Linear.Quaternion:$cexp from linear-1.19.1.3

Percentage Accurate: 99.8% → 99.8%

Time: 15.7s

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: 64.3% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ \frac{0 - y}{y \cdot \left(-1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)} \cdot x \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (* (/ (- 0.0 y) (* y (+ -1.0 (* -0.16666666666666666 (* y y))))) x))

C

double code(double x, double y) {
	return ((0.0 - y) / (y * (-1.0 + (-0.16666666666666666 * (y * y))))) * x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((0.0d0 - y) / (y * ((-1.0d0) + ((-0.16666666666666666d0) * (y * y))))) * x
end function

Java

public static double code(double x, double y) {
	return ((0.0 - y) / (y * (-1.0 + (-0.16666666666666666 * (y * y))))) * x;
}

Python

def code(x, y):
	return ((0.0 - y) / (y * (-1.0 + (-0.16666666666666666 * (y * y))))) * x

Julia

function code(x, y)
	return Float64(Float64(Float64(0.0 - y) / Float64(y * Float64(-1.0 + Float64(-0.16666666666666666 * Float64(y * y))))) * x)
end

MATLAB

function tmp = code(x, y)
	tmp = ((0.0 - y) / (y * (-1.0 + (-0.16666666666666666 * (y * y))))) * x;
end

Wolfram

code[x_, y_] := N[(N[(N[(0.0 - y), $MachinePrecision] / N[(y * N[(-1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in y around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

7. Applied egg-rr 0

   \[\leadsto expr\]

8. Taylor expanded in y around 0 0

   \[\leadsto expr\]

10. Simplified 0

    \[\leadsto expr\]

12. Applied egg-rr 0

    \[\leadsto expr\]
13. Add Preprocessing

Alternative 3: 57.9% accurate, 7.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 200000000000:\\ \;\;\;\;\left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \frac{x}{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 200000000000.0)
   (* (+ 1.0 (* -0.16666666666666666 (* y y))) x)
   (* 6.0 (/ x (* y y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 200000000000.0) {
		tmp = (1.0 + (-0.16666666666666666 * (y * y))) * x;
	} else {
		tmp = 6.0 * (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 <= 200000000000.0d0) then
        tmp = (1.0d0 + ((-0.16666666666666666d0) * (y * y))) * x
    else
        tmp = 6.0d0 * (x / (y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 200000000000.0) {
		tmp = (1.0 + (-0.16666666666666666 * (y * y))) * x;
	} else {
		tmp = 6.0 * (x / (y * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 200000000000.0:
		tmp = (1.0 + (-0.16666666666666666 * (y * y))) * x
	else:
		tmp = 6.0 * (x / (y * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 200000000000.0)
		tmp = Float64(Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y))) * x);
	else
		tmp = Float64(6.0 * Float64(x / Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 200000000000.0)
		tmp = (1.0 + (-0.16666666666666666 * (y * y))) * x;
	else
		tmp = 6.0 * (x / (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 200000000000.0], N[(N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(6.0 * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2e11

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 2e11 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 58.2% accurate, 8.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.45:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \frac{x}{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 2.45) x (* 6.0 (/ x (* y y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 2.45) {
		tmp = x;
	} else {
		tmp = 6.0 * (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 <= 2.45d0) then
        tmp = x
    else
        tmp = 6.0d0 * (x / (y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 2.45) {
		tmp = x;
	} else {
		tmp = 6.0 * (x / (y * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 2.45:
		tmp = x
	else:
		tmp = 6.0 * (x / (y * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 2.45)
		tmp = x;
	else
		tmp = Float64(6.0 * Float64(x / Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 2.45)
		tmp = x;
	else
		tmp = 6.0 * (x / (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 2.45], x, N[(6.0 * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.4500000000000002

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 2.4500000000000002 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 64.3% 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. Add Preprocessing

3. Taylor expanded in y around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

7. Applied egg-rr 0

   \[\leadsto expr\]

8. Taylor expanded in y around 0 0

   \[\leadsto expr\]

10. Simplified 0

    \[\leadsto expr\]

11. Taylor expanded in x around 0 0

    \[\leadsto expr\]

13. Simplified 0

    \[\leadsto expr\]
14. Add Preprocessing

Alternative 6: 57.9% accurate, 17.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.25 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 3.25e+50) x 0.0))

C

double code(double x, double y) {
	double tmp;
	if (y <= 3.25e+50) {
		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 <= 3.25d+50) 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 <= 3.25e+50) {
		tmp = x;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 3.25e+50:
		tmp = x
	else:
		tmp = 0.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 3.25e+50)
		tmp = x;
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 3.25e+50)
		tmp = x;
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 3.25e+50], x, 0.0]

Derivation

1. Split input into 2 regimes

2. if y < 3.2500000000000001e50

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 3.2500000000000001e50 < y

   1. Initial program 99.7%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 15.7% 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 0

   \[\leadsto expr\]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024110 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))