Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 90.3% → 95.4%

Time: 8.3s

Alternatives: 10

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: 90.3% 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: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ z_s \cdot \begin{array}{l} \mathbf{if}\;z_m \leq 3.4 \cdot 10^{+158}:\\ \;\;\;\;\frac{x \cdot 2}{z_m \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z_m}}{\left(y - t\right) \cdot 0.5}\\ \end{array} \end{array} \]

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 3.4e+158)
    (/ (* 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 <= 3.4e+158) {
		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 <= 3.4d+158) 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 <= 3.4e+158) {
		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 <= 3.4e+158:
		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 <= 3.4e+158)
		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 <= 3.4e+158)
		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, 3.4e+158], 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: 71.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ \begin{array}{l} t_1 := \frac{x}{z_m} \cdot \frac{-2}{t}\\ z_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z_m}\\ \mathbf{elif}\;t \leq -9.4 \cdot 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-105}:\\ \;\;\;\;\frac{x}{z_m} \cdot \frac{2}{y}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \frac{2}{z_m \cdot y}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{x}{z_m \cdot t}\\ \end{array} \end{array} \end{array} \]

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 (* (/ x z_m) (/ -2.0 t))))
   (*
    z_s
    (if (<= t -5e+59)
      t_1
      (if (<= t -2.8e-12)
        (* x (/ (/ 2.0 y) z_m))
        (if (<= t -9.4e-59)
          t_1
          (if (<= t -7e-105)
            (* (/ x z_m) (/ 2.0 y))
            (if (<= t 2.1e+85)
              (* x (/ 2.0 (* z_m y)))
              (* -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) {
	double t_1 = (x / z_m) * (-2.0 / t);
	double tmp;
	if (t <= -5e+59) {
		tmp = t_1;
	} else if (t <= -2.8e-12) {
		tmp = x * ((2.0 / y) / z_m);
	} else if (t <= -9.4e-59) {
		tmp = t_1;
	} else if (t <= -7e-105) {
		tmp = (x / z_m) * (2.0 / y);
	} else if (t <= 2.1e+85) {
		tmp = x * (2.0 / (z_m * y));
	} else {
		tmp = -2.0 * (x / (z_m * 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) :: t_1
    real(8) :: tmp
    t_1 = (x / z_m) * ((-2.0d0) / t)
    if (t <= (-5d+59)) then
        tmp = t_1
    else if (t <= (-2.8d-12)) then
        tmp = x * ((2.0d0 / y) / z_m)
    else if (t <= (-9.4d-59)) then
        tmp = t_1
    else if (t <= (-7d-105)) then
        tmp = (x / z_m) * (2.0d0 / y)
    else if (t <= 2.1d+85) then
        tmp = x * (2.0d0 / (z_m * y))
    else
        tmp = (-2.0d0) * (x / (z_m * 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 t_1 = (x / z_m) * (-2.0 / t);
	double tmp;
	if (t <= -5e+59) {
		tmp = t_1;
	} else if (t <= -2.8e-12) {
		tmp = x * ((2.0 / y) / z_m);
	} else if (t <= -9.4e-59) {
		tmp = t_1;
	} else if (t <= -7e-105) {
		tmp = (x / z_m) * (2.0 / y);
	} else if (t <= 2.1e+85) {
		tmp = x * (2.0 / (z_m * y));
	} else {
		tmp = -2.0 * (x / (z_m * 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):
	t_1 = (x / z_m) * (-2.0 / t)
	tmp = 0
	if t <= -5e+59:
		tmp = t_1
	elif t <= -2.8e-12:
		tmp = x * ((2.0 / y) / z_m)
	elif t <= -9.4e-59:
		tmp = t_1
	elif t <= -7e-105:
		tmp = (x / z_m) * (2.0 / y)
	elif t <= 2.1e+85:
		tmp = x * (2.0 / (z_m * y))
	else:
		tmp = -2.0 * (x / (z_m * 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)
	t_1 = Float64(Float64(x / z_m) * Float64(-2.0 / t))
	tmp = 0.0
	if (t <= -5e+59)
		tmp = t_1;
	elseif (t <= -2.8e-12)
		tmp = Float64(x * Float64(Float64(2.0 / y) / z_m));
	elseif (t <= -9.4e-59)
		tmp = t_1;
	elseif (t <= -7e-105)
		tmp = Float64(Float64(x / z_m) * Float64(2.0 / y));
	elseif (t <= 2.1e+85)
		tmp = Float64(x * Float64(2.0 / Float64(z_m * y)));
	else
		tmp = Float64(-2.0 * Float64(x / Float64(z_m * 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)
	t_1 = (x / z_m) * (-2.0 / t);
	tmp = 0.0;
	if (t <= -5e+59)
		tmp = t_1;
	elseif (t <= -2.8e-12)
		tmp = x * ((2.0 / y) / z_m);
	elseif (t <= -9.4e-59)
		tmp = t_1;
	elseif (t <= -7e-105)
		tmp = (x / z_m) * (2.0 / y);
	elseif (t <= 2.1e+85)
		tmp = x * (2.0 / (z_m * y));
	else
		tmp = -2.0 * (x / (z_m * 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_] := Block[{t$95$1 = N[(N[(x / z$95$m), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]}, N[(z$95$s * If[LessEqual[t, -5e+59], t$95$1, If[LessEqual[t, -2.8e-12], N[(x * N[(N[(2.0 / y), $MachinePrecision] / z$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.4e-59], t$95$1, If[LessEqual[t, -7e-105], N[(N[(x / z$95$m), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e+85], N[(x * N[(2.0 / N[(z$95$m * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(x / N[(z$95$m * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]), $MachinePrecision]]

Derivation

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

Alternative 3: 71.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{2}{y}}{z_m}\\ t_2 := \frac{x}{z_m} \cdot \frac{-2}{t}\\ z_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.92 \cdot 10^{+62}:\\ \;\;\;\;\frac{2}{y \cdot \frac{z_m}{x}}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{x}{z_m \cdot t}\\ \end{array} \end{array} \end{array} \]

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 (* x (/ (/ 2.0 y) z_m))) (t_2 (* (/ x z_m) (/ -2.0 t))))
   (*
    z_s
    (if (<= t -4.5e+59)
      t_2
      (if (<= t -1.25e-8)
        t_1
        (if (<= t -7e-59)
          t_2
          (if (<= t 1.92e+62)
            (/ 2.0 (* y (/ z_m x)))
            (if (<= t 4.8e+86) t_1 (* -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) {
	double t_1 = x * ((2.0 / y) / z_m);
	double t_2 = (x / z_m) * (-2.0 / t);
	double tmp;
	if (t <= -4.5e+59) {
		tmp = t_2;
	} else if (t <= -1.25e-8) {
		tmp = t_1;
	} else if (t <= -7e-59) {
		tmp = t_2;
	} else if (t <= 1.92e+62) {
		tmp = 2.0 / (y * (z_m / x));
	} else if (t <= 4.8e+86) {
		tmp = t_1;
	} else {
		tmp = -2.0 * (x / (z_m * 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((2.0d0 / y) / z_m)
    t_2 = (x / z_m) * ((-2.0d0) / t)
    if (t <= (-4.5d+59)) then
        tmp = t_2
    else if (t <= (-1.25d-8)) then
        tmp = t_1
    else if (t <= (-7d-59)) then
        tmp = t_2
    else if (t <= 1.92d+62) then
        tmp = 2.0d0 / (y * (z_m / x))
    else if (t <= 4.8d+86) then
        tmp = t_1
    else
        tmp = (-2.0d0) * (x / (z_m * 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 t_1 = x * ((2.0 / y) / z_m);
	double t_2 = (x / z_m) * (-2.0 / t);
	double tmp;
	if (t <= -4.5e+59) {
		tmp = t_2;
	} else if (t <= -1.25e-8) {
		tmp = t_1;
	} else if (t <= -7e-59) {
		tmp = t_2;
	} else if (t <= 1.92e+62) {
		tmp = 2.0 / (y * (z_m / x));
	} else if (t <= 4.8e+86) {
		tmp = t_1;
	} else {
		tmp = -2.0 * (x / (z_m * 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):
	t_1 = x * ((2.0 / y) / z_m)
	t_2 = (x / z_m) * (-2.0 / t)
	tmp = 0
	if t <= -4.5e+59:
		tmp = t_2
	elif t <= -1.25e-8:
		tmp = t_1
	elif t <= -7e-59:
		tmp = t_2
	elif t <= 1.92e+62:
		tmp = 2.0 / (y * (z_m / x))
	elif t <= 4.8e+86:
		tmp = t_1
	else:
		tmp = -2.0 * (x / (z_m * 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)
	t_1 = Float64(x * Float64(Float64(2.0 / y) / z_m))
	t_2 = Float64(Float64(x / z_m) * Float64(-2.0 / t))
	tmp = 0.0
	if (t <= -4.5e+59)
		tmp = t_2;
	elseif (t <= -1.25e-8)
		tmp = t_1;
	elseif (t <= -7e-59)
		tmp = t_2;
	elseif (t <= 1.92e+62)
		tmp = Float64(2.0 / Float64(y * Float64(z_m / x)));
	elseif (t <= 4.8e+86)
		tmp = t_1;
	else
		tmp = Float64(-2.0 * Float64(x / Float64(z_m * 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)
	t_1 = x * ((2.0 / y) / z_m);
	t_2 = (x / z_m) * (-2.0 / t);
	tmp = 0.0;
	if (t <= -4.5e+59)
		tmp = t_2;
	elseif (t <= -1.25e-8)
		tmp = t_1;
	elseif (t <= -7e-59)
		tmp = t_2;
	elseif (t <= 1.92e+62)
		tmp = 2.0 / (y * (z_m / x));
	elseif (t <= 4.8e+86)
		tmp = t_1;
	else
		tmp = -2.0 * (x / (z_m * 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_] := Block[{t$95$1 = N[(x * N[(N[(2.0 / y), $MachinePrecision] / z$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / z$95$m), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]}, N[(z$95$s * If[LessEqual[t, -4.5e+59], t$95$2, If[LessEqual[t, -1.25e-8], t$95$1, If[LessEqual[t, -7e-59], t$95$2, If[LessEqual[t, 1.92e+62], N[(2.0 / N[(y * N[(z$95$m / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e+86], t$95$1, N[(-2.0 * N[(x / N[(z$95$m * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]), $MachinePrecision]]]

Derivation

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

Alternative 4: 71.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{2}{y}}{z_m}\\ z_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+61}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{z_m}}{t}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-58}:\\ \;\;\;\;\frac{x}{z_m} \cdot \frac{-2}{t}\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{+60}:\\ \;\;\;\;\frac{2}{y \cdot \frac{z_m}{x}}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{x}{z_m \cdot t}\\ \end{array} \end{array} \end{array} \]

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 (* x (/ (/ 2.0 y) z_m))))
   (*
    z_s
    (if (<= t -3.4e+61)
      (/ (/ (* x -2.0) z_m) t)
      (if (<= t -1.7e-8)
        t_1
        (if (<= t -1e-58)
          (* (/ x z_m) (/ -2.0 t))
          (if (<= t 6.1e+60)
            (/ 2.0 (* y (/ z_m x)))
            (if (<= t 5.2e+85) t_1 (* -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) {
	double t_1 = x * ((2.0 / y) / z_m);
	double tmp;
	if (t <= -3.4e+61) {
		tmp = ((x * -2.0) / z_m) / t;
	} else if (t <= -1.7e-8) {
		tmp = t_1;
	} else if (t <= -1e-58) {
		tmp = (x / z_m) * (-2.0 / t);
	} else if (t <= 6.1e+60) {
		tmp = 2.0 / (y * (z_m / x));
	} else if (t <= 5.2e+85) {
		tmp = t_1;
	} else {
		tmp = -2.0 * (x / (z_m * 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) :: t_1
    real(8) :: tmp
    t_1 = x * ((2.0d0 / y) / z_m)
    if (t <= (-3.4d+61)) then
        tmp = ((x * (-2.0d0)) / z_m) / t
    else if (t <= (-1.7d-8)) then
        tmp = t_1
    else if (t <= (-1d-58)) then
        tmp = (x / z_m) * ((-2.0d0) / t)
    else if (t <= 6.1d+60) then
        tmp = 2.0d0 / (y * (z_m / x))
    else if (t <= 5.2d+85) then
        tmp = t_1
    else
        tmp = (-2.0d0) * (x / (z_m * 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 t_1 = x * ((2.0 / y) / z_m);
	double tmp;
	if (t <= -3.4e+61) {
		tmp = ((x * -2.0) / z_m) / t;
	} else if (t <= -1.7e-8) {
		tmp = t_1;
	} else if (t <= -1e-58) {
		tmp = (x / z_m) * (-2.0 / t);
	} else if (t <= 6.1e+60) {
		tmp = 2.0 / (y * (z_m / x));
	} else if (t <= 5.2e+85) {
		tmp = t_1;
	} else {
		tmp = -2.0 * (x / (z_m * 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):
	t_1 = x * ((2.0 / y) / z_m)
	tmp = 0
	if t <= -3.4e+61:
		tmp = ((x * -2.0) / z_m) / t
	elif t <= -1.7e-8:
		tmp = t_1
	elif t <= -1e-58:
		tmp = (x / z_m) * (-2.0 / t)
	elif t <= 6.1e+60:
		tmp = 2.0 / (y * (z_m / x))
	elif t <= 5.2e+85:
		tmp = t_1
	else:
		tmp = -2.0 * (x / (z_m * 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)
	t_1 = Float64(x * Float64(Float64(2.0 / y) / z_m))
	tmp = 0.0
	if (t <= -3.4e+61)
		tmp = Float64(Float64(Float64(x * -2.0) / z_m) / t);
	elseif (t <= -1.7e-8)
		tmp = t_1;
	elseif (t <= -1e-58)
		tmp = Float64(Float64(x / z_m) * Float64(-2.0 / t));
	elseif (t <= 6.1e+60)
		tmp = Float64(2.0 / Float64(y * Float64(z_m / x)));
	elseif (t <= 5.2e+85)
		tmp = t_1;
	else
		tmp = Float64(-2.0 * Float64(x / Float64(z_m * 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)
	t_1 = x * ((2.0 / y) / z_m);
	tmp = 0.0;
	if (t <= -3.4e+61)
		tmp = ((x * -2.0) / z_m) / t;
	elseif (t <= -1.7e-8)
		tmp = t_1;
	elseif (t <= -1e-58)
		tmp = (x / z_m) * (-2.0 / t);
	elseif (t <= 6.1e+60)
		tmp = 2.0 / (y * (z_m / x));
	elseif (t <= 5.2e+85)
		tmp = t_1;
	else
		tmp = -2.0 * (x / (z_m * 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_] := Block[{t$95$1 = N[(x * N[(N[(2.0 / y), $MachinePrecision] / z$95$m), $MachinePrecision]), $MachinePrecision]}, N[(z$95$s * If[LessEqual[t, -3.4e+61], N[(N[(N[(x * -2.0), $MachinePrecision] / z$95$m), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, -1.7e-8], t$95$1, If[LessEqual[t, -1e-58], N[(N[(x / z$95$m), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.1e+60], N[(2.0 / N[(y * N[(z$95$m / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+85], t$95$1, N[(-2.0 * N[(x / N[(z$95$m * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]), $MachinePrecision]]

Derivation

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

Alternative 5: 72.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ z_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{+61} \lor \neg \left(t \leq 1.65 \cdot 10^{+85}\right):\\ \;\;\;\;-2 \cdot \frac{x}{z_m \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{2}{z_m \cdot y}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
z_s = (copysign.f64 1 z)
(FPCore (z_s x y z_m t)
 :precision binary64
 (*
  z_s
  (if (or (<= t -2.55e+61) (not (<= t 1.65e+85)))
    (* -2.0 (/ x (* z_m t)))
    (* x (/ 2.0 (* 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 t) {
	double tmp;
	if ((t <= -2.55e+61) || !(t <= 1.65e+85)) {
		tmp = -2.0 * (x / (z_m * t));
	} else {
		tmp = x * (2.0 / (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, 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 <= (-2.55d+61)) .or. (.not. (t <= 1.65d+85))) then
        tmp = (-2.0d0) * (x / (z_m * t))
    else
        tmp = x * (2.0d0 / (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 t) {
	double tmp;
	if ((t <= -2.55e+61) || !(t <= 1.65e+85)) {
		tmp = -2.0 * (x / (z_m * t));
	} else {
		tmp = x * (2.0 / (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, t):
	tmp = 0
	if (t <= -2.55e+61) or not (t <= 1.65e+85):
		tmp = -2.0 * (x / (z_m * t))
	else:
		tmp = x * (2.0 / (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, t)
	tmp = 0.0
	if ((t <= -2.55e+61) || !(t <= 1.65e+85))
		tmp = Float64(-2.0 * Float64(x / Float64(z_m * t)));
	else
		tmp = Float64(x * Float64(2.0 / 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, t)
	tmp = 0.0;
	if ((t <= -2.55e+61) || ~((t <= 1.65e+85)))
		tmp = -2.0 * (x / (z_m * t));
	else
		tmp = x * (2.0 / (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_, t_] := N[(z$95$s * If[Or[LessEqual[t, -2.55e+61], N[Not[LessEqual[t, 1.65e+85]], $MachinePrecision]], N[(-2.0 * N[(x / N[(z$95$m * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(2.0 / N[(z$95$m * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 6: 72.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ z_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+61}:\\ \;\;\;\;\frac{x}{z_m} \cdot \frac{-2}{t}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \frac{2}{z_m \cdot y}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{x}{z_m \cdot t}\\ \end{array} \end{array} \]

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 (<= t -2.9e+61)
    (* (/ x z_m) (/ -2.0 t))
    (if (<= t 9.6e+84) (* x (/ 2.0 (* z_m y))) (* -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) {
	double tmp;
	if (t <= -2.9e+61) {
		tmp = (x / z_m) * (-2.0 / t);
	} else if (t <= 9.6e+84) {
		tmp = x * (2.0 / (z_m * y));
	} else {
		tmp = -2.0 * (x / (z_m * 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 (t <= (-2.9d+61)) then
        tmp = (x / z_m) * ((-2.0d0) / t)
    else if (t <= 9.6d+84) then
        tmp = x * (2.0d0 / (z_m * y))
    else
        tmp = (-2.0d0) * (x / (z_m * 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 (t <= -2.9e+61) {
		tmp = (x / z_m) * (-2.0 / t);
	} else if (t <= 9.6e+84) {
		tmp = x * (2.0 / (z_m * y));
	} else {
		tmp = -2.0 * (x / (z_m * 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 t <= -2.9e+61:
		tmp = (x / z_m) * (-2.0 / t)
	elif t <= 9.6e+84:
		tmp = x * (2.0 / (z_m * y))
	else:
		tmp = -2.0 * (x / (z_m * 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 (t <= -2.9e+61)
		tmp = Float64(Float64(x / z_m) * Float64(-2.0 / t));
	elseif (t <= 9.6e+84)
		tmp = Float64(x * Float64(2.0 / Float64(z_m * y)));
	else
		tmp = Float64(-2.0 * Float64(x / Float64(z_m * 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 (t <= -2.9e+61)
		tmp = (x / z_m) * (-2.0 / t);
	elseif (t <= 9.6e+84)
		tmp = x * (2.0 / (z_m * y));
	else
		tmp = -2.0 * (x / (z_m * 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[t, -2.9e+61], N[(N[(x / z$95$m), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.6e+84], N[(x * N[(2.0 / N[(z$95$m * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(x / N[(z$95$m * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 7: 96.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ \begin{array}{l} t_1 := \frac{2}{y - t}\\ z_s \cdot \begin{array}{l} \mathbf{if}\;z_m \leq 2 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \frac{t_1}{z_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z_m} \cdot t_1\\ \end{array} \end{array} \end{array} \]

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 2e+53) (* 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 <= 2e+53) {
		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 <= 2d+53) 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 <= 2e+53) {
		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 <= 2e+53:
		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 <= 2e+53)
		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 <= 2e+53)
		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, 2e+53], 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 8: 95.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ z_s = \mathsf{copysign}\left(1, z\right) \\ z_s \cdot \begin{array}{l} \mathbf{if}\;z_m \leq 2.5 \cdot 10^{+140}:\\ \;\;\;\;\frac{x \cdot 2}{z_m \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z_m} \cdot \frac{2}{y - t}\\ \end{array} \end{array} \]

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 2.5e+140)
    (/ (* 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 <= 2.5e+140) {
		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 <= 2.5d+140) 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 <= 2.5e+140) {
		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 <= 2.5e+140:
		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 <= 2.5e+140)
		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 <= 2.5e+140)
		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, 2.5e+140], 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 9: 92.5% 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 10: 53.2% 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 2023343 
(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))))