Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3

Percentage Accurate: 96.7% → 98.0%

Time: 8.4s

Alternatives: 9

Speedup: 1.3×

• 24.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot y - z \cdot y\right) \cdot t \end{array} \]

FPCore

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

C

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

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 * y) - (z * y)) * t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot y - z \cdot y\right) \cdot t \end{array} \]

FPCore

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

C

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

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 * y) - (z * y)) * t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t_s \cdot \left(y_s \cdot \begin{array}{l} \mathbf{if}\;t_m \leq 5 \cdot 10^{-52}:\\ \;\;\;\;y_m \cdot \left(\left(x - z\right) \cdot t_m\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y_m \cdot t_m\right)\\ \end{array}\right) \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
(FPCore (t_s y_s x y_m z t_m)
 :precision binary64
 (*
  t_s
  (* y_s (if (<= t_m 5e-52) (* y_m (* (- x z) t_m)) (* (- x z) (* y_m t_m))))))

C

y_m = fabs(y);
y_s = copysign(1.0, y);
t_m = fabs(t);
t_s = copysign(1.0, t);
assert(x < y_m && y_m < z && z < t_m);
double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	double tmp;
	if (t_m <= 5e-52) {
		tmp = y_m * ((x - z) * t_m);
	} else {
		tmp = (x - z) * (y_m * t_m);
	}
	return t_s * (y_s * tmp);
}

Fortran

y_m = abs(y)
y_s = copysign(1.0d0, y)
t_m = abs(t)
t_s = copysign(1.0d0, t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
real(8) function code(t_s, y_s, x, y_m, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if (t_m <= 5d-52) then
        tmp = y_m * ((x - z) * t_m)
    else
        tmp = (x - z) * (y_m * t_m)
    end if
    code = t_s * (y_s * tmp)
end function

Java

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
t_m = Math.abs(t);
t_s = Math.copySign(1.0, t);
assert x < y_m && y_m < z && z < t_m;
public static double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	double tmp;
	if (t_m <= 5e-52) {
		tmp = y_m * ((x - z) * t_m);
	} else {
		tmp = (x - z) * (y_m * t_m);
	}
	return t_s * (y_s * tmp);
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
[x, y_m, z, t_m] = sort([x, y_m, z, t_m])
def code(t_s, y_s, x, y_m, z, t_m):
	tmp = 0
	if t_m <= 5e-52:
		tmp = y_m * ((x - z) * t_m)
	else:
		tmp = (x - z) * (y_m * t_m)
	return t_s * (y_s * tmp)

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
t_m = abs(t)
t_s = copysign(1.0, t)
x, y_m, z, t_m = sort([x, y_m, z, t_m])
function code(t_s, y_s, x, y_m, z, t_m)
	tmp = 0.0
	if (t_m <= 5e-52)
		tmp = Float64(y_m * Float64(Float64(x - z) * t_m));
	else
		tmp = Float64(Float64(x - z) * Float64(y_m * t_m));
	end
	return Float64(t_s * Float64(y_s * tmp))
end

MATLAB

y_m = abs(y);
y_s = sign(y) * abs(1.0);
t_m = abs(t);
t_s = sign(t) * abs(1.0);
x, y_m, z, t_m = num2cell(sort([x, y_m, z, t_m])){:}
function tmp_2 = code(t_s, y_s, x, y_m, z, t_m)
	tmp = 0.0;
	if (t_m <= 5e-52)
		tmp = y_m * ((x - z) * t_m);
	else
		tmp = (x - z) * (y_m * t_m);
	end
	tmp_2 = t_s * (y_s * tmp);
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
t_m = N[Abs[t], $MachinePrecision]
t_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
code[t$95$s_, y$95$s_, x_, y$95$m_, z_, t$95$m_] := N[(t$95$s * N[(y$95$s * If[LessEqual[t$95$m, 5e-52], N[(y$95$m * N[(N[(x - z), $MachinePrecision] * t$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(x - z), $MachinePrecision] * N[(y$95$m * t$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 2: 77.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ \begin{array}{l} t_2 := \left(y_m \cdot z\right) \cdot \left(-t_m\right)\\ t_s \cdot \left(y_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(y_m \cdot t_m\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-16}:\\ \;\;\;\;-y_m \cdot \left(z \cdot t_m\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-66} \lor \neg \left(z \leq 0.000285\right) \land z \leq 2.6 \cdot 10^{+58}:\\ \;\;\;\;t_m \cdot \left(y_m \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array}\right) \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
(FPCore (t_s y_s x y_m z t_m)
 :precision binary64
 (let* ((t_2 (* (* y_m z) (- t_m))))
   (*
    t_s
    (*
     y_s
     (if (<= z -1.8e+49)
       t_2
       (if (<= z -1.45e+16)
         (* x (* y_m t_m))
         (if (<= z -1.15e-16)
           (- (* y_m (* z t_m)))
           (if (or (<= z 8e-66) (and (not (<= z 0.000285)) (<= z 2.6e+58)))
             (* t_m (* y_m x))
             t_2))))))))

C

y_m = fabs(y);
y_s = copysign(1.0, y);
t_m = fabs(t);
t_s = copysign(1.0, t);
assert(x < y_m && y_m < z && z < t_m);
double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	double t_2 = (y_m * z) * -t_m;
	double tmp;
	if (z <= -1.8e+49) {
		tmp = t_2;
	} else if (z <= -1.45e+16) {
		tmp = x * (y_m * t_m);
	} else if (z <= -1.15e-16) {
		tmp = -(y_m * (z * t_m));
	} else if ((z <= 8e-66) || (!(z <= 0.000285) && (z <= 2.6e+58))) {
		tmp = t_m * (y_m * x);
	} else {
		tmp = t_2;
	}
	return t_s * (y_s * tmp);
}

Fortran

y_m = abs(y)
y_s = copysign(1.0d0, y)
t_m = abs(t)
t_s = copysign(1.0d0, t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
real(8) function code(t_s, y_s, x, y_m, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: t_2
    real(8) :: tmp
    t_2 = (y_m * z) * -t_m
    if (z <= (-1.8d+49)) then
        tmp = t_2
    else if (z <= (-1.45d+16)) then
        tmp = x * (y_m * t_m)
    else if (z <= (-1.15d-16)) then
        tmp = -(y_m * (z * t_m))
    else if ((z <= 8d-66) .or. (.not. (z <= 0.000285d0)) .and. (z <= 2.6d+58)) then
        tmp = t_m * (y_m * x)
    else
        tmp = t_2
    end if
    code = t_s * (y_s * tmp)
end function

Java

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
t_m = Math.abs(t);
t_s = Math.copySign(1.0, t);
assert x < y_m && y_m < z && z < t_m;
public static double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	double t_2 = (y_m * z) * -t_m;
	double tmp;
	if (z <= -1.8e+49) {
		tmp = t_2;
	} else if (z <= -1.45e+16) {
		tmp = x * (y_m * t_m);
	} else if (z <= -1.15e-16) {
		tmp = -(y_m * (z * t_m));
	} else if ((z <= 8e-66) || (!(z <= 0.000285) && (z <= 2.6e+58))) {
		tmp = t_m * (y_m * x);
	} else {
		tmp = t_2;
	}
	return t_s * (y_s * tmp);
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
[x, y_m, z, t_m] = sort([x, y_m, z, t_m])
def code(t_s, y_s, x, y_m, z, t_m):
	t_2 = (y_m * z) * -t_m
	tmp = 0
	if z <= -1.8e+49:
		tmp = t_2
	elif z <= -1.45e+16:
		tmp = x * (y_m * t_m)
	elif z <= -1.15e-16:
		tmp = -(y_m * (z * t_m))
	elif (z <= 8e-66) or (not (z <= 0.000285) and (z <= 2.6e+58)):
		tmp = t_m * (y_m * x)
	else:
		tmp = t_2
	return t_s * (y_s * tmp)

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
t_m = abs(t)
t_s = copysign(1.0, t)
x, y_m, z, t_m = sort([x, y_m, z, t_m])
function code(t_s, y_s, x, y_m, z, t_m)
	t_2 = Float64(Float64(y_m * z) * Float64(-t_m))
	tmp = 0.0
	if (z <= -1.8e+49)
		tmp = t_2;
	elseif (z <= -1.45e+16)
		tmp = Float64(x * Float64(y_m * t_m));
	elseif (z <= -1.15e-16)
		tmp = Float64(-Float64(y_m * Float64(z * t_m)));
	elseif ((z <= 8e-66) || (!(z <= 0.000285) && (z <= 2.6e+58)))
		tmp = Float64(t_m * Float64(y_m * x));
	else
		tmp = t_2;
	end
	return Float64(t_s * Float64(y_s * tmp))
end

MATLAB

y_m = abs(y);
y_s = sign(y) * abs(1.0);
t_m = abs(t);
t_s = sign(t) * abs(1.0);
x, y_m, z, t_m = num2cell(sort([x, y_m, z, t_m])){:}
function tmp_2 = code(t_s, y_s, x, y_m, z, t_m)
	t_2 = (y_m * z) * -t_m;
	tmp = 0.0;
	if (z <= -1.8e+49)
		tmp = t_2;
	elseif (z <= -1.45e+16)
		tmp = x * (y_m * t_m);
	elseif (z <= -1.15e-16)
		tmp = -(y_m * (z * t_m));
	elseif ((z <= 8e-66) || (~((z <= 0.000285)) && (z <= 2.6e+58)))
		tmp = t_m * (y_m * x);
	else
		tmp = t_2;
	end
	tmp_2 = t_s * (y_s * tmp);
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
t_m = N[Abs[t], $MachinePrecision]
t_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
code[t$95$s_, y$95$s_, x_, y$95$m_, z_, t$95$m_] := Block[{t$95$2 = N[(N[(y$95$m * z), $MachinePrecision] * (-t$95$m)), $MachinePrecision]}, N[(t$95$s * N[(y$95$s * If[LessEqual[z, -1.8e+49], t$95$2, If[LessEqual[z, -1.45e+16], N[(x * N[(y$95$m * t$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.15e-16], (-N[(y$95$m * N[(z * t$95$m), $MachinePrecision]), $MachinePrecision]), If[Or[LessEqual[z, 8e-66], And[N[Not[LessEqual[z, 0.000285]], $MachinePrecision], LessEqual[z, 2.6e+58]]], N[(t$95$m * N[(y$95$m * x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 3: 89.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t_s \cdot \left(y_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+202} \lor \neg \left(z \leq 1.9 \cdot 10^{+95}\right):\\ \;\;\;\;\left(y_m \cdot z\right) \cdot \left(-t_m\right)\\ \mathbf{else}:\\ \;\;\;\;y_m \cdot \left(\left(x - z\right) \cdot t_m\right)\\ \end{array}\right) \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
(FPCore (t_s y_s x y_m z t_m)
 :precision binary64
 (*
  t_s
  (*
   y_s
   (if (or (<= z -6.5e+202) (not (<= z 1.9e+95)))
     (* (* y_m z) (- t_m))
     (* y_m (* (- x z) t_m))))))

C

y_m = fabs(y);
y_s = copysign(1.0, y);
t_m = fabs(t);
t_s = copysign(1.0, t);
assert(x < y_m && y_m < z && z < t_m);
double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	double tmp;
	if ((z <= -6.5e+202) || !(z <= 1.9e+95)) {
		tmp = (y_m * z) * -t_m;
	} else {
		tmp = y_m * ((x - z) * t_m);
	}
	return t_s * (y_s * tmp);
}

Fortran

y_m = abs(y)
y_s = copysign(1.0d0, y)
t_m = abs(t)
t_s = copysign(1.0d0, t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
real(8) function code(t_s, y_s, x, y_m, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if ((z <= (-6.5d+202)) .or. (.not. (z <= 1.9d+95))) then
        tmp = (y_m * z) * -t_m
    else
        tmp = y_m * ((x - z) * t_m)
    end if
    code = t_s * (y_s * tmp)
end function

Java

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
t_m = Math.abs(t);
t_s = Math.copySign(1.0, t);
assert x < y_m && y_m < z && z < t_m;
public static double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	double tmp;
	if ((z <= -6.5e+202) || !(z <= 1.9e+95)) {
		tmp = (y_m * z) * -t_m;
	} else {
		tmp = y_m * ((x - z) * t_m);
	}
	return t_s * (y_s * tmp);
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
[x, y_m, z, t_m] = sort([x, y_m, z, t_m])
def code(t_s, y_s, x, y_m, z, t_m):
	tmp = 0
	if (z <= -6.5e+202) or not (z <= 1.9e+95):
		tmp = (y_m * z) * -t_m
	else:
		tmp = y_m * ((x - z) * t_m)
	return t_s * (y_s * tmp)

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
t_m = abs(t)
t_s = copysign(1.0, t)
x, y_m, z, t_m = sort([x, y_m, z, t_m])
function code(t_s, y_s, x, y_m, z, t_m)
	tmp = 0.0
	if ((z <= -6.5e+202) || !(z <= 1.9e+95))
		tmp = Float64(Float64(y_m * z) * Float64(-t_m));
	else
		tmp = Float64(y_m * Float64(Float64(x - z) * t_m));
	end
	return Float64(t_s * Float64(y_s * tmp))
end

MATLAB

y_m = abs(y);
y_s = sign(y) * abs(1.0);
t_m = abs(t);
t_s = sign(t) * abs(1.0);
x, y_m, z, t_m = num2cell(sort([x, y_m, z, t_m])){:}
function tmp_2 = code(t_s, y_s, x, y_m, z, t_m)
	tmp = 0.0;
	if ((z <= -6.5e+202) || ~((z <= 1.9e+95)))
		tmp = (y_m * z) * -t_m;
	else
		tmp = y_m * ((x - z) * t_m);
	end
	tmp_2 = t_s * (y_s * tmp);
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
t_m = N[Abs[t], $MachinePrecision]
t_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
code[t$95$s_, y$95$s_, x_, y$95$m_, z_, t$95$m_] := N[(t$95$s * N[(y$95$s * If[Or[LessEqual[z, -6.5e+202], N[Not[LessEqual[z, 1.9e+95]], $MachinePrecision]], N[(N[(y$95$m * z), $MachinePrecision] * (-t$95$m)), $MachinePrecision], N[(y$95$m * N[(N[(x - z), $MachinePrecision] * t$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 4: 72.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t_s \cdot \left(y_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+43} \lor \neg \left(x \leq 9 \cdot 10^{+129}\right):\\ \;\;\;\;t_m \cdot \left(y_m \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;-y_m \cdot \left(z \cdot t_m\right)\\ \end{array}\right) \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
(FPCore (t_s y_s x y_m z t_m)
 :precision binary64
 (*
  t_s
  (*
   y_s
   (if (or (<= x -5.8e+43) (not (<= x 9e+129)))
     (* t_m (* y_m x))
     (- (* y_m (* z t_m)))))))

C

y_m = fabs(y);
y_s = copysign(1.0, y);
t_m = fabs(t);
t_s = copysign(1.0, t);
assert(x < y_m && y_m < z && z < t_m);
double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	double tmp;
	if ((x <= -5.8e+43) || !(x <= 9e+129)) {
		tmp = t_m * (y_m * x);
	} else {
		tmp = -(y_m * (z * t_m));
	}
	return t_s * (y_s * tmp);
}

Fortran

y_m = abs(y)
y_s = copysign(1.0d0, y)
t_m = abs(t)
t_s = copysign(1.0d0, t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
real(8) function code(t_s, y_s, x, y_m, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if ((x <= (-5.8d+43)) .or. (.not. (x <= 9d+129))) then
        tmp = t_m * (y_m * x)
    else
        tmp = -(y_m * (z * t_m))
    end if
    code = t_s * (y_s * tmp)
end function

Java

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
t_m = Math.abs(t);
t_s = Math.copySign(1.0, t);
assert x < y_m && y_m < z && z < t_m;
public static double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	double tmp;
	if ((x <= -5.8e+43) || !(x <= 9e+129)) {
		tmp = t_m * (y_m * x);
	} else {
		tmp = -(y_m * (z * t_m));
	}
	return t_s * (y_s * tmp);
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
[x, y_m, z, t_m] = sort([x, y_m, z, t_m])
def code(t_s, y_s, x, y_m, z, t_m):
	tmp = 0
	if (x <= -5.8e+43) or not (x <= 9e+129):
		tmp = t_m * (y_m * x)
	else:
		tmp = -(y_m * (z * t_m))
	return t_s * (y_s * tmp)

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
t_m = abs(t)
t_s = copysign(1.0, t)
x, y_m, z, t_m = sort([x, y_m, z, t_m])
function code(t_s, y_s, x, y_m, z, t_m)
	tmp = 0.0
	if ((x <= -5.8e+43) || !(x <= 9e+129))
		tmp = Float64(t_m * Float64(y_m * x));
	else
		tmp = Float64(-Float64(y_m * Float64(z * t_m)));
	end
	return Float64(t_s * Float64(y_s * tmp))
end

MATLAB

y_m = abs(y);
y_s = sign(y) * abs(1.0);
t_m = abs(t);
t_s = sign(t) * abs(1.0);
x, y_m, z, t_m = num2cell(sort([x, y_m, z, t_m])){:}
function tmp_2 = code(t_s, y_s, x, y_m, z, t_m)
	tmp = 0.0;
	if ((x <= -5.8e+43) || ~((x <= 9e+129)))
		tmp = t_m * (y_m * x);
	else
		tmp = -(y_m * (z * t_m));
	end
	tmp_2 = t_s * (y_s * tmp);
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
t_m = N[Abs[t], $MachinePrecision]
t_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
code[t$95$s_, y$95$s_, x_, y$95$m_, z_, t$95$m_] := N[(t$95$s * N[(y$95$s * If[Or[LessEqual[x, -5.8e+43], N[Not[LessEqual[x, 9e+129]], $MachinePrecision]], N[(t$95$m * N[(y$95$m * x), $MachinePrecision]), $MachinePrecision], (-N[(y$95$m * N[(z * t$95$m), $MachinePrecision]), $MachinePrecision])]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 5: 72.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t_s \cdot \left(y_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+75} \lor \neg \left(x \leq 6.2 \cdot 10^{+178}\right):\\ \;\;\;\;t_m \cdot \left(y_m \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y_m \cdot \left(-t_m\right)\right)\\ \end{array}\right) \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
(FPCore (t_s y_s x y_m z t_m)
 :precision binary64
 (*
  t_s
  (*
   y_s
   (if (or (<= x -6.5e+75) (not (<= x 6.2e+178)))
     (* t_m (* y_m x))
     (* z (* y_m (- t_m)))))))

C

y_m = fabs(y);
y_s = copysign(1.0, y);
t_m = fabs(t);
t_s = copysign(1.0, t);
assert(x < y_m && y_m < z && z < t_m);
double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	double tmp;
	if ((x <= -6.5e+75) || !(x <= 6.2e+178)) {
		tmp = t_m * (y_m * x);
	} else {
		tmp = z * (y_m * -t_m);
	}
	return t_s * (y_s * tmp);
}

Fortran

y_m = abs(y)
y_s = copysign(1.0d0, y)
t_m = abs(t)
t_s = copysign(1.0d0, t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
real(8) function code(t_s, y_s, x, y_m, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if ((x <= (-6.5d+75)) .or. (.not. (x <= 6.2d+178))) then
        tmp = t_m * (y_m * x)
    else
        tmp = z * (y_m * -t_m)
    end if
    code = t_s * (y_s * tmp)
end function

Java

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
t_m = Math.abs(t);
t_s = Math.copySign(1.0, t);
assert x < y_m && y_m < z && z < t_m;
public static double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	double tmp;
	if ((x <= -6.5e+75) || !(x <= 6.2e+178)) {
		tmp = t_m * (y_m * x);
	} else {
		tmp = z * (y_m * -t_m);
	}
	return t_s * (y_s * tmp);
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
[x, y_m, z, t_m] = sort([x, y_m, z, t_m])
def code(t_s, y_s, x, y_m, z, t_m):
	tmp = 0
	if (x <= -6.5e+75) or not (x <= 6.2e+178):
		tmp = t_m * (y_m * x)
	else:
		tmp = z * (y_m * -t_m)
	return t_s * (y_s * tmp)

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
t_m = abs(t)
t_s = copysign(1.0, t)
x, y_m, z, t_m = sort([x, y_m, z, t_m])
function code(t_s, y_s, x, y_m, z, t_m)
	tmp = 0.0
	if ((x <= -6.5e+75) || !(x <= 6.2e+178))
		tmp = Float64(t_m * Float64(y_m * x));
	else
		tmp = Float64(z * Float64(y_m * Float64(-t_m)));
	end
	return Float64(t_s * Float64(y_s * tmp))
end

MATLAB

y_m = abs(y);
y_s = sign(y) * abs(1.0);
t_m = abs(t);
t_s = sign(t) * abs(1.0);
x, y_m, z, t_m = num2cell(sort([x, y_m, z, t_m])){:}
function tmp_2 = code(t_s, y_s, x, y_m, z, t_m)
	tmp = 0.0;
	if ((x <= -6.5e+75) || ~((x <= 6.2e+178)))
		tmp = t_m * (y_m * x);
	else
		tmp = z * (y_m * -t_m);
	end
	tmp_2 = t_s * (y_s * tmp);
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
t_m = N[Abs[t], $MachinePrecision]
t_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
code[t$95$s_, y$95$s_, x_, y$95$m_, z_, t$95$m_] := N[(t$95$s * N[(y$95$s * If[Or[LessEqual[x, -6.5e+75], N[Not[LessEqual[x, 6.2e+178]], $MachinePrecision]], N[(t$95$m * N[(y$95$m * x), $MachinePrecision]), $MachinePrecision], N[(z * N[(y$95$m * (-t$95$m)), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 6: 57.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t_s \cdot \left(y_s \cdot \begin{array}{l} \mathbf{if}\;t_m \leq 5.2 \cdot 10^{-84}:\\ \;\;\;\;y_m \cdot \left(x \cdot t_m\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y_m \cdot t_m\right)\\ \end{array}\right) \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
(FPCore (t_s y_s x y_m z t_m)
 :precision binary64
 (* t_s (* y_s (if (<= t_m 5.2e-84) (* y_m (* x t_m)) (* x (* y_m t_m))))))

C

y_m = fabs(y);
y_s = copysign(1.0, y);
t_m = fabs(t);
t_s = copysign(1.0, t);
assert(x < y_m && y_m < z && z < t_m);
double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	double tmp;
	if (t_m <= 5.2e-84) {
		tmp = y_m * (x * t_m);
	} else {
		tmp = x * (y_m * t_m);
	}
	return t_s * (y_s * tmp);
}

Fortran

y_m = abs(y)
y_s = copysign(1.0d0, y)
t_m = abs(t)
t_s = copysign(1.0d0, t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
real(8) function code(t_s, y_s, x, y_m, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if (t_m <= 5.2d-84) then
        tmp = y_m * (x * t_m)
    else
        tmp = x * (y_m * t_m)
    end if
    code = t_s * (y_s * tmp)
end function

Java

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
t_m = Math.abs(t);
t_s = Math.copySign(1.0, t);
assert x < y_m && y_m < z && z < t_m;
public static double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	double tmp;
	if (t_m <= 5.2e-84) {
		tmp = y_m * (x * t_m);
	} else {
		tmp = x * (y_m * t_m);
	}
	return t_s * (y_s * tmp);
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
[x, y_m, z, t_m] = sort([x, y_m, z, t_m])
def code(t_s, y_s, x, y_m, z, t_m):
	tmp = 0
	if t_m <= 5.2e-84:
		tmp = y_m * (x * t_m)
	else:
		tmp = x * (y_m * t_m)
	return t_s * (y_s * tmp)

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
t_m = abs(t)
t_s = copysign(1.0, t)
x, y_m, z, t_m = sort([x, y_m, z, t_m])
function code(t_s, y_s, x, y_m, z, t_m)
	tmp = 0.0
	if (t_m <= 5.2e-84)
		tmp = Float64(y_m * Float64(x * t_m));
	else
		tmp = Float64(x * Float64(y_m * t_m));
	end
	return Float64(t_s * Float64(y_s * tmp))
end

MATLAB

y_m = abs(y);
y_s = sign(y) * abs(1.0);
t_m = abs(t);
t_s = sign(t) * abs(1.0);
x, y_m, z, t_m = num2cell(sort([x, y_m, z, t_m])){:}
function tmp_2 = code(t_s, y_s, x, y_m, z, t_m)
	tmp = 0.0;
	if (t_m <= 5.2e-84)
		tmp = y_m * (x * t_m);
	else
		tmp = x * (y_m * t_m);
	end
	tmp_2 = t_s * (y_s * tmp);
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
t_m = N[Abs[t], $MachinePrecision]
t_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
code[t$95$s_, y$95$s_, x_, y$95$m_, z_, t$95$m_] := N[(t$95$s * N[(y$95$s * If[LessEqual[t$95$m, 5.2e-84], N[(y$95$m * N[(x * t$95$m), $MachinePrecision]), $MachinePrecision], N[(x * N[(y$95$m * t$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 7: 97.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t_s \cdot \left(y_s \cdot \left(\left(y_m \cdot \left(x - z\right)\right) \cdot t_m\right)\right) \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
(FPCore (t_s y_s x y_m z t_m)
 :precision binary64
 (* t_s (* y_s (* (* y_m (- x z)) t_m))))

C

y_m = fabs(y);
y_s = copysign(1.0, y);
t_m = fabs(t);
t_s = copysign(1.0, t);
assert(x < y_m && y_m < z && z < t_m);
double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	return t_s * (y_s * ((y_m * (x - z)) * t_m));
}

Fortran

y_m = abs(y)
y_s = copysign(1.0d0, y)
t_m = abs(t)
t_s = copysign(1.0d0, t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
real(8) function code(t_s, y_s, x, y_m, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    code = t_s * (y_s * ((y_m * (x - z)) * t_m))
end function

Java

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
t_m = Math.abs(t);
t_s = Math.copySign(1.0, t);
assert x < y_m && y_m < z && z < t_m;
public static double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	return t_s * (y_s * ((y_m * (x - z)) * t_m));
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
[x, y_m, z, t_m] = sort([x, y_m, z, t_m])
def code(t_s, y_s, x, y_m, z, t_m):
	return t_s * (y_s * ((y_m * (x - z)) * t_m))

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
t_m = abs(t)
t_s = copysign(1.0, t)
x, y_m, z, t_m = sort([x, y_m, z, t_m])
function code(t_s, y_s, x, y_m, z, t_m)
	return Float64(t_s * Float64(y_s * Float64(Float64(y_m * Float64(x - z)) * t_m)))
end

MATLAB

y_m = abs(y);
y_s = sign(y) * abs(1.0);
t_m = abs(t);
t_s = sign(t) * abs(1.0);
x, y_m, z, t_m = num2cell(sort([x, y_m, z, t_m])){:}
function tmp = code(t_s, y_s, x, y_m, z, t_m)
	tmp = t_s * (y_s * ((y_m * (x - z)) * t_m));
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
t_m = N[Abs[t], $MachinePrecision]
t_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
code[t$95$s_, y$95$s_, x_, y$95$m_, z_, t$95$m_] := N[(t$95$s * N[(y$95$s * N[(N[(y$95$m * N[(x - z), $MachinePrecision]), $MachinePrecision] * t$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 8: 51.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t_s \cdot \left(y_s \cdot \left(y_m \cdot \left(x \cdot t_m\right)\right)\right) \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
(FPCore (t_s y_s x y_m z t_m)
 :precision binary64
 (* t_s (* y_s (* y_m (* x t_m)))))

C

y_m = fabs(y);
y_s = copysign(1.0, y);
t_m = fabs(t);
t_s = copysign(1.0, t);
assert(x < y_m && y_m < z && z < t_m);
double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	return t_s * (y_s * (y_m * (x * t_m)));
}

Fortran

y_m = abs(y)
y_s = copysign(1.0d0, y)
t_m = abs(t)
t_s = copysign(1.0d0, t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
real(8) function code(t_s, y_s, x, y_m, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    code = t_s * (y_s * (y_m * (x * t_m)))
end function

Java

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
t_m = Math.abs(t);
t_s = Math.copySign(1.0, t);
assert x < y_m && y_m < z && z < t_m;
public static double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	return t_s * (y_s * (y_m * (x * t_m)));
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
[x, y_m, z, t_m] = sort([x, y_m, z, t_m])
def code(t_s, y_s, x, y_m, z, t_m):
	return t_s * (y_s * (y_m * (x * t_m)))

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
t_m = abs(t)
t_s = copysign(1.0, t)
x, y_m, z, t_m = sort([x, y_m, z, t_m])
function code(t_s, y_s, x, y_m, z, t_m)
	return Float64(t_s * Float64(y_s * Float64(y_m * Float64(x * t_m))))
end

MATLAB

y_m = abs(y);
y_s = sign(y) * abs(1.0);
t_m = abs(t);
t_s = sign(t) * abs(1.0);
x, y_m, z, t_m = num2cell(sort([x, y_m, z, t_m])){:}
function tmp = code(t_s, y_s, x, y_m, z, t_m)
	tmp = t_s * (y_s * (y_m * (x * t_m)));
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
t_m = N[Abs[t], $MachinePrecision]
t_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
code[t$95$s_, y$95$s_, x_, y$95$m_, z_, t$95$m_] := N[(t$95$s * N[(y$95$s * N[(y$95$m * N[(x * t$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 9: 56.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t_s \cdot \left(y_s \cdot \left(t_m \cdot \left(y_m \cdot x\right)\right)\right) \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
(FPCore (t_s y_s x y_m z t_m)
 :precision binary64
 (* t_s (* y_s (* t_m (* y_m x)))))

C

y_m = fabs(y);
y_s = copysign(1.0, y);
t_m = fabs(t);
t_s = copysign(1.0, t);
assert(x < y_m && y_m < z && z < t_m);
double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	return t_s * (y_s * (t_m * (y_m * x)));
}

Fortran

y_m = abs(y)
y_s = copysign(1.0d0, y)
t_m = abs(t)
t_s = copysign(1.0d0, t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
real(8) function code(t_s, y_s, x, y_m, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    code = t_s * (y_s * (t_m * (y_m * x)))
end function

Java

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
t_m = Math.abs(t);
t_s = Math.copySign(1.0, t);
assert x < y_m && y_m < z && z < t_m;
public static double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	return t_s * (y_s * (t_m * (y_m * x)));
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
[x, y_m, z, t_m] = sort([x, y_m, z, t_m])
def code(t_s, y_s, x, y_m, z, t_m):
	return t_s * (y_s * (t_m * (y_m * x)))

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
t_m = abs(t)
t_s = copysign(1.0, t)
x, y_m, z, t_m = sort([x, y_m, z, t_m])
function code(t_s, y_s, x, y_m, z, t_m)
	return Float64(t_s * Float64(y_s * Float64(t_m * Float64(y_m * x))))
end

MATLAB

y_m = abs(y);
y_s = sign(y) * abs(1.0);
t_m = abs(t);
t_s = sign(t) * abs(1.0);
x, y_m, z, t_m = num2cell(sort([x, y_m, z, t_m])){:}
function tmp = code(t_s, y_s, x, y_m, z, t_m)
	tmp = t_s * (y_s * (t_m * (y_m * x)));
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
t_m = N[Abs[t], $MachinePrecision]
t_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
code[t$95$s_, y$95$s_, x_, y$95$m_, z_, t$95$m_] := N[(t$95$s * N[(y$95$s * N[(t$95$m * N[(y$95$m * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Developer target: 95.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t < -9.231879582886777 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t < 2.543067051564877 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (< t -9.231879582886777e-80)
   (* (* y t) (- x z))
   (if (< t 2.543067051564877e+83) (* y (* t (- x z))) (* (* y (- x z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t < -9.231879582886777e-80) {
		tmp = (y * t) * (x - z);
	} else if (t < 2.543067051564877e+83) {
		tmp = y * (t * (x - z));
	} else {
		tmp = (y * (x - z)) * t;
	}
	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) :: tmp
    if (t < (-9.231879582886777d-80)) then
        tmp = (y * t) * (x - z)
    else if (t < 2.543067051564877d+83) then
        tmp = y * (t * (x - z))
    else
        tmp = (y * (x - z)) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t < -9.231879582886777e-80) {
		tmp = (y * t) * (x - z);
	} else if (t < 2.543067051564877e+83) {
		tmp = y * (t * (x - z));
	} else {
		tmp = (y * (x - z)) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t < -9.231879582886777e-80:
		tmp = (y * t) * (x - z)
	elif t < 2.543067051564877e+83:
		tmp = y * (t * (x - z))
	else:
		tmp = (y * (x - z)) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t < -9.231879582886777e-80)
		tmp = Float64(Float64(y * t) * Float64(x - z));
	elseif (t < 2.543067051564877e+83)
		tmp = Float64(y * Float64(t * Float64(x - z)));
	else
		tmp = Float64(Float64(y * Float64(x - z)) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t < -9.231879582886777e-80)
		tmp = (y * t) * (x - z);
	elseif (t < 2.543067051564877e+83)
		tmp = y * (t * (x - z));
	else
		tmp = (y * (x - z)) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Less[t, -9.231879582886777e-80], N[(N[(y * t), $MachinePrecision] * N[(x - z), $MachinePrecision]), $MachinePrecision], If[Less[t, 2.543067051564877e+83], N[(y * N[(t * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023350 
(FPCore (x y z t)
  :name "Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -9.231879582886777e-80) (* (* y t) (- x z)) (if (< t 2.543067051564877e+83) (* y (* t (- x z))) (* (* y (- x z)) t)))

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