Linear.Quaternion:$csinh from linear-1.19.1.3

Percentage Accurate: 99.9% → 99.9%

Time: 7.7s

Alternatives: 7

Speedup: 1.0×

• 51.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 2: 86.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\cosh x \leq 1.35:\\ \;\;\;\;\frac{\sin y}{y}\\ \mathbf{else}:\\ \;\;\;\;\cosh x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (cosh x) 1.35) (/ (sin y) y) (cosh x)))

C

double code(double x, double y) {
	double tmp;
	if (cosh(x) <= 1.35) {
		tmp = sin(y) / y;
	} else {
		tmp = cosh(x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (cosh(x) <= 1.35d0) then
        tmp = sin(y) / y
    else
        tmp = cosh(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.cosh(x) <= 1.35) {
		tmp = Math.sin(y) / y;
	} else {
		tmp = Math.cosh(x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.cosh(x) <= 1.35:
		tmp = math.sin(y) / y
	else:
		tmp = math.cosh(x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (cosh(x) <= 1.35)
		tmp = Float64(sin(y) / y);
	else
		tmp = cosh(x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (cosh(x) <= 1.35)
		tmp = sin(y) / y;
	else
		tmp = cosh(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Cosh[x], $MachinePrecision], 1.35], N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision], N[Cosh[x], $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 3: 63.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \cosh x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (cosh x))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return math.cosh(x)

Julia

function code(x, y)
	return cosh(x)
end

MATLAB

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

Wolfram

code[x_, y_] := N[Cosh[x], $MachinePrecision]

Derivation

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Alternative 4: 32.7% accurate, 12.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.0015:\\ \;\;\;\;\frac{-1}{y \cdot \left(\frac{-1}{y} + y \cdot -0.16666666666666666\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{y}}{y \cdot 0.16666666666666666}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.0015)
   (/ -1.0 (* y (+ (/ -1.0 y) (* y -0.16666666666666666))))
   (/ (/ 1.0 y) (* y 0.16666666666666666))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.0015) {
		tmp = -1.0 / (y * ((-1.0 / y) + (y * -0.16666666666666666)));
	} else {
		tmp = (1.0 / y) / (y * 0.16666666666666666);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 0.0015d0) then
        tmp = (-1.0d0) / (y * (((-1.0d0) / y) + (y * (-0.16666666666666666d0))))
    else
        tmp = (1.0d0 / y) / (y * 0.16666666666666666d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.0015) {
		tmp = -1.0 / (y * ((-1.0 / y) + (y * -0.16666666666666666)));
	} else {
		tmp = (1.0 / y) / (y * 0.16666666666666666);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.0015:
		tmp = -1.0 / (y * ((-1.0 / y) + (y * -0.16666666666666666)))
	else:
		tmp = (1.0 / y) / (y * 0.16666666666666666)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.0015)
		tmp = Float64(-1.0 / Float64(y * Float64(Float64(-1.0 / y) + Float64(y * -0.16666666666666666))));
	else
		tmp = Float64(Float64(1.0 / y) / Float64(y * 0.16666666666666666));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.0015)
		tmp = -1.0 / (y * ((-1.0 / y) + (y * -0.16666666666666666)));
	else
		tmp = (1.0 / y) / (y * 0.16666666666666666);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.0015], N[(-1.0 / N[(y * N[(N[(-1.0 / y), $MachinePrecision] + N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / y), $MachinePrecision] / N[(y * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 5: 32.8% accurate, 12.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 6.8 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{1}{y}}{\frac{1}{y} + y \cdot 0.16666666666666666}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{y}}{y \cdot 0.16666666666666666}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 6.8e-5)
   (/ (/ 1.0 y) (+ (/ 1.0 y) (* y 0.16666666666666666)))
   (/ (/ 1.0 y) (* y 0.16666666666666666))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 6.8e-5) {
		tmp = (1.0 / y) / ((1.0 / y) + (y * 0.16666666666666666));
	} else {
		tmp = (1.0 / y) / (y * 0.16666666666666666);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 6.8d-5) then
        tmp = (1.0d0 / y) / ((1.0d0 / y) + (y * 0.16666666666666666d0))
    else
        tmp = (1.0d0 / y) / (y * 0.16666666666666666d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 6.8e-5) {
		tmp = (1.0 / y) / ((1.0 / y) + (y * 0.16666666666666666));
	} else {
		tmp = (1.0 / y) / (y * 0.16666666666666666);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 6.8e-5:
		tmp = (1.0 / y) / ((1.0 / y) + (y * 0.16666666666666666))
	else:
		tmp = (1.0 / y) / (y * 0.16666666666666666)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 6.8e-5)
		tmp = Float64(Float64(1.0 / y) / Float64(Float64(1.0 / y) + Float64(y * 0.16666666666666666)));
	else
		tmp = Float64(Float64(1.0 / y) / Float64(y * 0.16666666666666666));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 6.8e-5)
		tmp = (1.0 / y) / ((1.0 / y) + (y * 0.16666666666666666));
	else
		tmp = (1.0 / y) / (y * 0.16666666666666666);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 6.8e-5], N[(N[(1.0 / y), $MachinePrecision] / N[(N[(1.0 / y), $MachinePrecision] + N[(y * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / y), $MachinePrecision] / N[(y * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 6: 32.1% accurate, 17.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 6.8 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{y}}{y \cdot 0.16666666666666666}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 6.8e-5) 1.0 (/ (/ 1.0 y) (* y 0.16666666666666666))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 6.8e-5) {
		tmp = 1.0;
	} else {
		tmp = (1.0 / y) / (y * 0.16666666666666666);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 6.8d-5) then
        tmp = 1.0d0
    else
        tmp = (1.0d0 / y) / (y * 0.16666666666666666d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 6.8e-5) {
		tmp = 1.0;
	} else {
		tmp = (1.0 / y) / (y * 0.16666666666666666);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 6.8e-5:
		tmp = 1.0
	else:
		tmp = (1.0 / y) / (y * 0.16666666666666666)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 6.8e-5)
		tmp = 1.0;
	else
		tmp = Float64(Float64(1.0 / y) / Float64(y * 0.16666666666666666));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 6.8e-5)
		tmp = 1.0;
	else
		tmp = (1.0 / y) / (y * 0.16666666666666666);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 6.8e-5], 1.0, N[(N[(1.0 / y), $MachinePrecision] / N[(y * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 26.0% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_] := 1.0

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Developer target: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024006 
(FPCore (x y)
  :name "Linear.Quaternion:$csinh from linear-1.19.1.3"
  :precision binary64

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

  (* (cosh x) (/ (sin y) y)))