Radioactive exchange between two surfaces

Percentage Accurate: 86.1% → 94.9%

Time: 3.2s

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: 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: 94.9% accurate, 12.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot x + y \cdot y\\ \mathbf{if}\;x \leq -8 \cdot 10^{+179}:\\ \;\;\;\;\left(x \cdot x\right) \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \left(x \cdot x - y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (* x x) (* y y))))
   (if (<= x -8e+179) (* (* x x) t_0) (* t_0 (- (* x x) (* y y))))))

C

double code(double x, double y) {
	double t_0 = (x * x) + (y * y);
	double tmp;
	if (x <= -8e+179) {
		tmp = (x * x) * t_0;
	} else {
		tmp = t_0 * ((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) :: t_0
    real(8) :: tmp
    t_0 = (x * x) + (y * y)
    if (x <= (-8d+179)) then
        tmp = (x * x) * t_0
    else
        tmp = t_0 * ((x * x) - (y * y))
    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 <= -8e+179) {
		tmp = (x * x) * t_0;
	} else {
		tmp = t_0 * ((x * x) - (y * y));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x * x) + (y * y)
	tmp = 0
	if x <= -8e+179:
		tmp = (x * x) * t_0
	else:
		tmp = t_0 * ((x * x) - (y * y))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x * x) + Float64(y * y))
	tmp = 0.0
	if (x <= -8e+179)
		tmp = Float64(Float64(x * x) * t_0);
	else
		tmp = Float64(t_0 * Float64(Float64(x * x) - Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x * x) + (y * y);
	tmp = 0.0;
	if (x <= -8e+179)
		tmp = (x * x) * t_0;
	else
		tmp = t_0 * ((x * x) - (y * y));
	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, -8e+179], N[(N[(x * x), $MachinePrecision] * t$95$0), $MachinePrecision], N[(t$95$0 * N[(N[(x * x), $MachinePrecision] - N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.99999999999999984e179

   1. Initial program 62.5%

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

      1. sqr-pow 62.5%

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

      2. sqr-pow 62.5%

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

      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 95.8%

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

      1. unpow2 95.8%

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

   6. Simplified 95.8%

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

   if -7.99999999999999984e179 < x

   1. Initial program 90.1%

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

      1. sqr-pow 90.0%

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

      2. sqr-pow 89.9%

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

      3. difference-of-squares 96.3%

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

      4. metadata-eval 96.3%

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

      5. pow2 96.3%

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

      6. metadata-eval 96.3%

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

      7. pow2 96.3%

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

      8. metadata-eval 96.3%

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

      9. pow2 96.3%

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

      10. metadata-eval 96.3%

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

      11. pow2 96.3%

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

   3. Applied egg-rr 96.3%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+179}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(x \cdot x + y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x + y \cdot y\right) \cdot \left(x \cdot x - y \cdot y\right)\\ \end{array} \]

Alternative 2: 82.0% accurate, 12.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+43} \lor \neg \left(y \leq 1.2 \cdot 10^{+16}\right):\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(y \cdot \left(-y\right) - x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(x \cdot x + y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.25e+43) (not (<= y 1.2e+16)))
   (* (* y y) (- (* y (- y)) (* x x)))
   (* (* x x) (+ (* x x) (* y y)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.25e+43) || !(y <= 1.2e+16)) {
		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 <= (-1.25d+43)) .or. (.not. (y <= 1.2d+16))) 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 <= -1.25e+43) || !(y <= 1.2e+16)) {
		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 <= -1.25e+43) or not (y <= 1.2e+16):
		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 <= -1.25e+43) || !(y <= 1.2e+16))
		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 <= -1.25e+43) || ~((y <= 1.2e+16)))
		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, -1.25e+43], N[Not[LessEqual[y, 1.2e+16]], $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 < -1.2500000000000001e43 or 1.2e16 < y

   1. Initial program 70.6%

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

      1. sqr-pow 70.6%

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

      2. sqr-pow 70.5%

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

      3. difference-of-squares 87.1%

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

      4. metadata-eval 87.1%

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

      5. pow2 87.1%

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

      6. metadata-eval 87.1%

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

      7. pow2 87.1%

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

      8. metadata-eval 87.1%

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

      9. pow2 87.1%

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

      10. metadata-eval 87.1%

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

      11. pow2 87.1%

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

   3. Applied egg-rr 87.1%

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

   4. Taylor expanded in x around 0 81.6%

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

      1. unpow2 81.6%

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

      2. mul-1-neg 81.6%

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

      3. distribute-rgt-neg-out 81.6%

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

   6. Simplified 81.6%

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

   if -1.2500000000000001e43 < y < 1.2e16

   1. Initial program 100.0%

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

      1. sqr-pow 99.8%

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

      2. sqr-pow 99.8%

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

      3. difference-of-squares 99.8%

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

      4. metadata-eval 99.8%

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

      5. pow2 99.8%

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

      6. metadata-eval 99.8%

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

      7. pow2 99.8%

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

      8. metadata-eval 99.8%

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

      9. pow2 99.8%

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

      10. metadata-eval 99.8%

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

      11. pow2 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in x around inf 90.1%

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

      1. unpow2 90.1%

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

   6. Simplified 90.1%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+43} \lor \neg \left(y \leq 1.2 \cdot 10^{+16}\right):\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(y \cdot \left(-y\right) - x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(x \cdot x + y \cdot y\right)\\ \end{array} \]

Alternative 3: 69.8% accurate, 13.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+137} \lor \neg \left(y \leq 1.8 \cdot 10^{+151}\right):\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(y \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(x \cdot x + y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5.3e+137) (not (<= y 1.8e+151)))
   (* (* x x) (* y (- y)))
   (* (* x x) (+ (* x x) (* y y)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5.3e+137) || !(y <= 1.8e+151)) {
		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 <= (-5.3d+137)) .or. (.not. (y <= 1.8d+151))) 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 <= -5.3e+137) || !(y <= 1.8e+151)) {
		tmp = (x * x) * (y * -y);
	} else {
		tmp = (x * x) * ((x * x) + (y * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -5.3e+137) or not (y <= 1.8e+151):
		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 <= -5.3e+137) || !(y <= 1.8e+151))
		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 <= -5.3e+137) || ~((y <= 1.8e+151)))
		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, -5.3e+137], N[Not[LessEqual[y, 1.8e+151]], $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 < -5.29999999999999968e137 or 1.8e151 < y

   1. Initial program 67.2%

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

      1. sqr-pow 67.2%

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

      2. sqr-pow 67.2%

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

      3. difference-of-squares 78.1%

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

      4. metadata-eval 78.1%

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

      5. pow2 78.1%

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

      6. metadata-eval 78.1%

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

      7. pow2 78.1%

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

      8. metadata-eval 78.1%

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

      9. pow2 78.1%

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

      10. metadata-eval 78.1%

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

      11. pow2 78.1%

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

   3. Applied egg-rr 78.1%

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

   4. Taylor expanded in x around 0 87.5%

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

      1. unpow2 87.5%

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

      2. mul-1-neg 87.5%

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

      3. distribute-rgt-neg-out 87.5%

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

   6. Simplified 87.5%

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

   7. Taylor expanded in x around inf 48.7%

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

      1. mul-1-neg 48.7%

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

      2. unpow2 48.7%

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

      3. unpow2 48.7%

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

      4. *-commutative 48.7%

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

   9. Simplified 48.7%

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

   if -5.29999999999999968e137 < y < 1.8e151

   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 99.8%

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

      4. metadata-eval 99.8%

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

      5. pow2 99.8%

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

      6. metadata-eval 99.8%

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

      7. pow2 99.8%

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

      8. metadata-eval 99.8%

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

      9. pow2 99.8%

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

      10. metadata-eval 99.8%

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

      11. pow2 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in x around inf 75.4%

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

      1. unpow2 75.4%

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

   6. Simplified 75.4%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+137} \lor \neg \left(y \leq 1.8 \cdot 10^{+151}\right):\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(y \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(x \cdot x + y \cdot y\right)\\ \end{array} \]

Alternative 4: 44.7% accurate, 16.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+150} \lor \neg \left(x \leq 4.6 \cdot 10^{+115}\right):\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(y \cdot \left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -5.2e+150) (not (<= x 4.6e+115)))
   (* (* x x) (* y y))
   (* (* x x) (* y (- y)))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -5.2e+150) || !(x <= 4.6e+115)) {
		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 ((x <= (-5.2d+150)) .or. (.not. (x <= 4.6d+115))) 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 ((x <= -5.2e+150) || !(x <= 4.6e+115)) {
		tmp = (x * x) * (y * y);
	} else {
		tmp = (x * x) * (y * -y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -5.2e+150) or not (x <= 4.6e+115):
		tmp = (x * x) * (y * y)
	else:
		tmp = (x * x) * (y * -y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -5.2e+150) || !(x <= 4.6e+115))
		tmp = Float64(Float64(x * x) * Float64(y * y));
	else
		tmp = Float64(Float64(x * x) * Float64(y * Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -5.2e+150) || ~((x <= 4.6e+115)))
		tmp = (x * x) * (y * y);
	else
		tmp = (x * x) * (y * -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -5.2e+150], N[Not[LessEqual[x, 4.6e+115]], $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 x < -5.20000000000000012e150 or 4.60000000000000007e115 < x

   1. Initial program 68.0%

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

      1. sqr-pow 68.0%

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

      2. sqr-pow 68.0%

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

      3. difference-of-squares 81.3%

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

      4. metadata-eval 81.3%

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

      5. pow2 81.3%

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

      6. metadata-eval 81.3%

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

      7. pow2 81.3%

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

      8. metadata-eval 81.3%

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

      9. pow2 81.3%

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

      10. metadata-eval 81.3%

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

      11. pow2 81.3%

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

   3. Applied egg-rr 81.3%

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

   4. Taylor expanded in x around inf 92.0%

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

      1. unpow2 92.0%

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

   6. Simplified 92.0%

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

   7. Taylor expanded in x around 0 57.6%

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

      1. unpow2 57.6%

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

      2. unpow2 57.6%

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

      3. *-commutative 57.6%

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

   9. Simplified 57.6%

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

   if -5.20000000000000012e150 < x < 4.60000000000000007e115

   1. Initial program 95.6%

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

      1. sqr-pow 95.4%

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

      2. sqr-pow 95.3%

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

      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 0 80.6%

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

      1. unpow2 80.6%

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

      2. mul-1-neg 80.6%

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

      3. distribute-rgt-neg-out 80.6%

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

   6. Simplified 80.6%

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

   7. Taylor expanded in x around inf 43.1%

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

      1. mul-1-neg 43.1%

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

      2. unpow2 43.1%

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

      3. unpow2 43.1%

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

      4. *-commutative 43.1%

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

   9. Simplified 43.1%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+150} \lor \neg \left(x \leq 4.6 \cdot 10^{+115}\right):\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(y \cdot \left(-y\right)\right)\\ \end{array} \]

Alternative 5: 32.0% 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 87.5%

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

   1. sqr-pow 87.4%

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

   2. sqr-pow 87.3%

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

   3. difference-of-squares 94.3%

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

   4. metadata-eval 94.3%

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

   5. pow2 94.3%

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

   6. metadata-eval 94.3%

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

   7. pow2 94.3%

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

   8. metadata-eval 94.3%

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

   9. pow2 94.3%

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

   10. metadata-eval 94.3%

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

   11. pow2 94.3%

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

3. Applied egg-rr 94.3%

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

4. Taylor expanded in x around inf 59.7%

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

   1. unpow2 59.7%

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

6. Simplified 59.7%

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

7. Taylor expanded in x around 0 36.2%

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

   1. unpow2 36.2%

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

   2. unpow2 36.2%

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

   3. *-commutative 36.2%

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

9. Simplified 36.2%

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

10. Final simplification 36.2%

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

Reproduce

herbie shell --seed 2023182 
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  :precision binary64
  (- (pow x 4.0) (pow y 4.0)))