Linear.Quaternion:$ccosh from linear-1.19.1.3

Percentage Accurate: 88.9% → 99.9%

Time: 8.0s

Alternatives: 7

Speedup: 1.0×

• 49.3% 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: 88.9% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.1%

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

   1. associate-*l/ 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 86.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq -4 \cdot 10^{-6} \lor \neg \left(\sinh y \leq 0.02\right):\\ \;\;\;\;\sinh y\\ \mathbf{else}:\\ \;\;\;\;\sin x \cdot \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= (sinh y) -4e-6) (not (<= (sinh y) 0.02)))
   (sinh y)
   (* (sin x) (/ y x))))

C

double code(double x, double y) {
	double tmp;
	if ((sinh(y) <= -4e-6) || !(sinh(y) <= 0.02)) {
		tmp = sinh(y);
	} else {
		tmp = sin(x) * (y / x);
	}
	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-6)) .or. (.not. (sinh(y) <= 0.02d0))) then
        tmp = sinh(y)
    else
        tmp = sin(x) * (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((Math.sinh(y) <= -4e-6) || !(Math.sinh(y) <= 0.02)) {
		tmp = Math.sinh(y);
	} else {
		tmp = Math.sin(x) * (y / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (math.sinh(y) <= -4e-6) or not (math.sinh(y) <= 0.02):
		tmp = math.sinh(y)
	else:
		tmp = math.sin(x) * (y / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((sinh(y) <= -4e-6) || !(sinh(y) <= 0.02))
		tmp = sinh(y);
	else
		tmp = Float64(sin(x) * Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((sinh(y) <= -4e-6) || ~((sinh(y) <= 0.02)))
		tmp = sinh(y);
	else
		tmp = sin(x) * (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[N[Sinh[y], $MachinePrecision], -4e-6], N[Not[LessEqual[N[Sinh[y], $MachinePrecision], 0.02]], $MachinePrecision]], N[Sinh[y], $MachinePrecision], N[(N[Sin[x], $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < -3.99999999999999982e-6 or 0.0200000000000000004 < (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%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 82.5%

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

   if -3.99999999999999982e-6 < (sinh.f64 y) < 0.0200000000000000004

   1. Initial program 83.8%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 83.4%

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

      1. associate-/l* 99.4%

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

      2. associate-/r/ 99.3%

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

   6. Simplified 99.3%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sinh y \leq -4 \cdot 10^{-6} \lor \neg \left(\sinh y \leq 0.02\right):\\ \;\;\;\;\sinh y\\ \mathbf{else}:\\ \;\;\;\;\sin x \cdot \frac{y}{x}\\ \end{array} \]

Alternative 3: 74.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq -4 \cdot 10^{-53} \lor \neg \left(\sinh y \leq 2 \cdot 10^{-87}\right):\\ \;\;\;\;\sinh y\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x}{y} \cdot \frac{1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= (sinh y) -4e-53) (not (<= (sinh y) 2e-87)))
   (sinh y)
   (/ 1.0 (* (/ x y) (/ 1.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if ((sinh(y) <= -4e-53) || !(sinh(y) <= 2e-87)) {
		tmp = sinh(y);
	} else {
		tmp = 1.0 / ((x / y) * (1.0 / x));
	}
	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-53)) .or. (.not. (sinh(y) <= 2d-87))) then
        tmp = sinh(y)
    else
        tmp = 1.0d0 / ((x / y) * (1.0d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((Math.sinh(y) <= -4e-53) || !(Math.sinh(y) <= 2e-87)) {
		tmp = Math.sinh(y);
	} else {
		tmp = 1.0 / ((x / y) * (1.0 / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (math.sinh(y) <= -4e-53) or not (math.sinh(y) <= 2e-87):
		tmp = math.sinh(y)
	else:
		tmp = 1.0 / ((x / y) * (1.0 / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((sinh(y) <= -4e-53) || !(sinh(y) <= 2e-87))
		tmp = sinh(y);
	else
		tmp = Float64(1.0 / Float64(Float64(x / y) * Float64(1.0 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((sinh(y) <= -4e-53) || ~((sinh(y) <= 2e-87)))
		tmp = sinh(y);
	else
		tmp = 1.0 / ((x / y) * (1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[N[Sinh[y], $MachinePrecision], -4e-53], N[Not[LessEqual[N[Sinh[y], $MachinePrecision], 2e-87]], $MachinePrecision]], N[Sinh[y], $MachinePrecision], N[(1.0 / N[(N[(x / y), $MachinePrecision] * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < -4.00000000000000012e-53 or 2.00000000000000004e-87 < (sinh.f64 y)

   1. Initial program 98.5%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 78.8%

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

   if -4.00000000000000012e-53 < (sinh.f64 y) < 2.00000000000000004e-87

   1. Initial program 81.7%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 81.7%

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

      1. associate-/l* 99.9%

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

      2. associate-/r/ 99.7%

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

   6. Simplified 99.7%

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

      1. clear-num 99.6%

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

      2. associate-/r/ 99.6%

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

      3. associate-/l/ 81.6%

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

   8. Applied egg-rr 81.6%

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

   9. Taylor expanded in x around 0 27.6%

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

       1. *-commutative 27.6%

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

   11. Simplified 27.6%

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

       1. associate-/r* 81.6%

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

       2. div-inv 81.7%

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

   13. Applied egg-rr 81.7%

       \[\leadsto \frac{1}{\color{blue}{\frac{x}{y} \cdot \frac{1}{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sinh y \leq -4 \cdot 10^{-53} \lor \neg \left(\sinh y \leq 2 \cdot 10^{-87}\right):\\ \;\;\;\;\sinh y\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x}{y} \cdot \frac{1}{x}}\\ \end{array} \]

Alternative 4: 86.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3300000 \lor \neg \left(y \leq 0.14\right):\\ \;\;\;\;\sinh y\\ \mathbf{else}:\\ \;\;\;\;\frac{\sin x}{-0.16666666666666666 \cdot \left(x \cdot y\right) + \frac{x}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3300000.0) (not (<= y 0.14)))
   (sinh y)
   (/ (sin x) (+ (* -0.16666666666666666 (* x y)) (/ x y)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3300000.0) || !(y <= 0.14)) {
		tmp = sinh(y);
	} else {
		tmp = sin(x) / ((-0.16666666666666666 * (x * y)) + (x / 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 <= (-3300000.0d0)) .or. (.not. (y <= 0.14d0))) then
        tmp = sinh(y)
    else
        tmp = sin(x) / (((-0.16666666666666666d0) * (x * y)) + (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -3300000.0) || !(y <= 0.14)) {
		tmp = Math.sinh(y);
	} else {
		tmp = Math.sin(x) / ((-0.16666666666666666 * (x * y)) + (x / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3300000.0) or not (y <= 0.14):
		tmp = math.sinh(y)
	else:
		tmp = math.sin(x) / ((-0.16666666666666666 * (x * y)) + (x / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3300000.0) || !(y <= 0.14))
		tmp = sinh(y);
	else
		tmp = Float64(sin(x) / Float64(Float64(-0.16666666666666666 * Float64(x * y)) + Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -3300000.0) || ~((y <= 0.14)))
		tmp = sinh(y);
	else
		tmp = sin(x) / ((-0.16666666666666666 * (x * y)) + (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3300000.0], N[Not[LessEqual[y, 0.14]], $MachinePrecision]], N[Sinh[y], $MachinePrecision], N[(N[Sin[x], $MachinePrecision] / N[(N[(-0.16666666666666666 * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3e6 or 0.14000000000000001 < y

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 84.1%

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

   if -3.3e6 < y < 0.14000000000000001

   1. Initial program 84.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 97.9%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3300000 \lor \neg \left(y \leq 0.14\right):\\ \;\;\;\;\sinh y\\ \mathbf{else}:\\ \;\;\;\;\frac{\sin x}{-0.16666666666666666 \cdot \left(x \cdot y\right) + \frac{x}{y}}\\ \end{array} \]

Alternative 5: 86.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-6} \lor \neg \left(y \leq 0.0116\right):\\ \;\;\;\;\sinh y\\ \mathbf{else}:\\ \;\;\;\;\frac{\sin x}{x} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4e-6) (not (<= y 0.0116))) (sinh y) (* (/ (sin x) x) y)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4e-6) || !(y <= 0.0116)) {
		tmp = sinh(y);
	} else {
		tmp = (sin(x) / x) * 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 <= (-4d-6)) .or. (.not. (y <= 0.0116d0))) then
        tmp = sinh(y)
    else
        tmp = (sin(x) / x) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -4e-6) || !(y <= 0.0116)) {
		tmp = Math.sinh(y);
	} else {
		tmp = (Math.sin(x) / x) * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4e-6) or not (y <= 0.0116):
		tmp = math.sinh(y)
	else:
		tmp = (math.sin(x) / x) * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4e-6) || !(y <= 0.0116))
		tmp = sinh(y);
	else
		tmp = Float64(Float64(sin(x) / x) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -4e-6) || ~((y <= 0.0116)))
		tmp = sinh(y);
	else
		tmp = (sin(x) / x) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4e-6], N[Not[LessEqual[y, 0.0116]], $MachinePrecision]], N[Sinh[y], $MachinePrecision], N[(N[(N[Sin[x], $MachinePrecision] / x), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.99999999999999982e-6 or 0.0116 < y

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 82.5%

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

   if -3.99999999999999982e-6 < y < 0.0116

   1. Initial program 83.8%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 83.4%

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

      1. associate-/l* 99.4%

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

   6. Simplified 99.4%

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

      1. clear-num 99.2%

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

      2. associate-/r/ 99.4%

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

      3. clear-num 99.4%

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

   8. Applied egg-rr 99.4%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-6} \lor \neg \left(y \leq 0.0116\right):\\ \;\;\;\;\sinh y\\ \mathbf{else}:\\ \;\;\;\;\frac{\sin x}{x} \cdot y\\ \end{array} \]

Alternative 6: 50.5% 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 92.1%

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

   1. associate-*l/ 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in y around 0 43.8%

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

   1. associate-/l* 51.7%

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

   2. associate-/r/ 64.7%

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

6. Simplified 64.7%

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

   1. clear-num 64.7%

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

   2. associate-/r/ 63.9%

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

   3. associate-/l/ 43.8%

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

8. Applied egg-rr 43.8%

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

9. Taylor expanded in x around 0 26.0%

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

    1. *-commutative 26.0%

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

11. Simplified 26.0%

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

    1. associate-/r* 53.0%

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

    2. associate-/r/ 53.8%

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

    3. clear-num 53.5%

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

13. Applied egg-rr 53.5%

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

14. Final simplification 53.5%

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

Alternative 7: 28.0% 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 92.1%

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

   1. associate-*l/ 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in y around 0 43.8%

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

   1. associate-/l* 51.7%

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

   2. associate-/r/ 64.7%

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

6. Simplified 64.7%

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

7. Taylor expanded in x around 0 27.0%

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

8. Final simplification 27.0%

   \[\leadsto y \]

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 2023306 
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (* (sin x) (/ (sinh y) x))

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