Linear.Quaternion:$ccosh from linear-1.19.1.3

Percentage Accurate: 89.1% → 99.8%

Time: 9.7s

Alternatives: 6

Speedup: 1.0×

• 49.5% 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: 89.1% 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: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{\sin x}{x}}{\frac{1}{\sinh y}} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (/ (sin x) x) (/ 1.0 (sinh y))))

C

double code(double x, double y) {
	return (sin(x) / x) / (1.0 / sinh(y));
}

Fortran

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

Java

public static double code(double x, double y) {
	return (Math.sin(x) / x) / (1.0 / Math.sinh(y));
}

Python

def code(x, y):
	return (math.sin(x) / x) / (1.0 / math.sinh(y))

Julia

function code(x, y)
	return Float64(Float64(sin(x) / x) / Float64(1.0 / sinh(y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (sin(x) / x) / (1.0 / sinh(y));
end

Wolfram

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

Derivation

1. Initial program 88.5%

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

   1. associate-/l* 99.5%

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

3. Simplified 99.5%

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

   1. clear-num 98.9%

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

   2. un-div-inv 99.3%

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

6. Applied egg-rr 99.3%

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

   1. *-un-lft-identity 99.3%

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

   2. div-inv 99.2%

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

   3. times-frac 88.4%

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

8. Applied egg-rr 88.4%

   \[\leadsto \color{blue}{\frac{1}{x} \cdot \frac{\sin x}{\frac{1}{\sinh y}}} \]
9. Step-by-step derivation

   1. associate-*r/ 99.8%

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

   2. associate-*l/ 99.9%

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

   3. *-un-lft-identity 99.9%

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

10. Applied egg-rr 99.9%

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

11. Final simplification 99.9%

    \[\leadsto \frac{\frac{\sin x}{x}}{\frac{1}{\sinh y}} \]
12. Add Preprocessing

Alternative 2: 69.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq 4 \cdot 10^{-5}:\\ \;\;\;\;\frac{\sin x}{x} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) 4e-5) (* (/ (sin x) x) y) (sinh y)))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= 4e-5) {
		tmp = (sin(x) / x) * y;
	} 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) <= 4d-5) then
        tmp = (sin(x) / x) * y
    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) <= 4e-5) {
		tmp = (Math.sin(x) / x) * y;
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= 4e-5:
		tmp = (math.sin(x) / x) * y
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= 4e-5)
		tmp = Float64(Float64(sin(x) / x) * y);
	else
		tmp = sinh(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= 4e-5)
		tmp = (sin(x) / x) * y;
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], 4e-5], N[(N[(N[Sin[x], $MachinePrecision] / x), $MachinePrecision] * y), $MachinePrecision], N[Sinh[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < 4.00000000000000033e-5

   1. Initial program 84.5%

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

      1. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in y around 0 52.0%

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

      1. associate-/l* 67.5%

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

   7. Simplified 67.5%

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

   if 4.00000000000000033e-5 < (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. associate-*r/ 100.0%

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

      2. clear-num 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/r* 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 62.0%

      \[\leadsto \frac{1}{\color{blue}{\frac{2}{e^{y} - \frac{1}{e^{y}}}}} \]
   8. Step-by-step derivation

      1. metadata-eval 62.0%

         \[\leadsto \frac{1}{\frac{\color{blue}{1 \cdot 2}}{e^{y} - \frac{1}{e^{y}}}} \]

      2. associate-*l/ 62.0%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{e^{y} - \frac{1}{e^{y}}} \cdot 2}} \]

      3. associate-/r/ 62.0%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{e^{y} - \frac{1}{e^{y}}}{2}}}} \]

      4. rec-exp 62.0%

         \[\leadsto \frac{1}{\frac{1}{\frac{e^{y} - \color{blue}{e^{-y}}}{2}}} \]

      5. sinh-def 62.2%

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

   9. Simplified 62.2%

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

       1. remove-double-div 62.2%

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

       2. sinh-def 62.0%

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

       3. div-sub 62.0%

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

   11. Applied egg-rr 62.0%

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

       1. div-sub 62.0%

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

       2. sinh-def 62.2%

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

   13. Simplified 62.2%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sinh y \leq 4 \cdot 10^{-5}:\\ \;\;\;\;\frac{\sin x}{x} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq 2 \cdot 10^{-46}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) 2e-46) (* x (/ y x)) (sinh y)))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= 2e-46) {
		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) <= 2d-46) 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) <= 2e-46) {
		tmp = x * (y / x);
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= 2e-46:
		tmp = x * (y / x)
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= 2e-46)
		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) <= 2e-46)
		tmp = x * (y / x);
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], 2e-46], N[(x * N[(y / x), $MachinePrecision]), $MachinePrecision], N[Sinh[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < 2.00000000000000005e-46

   1. Initial program 84.0%

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

   3. Taylor expanded in y around 0 50.1%

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

   4. Taylor expanded in x around 0 26.7%

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

      1. *-commutative 26.7%

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

   6. Simplified 26.7%

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

      1. *-commutative 26.7%

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

      2. associate-/l* 59.2%

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

   8. Applied egg-rr 59.2%

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

   if 2.00000000000000005e-46 < (sinh.f64 y)

   1. Initial program 99.5%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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. associate-*r/ 99.5%

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

      2. clear-num 99.5%

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

      3. *-commutative 99.5%

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

      4. associate-/r* 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 56.5%

      \[\leadsto \frac{1}{\color{blue}{\frac{2}{e^{y} - \frac{1}{e^{y}}}}} \]
   8. Step-by-step derivation

      1. metadata-eval 56.5%

         \[\leadsto \frac{1}{\frac{\color{blue}{1 \cdot 2}}{e^{y} - \frac{1}{e^{y}}}} \]

      2. associate-*l/ 56.5%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{e^{y} - \frac{1}{e^{y}}} \cdot 2}} \]

      3. associate-/r/ 56.5%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{e^{y} - \frac{1}{e^{y}}}{2}}}} \]

      4. rec-exp 56.6%

         \[\leadsto \frac{1}{\frac{1}{\frac{e^{y} - \color{blue}{e^{-y}}}{2}}} \]

      5. sinh-def 63.6%

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

   9. Simplified 63.6%

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

       1. remove-double-div 63.6%

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

       2. sinh-def 56.6%

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

       3. div-sub 56.6%

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

   11. Applied egg-rr 56.6%

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

       1. div-sub 56.6%

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

       2. sinh-def 63.6%

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

   13. Simplified 63.6%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sinh y \leq 2 \cdot 10^{-46}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.8% 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 88.5%

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

   1. associate-/l* 99.5%

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

3. Simplified 99.5%

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

5. Final simplification 99.5%

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

Alternative 5: 49.5% 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 88.5%

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

3. Taylor expanded in y around 0 39.9%

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

4. Taylor expanded in x around 0 24.1%

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

   1. *-commutative 24.1%

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

6. Simplified 24.1%

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

   1. *-commutative 24.1%

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

   2. associate-/l* 51.7%

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

8. Applied egg-rr 51.7%

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

9. Final simplification 51.7%

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

Alternative 6: 27.9% 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 88.5%

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

   1. associate-/l* 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in y around 0 39.9%

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

   1. associate-/l* 51.4%

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

7. Simplified 51.4%

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

8. Taylor expanded in x around 0 29.7%

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

9. Final simplification 29.7%

   \[\leadsto y \]
10. Add Preprocessing

Developer target: 99.8% 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 2024080 
(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))