Linear.Quaternion:$ctanh from linear-1.19.1.3

Percentage Accurate: 96.1% → 99.3%

Time: 9.1s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * (sin(y) / y)) / 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 = (x * (sin(y) / y)) / z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * (sin(y) / y)) / 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 = (x * (sin(y) / y)) / z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ \begin{array}{l} t_0 := \frac{\sin y}{y}\\ z_s \cdot \begin{array}{l} \mathbf{if}\;z_m \leq 1.22 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{\frac{z_m}{t_0}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t_0}{z_m}\\ \end{array} \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m)
 :precision binary64
 (let* ((t_0 (/ (sin y) y)))
   (* z_s (if (<= z_m 1.22e-92) (/ x (/ z_m t_0)) (/ (* x t_0) z_m)))))

C

z_m = fabs(z);
z_s = copysign(1.0, z);
double code(double z_s, double x, double y, double z_m) {
	double t_0 = sin(y) / y;
	double tmp;
	if (z_m <= 1.22e-92) {
		tmp = x / (z_m / t_0);
	} else {
		tmp = (x * t_0) / z_m;
	}
	return z_s * tmp;
}

Fortran

z_m = abs(z)
z_s = copysign(1.0d0, z)
real(8) function code(z_s, x, y, z_m)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sin(y) / y
    if (z_m <= 1.22d-92) then
        tmp = x / (z_m / t_0)
    else
        tmp = (x * t_0) / z_m
    end if
    code = z_s * tmp
end function

Java

z_m = Math.abs(z);
z_s = Math.copySign(1.0, z);
public static double code(double z_s, double x, double y, double z_m) {
	double t_0 = Math.sin(y) / y;
	double tmp;
	if (z_m <= 1.22e-92) {
		tmp = x / (z_m / t_0);
	} else {
		tmp = (x * t_0) / z_m;
	}
	return z_s * tmp;
}

Python

z_m = math.fabs(z)
z_s = math.copysign(1.0, z)
def code(z_s, x, y, z_m):
	t_0 = math.sin(y) / y
	tmp = 0
	if z_m <= 1.22e-92:
		tmp = x / (z_m / t_0)
	else:
		tmp = (x * t_0) / z_m
	return z_s * tmp

Julia

z_m = abs(z)
z_s = copysign(1.0, z)
function code(z_s, x, y, z_m)
	t_0 = Float64(sin(y) / y)
	tmp = 0.0
	if (z_m <= 1.22e-92)
		tmp = Float64(x / Float64(z_m / t_0));
	else
		tmp = Float64(Float64(x * t_0) / z_m);
	end
	return Float64(z_s * tmp)
end

MATLAB

z_m = abs(z);
z_s = sign(z) * abs(1.0);
function tmp_2 = code(z_s, x, y, z_m)
	t_0 = sin(y) / y;
	tmp = 0.0;
	if (z_m <= 1.22e-92)
		tmp = x / (z_m / t_0);
	else
		tmp = (x * t_0) / z_m;
	end
	tmp_2 = z_s * tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
z_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[z$95$s_, x_, y_, z$95$m_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]}, N[(z$95$s * If[LessEqual[z$95$m, 1.22e-92], N[(x / N[(z$95$m / t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[(x * t$95$0), $MachinePrecision] / z$95$m), $MachinePrecision]]), $MachinePrecision]]

Derivation

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

Alternative 2: 77.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ z_s \cdot \begin{array}{l} \mathbf{if}\;y \leq 1.45 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{z_m}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\sin y}{z_m \cdot y}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m)
 :precision binary64
 (* z_s (if (<= y 1.45e-17) (/ x z_m) (* x (/ (sin y) (* z_m y))))))

C

z_m = fabs(z);
z_s = copysign(1.0, z);
double code(double z_s, double x, double y, double z_m) {
	double tmp;
	if (y <= 1.45e-17) {
		tmp = x / z_m;
	} else {
		tmp = x * (sin(y) / (z_m * y));
	}
	return z_s * tmp;
}

Fortran

z_m = abs(z)
z_s = copysign(1.0d0, z)
real(8) function code(z_s, x, y, z_m)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8) :: tmp
    if (y <= 1.45d-17) then
        tmp = x / z_m
    else
        tmp = x * (sin(y) / (z_m * y))
    end if
    code = z_s * tmp
end function

Java

z_m = Math.abs(z);
z_s = Math.copySign(1.0, z);
public static double code(double z_s, double x, double y, double z_m) {
	double tmp;
	if (y <= 1.45e-17) {
		tmp = x / z_m;
	} else {
		tmp = x * (Math.sin(y) / (z_m * y));
	}
	return z_s * tmp;
}

Python

z_m = math.fabs(z)
z_s = math.copysign(1.0, z)
def code(z_s, x, y, z_m):
	tmp = 0
	if y <= 1.45e-17:
		tmp = x / z_m
	else:
		tmp = x * (math.sin(y) / (z_m * y))
	return z_s * tmp

Julia

z_m = abs(z)
z_s = copysign(1.0, z)
function code(z_s, x, y, z_m)
	tmp = 0.0
	if (y <= 1.45e-17)
		tmp = Float64(x / z_m);
	else
		tmp = Float64(x * Float64(sin(y) / Float64(z_m * y)));
	end
	return Float64(z_s * tmp)
end

MATLAB

z_m = abs(z);
z_s = sign(z) * abs(1.0);
function tmp_2 = code(z_s, x, y, z_m)
	tmp = 0.0;
	if (y <= 1.45e-17)
		tmp = x / z_m;
	else
		tmp = x * (sin(y) / (z_m * y));
	end
	tmp_2 = z_s * tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
z_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[z$95$s_, x_, y_, z$95$m_] := N[(z$95$s * If[LessEqual[y, 1.45e-17], N[(x / z$95$m), $MachinePrecision], N[(x * N[(N[Sin[y], $MachinePrecision] / N[(z$95$m * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 3: 95.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ z_s \cdot \begin{array}{l} \mathbf{if}\;x \leq 9.8 \cdot 10^{+188}:\\ \;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z_m}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\sin y}{z_m \cdot y}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m)
 :precision binary64
 (*
  z_s
  (if (<= x 9.8e+188)
    (* (/ (sin y) y) (/ x z_m))
    (* x (/ (sin y) (* z_m y))))))

C

z_m = fabs(z);
z_s = copysign(1.0, z);
double code(double z_s, double x, double y, double z_m) {
	double tmp;
	if (x <= 9.8e+188) {
		tmp = (sin(y) / y) * (x / z_m);
	} else {
		tmp = x * (sin(y) / (z_m * y));
	}
	return z_s * tmp;
}

Fortran

z_m = abs(z)
z_s = copysign(1.0d0, z)
real(8) function code(z_s, x, y, z_m)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8) :: tmp
    if (x <= 9.8d+188) then
        tmp = (sin(y) / y) * (x / z_m)
    else
        tmp = x * (sin(y) / (z_m * y))
    end if
    code = z_s * tmp
end function

Java

z_m = Math.abs(z);
z_s = Math.copySign(1.0, z);
public static double code(double z_s, double x, double y, double z_m) {
	double tmp;
	if (x <= 9.8e+188) {
		tmp = (Math.sin(y) / y) * (x / z_m);
	} else {
		tmp = x * (Math.sin(y) / (z_m * y));
	}
	return z_s * tmp;
}

Python

z_m = math.fabs(z)
z_s = math.copysign(1.0, z)
def code(z_s, x, y, z_m):
	tmp = 0
	if x <= 9.8e+188:
		tmp = (math.sin(y) / y) * (x / z_m)
	else:
		tmp = x * (math.sin(y) / (z_m * y))
	return z_s * tmp

Julia

z_m = abs(z)
z_s = copysign(1.0, z)
function code(z_s, x, y, z_m)
	tmp = 0.0
	if (x <= 9.8e+188)
		tmp = Float64(Float64(sin(y) / y) * Float64(x / z_m));
	else
		tmp = Float64(x * Float64(sin(y) / Float64(z_m * y)));
	end
	return Float64(z_s * tmp)
end

MATLAB

z_m = abs(z);
z_s = sign(z) * abs(1.0);
function tmp_2 = code(z_s, x, y, z_m)
	tmp = 0.0;
	if (x <= 9.8e+188)
		tmp = (sin(y) / y) * (x / z_m);
	else
		tmp = x * (sin(y) / (z_m * y));
	end
	tmp_2 = z_s * tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
z_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[z$95$s_, x_, y_, z$95$m_] := N[(z$95$s * If[LessEqual[x, 9.8e+188], N[(N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision] * N[(x / z$95$m), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Sin[y], $MachinePrecision] / N[(z$95$m * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 4: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ z_s \cdot \begin{array}{l} \mathbf{if}\;z_m \leq 1.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{z_m \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z_m}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m)
 :precision binary64
 (*
  z_s
  (if (<= z_m 1.2e-36)
    (/ x (* z_m (/ y (sin y))))
    (* (/ (sin y) y) (/ x z_m)))))

C

z_m = fabs(z);
z_s = copysign(1.0, z);
double code(double z_s, double x, double y, double z_m) {
	double tmp;
	if (z_m <= 1.2e-36) {
		tmp = x / (z_m * (y / sin(y)));
	} else {
		tmp = (sin(y) / y) * (x / z_m);
	}
	return z_s * tmp;
}

Fortran

z_m = abs(z)
z_s = copysign(1.0d0, z)
real(8) function code(z_s, x, y, z_m)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8) :: tmp
    if (z_m <= 1.2d-36) then
        tmp = x / (z_m * (y / sin(y)))
    else
        tmp = (sin(y) / y) * (x / z_m)
    end if
    code = z_s * tmp
end function

Java

z_m = Math.abs(z);
z_s = Math.copySign(1.0, z);
public static double code(double z_s, double x, double y, double z_m) {
	double tmp;
	if (z_m <= 1.2e-36) {
		tmp = x / (z_m * (y / Math.sin(y)));
	} else {
		tmp = (Math.sin(y) / y) * (x / z_m);
	}
	return z_s * tmp;
}

Python

z_m = math.fabs(z)
z_s = math.copysign(1.0, z)
def code(z_s, x, y, z_m):
	tmp = 0
	if z_m <= 1.2e-36:
		tmp = x / (z_m * (y / math.sin(y)))
	else:
		tmp = (math.sin(y) / y) * (x / z_m)
	return z_s * tmp

Julia

z_m = abs(z)
z_s = copysign(1.0, z)
function code(z_s, x, y, z_m)
	tmp = 0.0
	if (z_m <= 1.2e-36)
		tmp = Float64(x / Float64(z_m * Float64(y / sin(y))));
	else
		tmp = Float64(Float64(sin(y) / y) * Float64(x / z_m));
	end
	return Float64(z_s * tmp)
end

MATLAB

z_m = abs(z);
z_s = sign(z) * abs(1.0);
function tmp_2 = code(z_s, x, y, z_m)
	tmp = 0.0;
	if (z_m <= 1.2e-36)
		tmp = x / (z_m * (y / sin(y)));
	else
		tmp = (sin(y) / y) * (x / z_m);
	end
	tmp_2 = z_s * tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
z_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[z$95$s_, x_, y_, z$95$m_] := N[(z$95$s * If[LessEqual[z$95$m, 1.2e-36], N[(x / N[(z$95$m * N[(y / N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision] * N[(x / z$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 5: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ \begin{array}{l} t_0 := \frac{\sin y}{y}\\ z_s \cdot \begin{array}{l} \mathbf{if}\;z_m \leq 2 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{\frac{z_m}{t_0}}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \frac{x}{z_m}\\ \end{array} \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m)
 :precision binary64
 (let* ((t_0 (/ (sin y) y)))
   (* z_s (if (<= z_m 2e-40) (/ x (/ z_m t_0)) (* t_0 (/ x z_m))))))

C

z_m = fabs(z);
z_s = copysign(1.0, z);
double code(double z_s, double x, double y, double z_m) {
	double t_0 = sin(y) / y;
	double tmp;
	if (z_m <= 2e-40) {
		tmp = x / (z_m / t_0);
	} else {
		tmp = t_0 * (x / z_m);
	}
	return z_s * tmp;
}

Fortran

z_m = abs(z)
z_s = copysign(1.0d0, z)
real(8) function code(z_s, x, y, z_m)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sin(y) / y
    if (z_m <= 2d-40) then
        tmp = x / (z_m / t_0)
    else
        tmp = t_0 * (x / z_m)
    end if
    code = z_s * tmp
end function

Java

z_m = Math.abs(z);
z_s = Math.copySign(1.0, z);
public static double code(double z_s, double x, double y, double z_m) {
	double t_0 = Math.sin(y) / y;
	double tmp;
	if (z_m <= 2e-40) {
		tmp = x / (z_m / t_0);
	} else {
		tmp = t_0 * (x / z_m);
	}
	return z_s * tmp;
}

Python

z_m = math.fabs(z)
z_s = math.copysign(1.0, z)
def code(z_s, x, y, z_m):
	t_0 = math.sin(y) / y
	tmp = 0
	if z_m <= 2e-40:
		tmp = x / (z_m / t_0)
	else:
		tmp = t_0 * (x / z_m)
	return z_s * tmp

Julia

z_m = abs(z)
z_s = copysign(1.0, z)
function code(z_s, x, y, z_m)
	t_0 = Float64(sin(y) / y)
	tmp = 0.0
	if (z_m <= 2e-40)
		tmp = Float64(x / Float64(z_m / t_0));
	else
		tmp = Float64(t_0 * Float64(x / z_m));
	end
	return Float64(z_s * tmp)
end

MATLAB

z_m = abs(z);
z_s = sign(z) * abs(1.0);
function tmp_2 = code(z_s, x, y, z_m)
	t_0 = sin(y) / y;
	tmp = 0.0;
	if (z_m <= 2e-40)
		tmp = x / (z_m / t_0);
	else
		tmp = t_0 * (x / z_m);
	end
	tmp_2 = z_s * tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
z_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[z$95$s_, x_, y_, z$95$m_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]}, N[(z$95$s * If[LessEqual[z$95$m, 2e-40], N[(x / N[(z$95$m / t$95$0), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(x / z$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

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

Alternative 6: 62.6% accurate, 7.1× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ z_s \cdot \begin{array}{l} \mathbf{if}\;y \leq 2.45 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{z_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z_m \cdot \left(y \cdot 0.16666666666666666 + \frac{1}{y}\right)}}{y}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m)
 :precision binary64
 (*
  z_s
  (if (<= y 2.45e-8)
    (/ x z_m)
    (/ (/ x (* z_m (+ (* y 0.16666666666666666) (/ 1.0 y)))) y))))

C

z_m = fabs(z);
z_s = copysign(1.0, z);
double code(double z_s, double x, double y, double z_m) {
	double tmp;
	if (y <= 2.45e-8) {
		tmp = x / z_m;
	} else {
		tmp = (x / (z_m * ((y * 0.16666666666666666) + (1.0 / y)))) / y;
	}
	return z_s * tmp;
}

Fortran

z_m = abs(z)
z_s = copysign(1.0d0, z)
real(8) function code(z_s, x, y, z_m)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8) :: tmp
    if (y <= 2.45d-8) then
        tmp = x / z_m
    else
        tmp = (x / (z_m * ((y * 0.16666666666666666d0) + (1.0d0 / y)))) / y
    end if
    code = z_s * tmp
end function

Java

z_m = Math.abs(z);
z_s = Math.copySign(1.0, z);
public static double code(double z_s, double x, double y, double z_m) {
	double tmp;
	if (y <= 2.45e-8) {
		tmp = x / z_m;
	} else {
		tmp = (x / (z_m * ((y * 0.16666666666666666) + (1.0 / y)))) / y;
	}
	return z_s * tmp;
}

Python

z_m = math.fabs(z)
z_s = math.copysign(1.0, z)
def code(z_s, x, y, z_m):
	tmp = 0
	if y <= 2.45e-8:
		tmp = x / z_m
	else:
		tmp = (x / (z_m * ((y * 0.16666666666666666) + (1.0 / y)))) / y
	return z_s * tmp

Julia

z_m = abs(z)
z_s = copysign(1.0, z)
function code(z_s, x, y, z_m)
	tmp = 0.0
	if (y <= 2.45e-8)
		tmp = Float64(x / z_m);
	else
		tmp = Float64(Float64(x / Float64(z_m * Float64(Float64(y * 0.16666666666666666) + Float64(1.0 / y)))) / y);
	end
	return Float64(z_s * tmp)
end

MATLAB

z_m = abs(z);
z_s = sign(z) * abs(1.0);
function tmp_2 = code(z_s, x, y, z_m)
	tmp = 0.0;
	if (y <= 2.45e-8)
		tmp = x / z_m;
	else
		tmp = (x / (z_m * ((y * 0.16666666666666666) + (1.0 / y)))) / y;
	end
	tmp_2 = z_s * tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
z_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[z$95$s_, x_, y_, z$95$m_] := N[(z$95$s * If[LessEqual[y, 2.45e-8], N[(x / z$95$m), $MachinePrecision], N[(N[(x / N[(z$95$m * N[(N[(y * 0.16666666666666666), $MachinePrecision] + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 7: 62.6% accurate, 7.1× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ z_s \cdot \begin{array}{l} \mathbf{if}\;y \leq 6.8 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{z_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\left(z_m \cdot y\right) \cdot 0.16666666666666666 + \frac{z_m}{y}}}{y}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m)
 :precision binary64
 (*
  z_s
  (if (<= y 6.8e-8)
    (/ x z_m)
    (/ (/ x (+ (* (* z_m y) 0.16666666666666666) (/ z_m y))) y))))

C

z_m = fabs(z);
z_s = copysign(1.0, z);
double code(double z_s, double x, double y, double z_m) {
	double tmp;
	if (y <= 6.8e-8) {
		tmp = x / z_m;
	} else {
		tmp = (x / (((z_m * y) * 0.16666666666666666) + (z_m / y))) / y;
	}
	return z_s * tmp;
}

Fortran

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

Java

z_m = Math.abs(z);
z_s = Math.copySign(1.0, z);
public static double code(double z_s, double x, double y, double z_m) {
	double tmp;
	if (y <= 6.8e-8) {
		tmp = x / z_m;
	} else {
		tmp = (x / (((z_m * y) * 0.16666666666666666) + (z_m / y))) / y;
	}
	return z_s * tmp;
}

Python

z_m = math.fabs(z)
z_s = math.copysign(1.0, z)
def code(z_s, x, y, z_m):
	tmp = 0
	if y <= 6.8e-8:
		tmp = x / z_m
	else:
		tmp = (x / (((z_m * y) * 0.16666666666666666) + (z_m / y))) / y
	return z_s * tmp

Julia

z_m = abs(z)
z_s = copysign(1.0, z)
function code(z_s, x, y, z_m)
	tmp = 0.0
	if (y <= 6.8e-8)
		tmp = Float64(x / z_m);
	else
		tmp = Float64(Float64(x / Float64(Float64(Float64(z_m * y) * 0.16666666666666666) + Float64(z_m / y))) / y);
	end
	return Float64(z_s * tmp)
end

MATLAB

z_m = abs(z);
z_s = sign(z) * abs(1.0);
function tmp_2 = code(z_s, x, y, z_m)
	tmp = 0.0;
	if (y <= 6.8e-8)
		tmp = x / z_m;
	else
		tmp = (x / (((z_m * y) * 0.16666666666666666) + (z_m / y))) / y;
	end
	tmp_2 = z_s * tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
z_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[z$95$s_, x_, y_, z$95$m_] := N[(z$95$s * If[LessEqual[y, 6.8e-8], N[(x / z$95$m), $MachinePrecision], N[(N[(x / N[(N[(N[(z$95$m * y), $MachinePrecision] * 0.16666666666666666), $MachinePrecision] + N[(z$95$m / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 8: 62.4% accurate, 9.7× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ z_s \cdot \begin{array}{l} \mathbf{if}\;y \leq 2.5:\\ \;\;\;\;\frac{x}{z_m}\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \frac{\frac{x}{z_m \cdot y}}{y}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m)
 :precision binary64
 (* z_s (if (<= y 2.5) (/ x z_m) (* 6.0 (/ (/ x (* z_m y)) y)))))

C

z_m = fabs(z);
z_s = copysign(1.0, z);
double code(double z_s, double x, double y, double z_m) {
	double tmp;
	if (y <= 2.5) {
		tmp = x / z_m;
	} else {
		tmp = 6.0 * ((x / (z_m * y)) / y);
	}
	return z_s * tmp;
}

Fortran

z_m = abs(z)
z_s = copysign(1.0d0, z)
real(8) function code(z_s, x, y, z_m)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8) :: tmp
    if (y <= 2.5d0) then
        tmp = x / z_m
    else
        tmp = 6.0d0 * ((x / (z_m * y)) / y)
    end if
    code = z_s * tmp
end function

Java

z_m = Math.abs(z);
z_s = Math.copySign(1.0, z);
public static double code(double z_s, double x, double y, double z_m) {
	double tmp;
	if (y <= 2.5) {
		tmp = x / z_m;
	} else {
		tmp = 6.0 * ((x / (z_m * y)) / y);
	}
	return z_s * tmp;
}

Python

z_m = math.fabs(z)
z_s = math.copysign(1.0, z)
def code(z_s, x, y, z_m):
	tmp = 0
	if y <= 2.5:
		tmp = x / z_m
	else:
		tmp = 6.0 * ((x / (z_m * y)) / y)
	return z_s * tmp

Julia

z_m = abs(z)
z_s = copysign(1.0, z)
function code(z_s, x, y, z_m)
	tmp = 0.0
	if (y <= 2.5)
		tmp = Float64(x / z_m);
	else
		tmp = Float64(6.0 * Float64(Float64(x / Float64(z_m * y)) / y));
	end
	return Float64(z_s * tmp)
end

MATLAB

z_m = abs(z);
z_s = sign(z) * abs(1.0);
function tmp_2 = code(z_s, x, y, z_m)
	tmp = 0.0;
	if (y <= 2.5)
		tmp = x / z_m;
	else
		tmp = 6.0 * ((x / (z_m * y)) / y);
	end
	tmp_2 = z_s * tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
z_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[z$95$s_, x_, y_, z$95$m_] := N[(z$95$s * If[LessEqual[y, 2.5], N[(x / z$95$m), $MachinePrecision], N[(6.0 * N[(N[(x / N[(z$95$m * y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 9: 62.4% accurate, 9.7× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ z_s \cdot \begin{array}{l} \mathbf{if}\;y \leq 2.5:\\ \;\;\;\;\frac{x}{z_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{6}{y}}{z_m}}{y}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m)
 :precision binary64
 (* z_s (if (<= y 2.5) (/ x z_m) (/ (* x (/ (/ 6.0 y) z_m)) y))))

C

z_m = fabs(z);
z_s = copysign(1.0, z);
double code(double z_s, double x, double y, double z_m) {
	double tmp;
	if (y <= 2.5) {
		tmp = x / z_m;
	} else {
		tmp = (x * ((6.0 / y) / z_m)) / y;
	}
	return z_s * tmp;
}

Fortran

z_m = abs(z)
z_s = copysign(1.0d0, z)
real(8) function code(z_s, x, y, z_m)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8) :: tmp
    if (y <= 2.5d0) then
        tmp = x / z_m
    else
        tmp = (x * ((6.0d0 / y) / z_m)) / y
    end if
    code = z_s * tmp
end function

Java

z_m = Math.abs(z);
z_s = Math.copySign(1.0, z);
public static double code(double z_s, double x, double y, double z_m) {
	double tmp;
	if (y <= 2.5) {
		tmp = x / z_m;
	} else {
		tmp = (x * ((6.0 / y) / z_m)) / y;
	}
	return z_s * tmp;
}

Python

z_m = math.fabs(z)
z_s = math.copysign(1.0, z)
def code(z_s, x, y, z_m):
	tmp = 0
	if y <= 2.5:
		tmp = x / z_m
	else:
		tmp = (x * ((6.0 / y) / z_m)) / y
	return z_s * tmp

Julia

z_m = abs(z)
z_s = copysign(1.0, z)
function code(z_s, x, y, z_m)
	tmp = 0.0
	if (y <= 2.5)
		tmp = Float64(x / z_m);
	else
		tmp = Float64(Float64(x * Float64(Float64(6.0 / y) / z_m)) / y);
	end
	return Float64(z_s * tmp)
end

MATLAB

z_m = abs(z);
z_s = sign(z) * abs(1.0);
function tmp_2 = code(z_s, x, y, z_m)
	tmp = 0.0;
	if (y <= 2.5)
		tmp = x / z_m;
	else
		tmp = (x * ((6.0 / y) / z_m)) / y;
	end
	tmp_2 = z_s * tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
z_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[z$95$s_, x_, y_, z$95$m_] := N[(z$95$s * If[LessEqual[y, 2.5], N[(x / z$95$m), $MachinePrecision], N[(N[(x * N[(N[(6.0 / y), $MachinePrecision] / z$95$m), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 10: 62.5% accurate, 9.7× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ z_s \cdot \begin{array}{l} \mathbf{if}\;y \leq 2.4:\\ \;\;\;\;\frac{x}{z_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{6}{y \cdot \frac{z_m}{x}}}{y}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m)
 :precision binary64
 (* z_s (if (<= y 2.4) (/ x z_m) (/ (/ 6.0 (* y (/ z_m x))) y))))

C

z_m = fabs(z);
z_s = copysign(1.0, z);
double code(double z_s, double x, double y, double z_m) {
	double tmp;
	if (y <= 2.4) {
		tmp = x / z_m;
	} else {
		tmp = (6.0 / (y * (z_m / x))) / y;
	}
	return z_s * tmp;
}

Fortran

z_m = abs(z)
z_s = copysign(1.0d0, z)
real(8) function code(z_s, x, y, z_m)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8) :: tmp
    if (y <= 2.4d0) then
        tmp = x / z_m
    else
        tmp = (6.0d0 / (y * (z_m / x))) / y
    end if
    code = z_s * tmp
end function

Java

z_m = Math.abs(z);
z_s = Math.copySign(1.0, z);
public static double code(double z_s, double x, double y, double z_m) {
	double tmp;
	if (y <= 2.4) {
		tmp = x / z_m;
	} else {
		tmp = (6.0 / (y * (z_m / x))) / y;
	}
	return z_s * tmp;
}

Python

z_m = math.fabs(z)
z_s = math.copysign(1.0, z)
def code(z_s, x, y, z_m):
	tmp = 0
	if y <= 2.4:
		tmp = x / z_m
	else:
		tmp = (6.0 / (y * (z_m / x))) / y
	return z_s * tmp

Julia

z_m = abs(z)
z_s = copysign(1.0, z)
function code(z_s, x, y, z_m)
	tmp = 0.0
	if (y <= 2.4)
		tmp = Float64(x / z_m);
	else
		tmp = Float64(Float64(6.0 / Float64(y * Float64(z_m / x))) / y);
	end
	return Float64(z_s * tmp)
end

MATLAB

z_m = abs(z);
z_s = sign(z) * abs(1.0);
function tmp_2 = code(z_s, x, y, z_m)
	tmp = 0.0;
	if (y <= 2.4)
		tmp = x / z_m;
	else
		tmp = (6.0 / (y * (z_m / x))) / y;
	end
	tmp_2 = z_s * tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
z_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[z$95$s_, x_, y_, z$95$m_] := N[(z$95$s * If[LessEqual[y, 2.4], N[(x / z$95$m), $MachinePrecision], N[(N[(6.0 / N[(y * N[(z$95$m / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 11: 62.5% accurate, 9.7× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ z_s \cdot \begin{array}{l} \mathbf{if}\;y \leq 2.5:\\ \;\;\;\;\frac{x}{z_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x \cdot 6}{z_m}}{y}}{y}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m)
 :precision binary64
 (* z_s (if (<= y 2.5) (/ x z_m) (/ (/ (/ (* x 6.0) z_m) y) y))))

C

z_m = fabs(z);
z_s = copysign(1.0, z);
double code(double z_s, double x, double y, double z_m) {
	double tmp;
	if (y <= 2.5) {
		tmp = x / z_m;
	} else {
		tmp = (((x * 6.0) / z_m) / y) / y;
	}
	return z_s * tmp;
}

Fortran

z_m = abs(z)
z_s = copysign(1.0d0, z)
real(8) function code(z_s, x, y, z_m)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8) :: tmp
    if (y <= 2.5d0) then
        tmp = x / z_m
    else
        tmp = (((x * 6.0d0) / z_m) / y) / y
    end if
    code = z_s * tmp
end function

Java

z_m = Math.abs(z);
z_s = Math.copySign(1.0, z);
public static double code(double z_s, double x, double y, double z_m) {
	double tmp;
	if (y <= 2.5) {
		tmp = x / z_m;
	} else {
		tmp = (((x * 6.0) / z_m) / y) / y;
	}
	return z_s * tmp;
}

Python

z_m = math.fabs(z)
z_s = math.copysign(1.0, z)
def code(z_s, x, y, z_m):
	tmp = 0
	if y <= 2.5:
		tmp = x / z_m
	else:
		tmp = (((x * 6.0) / z_m) / y) / y
	return z_s * tmp

Julia

z_m = abs(z)
z_s = copysign(1.0, z)
function code(z_s, x, y, z_m)
	tmp = 0.0
	if (y <= 2.5)
		tmp = Float64(x / z_m);
	else
		tmp = Float64(Float64(Float64(Float64(x * 6.0) / z_m) / y) / y);
	end
	return Float64(z_s * tmp)
end

MATLAB

z_m = abs(z);
z_s = sign(z) * abs(1.0);
function tmp_2 = code(z_s, x, y, z_m)
	tmp = 0.0;
	if (y <= 2.5)
		tmp = x / z_m;
	else
		tmp = (((x * 6.0) / z_m) / y) / y;
	end
	tmp_2 = z_s * tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
z_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[z$95$s_, x_, y_, z$95$m_] := N[(z$95$s * If[LessEqual[y, 2.5], N[(x / z$95$m), $MachinePrecision], N[(N[(N[(N[(x * 6.0), $MachinePrecision] / z$95$m), $MachinePrecision] / y), $MachinePrecision] / y), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 12: 62.2% accurate, 11.8× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ z_s \cdot \begin{array}{l} \mathbf{if}\;y \leq 2.8 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{z_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y \cdot \frac{z_m}{x}}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m)
 :precision binary64
 (* z_s (if (<= y 2.8e-30) (/ x z_m) (/ y (* y (/ z_m x))))))

C

z_m = fabs(z);
z_s = copysign(1.0, z);
double code(double z_s, double x, double y, double z_m) {
	double tmp;
	if (y <= 2.8e-30) {
		tmp = x / z_m;
	} else {
		tmp = y / (y * (z_m / x));
	}
	return z_s * tmp;
}

Fortran

z_m = abs(z)
z_s = copysign(1.0d0, z)
real(8) function code(z_s, x, y, z_m)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8) :: tmp
    if (y <= 2.8d-30) then
        tmp = x / z_m
    else
        tmp = y / (y * (z_m / x))
    end if
    code = z_s * tmp
end function

Java

z_m = Math.abs(z);
z_s = Math.copySign(1.0, z);
public static double code(double z_s, double x, double y, double z_m) {
	double tmp;
	if (y <= 2.8e-30) {
		tmp = x / z_m;
	} else {
		tmp = y / (y * (z_m / x));
	}
	return z_s * tmp;
}

Python

z_m = math.fabs(z)
z_s = math.copysign(1.0, z)
def code(z_s, x, y, z_m):
	tmp = 0
	if y <= 2.8e-30:
		tmp = x / z_m
	else:
		tmp = y / (y * (z_m / x))
	return z_s * tmp

Julia

z_m = abs(z)
z_s = copysign(1.0, z)
function code(z_s, x, y, z_m)
	tmp = 0.0
	if (y <= 2.8e-30)
		tmp = Float64(x / z_m);
	else
		tmp = Float64(y / Float64(y * Float64(z_m / x)));
	end
	return Float64(z_s * tmp)
end

MATLAB

z_m = abs(z);
z_s = sign(z) * abs(1.0);
function tmp_2 = code(z_s, x, y, z_m)
	tmp = 0.0;
	if (y <= 2.8e-30)
		tmp = x / z_m;
	else
		tmp = y / (y * (z_m / x));
	end
	tmp_2 = z_s * tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
z_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[z$95$s_, x_, y_, z$95$m_] := N[(z$95$s * If[LessEqual[y, 2.8e-30], N[(x / z$95$m), $MachinePrecision], N[(y / N[(y * N[(z$95$m / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 13: 62.3% accurate, 11.8× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ z_s \cdot \begin{array}{l} \mathbf{if}\;y \leq 50000000000000:\\ \;\;\;\;\frac{x}{z_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z_m \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m)
 :precision binary64
 (* z_s (if (<= y 50000000000000.0) (/ x z_m) (/ y (* z_m (/ y x))))))

C

z_m = fabs(z);
z_s = copysign(1.0, z);
double code(double z_s, double x, double y, double z_m) {
	double tmp;
	if (y <= 50000000000000.0) {
		tmp = x / z_m;
	} else {
		tmp = y / (z_m * (y / x));
	}
	return z_s * tmp;
}

Fortran

z_m = abs(z)
z_s = copysign(1.0d0, z)
real(8) function code(z_s, x, y, z_m)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8) :: tmp
    if (y <= 50000000000000.0d0) then
        tmp = x / z_m
    else
        tmp = y / (z_m * (y / x))
    end if
    code = z_s * tmp
end function

Java

z_m = Math.abs(z);
z_s = Math.copySign(1.0, z);
public static double code(double z_s, double x, double y, double z_m) {
	double tmp;
	if (y <= 50000000000000.0) {
		tmp = x / z_m;
	} else {
		tmp = y / (z_m * (y / x));
	}
	return z_s * tmp;
}

Python

z_m = math.fabs(z)
z_s = math.copysign(1.0, z)
def code(z_s, x, y, z_m):
	tmp = 0
	if y <= 50000000000000.0:
		tmp = x / z_m
	else:
		tmp = y / (z_m * (y / x))
	return z_s * tmp

Julia

z_m = abs(z)
z_s = copysign(1.0, z)
function code(z_s, x, y, z_m)
	tmp = 0.0
	if (y <= 50000000000000.0)
		tmp = Float64(x / z_m);
	else
		tmp = Float64(y / Float64(z_m * Float64(y / x)));
	end
	return Float64(z_s * tmp)
end

MATLAB

z_m = abs(z);
z_s = sign(z) * abs(1.0);
function tmp_2 = code(z_s, x, y, z_m)
	tmp = 0.0;
	if (y <= 50000000000000.0)
		tmp = x / z_m;
	else
		tmp = y / (z_m * (y / x));
	end
	tmp_2 = z_s * tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
z_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[z$95$s_, x_, y_, z$95$m_] := N[(z$95$s * If[LessEqual[y, 50000000000000.0], N[(x / z$95$m), $MachinePrecision], N[(y / N[(z$95$m * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 14: 58.4% accurate, 35.7× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ z_s \cdot \frac{x}{z_m} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m) :precision binary64 (* z_s (/ x z_m)))

C

z_m = fabs(z);
z_s = copysign(1.0, z);
double code(double z_s, double x, double y, double z_m) {
	return z_s * (x / z_m);
}

Fortran

z_m = abs(z)
z_s = copysign(1.0d0, z)
real(8) function code(z_s, x, y, z_m)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    code = z_s * (x / z_m)
end function

Java

z_m = Math.abs(z);
z_s = Math.copySign(1.0, z);
public static double code(double z_s, double x, double y, double z_m) {
	return z_s * (x / z_m);
}

Python

z_m = math.fabs(z)
z_s = math.copysign(1.0, z)
def code(z_s, x, y, z_m):
	return z_s * (x / z_m)

Julia

z_m = abs(z)
z_s = copysign(1.0, z)
function code(z_s, x, y, z_m)
	return Float64(z_s * Float64(x / z_m))
end

MATLAB

z_m = abs(z);
z_s = sign(z) * abs(1.0);
function tmp = code(z_s, x, y, z_m)
	tmp = z_s * (x / z_m);
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
z_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[z$95$s_, x_, y_, z$95$m_] := N[(z$95$s * N[(x / z$95$m), $MachinePrecision]), $MachinePrecision]

Derivation

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

Developer target: 99.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{\sin y}\\ t_1 := \frac{x \cdot \frac{1}{t_0}}{z}\\ \mathbf{if}\;z < -4.2173720203427147 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{z \cdot t_0}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (sin y))) (t_1 (/ (* x (/ 1.0 t_0)) z)))
   (if (< z -4.2173720203427147e-29)
     t_1
     (if (< z 4.446702369113811e+64) (/ x (* z t_0)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = y / sin(y);
	double t_1 = (x * (1.0 / t_0)) / z;
	double tmp;
	if (z < -4.2173720203427147e-29) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x / (z * t_0);
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = y / sin(y)
    t_1 = (x * (1.0d0 / t_0)) / z
    if (z < (-4.2173720203427147d-29)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x / (z * t_0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y / Math.sin(y);
	double t_1 = (x * (1.0 / t_0)) / z;
	double tmp;
	if (z < -4.2173720203427147e-29) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x / (z * t_0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / math.sin(y)
	t_1 = (x * (1.0 / t_0)) / z
	tmp = 0
	if z < -4.2173720203427147e-29:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x / (z * t_0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / sin(y))
	t_1 = Float64(Float64(x * Float64(1.0 / t_0)) / z)
	tmp = 0.0
	if (z < -4.2173720203427147e-29)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x / Float64(z * t_0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / sin(y);
	t_1 = (x * (1.0 / t_0)) / z;
	tmp = 0.0;
	if (z < -4.2173720203427147e-29)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x / (z * t_0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y / N[Sin[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, If[Less[z, -4.2173720203427147e-29], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x / N[(z * t$95$0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2023343 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctanh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< z -4.2173720203427147e-29) (/ (* x (/ 1.0 (/ y (sin y)))) z) (if (< z 4.446702369113811e+64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1.0 (/ y (sin y)))) z)))

  (/ (* x (/ (sin y) y)) z))