Linear.Quaternion:$cexp from linear-1.19.1.3

Percentage Accurate: 99.8% → 99.8%

Time: 5.9s

Alternatives: 9

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x \cdot \frac{\sin y}{y} \]
2. Step-by-step derivation

   1. clear-num 99.7%

      \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{y}{\sin y}}} \]

   2. un-div-inv 99.8%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\sin y}}} \]

3. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\frac{x}{\frac{y}{\sin y}}} \]

4. Final simplification 99.8%

   \[\leadsto \frac{x}{\frac{y}{\sin y}} \]

Alternative 2: 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. Final simplification 99.8%

   \[\leadsto x \cdot \frac{\sin y}{y} \]

Alternative 3: 63.5% accurate, 8.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+15} \lor \neg \left(y \leq 1.3 \cdot 10^{+35}\right):\\ \;\;\;\;6 \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \left(y \cdot y\right) \cdot -0.16666666666666666\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1e+15) (not (<= y 1.3e+35)))
   (* 6.0 (/ x (* y y)))
   (* x (+ 1.0 (* (* y y) -0.16666666666666666)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1e+15) || !(y <= 1.3e+35)) {
		tmp = 6.0 * (x / (y * y));
	} else {
		tmp = x * (1.0 + ((y * y) * -0.16666666666666666));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1d+15)) .or. (.not. (y <= 1.3d+35))) then
        tmp = 6.0d0 * (x / (y * y))
    else
        tmp = x * (1.0d0 + ((y * y) * (-0.16666666666666666d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1e+15) || !(y <= 1.3e+35)) {
		tmp = 6.0 * (x / (y * y));
	} else {
		tmp = x * (1.0 + ((y * y) * -0.16666666666666666));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1e+15) or not (y <= 1.3e+35):
		tmp = 6.0 * (x / (y * y))
	else:
		tmp = x * (1.0 + ((y * y) * -0.16666666666666666))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1e+15) || !(y <= 1.3e+35))
		tmp = Float64(6.0 * Float64(x / Float64(y * y)));
	else
		tmp = Float64(x * Float64(1.0 + Float64(Float64(y * y) * -0.16666666666666666)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1e+15) || ~((y <= 1.3e+35)))
		tmp = 6.0 * (x / (y * y));
	else
		tmp = x * (1.0 + ((y * y) * -0.16666666666666666));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1e+15], N[Not[LessEqual[y, 1.3e+35]], $MachinePrecision]], N[(6.0 * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(N[(y * y), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1e15 or 1.30000000000000003e35 < y

   1. Initial program 99.6%

      \[x \cdot \frac{\sin y}{y} \]
   2. Step-by-step derivation

      1. clear-num 99.5%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{y}{\sin y}}} \]

      2. un-div-inv 99.6%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{\sin y}}} \]

   3. Applied egg-rr 99.6%

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

      1. clear-num 99.5%

         \[\leadsto \frac{x}{\color{blue}{\frac{1}{\frac{\sin y}{y}}}} \]

      2. associate-/r/ 99.6%

         \[\leadsto \frac{x}{\color{blue}{\frac{1}{\sin y} \cdot y}} \]

   5. Applied egg-rr 99.6%

      \[\leadsto \frac{x}{\color{blue}{\frac{1}{\sin y} \cdot y}} \]

   6. Taylor expanded in y around 0 27.4%

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

   7. Taylor expanded in y around inf 27.4%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{{y}^{2}}} \]
   8. Step-by-step derivation

      1. unpow2 27.4%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{y \cdot y}} \]

   9. Simplified 27.4%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{y \cdot y}} \]

   if -1e15 < y < 1.30000000000000003e35

   1. Initial program 99.9%

      \[x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in y around 0 93.0%

      \[\leadsto x \cdot \color{blue}{\left(1 + -0.16666666666666666 \cdot {y}^{2}\right)} \]
   3. Step-by-step derivation

      1. unpow2 93.0%

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

   4. Simplified 93.0%

      \[\leadsto x \cdot \color{blue}{\left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+15} \lor \neg \left(y \leq 1.3 \cdot 10^{+35}\right):\\ \;\;\;\;6 \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \left(y \cdot y\right) \cdot -0.16666666666666666\right)\\ \end{array} \]

Alternative 4: 63.6% accurate, 8.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+15} \lor \neg \left(y \leq 1.16 \cdot 10^{+35}\right):\\ \;\;\;\;6 \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot y\right) \cdot \left(x \cdot -0.16666666666666666\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1e+15) (not (<= y 1.16e+35)))
   (* 6.0 (/ x (* y y)))
   (+ x (* (* y y) (* x -0.16666666666666666)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1e+15) || !(y <= 1.16e+35)) {
		tmp = 6.0 * (x / (y * y));
	} else {
		tmp = x + ((y * y) * (x * -0.16666666666666666));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1d+15)) .or. (.not. (y <= 1.16d+35))) then
        tmp = 6.0d0 * (x / (y * y))
    else
        tmp = x + ((y * y) * (x * (-0.16666666666666666d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1e+15) || !(y <= 1.16e+35)) {
		tmp = 6.0 * (x / (y * y));
	} else {
		tmp = x + ((y * y) * (x * -0.16666666666666666));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1e+15) or not (y <= 1.16e+35):
		tmp = 6.0 * (x / (y * y))
	else:
		tmp = x + ((y * y) * (x * -0.16666666666666666))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1e+15) || !(y <= 1.16e+35))
		tmp = Float64(6.0 * Float64(x / Float64(y * y)));
	else
		tmp = Float64(x + Float64(Float64(y * y) * Float64(x * -0.16666666666666666)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1e+15) || ~((y <= 1.16e+35)))
		tmp = 6.0 * (x / (y * y));
	else
		tmp = x + ((y * y) * (x * -0.16666666666666666));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1e+15], N[Not[LessEqual[y, 1.16e+35]], $MachinePrecision]], N[(6.0 * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * y), $MachinePrecision] * N[(x * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1e15 or 1.1600000000000001e35 < y

   1. Initial program 99.6%

      \[x \cdot \frac{\sin y}{y} \]
   2. Step-by-step derivation

      1. clear-num 99.5%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{y}{\sin y}}} \]

      2. un-div-inv 99.6%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{\sin y}}} \]

   3. Applied egg-rr 99.6%

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

      1. clear-num 99.5%

         \[\leadsto \frac{x}{\color{blue}{\frac{1}{\frac{\sin y}{y}}}} \]

      2. associate-/r/ 99.6%

         \[\leadsto \frac{x}{\color{blue}{\frac{1}{\sin y} \cdot y}} \]

   5. Applied egg-rr 99.6%

      \[\leadsto \frac{x}{\color{blue}{\frac{1}{\sin y} \cdot y}} \]

   6. Taylor expanded in y around 0 27.4%

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

   7. Taylor expanded in y around inf 27.4%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{{y}^{2}}} \]
   8. Step-by-step derivation

      1. unpow2 27.4%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{y \cdot y}} \]

   9. Simplified 27.4%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{y \cdot y}} \]

   if -1e15 < y < 1.1600000000000001e35

   1. Initial program 99.9%

      \[x \cdot \frac{\sin y}{y} \]
   2. Step-by-step derivation

      1. add-cube-cbrt 97.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \frac{\sin y}{y}} \cdot \sqrt[3]{x \cdot \frac{\sin y}{y}}\right) \cdot \sqrt[3]{x \cdot \frac{\sin y}{y}}} \]

      2. pow3 97.8%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \frac{\sin y}{y}}\right)}^{3}} \]

   3. Applied egg-rr 97.8%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \frac{\sin y}{y}}\right)}^{3}} \]

   4. Taylor expanded in y around 0 93.1%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot x + {y}^{2} \cdot \left(-0.1111111111111111 \cdot \left({1}^{0.3333333333333333} \cdot x\right) + -0.05555555555555555 \cdot \left({1}^{0.3333333333333333} \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. pow-base-1 93.1%

         \[\leadsto \color{blue}{1} \cdot x + {y}^{2} \cdot \left(-0.1111111111111111 \cdot \left({1}^{0.3333333333333333} \cdot x\right) + -0.05555555555555555 \cdot \left({1}^{0.3333333333333333} \cdot x\right)\right) \]

      2. *-lft-identity 93.1%

         \[\leadsto \color{blue}{x} + {y}^{2} \cdot \left(-0.1111111111111111 \cdot \left({1}^{0.3333333333333333} \cdot x\right) + -0.05555555555555555 \cdot \left({1}^{0.3333333333333333} \cdot x\right)\right) \]

      3. unpow2 93.1%

         \[\leadsto x + \color{blue}{\left(y \cdot y\right)} \cdot \left(-0.1111111111111111 \cdot \left({1}^{0.3333333333333333} \cdot x\right) + -0.05555555555555555 \cdot \left({1}^{0.3333333333333333} \cdot x\right)\right) \]

      4. distribute-rgt-out 93.1%

         \[\leadsto x + \left(y \cdot y\right) \cdot \color{blue}{\left(\left({1}^{0.3333333333333333} \cdot x\right) \cdot \left(-0.1111111111111111 + -0.05555555555555555\right)\right)} \]

      5. pow-base-1 93.1%

         \[\leadsto x + \left(y \cdot y\right) \cdot \left(\left(\color{blue}{1} \cdot x\right) \cdot \left(-0.1111111111111111 + -0.05555555555555555\right)\right) \]

      6. *-lft-identity 93.1%

         \[\leadsto x + \left(y \cdot y\right) \cdot \left(\color{blue}{x} \cdot \left(-0.1111111111111111 + -0.05555555555555555\right)\right) \]

      7. metadata-eval 93.1%

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

   6. Simplified 93.1%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+15} \lor \neg \left(y \leq 1.16 \cdot 10^{+35}\right):\\ \;\;\;\;6 \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot y\right) \cdot \left(x \cdot -0.16666666666666666\right)\\ \end{array} \]

Alternative 5: 63.3% accurate, 9.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \lor \neg \left(y \leq 2.4\right):\\ \;\;\;\;6 \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.4) (not (<= y 2.4))) (* 6.0 (/ x (* y y))) x))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.4) || !(y <= 2.4)) {
		tmp = 6.0 * (x / (y * y));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-2.4d0)) .or. (.not. (y <= 2.4d0))) then
        tmp = 6.0d0 * (x / (y * y))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.4) || !(y <= 2.4)) {
		tmp = 6.0 * (x / (y * y));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.4) or not (y <= 2.4):
		tmp = 6.0 * (x / (y * y))
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.4) || !(y <= 2.4))
		tmp = Float64(6.0 * Float64(x / Float64(y * y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.4) || ~((y <= 2.4)))
		tmp = 6.0 * (x / (y * y));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.4], N[Not[LessEqual[y, 2.4]], $MachinePrecision]], N[(6.0 * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.39999999999999991 or 2.39999999999999991 < y

   1. Initial program 99.6%

      \[x \cdot \frac{\sin y}{y} \]
   2. Step-by-step derivation

      1. clear-num 99.5%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{y}{\sin y}}} \]

      2. un-div-inv 99.6%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{\sin y}}} \]

   3. Applied egg-rr 99.6%

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

      1. clear-num 99.5%

         \[\leadsto \frac{x}{\color{blue}{\frac{1}{\frac{\sin y}{y}}}} \]

      2. associate-/r/ 99.6%

         \[\leadsto \frac{x}{\color{blue}{\frac{1}{\sin y} \cdot y}} \]

   5. Applied egg-rr 99.6%

      \[\leadsto \frac{x}{\color{blue}{\frac{1}{\sin y} \cdot y}} \]

   6. Taylor expanded in y around 0 25.2%

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

   7. Taylor expanded in y around inf 25.2%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{{y}^{2}}} \]
   8. Step-by-step derivation

      1. unpow2 25.2%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{y \cdot y}} \]

   9. Simplified 25.2%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{y \cdot y}} \]

   if -2.39999999999999991 < y < 2.39999999999999991

   1. Initial program 100.0%

      \[x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in y around 0 98.9%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \lor \neg \left(y \leq 2.4\right):\\ \;\;\;\;6 \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 61.1% accurate, 11.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+161} \lor \neg \left(y \leq 4 \cdot 10^{+20}\right):\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.55e+161) (not (<= y 4e+20))) (* y (/ x y)) x))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.55e+161) || !(y <= 4e+20)) {
		tmp = y * (x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-2.55d+161)) .or. (.not. (y <= 4d+20))) then
        tmp = y * (x / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.55e+161) || !(y <= 4e+20)) {
		tmp = y * (x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.55e+161) or not (y <= 4e+20):
		tmp = y * (x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.55e+161) || !(y <= 4e+20))
		tmp = Float64(y * Float64(x / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.55e+161) || ~((y <= 4e+20)))
		tmp = y * (x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.55e+161], N[Not[LessEqual[y, 4e+20]], $MachinePrecision]], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.54999999999999982e161 or 4e20 < y

   1. Initial program 99.6%

      \[x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in x around 0 99.6%

      \[\leadsto \color{blue}{\frac{\sin y \cdot x}{y}} \]

   3. Taylor expanded in y around 0 4.3%

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

      1. associate-/l* 29.8%

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

      2. div-inv 29.8%

         \[\leadsto \color{blue}{y \cdot \frac{1}{\frac{y}{x}}} \]

      3. clear-num 28.2%

         \[\leadsto y \cdot \color{blue}{\frac{x}{y}} \]

   5. Applied egg-rr 28.2%

      \[\leadsto \color{blue}{y \cdot \frac{x}{y}} \]

   if -2.54999999999999982e161 < y < 4e20

   1. Initial program 99.9%

      \[x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in y around 0 80.7%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+161} \lor \neg \left(y \leq 4 \cdot 10^{+20}\right):\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 62.7% accurate, 11.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+59} \lor \neg \left(y \leq 5 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5e+59) (not (<= y 5e-19))) (/ y (/ y x)) x))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5e+59) || !(y <= 5e-19)) {
		tmp = y / (y / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-5d+59)) .or. (.not. (y <= 5d-19))) then
        tmp = y / (y / x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -5e+59) || !(y <= 5e-19)) {
		tmp = y / (y / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -5e+59) or not (y <= 5e-19):
		tmp = y / (y / x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -5e+59) || !(y <= 5e-19))
		tmp = Float64(y / Float64(y / x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -5e+59) || ~((y <= 5e-19)))
		tmp = y / (y / x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -5e+59], N[Not[LessEqual[y, 5e-19]], $MachinePrecision]], N[(y / N[(y / x), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.9999999999999997e59 or 5.0000000000000004e-19 < y

   1. Initial program 99.6%

      \[x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in x around 0 99.6%

      \[\leadsto \color{blue}{\frac{\sin y \cdot x}{y}} \]

   3. Taylor expanded in y around 0 8.7%

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

      1. associate-/l* 29.7%

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

      2. div-inv 29.7%

         \[\leadsto \color{blue}{y \cdot \frac{1}{\frac{y}{x}}} \]

      3. clear-num 26.9%

         \[\leadsto y \cdot \color{blue}{\frac{x}{y}} \]

   5. Applied egg-rr 26.9%

      \[\leadsto \color{blue}{y \cdot \frac{x}{y}} \]
   6. Step-by-step derivation

      1. clear-num 29.7%

         \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{y}{x}}} \]

      2. un-div-inv 29.7%

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

   7. Applied egg-rr 29.7%

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

   if -4.9999999999999997e59 < y < 5.0000000000000004e-19

   1. Initial program 99.9%

      \[x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in y around 0 91.6%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+59} \lor \neg \left(y \leq 5 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 63.6% accurate, 11.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x \cdot \frac{\sin y}{y} \]
2. Step-by-step derivation

   1. clear-num 99.7%

      \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{y}{\sin y}}} \]

   2. un-div-inv 99.8%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\sin y}}} \]

3. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\frac{x}{\frac{y}{\sin y}}} \]

4. Taylor expanded in y around 0 65.2%

   \[\leadsto \frac{x}{\color{blue}{1 + 0.16666666666666666 \cdot {y}^{2}}} \]
5. Step-by-step derivation

   1. *-commutative 65.2%

      \[\leadsto \frac{x}{1 + \color{blue}{{y}^{2} \cdot 0.16666666666666666}} \]

   2. unpow2 65.2%

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

6. Simplified 65.2%

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

7. Final simplification 65.2%

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

Alternative 9: 51.9% accurate, 105.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

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

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 99.8%

   \[x \cdot \frac{\sin y}{y} \]

2. Taylor expanded in y around 0 55.1%

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

3. Final simplification 55.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023173 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))