Linear.Quaternion:$ccosh from linear-1.19.1.3

Percentage Accurate: 88.8% → 99.9%

Time: 7.3s

Alternatives: 8

Speedup: 1.0×

• 49.0% 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: 88.8% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.0%

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

   1. *-commutative 92.0%

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

   2. associate-/l* 99.6%

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

4. Applied egg-rr 99.6%

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

5. Final simplification 99.6%

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

Alternative 2: 70.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq 5 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{\sin x}{x}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) 5e-7) (* y (/ (sin x) x)) (sinh y)))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= 5e-7) {
		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) <= 5d-7) 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) <= 5e-7) {
		tmp = y * (Math.sin(x) / x);
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= 5e-7:
		tmp = y * (math.sin(x) / x)
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= 5e-7)
		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) <= 5e-7)
		tmp = y * (sin(x) / x);
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], 5e-7], 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) < 4.99999999999999977e-7

   1. Initial program 89.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 51.9%

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

      1. associate-/l* 62.3%

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

   7. Simplified 62.3%

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

   if 4.99999999999999977e-7 < (sinh.f64 y)

   1. Initial program 98.6%

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

      1. *-commutative 98.6%

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

      2. associate-/l* 98.6%

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

   4. Applied egg-rr 98.6%

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

   5. Taylor expanded in x around 0 71.4%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sinh y \leq 5 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{\sin x}{x}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq 5 \cdot 10^{-77}:\\ \;\;\;\;\frac{\frac{y}{x}}{\frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) 5e-77) (/ (/ y x) (/ 1.0 x)) (sinh y)))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= 5e-77) {
		tmp = (y / x) / (1.0 / 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) <= 5d-77) then
        tmp = (y / x) / (1.0d0 / 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) <= 5e-77) {
		tmp = (y / x) / (1.0 / x);
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= 5e-77:
		tmp = (y / x) / (1.0 / x)
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= 5e-77)
		tmp = Float64(Float64(y / x) / Float64(1.0 / x));
	else
		tmp = sinh(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= 5e-77)
		tmp = (y / x) / (1.0 / x);
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], 5e-77], N[(N[(y / x), $MachinePrecision] / N[(1.0 / x), $MachinePrecision]), $MachinePrecision], N[Sinh[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < 4.99999999999999963e-77

   1. Initial program 88.8%

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

   3. Taylor expanded in y around 0 48.4%

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

      1. associate-/l* 70.2%

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

      2. *-commutative 70.2%

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

   5. Applied egg-rr 70.2%

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

      1. associate-/r/ 59.5%

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

      2. div-inv 59.4%

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

      3. associate-/r* 70.1%

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

   7. Applied egg-rr 70.1%

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

   8. Taylor expanded in x around 0 55.9%

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

   if 4.99999999999999963e-77 < (sinh.f64 y)

   1. Initial program 98.6%

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

      1. *-commutative 98.6%

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

      2. associate-/l* 98.8%

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

   4. Applied egg-rr 98.8%

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

   5. Taylor expanded in x around 0 67.8%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sinh y \leq 5 \cdot 10^{-77}:\\ \;\;\;\;\frac{\frac{y}{x}}{\frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \]
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 92.0%

   \[\frac{\sin x \cdot \sinh y}{x} \]
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: 30.7% accurate, 17.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.5 \cdot 10^{+92}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x}{y \cdot x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x 3.5e+92) y (/ 1.0 (/ x (* y x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 3.5e+92) {
		tmp = y;
	} else {
		tmp = 1.0 / (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 (x <= 3.5d+92) then
        tmp = y
    else
        tmp = 1.0d0 / (x / (y * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 3.5e+92) {
		tmp = y;
	} else {
		tmp = 1.0 / (x / (y * x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 3.5e+92:
		tmp = y
	else:
		tmp = 1.0 / (x / (y * x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 3.5e+92)
		tmp = y;
	else
		tmp = Float64(1.0 / Float64(x / Float64(y * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 3.5e+92)
		tmp = y;
	else
		tmp = 1.0 / (x / (y * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 3.5e+92], y, N[(1.0 / N[(x / N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.49999999999999986e92

   1. Initial program 89.7%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around 0 35.2%

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

      1. associate-/l* 44.9%

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

   7. Simplified 44.9%

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

   8. Taylor expanded in x around 0 28.0%

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

   if 3.49999999999999986e92 < x

   1. Initial program 99.9%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 53.8%

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

      1. associate-/l* 53.8%

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

   7. Simplified 53.8%

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

      1. associate-*r/ 53.8%

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

      2. *-commutative 53.8%

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

      3. clear-num 52.4%

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

      4. associate-/r* 52.3%

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

   9. Applied egg-rr 52.3%

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

   10. Taylor expanded in x around inf 52.4%

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

   11. Taylor expanded in x around 0 17.3%

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

       1. *-commutative 17.3%

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

   13. Simplified 17.3%

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

4. Final simplification 25.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.5 \cdot 10^{+92}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x}{y \cdot x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 30.7% accurate, 20.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.85 \cdot 10^{+96}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x 1.85e+96) y (/ (* y x) x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 1.85e+96) {
		tmp = y;
	} else {
		tmp = (y * x) / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 1.85d+96) then
        tmp = y
    else
        tmp = (y * x) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 1.85e+96) {
		tmp = y;
	} else {
		tmp = (y * x) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 1.85e+96:
		tmp = y
	else:
		tmp = (y * x) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 1.85e+96)
		tmp = y;
	else
		tmp = Float64(Float64(y * x) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 1.85e+96)
		tmp = y;
	else
		tmp = (y * x) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 1.85e+96], y, N[(N[(y * x), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.84999999999999996e96

   1. Initial program 89.8%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around 0 35.5%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]
   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 27.8%

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

   if 1.84999999999999996e96 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 53.0%

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

   4. Taylor expanded in x around 0 17.5%

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

4. Final simplification 25.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.85 \cdot 10^{+96}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.4% accurate, 29.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.0%

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

3. Taylor expanded in y around 0 39.3%

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

   1. associate-/l* 60.2%

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

   2. *-commutative 60.2%

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

5. Applied egg-rr 60.2%

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

   1. associate-/r/ 46.9%

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

   2. div-inv 46.8%

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

   3. associate-/r* 60.2%

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

7. Applied egg-rr 60.2%

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

8. Taylor expanded in x around 0 47.9%

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

9. Final simplification 47.9%

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

Alternative 8: 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 92.0%

   \[\frac{\sin x \cdot \sinh y}{x} \]
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 39.3%

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

   1. associate-/l* 46.9%

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

7. Simplified 46.9%

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

8. Taylor expanded in x around 0 22.6%

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

9. Final simplification 22.6%

   \[\leadsto y \]
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 2024079 
(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))