Linear.Quaternion:$ccosh from linear-1.19.1.3

Percentage Accurate: 89.0% → 99.8%

Time: 9.7s

Alternatives: 8

Speedup: 1.0×

• Could not converge on a ground truth

  1. x = 1.518273698887744e+132
  2. y = 7.120487960924775e+291

• 48.6% 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: 89.0% 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

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

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 90.2%

   \[\frac{\sin x \cdot \sinh y}{x} \]
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: 69.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq 0.0005:\\ \;\;\;\;\frac{y}{\frac{x}{\sin x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \sinh y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) 0.0005) (/ y (/ x (sin x))) (/ (* x (sinh y)) x)))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= 0.0005) {
		tmp = y / (x / sin(x));
	} else {
		tmp = (x * sinh(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) <= 0.0005d0) then
        tmp = y / (x / sin(x))
    else
        tmp = (x * sinh(y)) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.sinh(y) <= 0.0005) {
		tmp = y / (x / Math.sin(x));
	} else {
		tmp = (x * Math.sinh(y)) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= 0.0005:
		tmp = y / (x / math.sin(x))
	else:
		tmp = (x * math.sinh(y)) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= 0.0005)
		tmp = Float64(y / Float64(x / sin(x)));
	else
		tmp = Float64(Float64(x * sinh(y)) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= 0.0005)
		tmp = y / (x / sin(x));
	else
		tmp = (x * sinh(y)) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], 0.0005], N[(y / N[(x / N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Sinh[y], $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < 5.0000000000000001e-4

   1. Initial program 86.9%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 50.8%

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

      1. associate-/l* 63.7%

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

   7. Simplified 63.7%

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

      1. clear-num 63.7%

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

      2. un-div-inv 63.8%

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

   9. Applied egg-rr 63.8%

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

   if 5.0000000000000001e-4 < (sinh.f64 y)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 70.8%

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

Alternative 3: 69.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq 0.0005:\\ \;\;\;\;\frac{y}{\frac{x}{\sin x}}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) 0.0005) (/ y (/ x (sin x))) (sinh y)))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= 0.0005) {
		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) <= 0.0005d0) 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) <= 0.0005) {
		tmp = y / (x / Math.sin(x));
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= 0.0005:
		tmp = y / (x / math.sin(x))
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= 0.0005)
		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) <= 0.0005)
		tmp = y / (x / sin(x));
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], 0.0005], 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) < 5.0000000000000001e-4

   1. Initial program 86.9%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 50.8%

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

      1. associate-/l* 63.7%

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

   7. Simplified 63.7%

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

      1. clear-num 63.7%

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

      2. un-div-inv 63.8%

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

   9. Applied egg-rr 63.8%

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

   if 5.0000000000000001e-4 < (sinh.f64 y)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 70.8%

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

      1. *-commutative 70.8%

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

      2. associate-/l* 70.8%

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

   5. Applied egg-rr 70.8%

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

      1. *-inverses 70.8%

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

      2. *-rgt-identity 70.8%

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

   7. Simplified 70.8%

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

Alternative 4: 69.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq 0.0005:\\ \;\;\;\;y \cdot \frac{\sin x}{x}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) 0.0005) (* y (/ (sin x) x)) (sinh y)))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= 0.0005) {
		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) <= 0.0005d0) 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) <= 0.0005) {
		tmp = y * (Math.sin(x) / x);
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= 0.0005:
		tmp = y * (math.sin(x) / x)
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= 0.0005)
		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) <= 0.0005)
		tmp = y * (sin(x) / x);
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], 0.0005], 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) < 5.0000000000000001e-4

   1. Initial program 86.9%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 50.8%

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

      1. associate-/l* 63.7%

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

   7. Simplified 63.7%

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

   if 5.0000000000000001e-4 < (sinh.f64 y)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 70.8%

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

      1. *-commutative 70.8%

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

      2. associate-/l* 70.8%

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

   5. Applied egg-rr 70.8%

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

      1. *-inverses 70.8%

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

      2. *-rgt-identity 70.8%

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

   7. Simplified 70.8%

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

Alternative 5: 62.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq 5 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) 5e-81) (/ x (/ x y)) (sinh y)))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= 5e-81) {
		tmp = 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) <= 5d-81) then
        tmp = 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) <= 5e-81) {
		tmp = x / (x / y);
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= 5e-81:
		tmp = x / (x / y)
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= 5e-81)
		tmp = Float64(x / Float64(x / y));
	else
		tmp = sinh(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= 5e-81)
		tmp = x / (x / y);
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], 5e-81], N[(x / N[(x / y), $MachinePrecision]), $MachinePrecision], N[Sinh[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < 4.99999999999999981e-81

   1. Initial program 86.3%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 69.4%

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

   6. Taylor expanded in x around 0 51.5%

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

      1. clear-num 51.8%

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

      2. un-div-inv 50.2%

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

   8. Applied egg-rr 50.2%

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

   if 4.99999999999999981e-81 < (sinh.f64 y)

   1. Initial program 98.7%

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

   3. Taylor expanded in x around 0 62.4%

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

      1. *-commutative 62.4%

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

      2. associate-/l* 63.5%

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

   5. Applied egg-rr 63.5%

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

      1. *-inverses 63.5%

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

      2. *-rgt-identity 63.5%

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

   7. Simplified 63.5%

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

Alternative 6: 56.9% accurate, 14.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.55 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 2.55e+99)
   (* x (/ y x))
   (* y (+ 1.0 (* 0.16666666666666666 (* y y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 2.55e+99) {
		tmp = x * (y / x);
	} else {
		tmp = y * (1.0 + (0.16666666666666666 * (y * 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 <= 2.55d+99) then
        tmp = x * (y / x)
    else
        tmp = y * (1.0d0 + (0.16666666666666666d0 * (y * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 2.55e+99) {
		tmp = x * (y / x);
	} else {
		tmp = y * (1.0 + (0.16666666666666666 * (y * y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 2.55e+99:
		tmp = x * (y / x)
	else:
		tmp = y * (1.0 + (0.16666666666666666 * (y * y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 2.55e+99)
		tmp = Float64(x * Float64(y / x));
	else
		tmp = Float64(y * Float64(1.0 + Float64(0.16666666666666666 * Float64(y * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 2.55e+99)
		tmp = x * (y / x);
	else
		tmp = y * (1.0 + (0.16666666666666666 * (y * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 2.55e+99], N[(x * N[(y / x), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 + N[(0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.54999999999999976e99

   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 68.4%

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

   6. Taylor expanded in x around 0 48.1%

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

   if 2.54999999999999976e99 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 62.7%

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

   4. Taylor expanded in y around 0 62.7%

      \[\leadsto \color{blue}{y \cdot \left(1 + 0.16666666666666666 \cdot {y}^{2}\right)} \]
   5. Step-by-step derivation

      1. unpow2 62.7%

         \[\leadsto y \cdot \left(1 + 0.16666666666666666 \cdot \color{blue}{\left(y \cdot y\right)}\right) \]

   6. Applied egg-rr 62.7%

      \[\leadsto y \cdot \left(1 + 0.16666666666666666 \cdot \color{blue}{\left(y \cdot y\right)}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 50.6% 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 90.2%

   \[\frac{\sin x \cdot \sinh y}{x} \]
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 62.7%

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

6. Taylor expanded in x around 0 46.3%

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

Alternative 8: 28.6% 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 90.2%

   \[\frac{\sin x \cdot \sinh y}{x} \]
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 39.1%

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

   1. associate-/l* 48.8%

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

7. Simplified 48.8%

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

8. Taylor expanded in x around 0 24.3%

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

Developer Target 1: 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 2024165 
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (* (sin x) (/ (sinh y) x)))

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