Linear.Quaternion:$cexp from linear-1.19.1.3

Percentage Accurate: 99.8% → 99.8%

Time: 7.2s

Alternatives: 6

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. Final simplification 99.8%

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

Alternative 2: 52.9% accurate, 9.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. clear-num 99.7%

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

   2. div-inv 99.8%

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

   3. div-inv 99.6%

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

   4. associate-/r* 90.5%

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

4. Applied egg-rr 90.5%

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

5. Taylor expanded in y around 0 53.8%

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

6. Final simplification 53.8%

   \[\leadsto \frac{\frac{x}{y}}{y \cdot 0.16666666666666666 + \frac{1}{y}} \]
7. Add Preprocessing

Alternative 3: 52.1% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ y \cdot \frac{-1}{\frac{-y}{x}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in x around 0 89.6%

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

   1. *-commutative 89.6%

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

   2. associate-/l* 90.9%

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

5. Simplified 90.9%

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

6. Taylor expanded in y around 0 53.8%

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

   1. frac-2neg 53.8%

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

   2. div-inv 52.9%

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

   3. distribute-neg-frac 52.9%

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

8. Applied egg-rr 52.9%

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

9. Final simplification 52.9%

   \[\leadsto y \cdot \frac{-1}{\frac{-y}{x}} \]
10. Add Preprocessing

Alternative 4: 51.4% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in x around 0 89.6%

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

   1. *-commutative 89.6%

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

   2. associate-/l* 90.9%

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

5. Simplified 90.9%

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

6. Taylor expanded in y around 0 53.8%

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

   1. *-un-lft-identity 53.8%

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

   2. associate-*l/ 52.9%

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

   3. clear-num 52.3%

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

8. Applied egg-rr 52.3%

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

9. Final simplification 52.3%

   \[\leadsto y \cdot \frac{x}{y} \]
10. Add Preprocessing

Alternative 5: 52.9% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in x around 0 89.6%

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

   1. *-commutative 89.6%

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

   2. associate-/l* 90.9%

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

5. Simplified 90.9%

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

6. Taylor expanded in y around 0 53.8%

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

7. Final simplification 53.8%

   \[\leadsto \frac{y}{\frac{y}{x}} \]
8. Add Preprocessing

Alternative 6: 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. Add Preprocessing

3. Taylor expanded in y around 0 52.1%

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

4. Final simplification 52.1%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024033 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))