \]

      3. *-commutative 34.5%

         \[\leadsto \color{blue}{\left(x \cdot x\right) \cdot \left(y \cdot y\right)} \]

   9. Simplified 34.5%

      \[\leadsto \color{blue}{\left(x \cdot x\right) \cdot \left(y \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+109} \lor \neg \left(y \leq 1.25 \cdot 10^{+126}\right):\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(y \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(y \cdot y\right)\\ \end{array} \]

Alternative 5: 33.3% accurate, 29.3× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot x\right) \cdot \left(y \cdot y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (* x x) (* y y)))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (x * x) * (y * y)

Julia

function code(x, y)
	return Float64(Float64(x * x) * Float64(y * y))
end

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(x * x), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.3%

   \[{x}^{4} - {y}^{4} \]
2. Step-by-step derivation

   1. sqr-pow 86.2%

      \[\leadsto \color{blue}{{x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)}} - {y}^{4} \]

   2. sqr-pow 86.1%

      \[\leadsto {x}^{\left(\frac{4}{2}\right)} \cdot {x}^{\left(\frac{4}{2}\right)} - \color{blue}{{y}^{\left(\frac{4}{2}\right)} \cdot {y}^{\left(\frac{4}{2}\right)}} \]

   3. difference-of-squares 94.7%

      \[\leadsto \color{blue}{\left({x}^{\left(\frac{4}{2}\right)} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right)} \]

   4. metadata-eval 94.7%

      \[\leadsto \left({x}^{\color{blue}{2}} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

   5. pow2 94.7%

      \[\leadsto \left(\color{blue}{x \cdot x} + {y}^{\left(\frac{4}{2}\right)}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

   6. metadata-eval 94.7%

      \[\leadsto \left(x \cdot x + {y}^{\color{blue}{2}}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

   7. pow2 94.7%

      \[\leadsto \left(x \cdot x + \color{blue}{y \cdot y}\right) \cdot \left({x}^{\left(\frac{4}{2}\right)} - {y}^{\left(\frac{4}{2}\right)}\right) \]

   8. metadata-eval 94.7%

      \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left({x}^{\color{blue}{2}} - {y}^{\left(\frac{4}{2}\right)}\right) \]

   9. pow2 94.7%

      \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(\color{blue}{x \cdot x} - {y}^{\left(\frac{4}{2}\right)}\right) \]

   10. metadata-eval 94.7%

       \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - {y}^{\color{blue}{2}}\right) \]

   11. pow2 94.7%

       \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - \color{blue}{y \cdot y}\right) \]

3. Applied egg-rr 94.7%

   \[\leadsto \color{blue}{\left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - y \cdot y\right)} \]

4. Taylor expanded in x around inf 55.8%

   \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{{x}^{2}} \]
5. Step-by-step derivation

   1. unpow2 55.8%

      \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(x \cdot x\right)} \]

6. Simplified 55.8%

   \[\leadsto \left(x \cdot x + y \cdot y\right) \cdot \color{blue}{\left(x \cdot x\right)} \]

7. Taylor expanded in x around 0 26.9%

   \[\leadsto \color{blue}{{y}^{2} \cdot {x}^{2}} \]
8. Step-by-step derivation

   1. unpow2 26.9%

      \[\leadsto \color{blue}{\left(y \cdot y\right)} \cdot {x}^{2} \]

   2. unpow2 26.9%

      \[\leadsto \left(y \cdot y\right) \cdot \color{blue}{\left(x \cdot x\right)} \]

   3. *-commutative 26.9%

      \[\leadsto \color{blue}{\left(x \cdot x\right) \cdot \left(y \cdot y\right)} \]

9. Simplified 26.9%

   \[\leadsto \color{blue}{\left(x \cdot x\right) \cdot \left(y \cdot y\right)} \]

10. Final simplification 26.9%

    \[\leadsto \left(x \cdot x\right) \cdot \left(y \cdot y\right) \]

Reproduce

herbie shell --seed 2023178 
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  :precision binary64
  (- (pow x 4.0) (pow y 4.0)))