Linear.Quaternion:$ctan from linear-1.19.1.3

Percentage Accurate: 83.9% → 99.7%

Time: 7.9s

Alternatives: 13

Speedup: 1.0×

• 64.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 83.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ \begin{array}{l} t_0 := \cosh x_m \cdot \frac{y_m}{x_m}\\ y_s \cdot \left(x_s \cdot \begin{array}{l} \mathbf{if}\;t_0 \leq 5 \cdot 10^{+191}:\\ \;\;\;\;\frac{t_0}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y_m \cdot \frac{\cosh x_m}{z}}{x_m}\\ \end{array}\right) \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x_s x_m y_m z)
 :precision binary64
 (let* ((t_0 (* (cosh x_m) (/ y_m x_m))))
   (*
    y_s
    (* x_s (if (<= t_0 5e+191) (/ t_0 z) (/ (* y_m (/ (cosh x_m) z)) x_m))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x_s, double x_m, double y_m, double z) {
	double t_0 = cosh(x_m) * (y_m / x_m);
	double tmp;
	if (t_0 <= 5e+191) {
		tmp = t_0 / z;
	} else {
		tmp = (y_m * (cosh(x_m) / z)) / x_m;
	}
	return y_s * (x_s * tmp);
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x_s, x_m, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = cosh(x_m) * (y_m / x_m)
    if (t_0 <= 5d+191) then
        tmp = t_0 / z
    else
        tmp = (y_m * (cosh(x_m) / z)) / x_m
    end if
    code = y_s * (x_s * tmp)
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x_s, double x_m, double y_m, double z) {
	double t_0 = Math.cosh(x_m) * (y_m / x_m);
	double tmp;
	if (t_0 <= 5e+191) {
		tmp = t_0 / z;
	} else {
		tmp = (y_m * (Math.cosh(x_m) / z)) / x_m;
	}
	return y_s * (x_s * tmp);
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x_s, x_m, y_m, z):
	t_0 = math.cosh(x_m) * (y_m / x_m)
	tmp = 0
	if t_0 <= 5e+191:
		tmp = t_0 / z
	else:
		tmp = (y_m * (math.cosh(x_m) / z)) / x_m
	return y_s * (x_s * tmp)

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x_s, x_m, y_m, z)
	t_0 = Float64(cosh(x_m) * Float64(y_m / x_m))
	tmp = 0.0
	if (t_0 <= 5e+191)
		tmp = Float64(t_0 / z);
	else
		tmp = Float64(Float64(y_m * Float64(cosh(x_m) / z)) / x_m);
	end
	return Float64(y_s * Float64(x_s * tmp))
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp_2 = code(y_s, x_s, x_m, y_m, z)
	t_0 = cosh(x_m) * (y_m / x_m);
	tmp = 0.0;
	if (t_0 <= 5e+191)
		tmp = t_0 / z;
	else
		tmp = (y_m * (cosh(x_m) / z)) / x_m;
	end
	tmp_2 = y_s * (x_s * tmp);
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x$95$s_, x$95$m_, y$95$m_, z_] := Block[{t$95$0 = N[(N[Cosh[x$95$m], $MachinePrecision] * N[(y$95$m / x$95$m), $MachinePrecision]), $MachinePrecision]}, N[(y$95$s * N[(x$95$s * If[LessEqual[t$95$0, 5e+191], N[(t$95$0 / z), $MachinePrecision], N[(N[(y$95$m * N[(N[Cosh[x$95$m], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / x$95$m), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 2: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \left(x_s \cdot \begin{array}{l} \mathbf{if}\;y_m \leq 9.5 \cdot 10^{+118}:\\ \;\;\;\;\frac{y_m}{x_m} \cdot \frac{\cosh x_m}{z}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x_m \cdot y_m}{z} + \frac{y_m}{x_m \cdot z}\\ \end{array}\right) \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x_s x_m y_m z)
 :precision binary64
 (*
  y_s
  (*
   x_s
   (if (<= y_m 9.5e+118)
     (* (/ y_m x_m) (/ (cosh x_m) z))
     (+ (* 0.5 (/ (* x_m y_m) z)) (/ y_m (* x_m z)))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x_s, double x_m, double y_m, double z) {
	double tmp;
	if (y_m <= 9.5e+118) {
		tmp = (y_m / x_m) * (cosh(x_m) / z);
	} else {
		tmp = (0.5 * ((x_m * y_m) / z)) + (y_m / (x_m * z));
	}
	return y_s * (x_s * tmp);
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x_s, x_m, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y_m <= 9.5d+118) then
        tmp = (y_m / x_m) * (cosh(x_m) / z)
    else
        tmp = (0.5d0 * ((x_m * y_m) / z)) + (y_m / (x_m * z))
    end if
    code = y_s * (x_s * tmp)
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x_s, double x_m, double y_m, double z) {
	double tmp;
	if (y_m <= 9.5e+118) {
		tmp = (y_m / x_m) * (Math.cosh(x_m) / z);
	} else {
		tmp = (0.5 * ((x_m * y_m) / z)) + (y_m / (x_m * z));
	}
	return y_s * (x_s * tmp);
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x_s, x_m, y_m, z):
	tmp = 0
	if y_m <= 9.5e+118:
		tmp = (y_m / x_m) * (math.cosh(x_m) / z)
	else:
		tmp = (0.5 * ((x_m * y_m) / z)) + (y_m / (x_m * z))
	return y_s * (x_s * tmp)

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x_s, x_m, y_m, z)
	tmp = 0.0
	if (y_m <= 9.5e+118)
		tmp = Float64(Float64(y_m / x_m) * Float64(cosh(x_m) / z));
	else
		tmp = Float64(Float64(0.5 * Float64(Float64(x_m * y_m) / z)) + Float64(y_m / Float64(x_m * z)));
	end
	return Float64(y_s * Float64(x_s * tmp))
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp_2 = code(y_s, x_s, x_m, y_m, z)
	tmp = 0.0;
	if (y_m <= 9.5e+118)
		tmp = (y_m / x_m) * (cosh(x_m) / z);
	else
		tmp = (0.5 * ((x_m * y_m) / z)) + (y_m / (x_m * z));
	end
	tmp_2 = y_s * (x_s * tmp);
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x$95$s_, x$95$m_, y$95$m_, z_] := N[(y$95$s * N[(x$95$s * If[LessEqual[y$95$m, 9.5e+118], N[(N[(y$95$m / x$95$m), $MachinePrecision] * N[(N[Cosh[x$95$m], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * N[(N[(x$95$m * y$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y$95$m / N[(x$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 3: 96.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \left(x_s \cdot \begin{array}{l} \mathbf{if}\;y_m \leq 8.2 \cdot 10^{+118}:\\ \;\;\;\;\frac{y_m \cdot \frac{\cosh x_m}{x_m}}{z}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x_m \cdot y_m}{z} + \frac{y_m}{x_m \cdot z}\\ \end{array}\right) \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x_s x_m y_m z)
 :precision binary64
 (*
  y_s
  (*
   x_s
   (if (<= y_m 8.2e+118)
     (/ (* y_m (/ (cosh x_m) x_m)) z)
     (+ (* 0.5 (/ (* x_m y_m) z)) (/ y_m (* x_m z)))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x_s, double x_m, double y_m, double z) {
	double tmp;
	if (y_m <= 8.2e+118) {
		tmp = (y_m * (cosh(x_m) / x_m)) / z;
	} else {
		tmp = (0.5 * ((x_m * y_m) / z)) + (y_m / (x_m * z));
	}
	return y_s * (x_s * tmp);
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x_s, x_m, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y_m <= 8.2d+118) then
        tmp = (y_m * (cosh(x_m) / x_m)) / z
    else
        tmp = (0.5d0 * ((x_m * y_m) / z)) + (y_m / (x_m * z))
    end if
    code = y_s * (x_s * tmp)
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x_s, double x_m, double y_m, double z) {
	double tmp;
	if (y_m <= 8.2e+118) {
		tmp = (y_m * (Math.cosh(x_m) / x_m)) / z;
	} else {
		tmp = (0.5 * ((x_m * y_m) / z)) + (y_m / (x_m * z));
	}
	return y_s * (x_s * tmp);
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x_s, x_m, y_m, z):
	tmp = 0
	if y_m <= 8.2e+118:
		tmp = (y_m * (math.cosh(x_m) / x_m)) / z
	else:
		tmp = (0.5 * ((x_m * y_m) / z)) + (y_m / (x_m * z))
	return y_s * (x_s * tmp)

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x_s, x_m, y_m, z)
	tmp = 0.0
	if (y_m <= 8.2e+118)
		tmp = Float64(Float64(y_m * Float64(cosh(x_m) / x_m)) / z);
	else
		tmp = Float64(Float64(0.5 * Float64(Float64(x_m * y_m) / z)) + Float64(y_m / Float64(x_m * z)));
	end
	return Float64(y_s * Float64(x_s * tmp))
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp_2 = code(y_s, x_s, x_m, y_m, z)
	tmp = 0.0;
	if (y_m <= 8.2e+118)
		tmp = (y_m * (cosh(x_m) / x_m)) / z;
	else
		tmp = (0.5 * ((x_m * y_m) / z)) + (y_m / (x_m * z));
	end
	tmp_2 = y_s * (x_s * tmp);
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x$95$s_, x$95$m_, y$95$m_, z_] := N[(y$95$s * N[(x$95$s * If[LessEqual[y$95$m, 8.2e+118], N[(N[(y$95$m * N[(N[Cosh[x$95$m], $MachinePrecision] / x$95$m), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(0.5 * N[(N[(x$95$m * y$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y$95$m / N[(x$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 4: 68.6% accurate, 6.2× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ \begin{array}{l} t_0 := 0.5 \cdot \left(x_m \cdot y_m\right)\\ y_s \cdot \left(x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq 3.5 \cdot 10^{-69}:\\ \;\;\;\;\frac{\frac{y_m}{x_m} + t_0}{z}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+111}:\\ \;\;\;\;\frac{y_m + x_m \cdot t_0}{x_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x_m \cdot y_m}{z} + \frac{y_m}{x_m \cdot z}\\ \end{array}\right) \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x_s x_m y_m z)
 :precision binary64
 (let* ((t_0 (* 0.5 (* x_m y_m))))
   (*
    y_s
    (*
     x_s
     (if (<= z 3.5e-69)
       (/ (+ (/ y_m x_m) t_0) z)
       (if (<= z 1.95e+111)
         (/ (+ y_m (* x_m t_0)) (* x_m z))
         (+ (* 0.5 (/ (* x_m y_m) z)) (/ y_m (* x_m z)))))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x_s, double x_m, double y_m, double z) {
	double t_0 = 0.5 * (x_m * y_m);
	double tmp;
	if (z <= 3.5e-69) {
		tmp = ((y_m / x_m) + t_0) / z;
	} else if (z <= 1.95e+111) {
		tmp = (y_m + (x_m * t_0)) / (x_m * z);
	} else {
		tmp = (0.5 * ((x_m * y_m) / z)) + (y_m / (x_m * z));
	}
	return y_s * (x_s * tmp);
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x_s, x_m, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 0.5d0 * (x_m * y_m)
    if (z <= 3.5d-69) then
        tmp = ((y_m / x_m) + t_0) / z
    else if (z <= 1.95d+111) then
        tmp = (y_m + (x_m * t_0)) / (x_m * z)
    else
        tmp = (0.5d0 * ((x_m * y_m) / z)) + (y_m / (x_m * z))
    end if
    code = y_s * (x_s * tmp)
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x_s, double x_m, double y_m, double z) {
	double t_0 = 0.5 * (x_m * y_m);
	double tmp;
	if (z <= 3.5e-69) {
		tmp = ((y_m / x_m) + t_0) / z;
	} else if (z <= 1.95e+111) {
		tmp = (y_m + (x_m * t_0)) / (x_m * z);
	} else {
		tmp = (0.5 * ((x_m * y_m) / z)) + (y_m / (x_m * z));
	}
	return y_s * (x_s * tmp);
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x_s, x_m, y_m, z):
	t_0 = 0.5 * (x_m * y_m)
	tmp = 0
	if z <= 3.5e-69:
		tmp = ((y_m / x_m) + t_0) / z
	elif z <= 1.95e+111:
		tmp = (y_m + (x_m * t_0)) / (x_m * z)
	else:
		tmp = (0.5 * ((x_m * y_m) / z)) + (y_m / (x_m * z))
	return y_s * (x_s * tmp)

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x_s, x_m, y_m, z)
	t_0 = Float64(0.5 * Float64(x_m * y_m))
	tmp = 0.0
	if (z <= 3.5e-69)
		tmp = Float64(Float64(Float64(y_m / x_m) + t_0) / z);
	elseif (z <= 1.95e+111)
		tmp = Float64(Float64(y_m + Float64(x_m * t_0)) / Float64(x_m * z));
	else
		tmp = Float64(Float64(0.5 * Float64(Float64(x_m * y_m) / z)) + Float64(y_m / Float64(x_m * z)));
	end
	return Float64(y_s * Float64(x_s * tmp))
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp_2 = code(y_s, x_s, x_m, y_m, z)
	t_0 = 0.5 * (x_m * y_m);
	tmp = 0.0;
	if (z <= 3.5e-69)
		tmp = ((y_m / x_m) + t_0) / z;
	elseif (z <= 1.95e+111)
		tmp = (y_m + (x_m * t_0)) / (x_m * z);
	else
		tmp = (0.5 * ((x_m * y_m) / z)) + (y_m / (x_m * z));
	end
	tmp_2 = y_s * (x_s * tmp);
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x$95$s_, x$95$m_, y$95$m_, z_] := Block[{t$95$0 = N[(0.5 * N[(x$95$m * y$95$m), $MachinePrecision]), $MachinePrecision]}, N[(y$95$s * N[(x$95$s * If[LessEqual[z, 3.5e-69], N[(N[(N[(y$95$m / x$95$m), $MachinePrecision] + t$95$0), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.95e+111], N[(N[(y$95$m + N[(x$95$m * t$95$0), $MachinePrecision]), $MachinePrecision] / N[(x$95$m * z), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * N[(N[(x$95$m * y$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y$95$m / N[(x$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 5: 68.6% accurate, 6.2× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ \begin{array}{l} t_0 := 0.5 \cdot \frac{x_m \cdot y_m}{z}\\ y_s \cdot \left(x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq 3.7 \cdot 10^{-69}:\\ \;\;\;\;t_0 + \frac{\frac{y_m}{x_m}}{z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+110}:\\ \;\;\;\;\frac{y_m + x_m \cdot \left(0.5 \cdot \left(x_m \cdot y_m\right)\right)}{x_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{y_m}{x_m \cdot z}\\ \end{array}\right) \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x_s x_m y_m z)
 :precision binary64
 (let* ((t_0 (* 0.5 (/ (* x_m y_m) z))))
   (*
    y_s
    (*
     x_s
     (if (<= z 3.7e-69)
       (+ t_0 (/ (/ y_m x_m) z))
       (if (<= z 8e+110)
         (/ (+ y_m (* x_m (* 0.5 (* x_m y_m)))) (* x_m z))
         (+ t_0 (/ y_m (* x_m z)))))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x_s, double x_m, double y_m, double z) {
	double t_0 = 0.5 * ((x_m * y_m) / z);
	double tmp;
	if (z <= 3.7e-69) {
		tmp = t_0 + ((y_m / x_m) / z);
	} else if (z <= 8e+110) {
		tmp = (y_m + (x_m * (0.5 * (x_m * y_m)))) / (x_m * z);
	} else {
		tmp = t_0 + (y_m / (x_m * z));
	}
	return y_s * (x_s * tmp);
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x_s, x_m, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 0.5d0 * ((x_m * y_m) / z)
    if (z <= 3.7d-69) then
        tmp = t_0 + ((y_m / x_m) / z)
    else if (z <= 8d+110) then
        tmp = (y_m + (x_m * (0.5d0 * (x_m * y_m)))) / (x_m * z)
    else
        tmp = t_0 + (y_m / (x_m * z))
    end if
    code = y_s * (x_s * tmp)
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x_s, double x_m, double y_m, double z) {
	double t_0 = 0.5 * ((x_m * y_m) / z);
	double tmp;
	if (z <= 3.7e-69) {
		tmp = t_0 + ((y_m / x_m) / z);
	} else if (z <= 8e+110) {
		tmp = (y_m + (x_m * (0.5 * (x_m * y_m)))) / (x_m * z);
	} else {
		tmp = t_0 + (y_m / (x_m * z));
	}
	return y_s * (x_s * tmp);
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x_s, x_m, y_m, z):
	t_0 = 0.5 * ((x_m * y_m) / z)
	tmp = 0
	if z <= 3.7e-69:
		tmp = t_0 + ((y_m / x_m) / z)
	elif z <= 8e+110:
		tmp = (y_m + (x_m * (0.5 * (x_m * y_m)))) / (x_m * z)
	else:
		tmp = t_0 + (y_m / (x_m * z))
	return y_s * (x_s * tmp)

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x_s, x_m, y_m, z)
	t_0 = Float64(0.5 * Float64(Float64(x_m * y_m) / z))
	tmp = 0.0
	if (z <= 3.7e-69)
		tmp = Float64(t_0 + Float64(Float64(y_m / x_m) / z));
	elseif (z <= 8e+110)
		tmp = Float64(Float64(y_m + Float64(x_m * Float64(0.5 * Float64(x_m * y_m)))) / Float64(x_m * z));
	else
		tmp = Float64(t_0 + Float64(y_m / Float64(x_m * z)));
	end
	return Float64(y_s * Float64(x_s * tmp))
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp_2 = code(y_s, x_s, x_m, y_m, z)
	t_0 = 0.5 * ((x_m * y_m) / z);
	tmp = 0.0;
	if (z <= 3.7e-69)
		tmp = t_0 + ((y_m / x_m) / z);
	elseif (z <= 8e+110)
		tmp = (y_m + (x_m * (0.5 * (x_m * y_m)))) / (x_m * z);
	else
		tmp = t_0 + (y_m / (x_m * z));
	end
	tmp_2 = y_s * (x_s * tmp);
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x$95$s_, x$95$m_, y$95$m_, z_] := Block[{t$95$0 = N[(0.5 * N[(N[(x$95$m * y$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, N[(y$95$s * N[(x$95$s * If[LessEqual[z, 3.7e-69], N[(t$95$0 + N[(N[(y$95$m / x$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+110], N[(N[(y$95$m + N[(x$95$m * N[(0.5 * N[(x$95$m * y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x$95$m * z), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(y$95$m / N[(x$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 6: 69.5% accurate, 7.1× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \left(x_s \cdot \begin{array}{l} \mathbf{if}\;y_m \leq 2 \cdot 10^{+72}:\\ \;\;\;\;\frac{\frac{y_m}{x_m} + 0.5 \cdot \left(x_m \cdot y_m\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x_m \cdot y_m}{z} + \frac{y_m}{x_m \cdot z}\\ \end{array}\right) \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x_s x_m y_m z)
 :precision binary64
 (*
  y_s
  (*
   x_s
   (if (<= y_m 2e+72)
     (/ (+ (/ y_m x_m) (* 0.5 (* x_m y_m))) z)
     (+ (* 0.5 (/ (* x_m y_m) z)) (/ y_m (* x_m z)))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x_s, double x_m, double y_m, double z) {
	double tmp;
	if (y_m <= 2e+72) {
		tmp = ((y_m / x_m) + (0.5 * (x_m * y_m))) / z;
	} else {
		tmp = (0.5 * ((x_m * y_m) / z)) + (y_m / (x_m * z));
	}
	return y_s * (x_s * tmp);
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x_s, x_m, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y_m <= 2d+72) then
        tmp = ((y_m / x_m) + (0.5d0 * (x_m * y_m))) / z
    else
        tmp = (0.5d0 * ((x_m * y_m) / z)) + (y_m / (x_m * z))
    end if
    code = y_s * (x_s * tmp)
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x_s, double x_m, double y_m, double z) {
	double tmp;
	if (y_m <= 2e+72) {
		tmp = ((y_m / x_m) + (0.5 * (x_m * y_m))) / z;
	} else {
		tmp = (0.5 * ((x_m * y_m) / z)) + (y_m / (x_m * z));
	}
	return y_s * (x_s * tmp);
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x_s, x_m, y_m, z):
	tmp = 0
	if y_m <= 2e+72:
		tmp = ((y_m / x_m) + (0.5 * (x_m * y_m))) / z
	else:
		tmp = (0.5 * ((x_m * y_m) / z)) + (y_m / (x_m * z))
	return y_s * (x_s * tmp)

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x_s, x_m, y_m, z)
	tmp = 0.0
	if (y_m <= 2e+72)
		tmp = Float64(Float64(Float64(y_m / x_m) + Float64(0.5 * Float64(x_m * y_m))) / z);
	else
		tmp = Float64(Float64(0.5 * Float64(Float64(x_m * y_m) / z)) + Float64(y_m / Float64(x_m * z)));
	end
	return Float64(y_s * Float64(x_s * tmp))
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp_2 = code(y_s, x_s, x_m, y_m, z)
	tmp = 0.0;
	if (y_m <= 2e+72)
		tmp = ((y_m / x_m) + (0.5 * (x_m * y_m))) / z;
	else
		tmp = (0.5 * ((x_m * y_m) / z)) + (y_m / (x_m * z));
	end
	tmp_2 = y_s * (x_s * tmp);
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x$95$s_, x$95$m_, y$95$m_, z_] := N[(y$95$s * N[(x$95$s * If[LessEqual[y$95$m, 2e+72], N[(N[(N[(y$95$m / x$95$m), $MachinePrecision] + N[(0.5 * N[(x$95$m * y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(0.5 * N[(N[(x$95$m * y$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y$95$m / N[(x$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 7: 65.8% accurate, 9.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \left(x_s \cdot \frac{y_m \cdot \left(x_m \cdot 0.5 + \frac{1}{x_m}\right)}{z}\right) \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x_s x_m y_m z)
 :precision binary64
 (* y_s (* x_s (/ (* y_m (+ (* x_m 0.5) (/ 1.0 x_m))) z))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x_s, double x_m, double y_m, double z) {
	return y_s * (x_s * ((y_m * ((x_m * 0.5) + (1.0 / x_m))) / z));
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x_s, x_m, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    code = y_s * (x_s * ((y_m * ((x_m * 0.5d0) + (1.0d0 / x_m))) / z))
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x_s, double x_m, double y_m, double z) {
	return y_s * (x_s * ((y_m * ((x_m * 0.5) + (1.0 / x_m))) / z));
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x_s, x_m, y_m, z):
	return y_s * (x_s * ((y_m * ((x_m * 0.5) + (1.0 / x_m))) / z))

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x_s, x_m, y_m, z)
	return Float64(y_s * Float64(x_s * Float64(Float64(y_m * Float64(Float64(x_m * 0.5) + Float64(1.0 / x_m))) / z)))
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp = code(y_s, x_s, x_m, y_m, z)
	tmp = y_s * (x_s * ((y_m * ((x_m * 0.5) + (1.0 / x_m))) / z));
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x$95$s_, x$95$m_, y$95$m_, z_] := N[(y$95$s * N[(x$95$s * N[(N[(y$95$m * N[(N[(x$95$m * 0.5), $MachinePrecision] + N[(1.0 / x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 8: 65.8% accurate, 9.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \left(x_s \cdot \frac{\frac{y_m}{x_m} + 0.5 \cdot \left(x_m \cdot y_m\right)}{z}\right) \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x_s x_m y_m z)
 :precision binary64
 (* y_s (* x_s (/ (+ (/ y_m x_m) (* 0.5 (* x_m y_m))) z))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x_s, double x_m, double y_m, double z) {
	return y_s * (x_s * (((y_m / x_m) + (0.5 * (x_m * y_m))) / z));
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x_s, x_m, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    code = y_s * (x_s * (((y_m / x_m) + (0.5d0 * (x_m * y_m))) / z))
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x_s, double x_m, double y_m, double z) {
	return y_s * (x_s * (((y_m / x_m) + (0.5 * (x_m * y_m))) / z));
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x_s, x_m, y_m, z):
	return y_s * (x_s * (((y_m / x_m) + (0.5 * (x_m * y_m))) / z))

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x_s, x_m, y_m, z)
	return Float64(y_s * Float64(x_s * Float64(Float64(Float64(y_m / x_m) + Float64(0.5 * Float64(x_m * y_m))) / z)))
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp = code(y_s, x_s, x_m, y_m, z)
	tmp = y_s * (x_s * (((y_m / x_m) + (0.5 * (x_m * y_m))) / z));
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x$95$s_, x$95$m_, y$95$m_, z_] := N[(y$95$s * N[(x$95$s * N[(N[(N[(y$95$m / x$95$m), $MachinePrecision] + N[(0.5 * N[(x$95$m * y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 9: 65.8% accurate, 11.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \left(x_s \cdot \begin{array}{l} \mathbf{if}\;x_m \leq 1.4:\\ \;\;\;\;\frac{\frac{y_m}{z}}{x_m}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y_m \cdot \frac{x_m}{z}\right)\\ \end{array}\right) \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x_s x_m y_m z)
 :precision binary64
 (* y_s (* x_s (if (<= x_m 1.4) (/ (/ y_m z) x_m) (* 0.5 (* y_m (/ x_m z)))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x_s, double x_m, double y_m, double z) {
	double tmp;
	if (x_m <= 1.4) {
		tmp = (y_m / z) / x_m;
	} else {
		tmp = 0.5 * (y_m * (x_m / z));
	}
	return y_s * (x_s * tmp);
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x_s, x_m, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x_m <= 1.4d0) then
        tmp = (y_m / z) / x_m
    else
        tmp = 0.5d0 * (y_m * (x_m / z))
    end if
    code = y_s * (x_s * tmp)
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x_s, double x_m, double y_m, double z) {
	double tmp;
	if (x_m <= 1.4) {
		tmp = (y_m / z) / x_m;
	} else {
		tmp = 0.5 * (y_m * (x_m / z));
	}
	return y_s * (x_s * tmp);
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x_s, x_m, y_m, z):
	tmp = 0
	if x_m <= 1.4:
		tmp = (y_m / z) / x_m
	else:
		tmp = 0.5 * (y_m * (x_m / z))
	return y_s * (x_s * tmp)

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x_s, x_m, y_m, z)
	tmp = 0.0
	if (x_m <= 1.4)
		tmp = Float64(Float64(y_m / z) / x_m);
	else
		tmp = Float64(0.5 * Float64(y_m * Float64(x_m / z)));
	end
	return Float64(y_s * Float64(x_s * tmp))
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp_2 = code(y_s, x_s, x_m, y_m, z)
	tmp = 0.0;
	if (x_m <= 1.4)
		tmp = (y_m / z) / x_m;
	else
		tmp = 0.5 * (y_m * (x_m / z));
	end
	tmp_2 = y_s * (x_s * tmp);
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x$95$s_, x$95$m_, y$95$m_, z_] := N[(y$95$s * N[(x$95$s * If[LessEqual[x$95$m, 1.4], N[(N[(y$95$m / z), $MachinePrecision] / x$95$m), $MachinePrecision], N[(0.5 * N[(y$95$m * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 10: 66.0% accurate, 11.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \left(x_s \cdot \begin{array}{l} \mathbf{if}\;x_m \leq 1.4:\\ \;\;\;\;\frac{\frac{y_m}{z}}{x_m}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x_m \cdot y_m}{z}\\ \end{array}\right) \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x_s x_m y_m z)
 :precision binary64
 (* y_s (* x_s (if (<= x_m 1.4) (/ (/ y_m z) x_m) (* 0.5 (/ (* x_m y_m) z))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x_s, double x_m, double y_m, double z) {
	double tmp;
	if (x_m <= 1.4) {
		tmp = (y_m / z) / x_m;
	} else {
		tmp = 0.5 * ((x_m * y_m) / z);
	}
	return y_s * (x_s * tmp);
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x_s, x_m, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x_m <= 1.4d0) then
        tmp = (y_m / z) / x_m
    else
        tmp = 0.5d0 * ((x_m * y_m) / z)
    end if
    code = y_s * (x_s * tmp)
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x_s, double x_m, double y_m, double z) {
	double tmp;
	if (x_m <= 1.4) {
		tmp = (y_m / z) / x_m;
	} else {
		tmp = 0.5 * ((x_m * y_m) / z);
	}
	return y_s * (x_s * tmp);
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x_s, x_m, y_m, z):
	tmp = 0
	if x_m <= 1.4:
		tmp = (y_m / z) / x_m
	else:
		tmp = 0.5 * ((x_m * y_m) / z)
	return y_s * (x_s * tmp)

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x_s, x_m, y_m, z)
	tmp = 0.0
	if (x_m <= 1.4)
		tmp = Float64(Float64(y_m / z) / x_m);
	else
		tmp = Float64(0.5 * Float64(Float64(x_m * y_m) / z));
	end
	return Float64(y_s * Float64(x_s * tmp))
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp_2 = code(y_s, x_s, x_m, y_m, z)
	tmp = 0.0;
	if (x_m <= 1.4)
		tmp = (y_m / z) / x_m;
	else
		tmp = 0.5 * ((x_m * y_m) / z);
	end
	tmp_2 = y_s * (x_s * tmp);
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x$95$s_, x$95$m_, y$95$m_, z_] := N[(y$95$s * N[(x$95$s * If[LessEqual[x$95$m, 1.4], N[(N[(y$95$m / z), $MachinePrecision] / x$95$m), $MachinePrecision], N[(0.5 * N[(N[(x$95$m * y$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 11: 52.5% accurate, 15.2× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \left(x_s \cdot \begin{array}{l} \mathbf{if}\;y_m \leq 1.05 \cdot 10^{+78}:\\ \;\;\;\;\frac{\frac{y_m}{x_m}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y_m}{x_m \cdot z}\\ \end{array}\right) \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x_s x_m y_m z)
 :precision binary64
 (* y_s (* x_s (if (<= y_m 1.05e+78) (/ (/ y_m x_m) z) (/ y_m (* x_m z))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x_s, double x_m, double y_m, double z) {
	double tmp;
	if (y_m <= 1.05e+78) {
		tmp = (y_m / x_m) / z;
	} else {
		tmp = y_m / (x_m * z);
	}
	return y_s * (x_s * tmp);
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x_s, x_m, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y_m <= 1.05d+78) then
        tmp = (y_m / x_m) / z
    else
        tmp = y_m / (x_m * z)
    end if
    code = y_s * (x_s * tmp)
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x_s, double x_m, double y_m, double z) {
	double tmp;
	if (y_m <= 1.05e+78) {
		tmp = (y_m / x_m) / z;
	} else {
		tmp = y_m / (x_m * z);
	}
	return y_s * (x_s * tmp);
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x_s, x_m, y_m, z):
	tmp = 0
	if y_m <= 1.05e+78:
		tmp = (y_m / x_m) / z
	else:
		tmp = y_m / (x_m * z)
	return y_s * (x_s * tmp)

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x_s, x_m, y_m, z)
	tmp = 0.0
	if (y_m <= 1.05e+78)
		tmp = Float64(Float64(y_m / x_m) / z);
	else
		tmp = Float64(y_m / Float64(x_m * z));
	end
	return Float64(y_s * Float64(x_s * tmp))
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp_2 = code(y_s, x_s, x_m, y_m, z)
	tmp = 0.0;
	if (y_m <= 1.05e+78)
		tmp = (y_m / x_m) / z;
	else
		tmp = y_m / (x_m * z);
	end
	tmp_2 = y_s * (x_s * tmp);
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x$95$s_, x$95$m_, y$95$m_, z_] := N[(y$95$s * N[(x$95$s * If[LessEqual[y$95$m, 1.05e+78], N[(N[(y$95$m / x$95$m), $MachinePrecision] / z), $MachinePrecision], N[(y$95$m / N[(x$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 12: 56.4% accurate, 15.2× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \left(x_s \cdot \begin{array}{l} \mathbf{if}\;y_m \leq 1.2 \cdot 10^{-22}:\\ \;\;\;\;\frac{\frac{y_m}{x_m}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y_m}{z}}{x_m}\\ \end{array}\right) \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x_s x_m y_m z)
 :precision binary64
 (* y_s (* x_s (if (<= y_m 1.2e-22) (/ (/ y_m x_m) z) (/ (/ y_m z) x_m)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x_s, double x_m, double y_m, double z) {
	double tmp;
	if (y_m <= 1.2e-22) {
		tmp = (y_m / x_m) / z;
	} else {
		tmp = (y_m / z) / x_m;
	}
	return y_s * (x_s * tmp);
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x_s, x_m, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y_m <= 1.2d-22) then
        tmp = (y_m / x_m) / z
    else
        tmp = (y_m / z) / x_m
    end if
    code = y_s * (x_s * tmp)
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x_s, double x_m, double y_m, double z) {
	double tmp;
	if (y_m <= 1.2e-22) {
		tmp = (y_m / x_m) / z;
	} else {
		tmp = (y_m / z) / x_m;
	}
	return y_s * (x_s * tmp);
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x_s, x_m, y_m, z):
	tmp = 0
	if y_m <= 1.2e-22:
		tmp = (y_m / x_m) / z
	else:
		tmp = (y_m / z) / x_m
	return y_s * (x_s * tmp)

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x_s, x_m, y_m, z)
	tmp = 0.0
	if (y_m <= 1.2e-22)
		tmp = Float64(Float64(y_m / x_m) / z);
	else
		tmp = Float64(Float64(y_m / z) / x_m);
	end
	return Float64(y_s * Float64(x_s * tmp))
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp_2 = code(y_s, x_s, x_m, y_m, z)
	tmp = 0.0;
	if (y_m <= 1.2e-22)
		tmp = (y_m / x_m) / z;
	else
		tmp = (y_m / z) / x_m;
	end
	tmp_2 = y_s * (x_s * tmp);
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x$95$s_, x$95$m_, y$95$m_, z_] := N[(y$95$s * N[(x$95$s * If[LessEqual[y$95$m, 1.2e-22], N[(N[(y$95$m / x$95$m), $MachinePrecision] / z), $MachinePrecision], N[(N[(y$95$m / z), $MachinePrecision] / x$95$m), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 13: 49.0% accurate, 21.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y_s \cdot \left(x_s \cdot \frac{y_m}{x_m \cdot z}\right) \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x_s x_m y_m z)
 :precision binary64
 (* y_s (* x_s (/ y_m (* x_m z)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x_s, double x_m, double y_m, double z) {
	return y_s * (x_s * (y_m / (x_m * z)));
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x_s, x_m, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    code = y_s * (x_s * (y_m / (x_m * z)))
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x_s, double x_m, double y_m, double z) {
	return y_s * (x_s * (y_m / (x_m * z)));
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x_s, x_m, y_m, z):
	return y_s * (x_s * (y_m / (x_m * z)))

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x_s, x_m, y_m, z)
	return Float64(y_s * Float64(x_s * Float64(y_m / Float64(x_m * z))))
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp = code(y_s, x_s, x_m, y_m, z)
	tmp = y_s * (x_s * (y_m / (x_m * z)));
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x$95$s_, x$95$m_, y$95$m_, z_] := N[(y$95$s * N[(x$95$s * N[(y$95$m / N[(x$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Developer target: 96.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{if}\;y < -4.618902267687042 \cdot 10^{-52}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y < 1.038530535935153 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ (/ y z) x) (cosh x))))
   (if (< y -4.618902267687042e-52)
     t_0
     (if (< y 1.038530535935153e-39) (/ (/ (* (cosh x) y) x) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y / z) / x) * cosh(x);
	double tmp;
	if (y < -4.618902267687042e-52) {
		tmp = t_0;
	} else if (y < 1.038530535935153e-39) {
		tmp = ((cosh(x) * y) / x) / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((y / z) / x) * cosh(x)
    if (y < (-4.618902267687042d-52)) then
        tmp = t_0
    else if (y < 1.038530535935153d-39) then
        tmp = ((cosh(x) * y) / x) / z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y / z) / x) * Math.cosh(x);
	double tmp;
	if (y < -4.618902267687042e-52) {
		tmp = t_0;
	} else if (y < 1.038530535935153e-39) {
		tmp = ((Math.cosh(x) * y) / x) / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y / z) / x) * math.cosh(x)
	tmp = 0
	if y < -4.618902267687042e-52:
		tmp = t_0
	elif y < 1.038530535935153e-39:
		tmp = ((math.cosh(x) * y) / x) / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y / z) / x) * cosh(x))
	tmp = 0.0
	if (y < -4.618902267687042e-52)
		tmp = t_0;
	elseif (y < 1.038530535935153e-39)
		tmp = Float64(Float64(Float64(cosh(x) * y) / x) / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y / z) / x) * cosh(x);
	tmp = 0.0;
	if (y < -4.618902267687042e-52)
		tmp = t_0;
	elseif (y < 1.038530535935153e-39)
		tmp = ((cosh(x) * y) / x) / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision] * N[Cosh[x], $MachinePrecision]), $MachinePrecision]}, If[Less[y, -4.618902267687042e-52], t$95$0, If[Less[y, 1.038530535935153e-39], N[(N[(N[(N[Cosh[x], $MachinePrecision] * y), $MachinePrecision] / x), $MachinePrecision] / z), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024003 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctan from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< y -4.618902267687042e-52) (* (/ (/ y z) x) (cosh x)) (if (< y 1.038530535935153e-39) (/ (/ (* (cosh x) y) x) z) (* (/ (/ y z) x) (cosh x))))

  (/ (* (cosh x) (/ y x)) z))