Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 89.5% → 96.3%

Time: 10.1s

Alternatives: 12

Speedup: 1.2×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot 2}{y \cdot z - t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (* x 2.0) (- (* y z) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x * 2.0) / ((y * z) - (t * z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * 2.0d0) / ((y * z) - (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * 2.0) / ((y * z) - (t * z));
}

Python

def code(x, y, z, t):
	return (x * 2.0) / ((y * z) - (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x * 2.0) / Float64(Float64(y * z) - Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * 2.0) / ((y * z) - (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * 2.0), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 89.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot 2}{y \cdot z - t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (* x 2.0) (- (* y z) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x * 2.0) / ((y * z) - (t * z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * 2.0d0) / ((y * z) - (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * 2.0) / ((y * z) - (t * z));
}

Python

def code(x, y, z, t):
	return (x * 2.0) / ((y * z) - (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x * 2.0) / Float64(Float64(y * z) - Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * 2.0) / ((y * z) - (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * 2.0), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ z_s \cdot \begin{array}{l} \mathbf{if}\;z_m \leq 2.5 \cdot 10^{+104}:\\ \;\;\;\;\frac{x \cdot 2}{z_m \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z_m}}{\left(y - t\right) \cdot 0.5}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m t)
 :precision binary64
 (*
  z_s
  (if (<= z_m 2.5e+104)
    (/ (* x 2.0) (* z_m (- y t)))
    (/ (/ x z_m) (* (- y t) 0.5)))))

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) {
	double tmp;
	if (z_m <= 2.5e+104) {
		tmp = (x * 2.0) / (z_m * (y - t));
	} else {
		tmp = (x / z_m) / ((y - t) * 0.5);
	}
	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, t)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z_m <= 2.5d+104) then
        tmp = (x * 2.0d0) / (z_m * (y - t))
    else
        tmp = (x / z_m) / ((y - t) * 0.5d0)
    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) {
	double tmp;
	if (z_m <= 2.5e+104) {
		tmp = (x * 2.0) / (z_m * (y - t));
	} else {
		tmp = (x / z_m) / ((y - t) * 0.5);
	}
	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):
	tmp = 0
	if z_m <= 2.5e+104:
		tmp = (x * 2.0) / (z_m * (y - t))
	else:
		tmp = (x / z_m) / ((y - t) * 0.5)
	return z_s * tmp

Julia

z_m = abs(z)
z_s = copysign(1.0, z)
function code(z_s, x, y, z_m, t)
	tmp = 0.0
	if (z_m <= 2.5e+104)
		tmp = Float64(Float64(x * 2.0) / Float64(z_m * Float64(y - t)));
	else
		tmp = Float64(Float64(x / z_m) / Float64(Float64(y - t) * 0.5));
	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)
	tmp = 0.0;
	if (z_m <= 2.5e+104)
		tmp = (x * 2.0) / (z_m * (y - t));
	else
		tmp = (x / z_m) / ((y - t) * 0.5);
	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_, t_] := N[(z$95$s * If[LessEqual[z$95$m, 2.5e+104], N[(N[(x * 2.0), $MachinePrecision] / N[(z$95$m * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z$95$m), $MachinePrecision] / N[(N[(y - t), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 2: 73.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ z_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+68}:\\ \;\;\;\;\frac{x}{z_m} \cdot \frac{2}{y}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+32}:\\ \;\;\;\;-2 \cdot \frac{x}{z_m \cdot t}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-46} \lor \neg \left(y \leq 7.6 \cdot 10^{-28}\right):\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z_m} \cdot \frac{-2}{t}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m t)
 :precision binary64
 (*
  z_s
  (if (<= y -1.8e+68)
    (* (/ x z_m) (/ 2.0 y))
    (if (<= y -5.5e+32)
      (* -2.0 (/ x (* z_m t)))
      (if (or (<= y -1.8e-46) (not (<= y 7.6e-28)))
        (* x (/ (/ 2.0 y) z_m))
        (* (/ x z_m) (/ -2.0 t)))))))

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) {
	double tmp;
	if (y <= -1.8e+68) {
		tmp = (x / z_m) * (2.0 / y);
	} else if (y <= -5.5e+32) {
		tmp = -2.0 * (x / (z_m * t));
	} else if ((y <= -1.8e-46) || !(y <= 7.6e-28)) {
		tmp = x * ((2.0 / y) / z_m);
	} else {
		tmp = (x / z_m) * (-2.0 / t);
	}
	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, t)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.8d+68)) then
        tmp = (x / z_m) * (2.0d0 / y)
    else if (y <= (-5.5d+32)) then
        tmp = (-2.0d0) * (x / (z_m * t))
    else if ((y <= (-1.8d-46)) .or. (.not. (y <= 7.6d-28))) then
        tmp = x * ((2.0d0 / y) / z_m)
    else
        tmp = (x / z_m) * ((-2.0d0) / t)
    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) {
	double tmp;
	if (y <= -1.8e+68) {
		tmp = (x / z_m) * (2.0 / y);
	} else if (y <= -5.5e+32) {
		tmp = -2.0 * (x / (z_m * t));
	} else if ((y <= -1.8e-46) || !(y <= 7.6e-28)) {
		tmp = x * ((2.0 / y) / z_m);
	} else {
		tmp = (x / z_m) * (-2.0 / t);
	}
	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):
	tmp = 0
	if y <= -1.8e+68:
		tmp = (x / z_m) * (2.0 / y)
	elif y <= -5.5e+32:
		tmp = -2.0 * (x / (z_m * t))
	elif (y <= -1.8e-46) or not (y <= 7.6e-28):
		tmp = x * ((2.0 / y) / z_m)
	else:
		tmp = (x / z_m) * (-2.0 / t)
	return z_s * tmp

Julia

z_m = abs(z)
z_s = copysign(1.0, z)
function code(z_s, x, y, z_m, t)
	tmp = 0.0
	if (y <= -1.8e+68)
		tmp = Float64(Float64(x / z_m) * Float64(2.0 / y));
	elseif (y <= -5.5e+32)
		tmp = Float64(-2.0 * Float64(x / Float64(z_m * t)));
	elseif ((y <= -1.8e-46) || !(y <= 7.6e-28))
		tmp = Float64(x * Float64(Float64(2.0 / y) / z_m));
	else
		tmp = Float64(Float64(x / z_m) * Float64(-2.0 / t));
	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)
	tmp = 0.0;
	if (y <= -1.8e+68)
		tmp = (x / z_m) * (2.0 / y);
	elseif (y <= -5.5e+32)
		tmp = -2.0 * (x / (z_m * t));
	elseif ((y <= -1.8e-46) || ~((y <= 7.6e-28)))
		tmp = x * ((2.0 / y) / z_m);
	else
		tmp = (x / z_m) * (-2.0 / t);
	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_, t_] := N[(z$95$s * If[LessEqual[y, -1.8e+68], N[(N[(x / z$95$m), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.5e+32], N[(-2.0 * N[(x / N[(z$95$m * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.8e-46], N[Not[LessEqual[y, 7.6e-28]], $MachinePrecision]], N[(x * N[(N[(2.0 / y), $MachinePrecision] / z$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(x / z$95$m), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

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

Alternative 3: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ z_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+68}:\\ \;\;\;\;\frac{x}{z_m} \cdot \frac{2}{y}\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{+36}:\\ \;\;\;\;-2 \cdot \frac{x}{z_m \cdot t}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-48} \lor \neg \left(y \leq 3.1 \cdot 10^{-24}\right):\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2}{t \cdot \frac{z_m}{x}}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m t)
 :precision binary64
 (*
  z_s
  (if (<= y -1.8e+68)
    (* (/ x z_m) (/ 2.0 y))
    (if (<= y -4.9e+36)
      (* -2.0 (/ x (* z_m t)))
      (if (or (<= y -2.4e-48) (not (<= y 3.1e-24)))
        (* x (/ (/ 2.0 y) z_m))
        (/ -2.0 (* t (/ 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 t) {
	double tmp;
	if (y <= -1.8e+68) {
		tmp = (x / z_m) * (2.0 / y);
	} else if (y <= -4.9e+36) {
		tmp = -2.0 * (x / (z_m * t));
	} else if ((y <= -2.4e-48) || !(y <= 3.1e-24)) {
		tmp = x * ((2.0 / y) / z_m);
	} else {
		tmp = -2.0 / (t * (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, t)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.8d+68)) then
        tmp = (x / z_m) * (2.0d0 / y)
    else if (y <= (-4.9d+36)) then
        tmp = (-2.0d0) * (x / (z_m * t))
    else if ((y <= (-2.4d-48)) .or. (.not. (y <= 3.1d-24))) then
        tmp = x * ((2.0d0 / y) / z_m)
    else
        tmp = (-2.0d0) / (t * (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 t) {
	double tmp;
	if (y <= -1.8e+68) {
		tmp = (x / z_m) * (2.0 / y);
	} else if (y <= -4.9e+36) {
		tmp = -2.0 * (x / (z_m * t));
	} else if ((y <= -2.4e-48) || !(y <= 3.1e-24)) {
		tmp = x * ((2.0 / y) / z_m);
	} else {
		tmp = -2.0 / (t * (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, t):
	tmp = 0
	if y <= -1.8e+68:
		tmp = (x / z_m) * (2.0 / y)
	elif y <= -4.9e+36:
		tmp = -2.0 * (x / (z_m * t))
	elif (y <= -2.4e-48) or not (y <= 3.1e-24):
		tmp = x * ((2.0 / y) / z_m)
	else:
		tmp = -2.0 / (t * (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, t)
	tmp = 0.0
	if (y <= -1.8e+68)
		tmp = Float64(Float64(x / z_m) * Float64(2.0 / y));
	elseif (y <= -4.9e+36)
		tmp = Float64(-2.0 * Float64(x / Float64(z_m * t)));
	elseif ((y <= -2.4e-48) || !(y <= 3.1e-24))
		tmp = Float64(x * Float64(Float64(2.0 / y) / z_m));
	else
		tmp = Float64(-2.0 / Float64(t * 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, t)
	tmp = 0.0;
	if (y <= -1.8e+68)
		tmp = (x / z_m) * (2.0 / y);
	elseif (y <= -4.9e+36)
		tmp = -2.0 * (x / (z_m * t));
	elseif ((y <= -2.4e-48) || ~((y <= 3.1e-24)))
		tmp = x * ((2.0 / y) / z_m);
	else
		tmp = -2.0 / (t * (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_, t_] := N[(z$95$s * If[LessEqual[y, -1.8e+68], N[(N[(x / z$95$m), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.9e+36], N[(-2.0 * N[(x / N[(z$95$m * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -2.4e-48], N[Not[LessEqual[y, 3.1e-24]], $MachinePrecision]], N[(x * N[(N[(2.0 / y), $MachinePrecision] / z$95$m), $MachinePrecision]), $MachinePrecision], N[(-2.0 / N[(t * N[(z$95$m / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

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

Alternative 4: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ \begin{array}{l} t_1 := \frac{2}{y \cdot \frac{z_m}{x}}\\ z_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+36}:\\ \;\;\;\;-2 \cdot \frac{x}{z_m \cdot t}\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-28}:\\ \;\;\;\;\frac{-2}{t \cdot \frac{z_m}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z_m}\\ \end{array} \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* y (/ z_m x)))))
   (*
    z_s
    (if (<= y -2.1e+68)
      t_1
      (if (<= y -2.8e+36)
        (* -2.0 (/ x (* z_m t)))
        (if (<= y -1.22e-55)
          t_1
          (if (<= y 2.8e-28)
            (/ -2.0 (* t (/ z_m x)))
            (* x (/ (/ 2.0 y) 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) {
	double t_1 = 2.0 / (y * (z_m / x));
	double tmp;
	if (y <= -2.1e+68) {
		tmp = t_1;
	} else if (y <= -2.8e+36) {
		tmp = -2.0 * (x / (z_m * t));
	} else if (y <= -1.22e-55) {
		tmp = t_1;
	} else if (y <= 2.8e-28) {
		tmp = -2.0 / (t * (z_m / x));
	} else {
		tmp = x * ((2.0 / y) / 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, t)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 / (y * (z_m / x))
    if (y <= (-2.1d+68)) then
        tmp = t_1
    else if (y <= (-2.8d+36)) then
        tmp = (-2.0d0) * (x / (z_m * t))
    else if (y <= (-1.22d-55)) then
        tmp = t_1
    else if (y <= 2.8d-28) then
        tmp = (-2.0d0) / (t * (z_m / x))
    else
        tmp = x * ((2.0d0 / y) / 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) {
	double t_1 = 2.0 / (y * (z_m / x));
	double tmp;
	if (y <= -2.1e+68) {
		tmp = t_1;
	} else if (y <= -2.8e+36) {
		tmp = -2.0 * (x / (z_m * t));
	} else if (y <= -1.22e-55) {
		tmp = t_1;
	} else if (y <= 2.8e-28) {
		tmp = -2.0 / (t * (z_m / x));
	} else {
		tmp = x * ((2.0 / y) / 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):
	t_1 = 2.0 / (y * (z_m / x))
	tmp = 0
	if y <= -2.1e+68:
		tmp = t_1
	elif y <= -2.8e+36:
		tmp = -2.0 * (x / (z_m * t))
	elif y <= -1.22e-55:
		tmp = t_1
	elif y <= 2.8e-28:
		tmp = -2.0 / (t * (z_m / x))
	else:
		tmp = x * ((2.0 / y) / 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)
	t_1 = Float64(2.0 / Float64(y * Float64(z_m / x)))
	tmp = 0.0
	if (y <= -2.1e+68)
		tmp = t_1;
	elseif (y <= -2.8e+36)
		tmp = Float64(-2.0 * Float64(x / Float64(z_m * t)));
	elseif (y <= -1.22e-55)
		tmp = t_1;
	elseif (y <= 2.8e-28)
		tmp = Float64(-2.0 / Float64(t * Float64(z_m / x)));
	else
		tmp = Float64(x * Float64(Float64(2.0 / y) / 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)
	t_1 = 2.0 / (y * (z_m / x));
	tmp = 0.0;
	if (y <= -2.1e+68)
		tmp = t_1;
	elseif (y <= -2.8e+36)
		tmp = -2.0 * (x / (z_m * t));
	elseif (y <= -1.22e-55)
		tmp = t_1;
	elseif (y <= 2.8e-28)
		tmp = -2.0 / (t * (z_m / x));
	else
		tmp = x * ((2.0 / y) / 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_, t_] := Block[{t$95$1 = N[(2.0 / N[(y * N[(z$95$m / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(z$95$s * If[LessEqual[y, -2.1e+68], t$95$1, If[LessEqual[y, -2.8e+36], N[(-2.0 * N[(x / N[(z$95$m * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.22e-55], t$95$1, If[LessEqual[y, 2.8e-28], N[(-2.0 / N[(t * N[(z$95$m / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(2.0 / y), $MachinePrecision] / z$95$m), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]

Derivation

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

Alternative 5: 73.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ \begin{array}{l} t_1 := \frac{2}{y \cdot \frac{z_m}{x}}\\ z_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+36}:\\ \;\;\;\;-2 \cdot \frac{x}{z_m \cdot t}\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-28}:\\ \;\;\;\;\frac{\frac{-2}{t}}{\frac{z_m}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z_m}\\ \end{array} \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* y (/ z_m x)))))
   (*
    z_s
    (if (<= y -1.8e+68)
      t_1
      (if (<= y -4.5e+36)
        (* -2.0 (/ x (* z_m t)))
        (if (<= y -2.05e-51)
          t_1
          (if (<= y 7.6e-28)
            (/ (/ -2.0 t) (/ z_m x))
            (* x (/ (/ 2.0 y) 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) {
	double t_1 = 2.0 / (y * (z_m / x));
	double tmp;
	if (y <= -1.8e+68) {
		tmp = t_1;
	} else if (y <= -4.5e+36) {
		tmp = -2.0 * (x / (z_m * t));
	} else if (y <= -2.05e-51) {
		tmp = t_1;
	} else if (y <= 7.6e-28) {
		tmp = (-2.0 / t) / (z_m / x);
	} else {
		tmp = x * ((2.0 / y) / 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, t)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 / (y * (z_m / x))
    if (y <= (-1.8d+68)) then
        tmp = t_1
    else if (y <= (-4.5d+36)) then
        tmp = (-2.0d0) * (x / (z_m * t))
    else if (y <= (-2.05d-51)) then
        tmp = t_1
    else if (y <= 7.6d-28) then
        tmp = ((-2.0d0) / t) / (z_m / x)
    else
        tmp = x * ((2.0d0 / y) / 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) {
	double t_1 = 2.0 / (y * (z_m / x));
	double tmp;
	if (y <= -1.8e+68) {
		tmp = t_1;
	} else if (y <= -4.5e+36) {
		tmp = -2.0 * (x / (z_m * t));
	} else if (y <= -2.05e-51) {
		tmp = t_1;
	} else if (y <= 7.6e-28) {
		tmp = (-2.0 / t) / (z_m / x);
	} else {
		tmp = x * ((2.0 / y) / 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):
	t_1 = 2.0 / (y * (z_m / x))
	tmp = 0
	if y <= -1.8e+68:
		tmp = t_1
	elif y <= -4.5e+36:
		tmp = -2.0 * (x / (z_m * t))
	elif y <= -2.05e-51:
		tmp = t_1
	elif y <= 7.6e-28:
		tmp = (-2.0 / t) / (z_m / x)
	else:
		tmp = x * ((2.0 / y) / 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)
	t_1 = Float64(2.0 / Float64(y * Float64(z_m / x)))
	tmp = 0.0
	if (y <= -1.8e+68)
		tmp = t_1;
	elseif (y <= -4.5e+36)
		tmp = Float64(-2.0 * Float64(x / Float64(z_m * t)));
	elseif (y <= -2.05e-51)
		tmp = t_1;
	elseif (y <= 7.6e-28)
		tmp = Float64(Float64(-2.0 / t) / Float64(z_m / x));
	else
		tmp = Float64(x * Float64(Float64(2.0 / y) / 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)
	t_1 = 2.0 / (y * (z_m / x));
	tmp = 0.0;
	if (y <= -1.8e+68)
		tmp = t_1;
	elseif (y <= -4.5e+36)
		tmp = -2.0 * (x / (z_m * t));
	elseif (y <= -2.05e-51)
		tmp = t_1;
	elseif (y <= 7.6e-28)
		tmp = (-2.0 / t) / (z_m / x);
	else
		tmp = x * ((2.0 / y) / 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_, t_] := Block[{t$95$1 = N[(2.0 / N[(y * N[(z$95$m / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(z$95$s * If[LessEqual[y, -1.8e+68], t$95$1, If[LessEqual[y, -4.5e+36], N[(-2.0 * N[(x / N[(z$95$m * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.05e-51], t$95$1, If[LessEqual[y, 7.6e-28], N[(N[(-2.0 / t), $MachinePrecision] / N[(z$95$m / x), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(2.0 / y), $MachinePrecision] / z$95$m), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]

Derivation

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

Alternative 6: 73.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ \begin{array}{l} t_1 := \frac{2}{y \cdot \frac{z_m}{x}}\\ z_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+34}:\\ \;\;\;\;\frac{\frac{x}{z_m}}{t \cdot -0.5}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-30}:\\ \;\;\;\;\frac{\frac{-2}{t}}{\frac{z_m}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z_m}\\ \end{array} \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* y (/ z_m x)))))
   (*
    z_s
    (if (<= y -1.8e+68)
      t_1
      (if (<= y -5.5e+34)
        (/ (/ x z_m) (* t -0.5))
        (if (<= y -9e-48)
          t_1
          (if (<= y 1.05e-30)
            (/ (/ -2.0 t) (/ z_m x))
            (* x (/ (/ 2.0 y) 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) {
	double t_1 = 2.0 / (y * (z_m / x));
	double tmp;
	if (y <= -1.8e+68) {
		tmp = t_1;
	} else if (y <= -5.5e+34) {
		tmp = (x / z_m) / (t * -0.5);
	} else if (y <= -9e-48) {
		tmp = t_1;
	} else if (y <= 1.05e-30) {
		tmp = (-2.0 / t) / (z_m / x);
	} else {
		tmp = x * ((2.0 / y) / 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, t)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 / (y * (z_m / x))
    if (y <= (-1.8d+68)) then
        tmp = t_1
    else if (y <= (-5.5d+34)) then
        tmp = (x / z_m) / (t * (-0.5d0))
    else if (y <= (-9d-48)) then
        tmp = t_1
    else if (y <= 1.05d-30) then
        tmp = ((-2.0d0) / t) / (z_m / x)
    else
        tmp = x * ((2.0d0 / y) / 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) {
	double t_1 = 2.0 / (y * (z_m / x));
	double tmp;
	if (y <= -1.8e+68) {
		tmp = t_1;
	} else if (y <= -5.5e+34) {
		tmp = (x / z_m) / (t * -0.5);
	} else if (y <= -9e-48) {
		tmp = t_1;
	} else if (y <= 1.05e-30) {
		tmp = (-2.0 / t) / (z_m / x);
	} else {
		tmp = x * ((2.0 / y) / 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):
	t_1 = 2.0 / (y * (z_m / x))
	tmp = 0
	if y <= -1.8e+68:
		tmp = t_1
	elif y <= -5.5e+34:
		tmp = (x / z_m) / (t * -0.5)
	elif y <= -9e-48:
		tmp = t_1
	elif y <= 1.05e-30:
		tmp = (-2.0 / t) / (z_m / x)
	else:
		tmp = x * ((2.0 / y) / 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)
	t_1 = Float64(2.0 / Float64(y * Float64(z_m / x)))
	tmp = 0.0
	if (y <= -1.8e+68)
		tmp = t_1;
	elseif (y <= -5.5e+34)
		tmp = Float64(Float64(x / z_m) / Float64(t * -0.5));
	elseif (y <= -9e-48)
		tmp = t_1;
	elseif (y <= 1.05e-30)
		tmp = Float64(Float64(-2.0 / t) / Float64(z_m / x));
	else
		tmp = Float64(x * Float64(Float64(2.0 / y) / 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)
	t_1 = 2.0 / (y * (z_m / x));
	tmp = 0.0;
	if (y <= -1.8e+68)
		tmp = t_1;
	elseif (y <= -5.5e+34)
		tmp = (x / z_m) / (t * -0.5);
	elseif (y <= -9e-48)
		tmp = t_1;
	elseif (y <= 1.05e-30)
		tmp = (-2.0 / t) / (z_m / x);
	else
		tmp = x * ((2.0 / y) / 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_, t_] := Block[{t$95$1 = N[(2.0 / N[(y * N[(z$95$m / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(z$95$s * If[LessEqual[y, -1.8e+68], t$95$1, If[LessEqual[y, -5.5e+34], N[(N[(x / z$95$m), $MachinePrecision] / N[(t * -0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9e-48], t$95$1, If[LessEqual[y, 1.05e-30], N[(N[(-2.0 / t), $MachinePrecision] / N[(z$95$m / x), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(2.0 / y), $MachinePrecision] / z$95$m), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]

Derivation

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

Alternative 7: 73.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ z_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+77}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{z_m}}{y}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+36}:\\ \;\;\;\;\frac{\frac{x}{z_m}}{t \cdot -0.5}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-52}:\\ \;\;\;\;\frac{2}{y \cdot \frac{z_m}{x}}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-27}:\\ \;\;\;\;\frac{\frac{-2}{t}}{\frac{z_m}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z_m}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m t)
 :precision binary64
 (*
  z_s
  (if (<= y -1.95e+77)
    (/ (/ (* x 2.0) z_m) y)
    (if (<= y -5e+36)
      (/ (/ x z_m) (* t -0.5))
      (if (<= y -8e-52)
        (/ 2.0 (* y (/ z_m x)))
        (if (<= y 1.45e-27)
          (/ (/ -2.0 t) (/ z_m x))
          (* x (/ (/ 2.0 y) 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) {
	double tmp;
	if (y <= -1.95e+77) {
		tmp = ((x * 2.0) / z_m) / y;
	} else if (y <= -5e+36) {
		tmp = (x / z_m) / (t * -0.5);
	} else if (y <= -8e-52) {
		tmp = 2.0 / (y * (z_m / x));
	} else if (y <= 1.45e-27) {
		tmp = (-2.0 / t) / (z_m / x);
	} else {
		tmp = x * ((2.0 / y) / 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, t)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.95d+77)) then
        tmp = ((x * 2.0d0) / z_m) / y
    else if (y <= (-5d+36)) then
        tmp = (x / z_m) / (t * (-0.5d0))
    else if (y <= (-8d-52)) then
        tmp = 2.0d0 / (y * (z_m / x))
    else if (y <= 1.45d-27) then
        tmp = ((-2.0d0) / t) / (z_m / x)
    else
        tmp = x * ((2.0d0 / y) / 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) {
	double tmp;
	if (y <= -1.95e+77) {
		tmp = ((x * 2.0) / z_m) / y;
	} else if (y <= -5e+36) {
		tmp = (x / z_m) / (t * -0.5);
	} else if (y <= -8e-52) {
		tmp = 2.0 / (y * (z_m / x));
	} else if (y <= 1.45e-27) {
		tmp = (-2.0 / t) / (z_m / x);
	} else {
		tmp = x * ((2.0 / y) / 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):
	tmp = 0
	if y <= -1.95e+77:
		tmp = ((x * 2.0) / z_m) / y
	elif y <= -5e+36:
		tmp = (x / z_m) / (t * -0.5)
	elif y <= -8e-52:
		tmp = 2.0 / (y * (z_m / x))
	elif y <= 1.45e-27:
		tmp = (-2.0 / t) / (z_m / x)
	else:
		tmp = x * ((2.0 / y) / 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)
	tmp = 0.0
	if (y <= -1.95e+77)
		tmp = Float64(Float64(Float64(x * 2.0) / z_m) / y);
	elseif (y <= -5e+36)
		tmp = Float64(Float64(x / z_m) / Float64(t * -0.5));
	elseif (y <= -8e-52)
		tmp = Float64(2.0 / Float64(y * Float64(z_m / x)));
	elseif (y <= 1.45e-27)
		tmp = Float64(Float64(-2.0 / t) / Float64(z_m / x));
	else
		tmp = Float64(x * Float64(Float64(2.0 / y) / 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)
	tmp = 0.0;
	if (y <= -1.95e+77)
		tmp = ((x * 2.0) / z_m) / y;
	elseif (y <= -5e+36)
		tmp = (x / z_m) / (t * -0.5);
	elseif (y <= -8e-52)
		tmp = 2.0 / (y * (z_m / x));
	elseif (y <= 1.45e-27)
		tmp = (-2.0 / t) / (z_m / x);
	else
		tmp = x * ((2.0 / y) / 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_, t_] := N[(z$95$s * If[LessEqual[y, -1.95e+77], N[(N[(N[(x * 2.0), $MachinePrecision] / z$95$m), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -5e+36], N[(N[(x / z$95$m), $MachinePrecision] / N[(t * -0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8e-52], N[(2.0 / N[(y * N[(z$95$m / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e-27], N[(N[(-2.0 / t), $MachinePrecision] / N[(z$95$m / x), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(2.0 / y), $MachinePrecision] / z$95$m), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

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

Alternative 8: 72.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ z_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-128} \lor \neg \left(t \leq 2.32 \cdot 10^{+52}\right):\\ \;\;\;\;-2 \cdot \frac{x}{z_m \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z_m}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m t)
 :precision binary64
 (*
  z_s
  (if (or (<= t -1.4e-128) (not (<= t 2.32e+52)))
    (* -2.0 (/ x (* z_m t)))
    (* x (/ (/ 2.0 y) 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) {
	double tmp;
	if ((t <= -1.4e-128) || !(t <= 2.32e+52)) {
		tmp = -2.0 * (x / (z_m * t));
	} else {
		tmp = x * ((2.0 / y) / 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, t)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.4d-128)) .or. (.not. (t <= 2.32d+52))) then
        tmp = (-2.0d0) * (x / (z_m * t))
    else
        tmp = x * ((2.0d0 / y) / 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) {
	double tmp;
	if ((t <= -1.4e-128) || !(t <= 2.32e+52)) {
		tmp = -2.0 * (x / (z_m * t));
	} else {
		tmp = x * ((2.0 / y) / 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):
	tmp = 0
	if (t <= -1.4e-128) or not (t <= 2.32e+52):
		tmp = -2.0 * (x / (z_m * t))
	else:
		tmp = x * ((2.0 / y) / 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)
	tmp = 0.0
	if ((t <= -1.4e-128) || !(t <= 2.32e+52))
		tmp = Float64(-2.0 * Float64(x / Float64(z_m * t)));
	else
		tmp = Float64(x * Float64(Float64(2.0 / y) / 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)
	tmp = 0.0;
	if ((t <= -1.4e-128) || ~((t <= 2.32e+52)))
		tmp = -2.0 * (x / (z_m * t));
	else
		tmp = x * ((2.0 / y) / 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_, t_] := N[(z$95$s * If[Or[LessEqual[t, -1.4e-128], N[Not[LessEqual[t, 2.32e+52]], $MachinePrecision]], N[(-2.0 * N[(x / N[(z$95$m * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(2.0 / y), $MachinePrecision] / z$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 9: 96.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ \begin{array}{l} t_1 := \frac{2}{y - t}\\ z_s \cdot \begin{array}{l} \mathbf{if}\;z_m \leq 1.24 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \frac{t_1}{z_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z_m} \cdot t_1\\ \end{array} \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (- y t))))
   (* z_s (if (<= z_m 1.24e+104) (* x (/ t_1 z_m)) (* (/ x z_m) t_1)))))

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) {
	double t_1 = 2.0 / (y - t);
	double tmp;
	if (z_m <= 1.24e+104) {
		tmp = x * (t_1 / z_m);
	} else {
		tmp = (x / z_m) * t_1;
	}
	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, t)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 / (y - t)
    if (z_m <= 1.24d+104) then
        tmp = x * (t_1 / z_m)
    else
        tmp = (x / z_m) * t_1
    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) {
	double t_1 = 2.0 / (y - t);
	double tmp;
	if (z_m <= 1.24e+104) {
		tmp = x * (t_1 / z_m);
	} else {
		tmp = (x / z_m) * t_1;
	}
	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):
	t_1 = 2.0 / (y - t)
	tmp = 0
	if z_m <= 1.24e+104:
		tmp = x * (t_1 / z_m)
	else:
		tmp = (x / z_m) * t_1
	return z_s * tmp

Julia

z_m = abs(z)
z_s = copysign(1.0, z)
function code(z_s, x, y, z_m, t)
	t_1 = Float64(2.0 / Float64(y - t))
	tmp = 0.0
	if (z_m <= 1.24e+104)
		tmp = Float64(x * Float64(t_1 / z_m));
	else
		tmp = Float64(Float64(x / z_m) * t_1);
	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)
	t_1 = 2.0 / (y - t);
	tmp = 0.0;
	if (z_m <= 1.24e+104)
		tmp = x * (t_1 / z_m);
	else
		tmp = (x / z_m) * t_1;
	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_, t_] := Block[{t$95$1 = N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision]}, N[(z$95$s * If[LessEqual[z$95$m, 1.24e+104], N[(x * N[(t$95$1 / z$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(x / z$95$m), $MachinePrecision] * t$95$1), $MachinePrecision]]), $MachinePrecision]]

Derivation

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

Alternative 10: 96.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ z_s \cdot \begin{array}{l} \mathbf{if}\;z_m \leq 4.2 \cdot 10^{+103}:\\ \;\;\;\;\frac{x \cdot 2}{z_m \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z_m} \cdot \frac{2}{y - t}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m t)
 :precision binary64
 (*
  z_s
  (if (<= z_m 4.2e+103)
    (/ (* x 2.0) (* z_m (- y t)))
    (* (/ x z_m) (/ 2.0 (- y t))))))

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) {
	double tmp;
	if (z_m <= 4.2e+103) {
		tmp = (x * 2.0) / (z_m * (y - t));
	} else {
		tmp = (x / z_m) * (2.0 / (y - t));
	}
	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, t)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z_m <= 4.2d+103) then
        tmp = (x * 2.0d0) / (z_m * (y - t))
    else
        tmp = (x / z_m) * (2.0d0 / (y - t))
    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) {
	double tmp;
	if (z_m <= 4.2e+103) {
		tmp = (x * 2.0) / (z_m * (y - t));
	} else {
		tmp = (x / z_m) * (2.0 / (y - t));
	}
	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):
	tmp = 0
	if z_m <= 4.2e+103:
		tmp = (x * 2.0) / (z_m * (y - t))
	else:
		tmp = (x / z_m) * (2.0 / (y - t))
	return z_s * tmp

Julia

z_m = abs(z)
z_s = copysign(1.0, z)
function code(z_s, x, y, z_m, t)
	tmp = 0.0
	if (z_m <= 4.2e+103)
		tmp = Float64(Float64(x * 2.0) / Float64(z_m * Float64(y - t)));
	else
		tmp = Float64(Float64(x / z_m) * Float64(2.0 / Float64(y - t)));
	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)
	tmp = 0.0;
	if (z_m <= 4.2e+103)
		tmp = (x * 2.0) / (z_m * (y - t));
	else
		tmp = (x / z_m) * (2.0 / (y - t));
	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_, t_] := N[(z$95$s * If[LessEqual[z$95$m, 4.2e+103], N[(N[(x * 2.0), $MachinePrecision] / N[(z$95$m * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z$95$m), $MachinePrecision] * N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 11: 92.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ z_s \cdot \left(x \cdot \frac{\frac{2}{y - t}}{z_m}\right) \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m t)
 :precision binary64
 (* z_s (* x (/ (/ 2.0 (- y t)) 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) {
	return z_s * (x * ((2.0 / (y - t)) / z_m));
}

Fortran

z_m = abs(z)
z_s = copysign(1.0d0, z)
real(8) function code(z_s, x, y, z_m, t)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    code = z_s * (x * ((2.0d0 / (y - t)) / 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, double t) {
	return z_s * (x * ((2.0 / (y - t)) / z_m));
}

Python

z_m = math.fabs(z)
z_s = math.copysign(1.0, z)
def code(z_s, x, y, z_m, t):
	return z_s * (x * ((2.0 / (y - t)) / z_m))

Julia

z_m = abs(z)
z_s = copysign(1.0, z)
function code(z_s, x, y, z_m, t)
	return Float64(z_s * Float64(x * Float64(Float64(2.0 / Float64(y - t)) / z_m)))
end

MATLAB

z_m = abs(z);
z_s = sign(z) * abs(1.0);
function tmp = code(z_s, x, y, z_m, t)
	tmp = z_s * (x * ((2.0 / (y - t)) / 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_, t_] := N[(z$95$s * N[(x * N[(N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision] / z$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 12: 53.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ z_s \cdot \left(-2 \cdot \frac{x}{z_m \cdot t}\right) \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m t) :precision binary64 (* z_s (* -2.0 (/ x (* z_m t)))))

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) {
	return z_s * (-2.0 * (x / (z_m * t)));
}

Fortran

z_m = abs(z)
z_s = copysign(1.0d0, z)
real(8) function code(z_s, x, y, z_m, t)
    real(8), intent (in) :: z_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    code = z_s * ((-2.0d0) * (x / (z_m * t)))
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) {
	return z_s * (-2.0 * (x / (z_m * t)));
}

Python

z_m = math.fabs(z)
z_s = math.copysign(1.0, z)
def code(z_s, x, y, z_m, t):
	return z_s * (-2.0 * (x / (z_m * t)))

Julia

z_m = abs(z)
z_s = copysign(1.0, z)
function code(z_s, x, y, z_m, t)
	return Float64(z_s * Float64(-2.0 * Float64(x / Float64(z_m * t))))
end

MATLAB

z_m = abs(z);
z_s = sign(z) * abs(1.0);
function tmp = code(z_s, x, y, z_m, t)
	tmp = z_s * (-2.0 * (x / (z_m * t)));
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_, t_] := N[(z$95$s * N[(-2.0 * N[(x / N[(z$95$m * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Developer target: 97.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ t_2 := \frac{x \cdot 2}{y \cdot z - t \cdot z}\\ \mathbf{if}\;t_2 < -2.559141628295061 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 < 1.045027827330126 \cdot 10^{-269}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 2}{y - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x (* (- y t) z)) 2.0))
        (t_2 (/ (* x 2.0) (- (* y z) (* t z)))))
   (if (< t_2 -2.559141628295061e-13)
     t_1
     (if (< t_2 1.045027827330126e-269) (/ (* (/ x z) 2.0) (- y t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / ((y - t) * z)) * 2.0;
	double t_2 = (x * 2.0) / ((y * z) - (t * z));
	double tmp;
	if (t_2 < -2.559141628295061e-13) {
		tmp = t_1;
	} else if (t_2 < 1.045027827330126e-269) {
		tmp = ((x / z) * 2.0) / (y - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / ((y - t) * z)) * 2.0d0
    t_2 = (x * 2.0d0) / ((y * z) - (t * z))
    if (t_2 < (-2.559141628295061d-13)) then
        tmp = t_1
    else if (t_2 < 1.045027827330126d-269) then
        tmp = ((x / z) * 2.0d0) / (y - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / ((y - t) * z)) * 2.0;
	double t_2 = (x * 2.0) / ((y * z) - (t * z));
	double tmp;
	if (t_2 < -2.559141628295061e-13) {
		tmp = t_1;
	} else if (t_2 < 1.045027827330126e-269) {
		tmp = ((x / z) * 2.0) / (y - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / ((y - t) * z)) * 2.0
	t_2 = (x * 2.0) / ((y * z) - (t * z))
	tmp = 0
	if t_2 < -2.559141628295061e-13:
		tmp = t_1
	elif t_2 < 1.045027827330126e-269:
		tmp = ((x / z) * 2.0) / (y - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / Float64(Float64(y - t) * z)) * 2.0)
	t_2 = Float64(Float64(x * 2.0) / Float64(Float64(y * z) - Float64(t * z)))
	tmp = 0.0
	if (t_2 < -2.559141628295061e-13)
		tmp = t_1;
	elseif (t_2 < 1.045027827330126e-269)
		tmp = Float64(Float64(Float64(x / z) * 2.0) / Float64(y - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / ((y - t) * z)) * 2.0;
	t_2 = (x * 2.0) / ((y * z) - (t * z));
	tmp = 0.0;
	if (t_2 < -2.559141628295061e-13)
		tmp = t_1;
	elseif (t_2 < 1.045027827330126e-269)
		tmp = ((x / z) * 2.0) / (y - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 2.0), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -2.559141628295061e-13], t$95$1, If[Less[t$95$2, 1.045027827330126e-269], N[(N[(N[(x / z), $MachinePrecision] * 2.0), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2023347 
(FPCore (x y z t)
  :name "Linear.Projection:infinitePerspective from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (if (< (/ (* x 2.0) (- (* y z) (* t z))) -2.559141628295061e-13) (* (/ x (* (- y t) z)) 2.0) (if (< (/ (* x 2.0) (- (* y z) (* t z))) 1.045027827330126e-269) (/ (* (/ x z) 2.0) (- y t)) (* (/ x (* (- y t) z)) 2.0)))

  (/ (* x 2.0) (- (* y z) (* t z))))