Linear.Quaternion:$ccosh from linear-1.19.1.3

Percentage Accurate: 88.4% → 99.9%

Time: 9.0s

Alternatives: 6

Speedup: 1.0×

• 49.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.3%

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

   1. associate-/l* 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 70.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq 2 \cdot 10^{+20}:\\ \;\;\;\;\frac{y}{\frac{x}{\sin x}}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) 2e+20) (/ y (/ x (sin x))) (sinh y)))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= 2e+20) {
		tmp = y / (x / sin(x));
	} else {
		tmp = sinh(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (sinh(y) <= 2d+20) then
        tmp = y / (x / sin(x))
    else
        tmp = sinh(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.sinh(y) <= 2e+20) {
		tmp = y / (x / Math.sin(x));
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= 2e+20:
		tmp = y / (x / math.sin(x))
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= 2e+20)
		tmp = Float64(y / Float64(x / sin(x)));
	else
		tmp = sinh(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= 2e+20)
		tmp = y / (x / sin(x));
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], 2e+20], N[(y / N[(x / N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Sinh[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < 2e20

   1. Initial program 87.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 49.7%

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

      1. associate-/l* 61.8%

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

   7. Simplified 61.8%

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

      1. clear-num 61.8%

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

      2. un-div-inv 61.8%

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

   9. Applied egg-rr 61.8%

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

   if 2e20 < (sinh.f64 y)

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

      1. add-cube-cbrt 100.0%

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

      2. pow3 100.0%

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

   6. Applied egg-rr 100.0%

      \[\leadsto \sin x \cdot \color{blue}{{\left(\sqrt[3]{\frac{\sinh y}{x}}\right)}^{3}} \]
   7. Step-by-step derivation

      1. rem-cube-cbrt 100.0%

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

      2. clear-num 100.0%

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

      3. div-inv 100.0%

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

      4. div-inv 100.0%

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

      5. associate-/r* 100.0%

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

   8. Applied egg-rr 100.0%

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

   9. Taylor expanded in x around 0 77.0%

      \[\leadsto \frac{\color{blue}{1}}{\frac{1}{\sinh y}} \]
   10. Step-by-step derivation

       1. remove-double-div 77.0%

          \[\leadsto \color{blue}{\sinh y} \]

       2. sinh-def 77.0%

          \[\leadsto \color{blue}{\frac{e^{y} - e^{-y}}{2}} \]

       3. div-sub 77.0%

          \[\leadsto \color{blue}{\frac{e^{y}}{2} - \frac{e^{-y}}{2}} \]

   11. Applied egg-rr 77.0%

       \[\leadsto \color{blue}{\frac{e^{y}}{2} - \frac{e^{-y}}{2}} \]
   12. Step-by-step derivation

       1. div-sub 77.0%

          \[\leadsto \color{blue}{\frac{e^{y} - e^{-y}}{2}} \]

       2. sinh-def 77.0%

          \[\leadsto \color{blue}{\sinh y} \]

   13. Simplified 77.0%

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

Alternative 3: 70.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq 2 \cdot 10^{+20}:\\ \;\;\;\;y \cdot \frac{\sin x}{x}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) 2e+20) (* y (/ (sin x) x)) (sinh y)))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= 2e+20) {
		tmp = y * (sin(x) / x);
	} else {
		tmp = sinh(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (sinh(y) <= 2d+20) then
        tmp = y * (sin(x) / x)
    else
        tmp = sinh(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.sinh(y) <= 2e+20) {
		tmp = y * (Math.sin(x) / x);
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= 2e+20:
		tmp = y * (math.sin(x) / x)
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= 2e+20)
		tmp = Float64(y * Float64(sin(x) / x));
	else
		tmp = sinh(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= 2e+20)
		tmp = y * (sin(x) / x);
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], 2e+20], N[(y * N[(N[Sin[x], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[Sinh[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < 2e20

   1. Initial program 87.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 49.7%

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

      1. associate-/l* 61.8%

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

   7. Simplified 61.8%

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

   if 2e20 < (sinh.f64 y)

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

      1. add-cube-cbrt 100.0%

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

      2. pow3 100.0%

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

   6. Applied egg-rr 100.0%

      \[\leadsto \sin x \cdot \color{blue}{{\left(\sqrt[3]{\frac{\sinh y}{x}}\right)}^{3}} \]
   7. Step-by-step derivation

      1. rem-cube-cbrt 100.0%

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

      2. clear-num 100.0%

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

      3. div-inv 100.0%

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

      4. div-inv 100.0%

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

      5. associate-/r* 100.0%

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

   8. Applied egg-rr 100.0%

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

   9. Taylor expanded in x around 0 77.0%

      \[\leadsto \frac{\color{blue}{1}}{\frac{1}{\sinh y}} \]
   10. Step-by-step derivation

       1. remove-double-div 77.0%

          \[\leadsto \color{blue}{\sinh y} \]

       2. sinh-def 77.0%

          \[\leadsto \color{blue}{\frac{e^{y} - e^{-y}}{2}} \]

       3. div-sub 77.0%

          \[\leadsto \color{blue}{\frac{e^{y}}{2} - \frac{e^{-y}}{2}} \]

   11. Applied egg-rr 77.0%

       \[\leadsto \color{blue}{\frac{e^{y}}{2} - \frac{e^{-y}}{2}} \]
   12. Step-by-step derivation

       1. div-sub 77.0%

          \[\leadsto \color{blue}{\frac{e^{y} - e^{-y}}{2}} \]

       2. sinh-def 77.0%

          \[\leadsto \color{blue}{\sinh y} \]

   13. Simplified 77.0%

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

Alternative 4: 63.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq 10^{-30}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) 1e-30) (* x (/ y x)) (sinh y)))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= 1e-30) {
		tmp = x * (y / x);
	} else {
		tmp = sinh(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (sinh(y) <= 1d-30) then
        tmp = x * (y / x)
    else
        tmp = sinh(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.sinh(y) <= 1e-30) {
		tmp = x * (y / x);
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= 1e-30:
		tmp = x * (y / x)
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= 1e-30)
		tmp = Float64(x * Float64(y / x));
	else
		tmp = sinh(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= 1e-30)
		tmp = x * (y / x);
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], 1e-30], N[(x * N[(y / x), $MachinePrecision]), $MachinePrecision], N[Sinh[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < 1e-30

   1. Initial program 87.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 47.9%

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

   6. Taylor expanded in x around 0 21.0%

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

      1. *-commutative 21.0%

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

   8. Simplified 21.0%

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

      1. *-commutative 21.0%

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

      2. associate-/l* 56.2%

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

   10. Applied egg-rr 56.2%

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

   if 1e-30 < (sinh.f64 y)

   1. Initial program 100.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. add-cube-cbrt 99.8%

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

      2. pow3 99.8%

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

   6. Applied egg-rr 99.8%

      \[\leadsto \sin x \cdot \color{blue}{{\left(\sqrt[3]{\frac{\sinh y}{x}}\right)}^{3}} \]
   7. Step-by-step derivation

      1. rem-cube-cbrt 99.9%

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

      2. clear-num 99.2%

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

      3. div-inv 99.2%

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

      4. div-inv 99.1%

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

      5. associate-/r* 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in x around 0 71.1%

      \[\leadsto \frac{\color{blue}{1}}{\frac{1}{\sinh y}} \]
   10. Step-by-step derivation

       1. remove-double-div 71.1%

          \[\leadsto \color{blue}{\sinh y} \]

       2. sinh-def 70.3%

          \[\leadsto \color{blue}{\frac{e^{y} - e^{-y}}{2}} \]

       3. div-sub 70.3%

          \[\leadsto \color{blue}{\frac{e^{y}}{2} - \frac{e^{-y}}{2}} \]

   11. Applied egg-rr 70.3%

       \[\leadsto \color{blue}{\frac{e^{y}}{2} - \frac{e^{-y}}{2}} \]
   12. Step-by-step derivation

       1. div-sub 70.3%

          \[\leadsto \color{blue}{\frac{e^{y} - e^{-y}}{2}} \]

       2. sinh-def 71.1%

          \[\leadsto \color{blue}{\sinh y} \]

   13. Simplified 71.1%

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

Alternative 5: 51.0% accurate, 41.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.3%

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

   1. associate-/l* 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in y around 0 36.6%

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

6. Taylor expanded in x around 0 18.9%

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

   1. *-commutative 18.9%

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

8. Simplified 18.9%

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

   1. *-commutative 18.9%

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

   2. associate-/l* 47.6%

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

10. Applied egg-rr 47.6%

    \[\leadsto \color{blue}{x \cdot \frac{y}{x}} \]
11. Add Preprocessing

Alternative 6: 28.5% accurate, 205.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 y)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return y

Julia

function code(x, y)
	return y
end

MATLAB

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

Wolfram

code[x_, y_] := y

Derivation

1. Initial program 91.3%

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

   1. associate-/l* 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in y around 0 36.6%

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

   1. associate-/l* 45.2%

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

7. Simplified 45.2%

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

8. Taylor expanded in x around 0 20.5%

   \[\leadsto \color{blue}{y} \]
9. Add Preprocessing

Developer target: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024087 
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"
  :precision binary64

  :alt
  (* (sin x) (/ (sinh y) x))

  (/ (* (sin x) (sinh y)) x))