Linear.Quaternion:$cexp from linear-1.19.1.3

Percentage Accurate: 99.8% → 99.8%

Time: 10.9s

Alternatives: 7

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x \cdot \frac{\sin y}{y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

public static double code(double x, double y) {
	return x * (Math.sin(y) / y);
}

Python

def code(x, y):
	return x * (math.sin(y) / y)

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{\sin y}{y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

public static double code(double x, double y) {
	return x * (Math.sin(y) / y);
}

Python

def code(x, y):
	return x * (math.sin(y) / y)

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{\sin y}{y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

public static double code(double x, double y) {
	return x * (Math.sin(y) / y);
}

Python

def code(x, y):
	return x * (math.sin(y) / y)

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x \cdot \frac{\sin y}{y} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 56.8% accurate, 7.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 320000:\\ \;\;\;\;x + y \cdot \left(x \cdot \left(y \cdot -0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{0.16666666666666666 \cdot \left(y \cdot y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 320000.0)
   (+ x (* y (* x (* y -0.16666666666666666))))
   (/ x (* 0.16666666666666666 (* y y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 320000.0) {
		tmp = x + (y * (x * (y * -0.16666666666666666)));
	} else {
		tmp = x / (0.16666666666666666 * (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 <= 320000.0d0) then
        tmp = x + (y * (x * (y * (-0.16666666666666666d0))))
    else
        tmp = x / (0.16666666666666666d0 * (y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 320000.0) {
		tmp = x + (y * (x * (y * -0.16666666666666666)));
	} else {
		tmp = x / (0.16666666666666666 * (y * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 320000.0:
		tmp = x + (y * (x * (y * -0.16666666666666666)))
	else:
		tmp = x / (0.16666666666666666 * (y * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 320000.0)
		tmp = Float64(x + Float64(y * Float64(x * Float64(y * -0.16666666666666666))));
	else
		tmp = Float64(x / Float64(0.16666666666666666 * Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 320000.0)
		tmp = x + (y * (x * (y * -0.16666666666666666)));
	else
		tmp = x / (0.16666666666666666 * (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 320000.0], N[(x + N[(y * N[(x * N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.2e5

   1. Initial program 99.9%

      \[x \cdot \frac{\sin y}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + \frac{-1}{6} \cdot \left(x \cdot {y}^{2}\right)} \]
   4. Step-by-step derivation

      1. *-rgt-identity N/A

         \[\leadsto x \cdot 1 + \color{blue}{\frac{-1}{6}} \cdot \left(x \cdot {y}^{2}\right) \]

      2. *-commutative N/A

         \[\leadsto x \cdot 1 + \left(x \cdot {y}^{2}\right) \cdot \color{blue}{\frac{-1}{6}} \]

      3. associate-*l* N/A

         \[\leadsto x \cdot 1 + x \cdot \color{blue}{\left({y}^{2} \cdot \frac{-1}{6}\right)} \]

      4. *-commutative N/A

         \[\leadsto x \cdot 1 + x \cdot \left(\frac{-1}{6} \cdot \color{blue}{{y}^{2}}\right) \]

      5. distribute-lft-in N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + \frac{-1}{6} \cdot {y}^{2}\right)} \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + \frac{-1}{6} \cdot {y}^{2}\right)}\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{-1}{6} \cdot {y}^{2}\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{6}, \color{blue}{\left({y}^{2}\right)}\right)\right)\right) \]

      9. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{6}, \left(y \cdot \color{blue}{y}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 67.2%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right)\right) \]

   5. Simplified 67.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\left(\frac{-1}{6} \cdot y\right) \cdot \color{blue}{y}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\left(\frac{-1}{6} \cdot y\right), \color{blue}{y}\right)\right)\right) \]

      3. *-lowering-*.f64 67.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{-1}{6}, y\right), y\right)\right)\right) \]

   7. Applied egg-rr 67.2%

      \[\leadsto x \cdot \left(1 + \color{blue}{\left(-0.16666666666666666 \cdot y\right) \cdot y}\right) \]
   8. Step-by-step derivation

      1. distribute-lft-in N/A

         \[\leadsto x \cdot 1 + \color{blue}{x \cdot \left(\left(\frac{-1}{6} \cdot y\right) \cdot y\right)} \]

      2. *-rgt-identity N/A

         \[\leadsto x + \color{blue}{x} \cdot \left(\left(\frac{-1}{6} \cdot y\right) \cdot y\right) \]

      3. +-commutative N/A

         \[\leadsto x \cdot \left(\left(\frac{-1}{6} \cdot y\right) \cdot y\right) + \color{blue}{x} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\left(\frac{-1}{6} \cdot y\right) \cdot y\right)\right), \color{blue}{x}\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right), x\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot x\right), x\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\frac{-1}{6} \cdot y\right) \cdot y\right) \cdot x\right), x\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y \cdot \left(\frac{-1}{6} \cdot y\right)\right) \cdot x\right), x\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \left(\left(\frac{-1}{6} \cdot y\right) \cdot x\right)\right), x\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\left(\frac{-1}{6} \cdot y\right) \cdot x\right)\right), x\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\left(\frac{-1}{6} \cdot y\right), x\right)\right), x\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\left(y \cdot \frac{-1}{6}\right), x\right)\right), x\right) \]

      13. *-lowering-*.f64 67.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \frac{-1}{6}\right), x\right)\right), x\right) \]

   9. Applied egg-rr 67.2%

      \[\leadsto \color{blue}{y \cdot \left(\left(y \cdot -0.16666666666666666\right) \cdot x\right) + x} \]

   if 3.2e5 < y

   1. Initial program 99.6%

      \[x \cdot \frac{\sin y}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + \frac{-1}{6} \cdot \left(x \cdot {y}^{2}\right)} \]
   4. Step-by-step derivation

      1. *-rgt-identity N/A

         \[\leadsto x \cdot 1 + \color{blue}{\frac{-1}{6}} \cdot \left(x \cdot {y}^{2}\right) \]

      2. *-commutative N/A

         \[\leadsto x \cdot 1 + \left(x \cdot {y}^{2}\right) \cdot \color{blue}{\frac{-1}{6}} \]

      3. associate-*l* N/A

         \[\leadsto x \cdot 1 + x \cdot \color{blue}{\left({y}^{2} \cdot \frac{-1}{6}\right)} \]

      4. *-commutative N/A

         \[\leadsto x \cdot 1 + x \cdot \left(\frac{-1}{6} \cdot \color{blue}{{y}^{2}}\right) \]

      5. distribute-lft-in N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + \frac{-1}{6} \cdot {y}^{2}\right)} \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + \frac{-1}{6} \cdot {y}^{2}\right)}\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{-1}{6} \cdot {y}^{2}\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{6}, \color{blue}{\left({y}^{2}\right)}\right)\right)\right) \]

      9. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{6}, \left(y \cdot \color{blue}{y}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 2.3%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right)\right) \]

   5. Simplified 2.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(1 + \frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \color{blue}{x} \]

      2. flip-+ N/A

         \[\leadsto \frac{1 \cdot 1 - \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)}{1 - \frac{-1}{6} \cdot \left(y \cdot y\right)} \cdot x \]

      3. associate-*l/ N/A

         \[\leadsto \frac{\left(1 \cdot 1 - \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \cdot x}{\color{blue}{1 - \frac{-1}{6} \cdot \left(y \cdot y\right)}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(\left(1 \cdot 1 - \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \cdot x\right), \color{blue}{\left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(1 \cdot 1 - \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right), x\right), \left(\color{blue}{1} - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(1 - \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \left(\left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      8. swap-sqr N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \left(\left(\frac{-1}{6} \cdot \frac{-1}{6}\right) \cdot \left(\left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\left(\frac{-1}{6} \cdot \frac{-1}{6}\right), \left(\left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \left(\left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\left(y \cdot y\right), \left(y \cdot y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(y \cdot y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(y, y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      14. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(y, y\right)\right)\right)\right), x\right), \left(1 + \color{blue}{\left(\mathsf{neg}\left(\frac{-1}{6}\right)\right) \cdot \left(y \cdot y\right)}\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(y, y\right)\right)\right)\right), x\right), \mathsf{+.f64}\left(1, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{-1}{6}\right)\right) \cdot \left(y \cdot y\right)\right)}\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(y, y\right)\right)\right)\right), x\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(\frac{-1}{6}\right)\right), \color{blue}{\left(y \cdot y\right)}\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(y, y\right)\right)\right)\right), x\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{6}, \left(\color{blue}{y} \cdot y\right)\right)\right)\right) \]

      18. *-lowering-*.f64 1.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(y, y\right)\right)\right)\right), x\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right)\right) \]

   7. Applied egg-rr 1.3%

      \[\leadsto \color{blue}{\frac{\left(1 - 0.027777777777777776 \cdot \left(\left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)\right) \cdot x}{1 + 0.16666666666666666 \cdot \left(y \cdot y\right)}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, y\right)\right)\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 38.1%

       \[\leadsto \frac{\color{blue}{x}}{1 + 0.16666666666666666 \cdot \left(y \cdot y\right)} \]

   11. Taylor expanded in y around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{6} \cdot {y}^{2}\right)}\right) \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \color{blue}{\left({y}^{2}\right)}\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \left(y \cdot \color{blue}{y}\right)\right)\right) \]

       3. *-lowering-*.f64 38.1%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right) \]

   13. Simplified 38.1%

       \[\leadsto \frac{x}{\color{blue}{0.16666666666666666 \cdot \left(y \cdot y\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 320000:\\ \;\;\;\;x + y \cdot \left(x \cdot \left(y \cdot -0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{0.16666666666666666 \cdot \left(y \cdot y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 56.8% accurate, 7.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 320000:\\ \;\;\;\;x \cdot \left(1 + \left(y \cdot y\right) \cdot -0.16666666666666666\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{0.16666666666666666 \cdot \left(y \cdot y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 320000.0)
   (* x (+ 1.0 (* (* y y) -0.16666666666666666)))
   (/ x (* 0.16666666666666666 (* y y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 320000.0) {
		tmp = x * (1.0 + ((y * y) * -0.16666666666666666));
	} else {
		tmp = x / (0.16666666666666666 * (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 <= 320000.0d0) then
        tmp = x * (1.0d0 + ((y * y) * (-0.16666666666666666d0)))
    else
        tmp = x / (0.16666666666666666d0 * (y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 320000.0) {
		tmp = x * (1.0 + ((y * y) * -0.16666666666666666));
	} else {
		tmp = x / (0.16666666666666666 * (y * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 320000.0:
		tmp = x * (1.0 + ((y * y) * -0.16666666666666666))
	else:
		tmp = x / (0.16666666666666666 * (y * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 320000.0)
		tmp = Float64(x * Float64(1.0 + Float64(Float64(y * y) * -0.16666666666666666)));
	else
		tmp = Float64(x / Float64(0.16666666666666666 * Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 320000.0)
		tmp = x * (1.0 + ((y * y) * -0.16666666666666666));
	else
		tmp = x / (0.16666666666666666 * (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 320000.0], N[(x * N[(1.0 + N[(N[(y * y), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.2e5

   1. Initial program 99.9%

      \[x \cdot \frac{\sin y}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + \frac{-1}{6} \cdot \left(x \cdot {y}^{2}\right)} \]
   4. Step-by-step derivation

      1. *-rgt-identity N/A

         \[\leadsto x \cdot 1 + \color{blue}{\frac{-1}{6}} \cdot \left(x \cdot {y}^{2}\right) \]

      2. *-commutative N/A

         \[\leadsto x \cdot 1 + \left(x \cdot {y}^{2}\right) \cdot \color{blue}{\frac{-1}{6}} \]

      3. associate-*l* N/A

         \[\leadsto x \cdot 1 + x \cdot \color{blue}{\left({y}^{2} \cdot \frac{-1}{6}\right)} \]

      4. *-commutative N/A

         \[\leadsto x \cdot 1 + x \cdot \left(\frac{-1}{6} \cdot \color{blue}{{y}^{2}}\right) \]

      5. distribute-lft-in N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + \frac{-1}{6} \cdot {y}^{2}\right)} \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + \frac{-1}{6} \cdot {y}^{2}\right)}\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{-1}{6} \cdot {y}^{2}\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{6}, \color{blue}{\left({y}^{2}\right)}\right)\right)\right) \]

      9. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{6}, \left(y \cdot \color{blue}{y}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 67.2%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right)\right) \]

   5. Simplified 67.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)} \]

   if 3.2e5 < y

   1. Initial program 99.6%

      \[x \cdot \frac{\sin y}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + \frac{-1}{6} \cdot \left(x \cdot {y}^{2}\right)} \]
   4. Step-by-step derivation

      1. *-rgt-identity N/A

         \[\leadsto x \cdot 1 + \color{blue}{\frac{-1}{6}} \cdot \left(x \cdot {y}^{2}\right) \]

      2. *-commutative N/A

         \[\leadsto x \cdot 1 + \left(x \cdot {y}^{2}\right) \cdot \color{blue}{\frac{-1}{6}} \]

      3. associate-*l* N/A

         \[\leadsto x \cdot 1 + x \cdot \color{blue}{\left({y}^{2} \cdot \frac{-1}{6}\right)} \]

      4. *-commutative N/A

         \[\leadsto x \cdot 1 + x \cdot \left(\frac{-1}{6} \cdot \color{blue}{{y}^{2}}\right) \]

      5. distribute-lft-in N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + \frac{-1}{6} \cdot {y}^{2}\right)} \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + \frac{-1}{6} \cdot {y}^{2}\right)}\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{-1}{6} \cdot {y}^{2}\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{6}, \color{blue}{\left({y}^{2}\right)}\right)\right)\right) \]

      9. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{6}, \left(y \cdot \color{blue}{y}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 2.3%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right)\right) \]

   5. Simplified 2.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(1 + \frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \color{blue}{x} \]

      2. flip-+ N/A

         \[\leadsto \frac{1 \cdot 1 - \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)}{1 - \frac{-1}{6} \cdot \left(y \cdot y\right)} \cdot x \]

      3. associate-*l/ N/A

         \[\leadsto \frac{\left(1 \cdot 1 - \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \cdot x}{\color{blue}{1 - \frac{-1}{6} \cdot \left(y \cdot y\right)}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(\left(1 \cdot 1 - \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \cdot x\right), \color{blue}{\left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(1 \cdot 1 - \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right), x\right), \left(\color{blue}{1} - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(1 - \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \left(\left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      8. swap-sqr N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \left(\left(\frac{-1}{6} \cdot \frac{-1}{6}\right) \cdot \left(\left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\left(\frac{-1}{6} \cdot \frac{-1}{6}\right), \left(\left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \left(\left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\left(y \cdot y\right), \left(y \cdot y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(y \cdot y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(y, y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      14. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(y, y\right)\right)\right)\right), x\right), \left(1 + \color{blue}{\left(\mathsf{neg}\left(\frac{-1}{6}\right)\right) \cdot \left(y \cdot y\right)}\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(y, y\right)\right)\right)\right), x\right), \mathsf{+.f64}\left(1, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{-1}{6}\right)\right) \cdot \left(y \cdot y\right)\right)}\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(y, y\right)\right)\right)\right), x\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(\frac{-1}{6}\right)\right), \color{blue}{\left(y \cdot y\right)}\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(y, y\right)\right)\right)\right), x\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{6}, \left(\color{blue}{y} \cdot y\right)\right)\right)\right) \]

      18. *-lowering-*.f64 1.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(y, y\right)\right)\right)\right), x\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right)\right) \]

   7. Applied egg-rr 1.3%

      \[\leadsto \color{blue}{\frac{\left(1 - 0.027777777777777776 \cdot \left(\left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)\right) \cdot x}{1 + 0.16666666666666666 \cdot \left(y \cdot y\right)}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, y\right)\right)\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 38.1%

       \[\leadsto \frac{\color{blue}{x}}{1 + 0.16666666666666666 \cdot \left(y \cdot y\right)} \]

   11. Taylor expanded in y around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{6} \cdot {y}^{2}\right)}\right) \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \color{blue}{\left({y}^{2}\right)}\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \left(y \cdot \color{blue}{y}\right)\right)\right) \]

       3. *-lowering-*.f64 38.1%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right) \]

   13. Simplified 38.1%

       \[\leadsto \frac{x}{\color{blue}{0.16666666666666666 \cdot \left(y \cdot y\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 320000:\\ \;\;\;\;x \cdot \left(1 + \left(y \cdot y\right) \cdot -0.16666666666666666\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{0.16666666666666666 \cdot \left(y \cdot y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.1% accurate, 8.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{0.16666666666666666 \cdot \left(y \cdot y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 2.5) x (/ x (* 0.16666666666666666 (* y y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 2.5) {
		tmp = x;
	} else {
		tmp = x / (0.16666666666666666 * (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 <= 2.5d0) then
        tmp = x
    else
        tmp = x / (0.16666666666666666d0 * (y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 2.5) {
		tmp = x;
	} else {
		tmp = x / (0.16666666666666666 * (y * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 2.5:
		tmp = x
	else:
		tmp = x / (0.16666666666666666 * (y * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 2.5)
		tmp = x;
	else
		tmp = Float64(x / Float64(0.16666666666666666 * Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 2.5)
		tmp = x;
	else
		tmp = x / (0.16666666666666666 * (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 2.5], x, N[(x / N[(0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.5

   1. Initial program 99.9%

      \[x \cdot \frac{\sin y}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

   5. Simplified 67.7%

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

   if 2.5 < y

   1. Initial program 99.6%

      \[x \cdot \frac{\sin y}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + \frac{-1}{6} \cdot \left(x \cdot {y}^{2}\right)} \]
   4. Step-by-step derivation

      1. *-rgt-identity N/A

         \[\leadsto x \cdot 1 + \color{blue}{\frac{-1}{6}} \cdot \left(x \cdot {y}^{2}\right) \]

      2. *-commutative N/A

         \[\leadsto x \cdot 1 + \left(x \cdot {y}^{2}\right) \cdot \color{blue}{\frac{-1}{6}} \]

      3. associate-*l* N/A

         \[\leadsto x \cdot 1 + x \cdot \color{blue}{\left({y}^{2} \cdot \frac{-1}{6}\right)} \]

      4. *-commutative N/A

         \[\leadsto x \cdot 1 + x \cdot \left(\frac{-1}{6} \cdot \color{blue}{{y}^{2}}\right) \]

      5. distribute-lft-in N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + \frac{-1}{6} \cdot {y}^{2}\right)} \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + \frac{-1}{6} \cdot {y}^{2}\right)}\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{-1}{6} \cdot {y}^{2}\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{6}, \color{blue}{\left({y}^{2}\right)}\right)\right)\right) \]

      9. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{6}, \left(y \cdot \color{blue}{y}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 2.4%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right)\right) \]

   5. Simplified 2.4%

      \[\leadsto \color{blue}{x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(1 + \frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \color{blue}{x} \]

      2. flip-+ N/A

         \[\leadsto \frac{1 \cdot 1 - \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)}{1 - \frac{-1}{6} \cdot \left(y \cdot y\right)} \cdot x \]

      3. associate-*l/ N/A

         \[\leadsto \frac{\left(1 \cdot 1 - \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \cdot x}{\color{blue}{1 - \frac{-1}{6} \cdot \left(y \cdot y\right)}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(\left(1 \cdot 1 - \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \cdot x\right), \color{blue}{\left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(1 \cdot 1 - \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right), x\right), \left(\color{blue}{1} - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(1 - \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \left(\left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      8. swap-sqr N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \left(\left(\frac{-1}{6} \cdot \frac{-1}{6}\right) \cdot \left(\left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\left(\frac{-1}{6} \cdot \frac{-1}{6}\right), \left(\left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \left(\left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\left(y \cdot y\right), \left(y \cdot y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(y \cdot y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(y, y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

      14. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(y, y\right)\right)\right)\right), x\right), \left(1 + \color{blue}{\left(\mathsf{neg}\left(\frac{-1}{6}\right)\right) \cdot \left(y \cdot y\right)}\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(y, y\right)\right)\right)\right), x\right), \mathsf{+.f64}\left(1, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{-1}{6}\right)\right) \cdot \left(y \cdot y\right)\right)}\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(y, y\right)\right)\right)\right), x\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(\frac{-1}{6}\right)\right), \color{blue}{\left(y \cdot y\right)}\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(y, y\right)\right)\right)\right), x\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{6}, \left(\color{blue}{y} \cdot y\right)\right)\right)\right) \]

      18. *-lowering-*.f64 1.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(y, y\right)\right)\right)\right), x\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right)\right) \]

   7. Applied egg-rr 1.4%

      \[\leadsto \color{blue}{\frac{\left(1 - 0.027777777777777776 \cdot \left(\left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)\right) \cdot x}{1 + 0.16666666666666666 \cdot \left(y \cdot y\right)}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, y\right)\right)\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 37.6%

       \[\leadsto \frac{\color{blue}{x}}{1 + 0.16666666666666666 \cdot \left(y \cdot y\right)} \]

   11. Taylor expanded in y around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{6} \cdot {y}^{2}\right)}\right) \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \color{blue}{\left({y}^{2}\right)}\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \left(y \cdot \color{blue}{y}\right)\right)\right) \]

       3. *-lowering-*.f64 37.6%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right) \]

   13. Simplified 37.6%

       \[\leadsto \frac{x}{\color{blue}{0.16666666666666666 \cdot \left(y \cdot y\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 62.7% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \frac{x}{1 + 0.16666666666666666 \cdot \left(y \cdot y\right)} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (/ x (+ 1.0 (* 0.16666666666666666 (* y y)))))

C

double code(double x, double y) {
	return x / (1.0 + (0.16666666666666666 * (y * y)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x / (1.0d0 + (0.16666666666666666d0 * (y * y)))
end function

Java

public static double code(double x, double y) {
	return x / (1.0 + (0.16666666666666666 * (y * y)));
}

Python

def code(x, y):
	return x / (1.0 + (0.16666666666666666 * (y * y)))

Julia

function code(x, y)
	return Float64(x / Float64(1.0 + Float64(0.16666666666666666 * Float64(y * y))))
end

MATLAB

function tmp = code(x, y)
	tmp = x / (1.0 + (0.16666666666666666 * (y * y)));
end

Wolfram

code[x_, y_] := N[(x / N[(1.0 + N[(0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[x \cdot \frac{\sin y}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{x + \frac{-1}{6} \cdot \left(x \cdot {y}^{2}\right)} \]
4. Step-by-step derivation

   1. *-rgt-identity N/A

      \[\leadsto x \cdot 1 + \color{blue}{\frac{-1}{6}} \cdot \left(x \cdot {y}^{2}\right) \]

   2. *-commutative N/A

      \[\leadsto x \cdot 1 + \left(x \cdot {y}^{2}\right) \cdot \color{blue}{\frac{-1}{6}} \]

   3. associate-*l* N/A

      \[\leadsto x \cdot 1 + x \cdot \color{blue}{\left({y}^{2} \cdot \frac{-1}{6}\right)} \]

   4. *-commutative N/A

      \[\leadsto x \cdot 1 + x \cdot \left(\frac{-1}{6} \cdot \color{blue}{{y}^{2}}\right) \]

   5. distribute-lft-in N/A

      \[\leadsto x \cdot \color{blue}{\left(1 + \frac{-1}{6} \cdot {y}^{2}\right)} \]

   6. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + \frac{-1}{6} \cdot {y}^{2}\right)}\right) \]

   7. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{-1}{6} \cdot {y}^{2}\right)}\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{6}, \color{blue}{\left({y}^{2}\right)}\right)\right)\right) \]

   9. unpow2 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{6}, \left(y \cdot \color{blue}{y}\right)\right)\right)\right) \]

   10. *-lowering-*.f64 51.3%

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{6}, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right)\right) \]

5. Simplified 51.3%

   \[\leadsto \color{blue}{x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)} \]
6. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(1 + \frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \color{blue}{x} \]

   2. flip-+ N/A

      \[\leadsto \frac{1 \cdot 1 - \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)}{1 - \frac{-1}{6} \cdot \left(y \cdot y\right)} \cdot x \]

   3. associate-*l/ N/A

      \[\leadsto \frac{\left(1 \cdot 1 - \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \cdot x}{\color{blue}{1 - \frac{-1}{6} \cdot \left(y \cdot y\right)}} \]

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

      \[\leadsto \mathsf{/.f64}\left(\left(\left(1 \cdot 1 - \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \cdot x\right), \color{blue}{\left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)}\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(1 \cdot 1 - \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right), x\right), \left(\color{blue}{1} - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

   6. metadata-eval N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(1 - \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

   7. --lowering--.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \left(\left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right) \cdot \left(\frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

   8. swap-sqr N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \left(\left(\frac{-1}{6} \cdot \frac{-1}{6}\right) \cdot \left(\left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

   9. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\left(\frac{-1}{6} \cdot \frac{-1}{6}\right), \left(\left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

   10. metadata-eval N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \left(\left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

   11. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\left(y \cdot y\right), \left(y \cdot y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

   12. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(y \cdot y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

   13. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(y, y\right)\right)\right)\right), x\right), \left(1 - \frac{-1}{6} \cdot \left(y \cdot y\right)\right)\right) \]

   14. cancel-sign-sub-inv N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(y, y\right)\right)\right)\right), x\right), \left(1 + \color{blue}{\left(\mathsf{neg}\left(\frac{-1}{6}\right)\right) \cdot \left(y \cdot y\right)}\right)\right) \]

   15. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(y, y\right)\right)\right)\right), x\right), \mathsf{+.f64}\left(1, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{-1}{6}\right)\right) \cdot \left(y \cdot y\right)\right)}\right)\right) \]

   16. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(y, y\right)\right)\right)\right), x\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(\frac{-1}{6}\right)\right), \color{blue}{\left(y \cdot y\right)}\right)\right)\right) \]

   17. metadata-eval N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(y, y\right)\right)\right)\right), x\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{6}, \left(\color{blue}{y} \cdot y\right)\right)\right)\right) \]

   18. *-lowering-*.f64 50.8%

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{36}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(y, y\right)\right)\right)\right), x\right), \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right)\right) \]

7. Applied egg-rr 50.8%

   \[\leadsto \color{blue}{\frac{\left(1 - 0.027777777777777776 \cdot \left(\left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)\right) \cdot x}{1 + 0.16666666666666666 \cdot \left(y \cdot y\right)}} \]

8. Taylor expanded in y around 0

   \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, y\right)\right)\right)\right) \]
9. Step-by-step derivation

10. Simplified 66.6%

    \[\leadsto \frac{\color{blue}{x}}{1 + 0.16666666666666666 \cdot \left(y \cdot y\right)} \]
11. Add Preprocessing

Alternative 6: 56.9% accurate, 17.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.46 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 1.46e+44) x 0.0))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1.46e+44) {
		tmp = x;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 1.46d+44) then
        tmp = x
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 1.46e+44) {
		tmp = x;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 1.46e+44:
		tmp = x
	else:
		tmp = 0.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1.46e+44)
		tmp = x;
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 1.46e+44)
		tmp = x;
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1.46e+44], x, 0.0]

Derivation

1. Split input into 2 regimes

2. if y < 1.4599999999999999e44

   1. Initial program 99.8%

      \[x \cdot \frac{\sin y}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

   5. Simplified 65.2%

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

   if 1.4599999999999999e44 < y

   1. Initial program 99.7%

      \[x \cdot \frac{\sin y}{y} \]
   2. Add Preprocessing

   4. Applied egg-rr 41.8%

      \[\leadsto \color{blue}{0} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 15.2% accurate, 105.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 0.0)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 0.0

Julia

function code(x, y)
	return 0.0
end

MATLAB

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

Wolfram

code[x_, y_] := 0.0

Derivation

1. Initial program 99.8%

   \[x \cdot \frac{\sin y}{y} \]
2. Add Preprocessing

4. Applied egg-rr 18.2%

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

Reproduce

herbie shell --seed 2024158 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))