Radioactive exchange between two surfaces

Percentage Accurate: 85.0% → 99.8%

Time: 3.2s

Alternatives: 4

Speedup: 13.7×

• 60.2% 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: 85.0% 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: 99.8% accurate, 13.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.4%

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

   1. sqr-pow 84.2%

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

   2. sqr-pow 84.2%

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

   3. difference-of-squares 92.4%

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

   4. metadata-eval 92.4%

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

   5. pow2 92.4%

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

   6. metadata-eval 92.4%

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

   7. pow2 92.4%

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

   8. metadata-eval 92.4%

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

   9. pow2 92.4%

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

   10. metadata-eval 92.4%

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

   11. pow2 92.4%

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

3. Applied egg-rr 92.4%

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

   1. difference-of-squares 99.8%

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

   2. *-commutative 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

Alternative 2: 69.1% accurate, 11.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{+77} \lor \neg \left(y \leq 3.6 \cdot 10^{+100}\right) \land y \leq 2.4 \cdot 10^{+111}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(-\left(x \cdot x + y \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y 1.7e+77) (and (not (<= y 3.6e+100)) (<= y 2.4e+111)))
   (* (* x x) (* x x))
   (* (* y y) (- (+ (* x x) (* y y))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= 1.7e+77) || (!(y <= 3.6e+100) && (y <= 2.4e+111))) {
		tmp = (x * x) * (x * x);
	} else {
		tmp = (y * y) * -((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 <= 1.7d+77) .or. (.not. (y <= 3.6d+100)) .and. (y <= 2.4d+111)) then
        tmp = (x * x) * (x * x)
    else
        tmp = (y * y) * -((x * x) + (y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= 1.7e+77) || (!(y <= 3.6e+100) && (y <= 2.4e+111))) {
		tmp = (x * x) * (x * x);
	} else {
		tmp = (y * y) * -((x * x) + (y * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= 1.7e+77) or (not (y <= 3.6e+100) and (y <= 2.4e+111)):
		tmp = (x * x) * (x * x)
	else:
		tmp = (y * y) * -((x * x) + (y * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= 1.7e+77) || (!(y <= 3.6e+100) && (y <= 2.4e+111)))
		tmp = Float64(Float64(x * x) * Float64(x * x));
	else
		tmp = Float64(Float64(y * y) * Float64(-Float64(Float64(x * x) + Float64(y * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= 1.7e+77) || (~((y <= 3.6e+100)) && (y <= 2.4e+111)))
		tmp = (x * x) * (x * x);
	else
		tmp = (y * y) * -((x * x) + (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, 1.7e+77], And[N[Not[LessEqual[y, 3.6e+100]], $MachinePrecision], LessEqual[y, 2.4e+111]]], N[(N[(x * x), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision], N[(N[(y * y), $MachinePrecision] * (-N[(N[(x * x), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.69999999999999998e77 or 3.6e100 < y < 2.40000000000000006e111

   1. Initial program 90.0%

      \[{x}^{4} - {y}^{4} \]

   2. Taylor expanded in x around inf 68.5%

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

      1. sqr-pow 68.3%

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

      2. metadata-eval 68.3%

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

      3. pow2 68.3%

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

      4. metadata-eval 68.3%

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

      5. pow2 68.3%

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

   4. Applied egg-rr 68.3%

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

   if 1.69999999999999998e77 < y < 3.6e100 or 2.40000000000000006e111 < y

   1. Initial program 57.8%

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

      1. sqr-pow 57.8%

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

      2. sqr-pow 57.8%

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

      3. difference-of-squares 77.8%

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

      4. metadata-eval 77.8%

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

      5. pow2 77.8%

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

      6. metadata-eval 77.8%

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

      7. pow2 77.8%

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

      8. metadata-eval 77.8%

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

      9. pow2 77.8%

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

      10. metadata-eval 77.8%

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

      11. pow2 77.8%

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

   3. Applied egg-rr 77.8%

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

   4. Taylor expanded in x around 0 80.0%

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

      1. unpow2 80.0%

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

      2. mul-1-neg 80.0%

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

      3. distribute-rgt-neg-out 80.0%

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

   6. Simplified 80.0%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{+77} \lor \neg \left(y \leq 3.6 \cdot 10^{+100}\right) \land y \leq 2.4 \cdot 10^{+111}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(-\left(x \cdot x + y \cdot y\right)\right)\\ \end{array} \]

Alternative 3: 64.2% accurate, 20.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.3 \cdot 10^{+173}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(y \cdot \left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 3.3e+173) (* (* x x) (* x x)) (* (* x x) (* y (- y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 3.3e+173) {
		tmp = (x * x) * (x * x);
	} 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 <= 3.3d+173) then
        tmp = (x * x) * (x * x)
    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 <= 3.3e+173) {
		tmp = (x * x) * (x * x);
	} else {
		tmp = (x * x) * (y * -y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 3.3e+173:
		tmp = (x * x) * (x * x)
	else:
		tmp = (x * x) * (y * -y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 3.3e+173)
		tmp = Float64(Float64(x * x) * Float64(x * x));
	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 (y <= 3.3e+173)
		tmp = (x * x) * (x * x);
	else
		tmp = (x * x) * (y * -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 3.3e+173], N[(N[(x * x), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision], N[(N[(x * x), $MachinePrecision] * N[(y * (-y)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.29999999999999996e173

   1. Initial program 87.8%

      \[{x}^{4} - {y}^{4} \]

   2. Taylor expanded in x around inf 65.9%

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

      1. sqr-pow 65.8%

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

      2. metadata-eval 65.8%

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

      3. pow2 65.8%

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

      4. metadata-eval 65.8%

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

      5. pow2 65.8%

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

   4. Applied egg-rr 65.8%

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

   if 3.29999999999999996e173 < y

   1. Initial program 53.8%

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

      1. sqr-pow 53.8%

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

      2. sqr-pow 53.8%

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

      3. difference-of-squares 73.1%

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

      4. metadata-eval 73.1%

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

      5. pow2 73.1%

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

      6. metadata-eval 73.1%

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

      7. pow2 73.1%

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

      8. metadata-eval 73.1%

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

      9. pow2 73.1%

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

      10. metadata-eval 73.1%

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

      11. pow2 73.1%

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

   3. Applied egg-rr 73.1%

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

   4. Taylor expanded in x around 0 92.3%

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

      1. unpow2 92.3%

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

      2. mul-1-neg 92.3%

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

      3. distribute-rgt-neg-out 92.3%

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

   6. Simplified 92.3%

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

   7. Taylor expanded in x around inf 65.4%

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

      1. mul-1-neg 65.4%

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

      2. unpow2 65.4%

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

      3. unpow2 65.4%

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

      4. *-commutative 65.4%

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

   9. Simplified 65.4%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.3 \cdot 10^{+173}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot \left(y \cdot \left(-y\right)\right)\\ \end{array} \]

Alternative 4: 58.0% accurate, 29.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.4%

   \[{x}^{4} - {y}^{4} \]

2. Taylor expanded in x around inf 60.1%

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

   1. sqr-pow 59.9%

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

   2. metadata-eval 59.9%

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

   3. pow2 59.9%

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

   4. metadata-eval 59.9%

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

   5. pow2 59.9%

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

4. Applied egg-rr 59.9%

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

5. Final simplification 59.9%

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

Reproduce

herbie shell --seed 2023223 
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  :precision binary64
  (- (pow x 4.0) (pow y 4.0)))