Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3

Percentage Accurate: 96.2% → 99.5%

Time: 10.7s

Alternatives: 9

Speedup: 0.7×

• 25.2% 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: 96.2% 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: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ \begin{array}{l} t_2 := \left(x \cdot y\_m - y\_m \cdot z\right) \cdot t\_m\\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+32} \lor \neg \left(t\_2 \leq 0\right):\\ \;\;\;\;t\_m \cdot \left(y\_m \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y\_m \cdot \left(t\_m \cdot \left(x - z\right)\right)\\ \end{array}\right) \end{array} \end{array} \]

FPCore

y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) y)
t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) 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 (* (- (* x y_m) (* y_m z)) t_m)))
   (*
    t_s
    (*
     y_s
     (if (or (<= t_2 -2e+32) (not (<= t_2 0.0)))
       (* t_m (* y_m (- x z)))
       (* y_m (* t_m (- x z))))))))

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 = ((x * y_m) - (y_m * z)) * t_m;
	double tmp;
	if ((t_2 <= -2e+32) || !(t_2 <= 0.0)) {
		tmp = t_m * (y_m * (x - z));
	} else {
		tmp = y_m * (t_m * (x - z));
	}
	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 = ((x * y_m) - (y_m * z)) * t_m
    if ((t_2 <= (-2d+32)) .or. (.not. (t_2 <= 0.0d0))) then
        tmp = t_m * (y_m * (x - z))
    else
        tmp = y_m * (t_m * (x - z))
    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 = ((x * y_m) - (y_m * z)) * t_m;
	double tmp;
	if ((t_2 <= -2e+32) || !(t_2 <= 0.0)) {
		tmp = t_m * (y_m * (x - z));
	} else {
		tmp = y_m * (t_m * (x - z));
	}
	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 = ((x * y_m) - (y_m * z)) * t_m
	tmp = 0
	if (t_2 <= -2e+32) or not (t_2 <= 0.0):
		tmp = t_m * (y_m * (x - z))
	else:
		tmp = y_m * (t_m * (x - z))
	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(Float64(x * y_m) - Float64(y_m * z)) * t_m)
	tmp = 0.0
	if ((t_2 <= -2e+32) || !(t_2 <= 0.0))
		tmp = Float64(t_m * Float64(y_m * Float64(x - z)));
	else
		tmp = Float64(y_m * Float64(t_m * Float64(x - z)));
	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 = ((x * y_m) - (y_m * z)) * t_m;
	tmp = 0.0;
	if ((t_2 <= -2e+32) || ~((t_2 <= 0.0)))
		tmp = t_m * (y_m * (x - z));
	else
		tmp = y_m * (t_m * (x - z));
	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[(N[(x * y$95$m), $MachinePrecision] - N[(y$95$m * z), $MachinePrecision]), $MachinePrecision] * t$95$m), $MachinePrecision]}, N[(t$95$s * N[(y$95$s * If[Or[LessEqual[t$95$2, -2e+32], N[Not[LessEqual[t$95$2, 0.0]], $MachinePrecision]], N[(t$95$m * N[(y$95$m * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y$95$m * N[(t$95$m * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t) < -2.00000000000000011e32 or 0.0 < (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t)

   1. Initial program 90.6%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 92.6%

         \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right)} \cdot t \]

   3. Simplified 92.6%

      \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right) \cdot t} \]
   4. Add Preprocessing

   if -2.00000000000000011e32 < (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t) < 0.0

   1. Initial program 92.3%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 92.3%

         \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right)} \cdot t \]

      2. associate-*l* 97.3%

         \[\leadsto \color{blue}{y \cdot \left(\left(x - z\right) \cdot t\right)} \]

      3. *-commutative 97.3%

         \[\leadsto y \cdot \color{blue}{\left(t \cdot \left(x - z\right)\right)} \]

   3. Simplified 97.3%

      \[\leadsto \color{blue}{y \cdot \left(t \cdot \left(x - z\right)\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y - y \cdot z\right) \cdot t \leq -2 \cdot 10^{+32} \lor \neg \left(\left(x \cdot y - y \cdot z\right) \cdot t \leq 0\right):\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ \begin{array}{l} t_2 := y\_m \cdot \left(x \cdot t\_m\right)\\ t_3 := \left(y\_m \cdot z\right) \cdot \left(-t\_m\right)\\ t_4 := z \cdot \left(y\_m \cdot \left(-t\_m\right)\right)\\ t_5 := \left(x \cdot y\_m\right) \cdot t\_m\\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+153}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x \leq -5.9 \cdot 10^{+79}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-40}:\\ \;\;\;\;x \cdot \left(y\_m \cdot t\_m\right)\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-158}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -1.56 \cdot 10^{-177}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-110}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-103}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2200000000:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array}\right) \end{array} \end{array} \]

FPCore

y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) y)
t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) 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 (* x t_m)))
        (t_3 (* (* y_m z) (- t_m)))
        (t_4 (* z (* y_m (- t_m))))
        (t_5 (* (* x y_m) t_m)))
   (*
    t_s
    (*
     y_s
     (if (<= x -7.8e+153)
       t_5
       (if (<= x -5.9e+79)
         t_3
         (if (<= x -1.75e-40)
           (* x (* y_m t_m))
           (if (<= x -1e-158)
             t_3
             (if (<= x -1.56e-177)
               t_2
               (if (<= x 7.5e-110)
                 t_4
                 (if (<= x 1.3e-103)
                   t_2
                   (if (<= x 2200000000.0) t_4 t_5))))))))))))

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 * (x * t_m);
	double t_3 = (y_m * z) * -t_m;
	double t_4 = z * (y_m * -t_m);
	double t_5 = (x * y_m) * t_m;
	double tmp;
	if (x <= -7.8e+153) {
		tmp = t_5;
	} else if (x <= -5.9e+79) {
		tmp = t_3;
	} else if (x <= -1.75e-40) {
		tmp = x * (y_m * t_m);
	} else if (x <= -1e-158) {
		tmp = t_3;
	} else if (x <= -1.56e-177) {
		tmp = t_2;
	} else if (x <= 7.5e-110) {
		tmp = t_4;
	} else if (x <= 1.3e-103) {
		tmp = t_2;
	} else if (x <= 2200000000.0) {
		tmp = t_4;
	} else {
		tmp = t_5;
	}
	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) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_2 = y_m * (x * t_m)
    t_3 = (y_m * z) * -t_m
    t_4 = z * (y_m * -t_m)
    t_5 = (x * y_m) * t_m
    if (x <= (-7.8d+153)) then
        tmp = t_5
    else if (x <= (-5.9d+79)) then
        tmp = t_3
    else if (x <= (-1.75d-40)) then
        tmp = x * (y_m * t_m)
    else if (x <= (-1d-158)) then
        tmp = t_3
    else if (x <= (-1.56d-177)) then
        tmp = t_2
    else if (x <= 7.5d-110) then
        tmp = t_4
    else if (x <= 1.3d-103) then
        tmp = t_2
    else if (x <= 2200000000.0d0) then
        tmp = t_4
    else
        tmp = t_5
    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 * (x * t_m);
	double t_3 = (y_m * z) * -t_m;
	double t_4 = z * (y_m * -t_m);
	double t_5 = (x * y_m) * t_m;
	double tmp;
	if (x <= -7.8e+153) {
		tmp = t_5;
	} else if (x <= -5.9e+79) {
		tmp = t_3;
	} else if (x <= -1.75e-40) {
		tmp = x * (y_m * t_m);
	} else if (x <= -1e-158) {
		tmp = t_3;
	} else if (x <= -1.56e-177) {
		tmp = t_2;
	} else if (x <= 7.5e-110) {
		tmp = t_4;
	} else if (x <= 1.3e-103) {
		tmp = t_2;
	} else if (x <= 2200000000.0) {
		tmp = t_4;
	} else {
		tmp = t_5;
	}
	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 * (x * t_m)
	t_3 = (y_m * z) * -t_m
	t_4 = z * (y_m * -t_m)
	t_5 = (x * y_m) * t_m
	tmp = 0
	if x <= -7.8e+153:
		tmp = t_5
	elif x <= -5.9e+79:
		tmp = t_3
	elif x <= -1.75e-40:
		tmp = x * (y_m * t_m)
	elif x <= -1e-158:
		tmp = t_3
	elif x <= -1.56e-177:
		tmp = t_2
	elif x <= 7.5e-110:
		tmp = t_4
	elif x <= 1.3e-103:
		tmp = t_2
	elif x <= 2200000000.0:
		tmp = t_4
	else:
		tmp = t_5
	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(y_m * Float64(x * t_m))
	t_3 = Float64(Float64(y_m * z) * Float64(-t_m))
	t_4 = Float64(z * Float64(y_m * Float64(-t_m)))
	t_5 = Float64(Float64(x * y_m) * t_m)
	tmp = 0.0
	if (x <= -7.8e+153)
		tmp = t_5;
	elseif (x <= -5.9e+79)
		tmp = t_3;
	elseif (x <= -1.75e-40)
		tmp = Float64(x * Float64(y_m * t_m));
	elseif (x <= -1e-158)
		tmp = t_3;
	elseif (x <= -1.56e-177)
		tmp = t_2;
	elseif (x <= 7.5e-110)
		tmp = t_4;
	elseif (x <= 1.3e-103)
		tmp = t_2;
	elseif (x <= 2200000000.0)
		tmp = t_4;
	else
		tmp = t_5;
	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 * (x * t_m);
	t_3 = (y_m * z) * -t_m;
	t_4 = z * (y_m * -t_m);
	t_5 = (x * y_m) * t_m;
	tmp = 0.0;
	if (x <= -7.8e+153)
		tmp = t_5;
	elseif (x <= -5.9e+79)
		tmp = t_3;
	elseif (x <= -1.75e-40)
		tmp = x * (y_m * t_m);
	elseif (x <= -1e-158)
		tmp = t_3;
	elseif (x <= -1.56e-177)
		tmp = t_2;
	elseif (x <= 7.5e-110)
		tmp = t_4;
	elseif (x <= 1.3e-103)
		tmp = t_2;
	elseif (x <= 2200000000.0)
		tmp = t_4;
	else
		tmp = t_5;
	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[(y$95$m * N[(x * t$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y$95$m * z), $MachinePrecision] * (-t$95$m)), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(y$95$m * (-t$95$m)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x * y$95$m), $MachinePrecision] * t$95$m), $MachinePrecision]}, N[(t$95$s * N[(y$95$s * If[LessEqual[x, -7.8e+153], t$95$5, If[LessEqual[x, -5.9e+79], t$95$3, If[LessEqual[x, -1.75e-40], N[(x * N[(y$95$m * t$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1e-158], t$95$3, If[LessEqual[x, -1.56e-177], t$95$2, If[LessEqual[x, 7.5e-110], t$95$4, If[LessEqual[x, 1.3e-103], t$95$2, If[LessEqual[x, 2200000000.0], t$95$4, t$95$5]]]]]]]]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -7.79999999999999966e153 or 2.2e9 < x

   1. Initial program 87.1%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 90.2%

         \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right)} \cdot t \]

   3. Simplified 90.2%

      \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right) \cdot t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 79.7%

      \[\leadsto \color{blue}{\left(x \cdot y\right)} \cdot t \]
   6. Step-by-step derivation

      1. *-commutative 79.7%

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot t \]

   7. Simplified 79.7%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot t \]

   if -7.79999999999999966e153 < x < -5.9e79 or -1.7500000000000001e-40 < x < -1.00000000000000006e-158

   1. Initial program 97.6%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 99.7%

         \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right)} \cdot t \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right) \cdot t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 78.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot z\right)\right)} \cdot t \]
   6. Step-by-step derivation

      1. mul-1-neg 78.4%

         \[\leadsto \color{blue}{\left(-y \cdot z\right)} \cdot t \]

      2. distribute-rgt-neg-out 78.4%

         \[\leadsto \color{blue}{\left(y \cdot \left(-z\right)\right)} \cdot t \]

   7. Simplified 78.4%

      \[\leadsto \color{blue}{\left(y \cdot \left(-z\right)\right)} \cdot t \]

   if -5.9e79 < x < -1.7500000000000001e-40

   1. Initial program 89.2%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 89.2%

         \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right)} \cdot t \]

      2. associate-*l* 95.7%

         \[\leadsto \color{blue}{y \cdot \left(\left(x - z\right) \cdot t\right)} \]

      3. *-commutative 95.7%

         \[\leadsto y \cdot \color{blue}{\left(t \cdot \left(x - z\right)\right)} \]

   3. Simplified 95.7%

      \[\leadsto \color{blue}{y \cdot \left(t \cdot \left(x - z\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 95.6%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \frac{t \cdot \left(y \cdot z\right)}{x} + t \cdot y\right)} \]

   6. Taylor expanded in z around 0 68.2%

      \[\leadsto x \cdot \color{blue}{\left(t \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-commutative 68.2%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot t\right)} \]

   8. Simplified 68.2%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot t\right)} \]

   if -1.00000000000000006e-158 < x < -1.5600000000000001e-177 or 7.50000000000000053e-110 < x < 1.29999999999999998e-103

   1. Initial program 94.0%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 94.0%

         \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right)} \cdot t \]

      2. associate-*l* 78.7%

         \[\leadsto \color{blue}{y \cdot \left(\left(x - z\right) \cdot t\right)} \]

      3. *-commutative 78.7%

         \[\leadsto y \cdot \color{blue}{\left(t \cdot \left(x - z\right)\right)} \]

   3. Simplified 78.7%

      \[\leadsto \color{blue}{y \cdot \left(t \cdot \left(x - z\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 83.3%

      \[\leadsto \color{blue}{t \cdot \left(x \cdot y\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 67.9%

         \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot y} \]

      2. *-commutative 67.9%

         \[\leadsto \color{blue}{y \cdot \left(t \cdot x\right)} \]

   7. Simplified 67.9%

      \[\leadsto \color{blue}{y \cdot \left(t \cdot x\right)} \]

   if -1.5600000000000001e-177 < x < 7.50000000000000053e-110 or 1.29999999999999998e-103 < x < 2.2e9

   1. Initial program 92.0%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 92.0%

         \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right)} \cdot t \]

   3. Simplified 92.0%

      \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right) \cdot t} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. distribute-rgt-out-- 92.0%

         \[\leadsto \color{blue}{\left(x \cdot y - z \cdot y\right)} \cdot t \]

      2. add-cube-cbrt 91.2%

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{x \cdot y - z \cdot y} \cdot \sqrt[3]{x \cdot y - z \cdot y}\right) \cdot \sqrt[3]{x \cdot y - z \cdot y}\right)} \cdot t \]

      3. pow3 91.2%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot y - z \cdot y}\right)}^{3}} \cdot t \]

      4. distribute-rgt-out-- 91.2%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot \left(x - z\right)}}\right)}^{3} \cdot t \]

   6. Applied egg-rr 91.2%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{y \cdot \left(x - z\right)}\right)}^{3}} \cdot t \]

   7. Taylor expanded in x around 0 82.7%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 82.7%

         \[\leadsto \color{blue}{-t \cdot \left(y \cdot z\right)} \]

      2. *-commutative 82.7%

         \[\leadsto -\color{blue}{\left(y \cdot z\right) \cdot t} \]

      3. *-commutative 82.7%

         \[\leadsto -\color{blue}{\left(z \cdot y\right)} \cdot t \]

      4. associate-*r* 87.1%

         \[\leadsto -\color{blue}{z \cdot \left(y \cdot t\right)} \]

      5. distribute-rgt-neg-in 87.1%

         \[\leadsto \color{blue}{z \cdot \left(-y \cdot t\right)} \]

      6. *-commutative 87.1%

         \[\leadsto z \cdot \left(-\color{blue}{t \cdot y}\right) \]

      7. distribute-lft-neg-in 87.1%

         \[\leadsto z \cdot \color{blue}{\left(\left(-t\right) \cdot y\right)} \]

   9. Simplified 87.1%

      \[\leadsto \color{blue}{z \cdot \left(\left(-t\right) \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+153}:\\ \;\;\;\;\left(x \cdot y\right) \cdot t\\ \mathbf{elif}\;x \leq -5.9 \cdot 10^{+79}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-40}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-158}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq -1.56 \cdot 10^{-177}:\\ \;\;\;\;y \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-110}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-103}:\\ \;\;\;\;y \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq 2200000000:\\ \;\;\;\;z \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+104} \lor \neg \left(x \leq -1.32 \cdot 10^{+69} \lor \neg \left(x \leq -2 \cdot 10^{-28}\right) \land x \leq 6200000000000\right):\\ \;\;\;\;\left(x \cdot y\_m\right) \cdot t\_m\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y\_m \cdot \left(-t\_m\right)\right)\\ \end{array}\right) \end{array} \]

FPCore

y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) y)
t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) 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 -1.22e+104)
           (not
            (or (<= x -1.32e+69)
                (and (not (<= x -2e-28)) (<= x 6200000000000.0)))))
     (* (* x y_m) t_m)
     (* 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 <= -1.22e+104) || !((x <= -1.32e+69) || (!(x <= -2e-28) && (x <= 6200000000000.0)))) {
		tmp = (x * y_m) * t_m;
	} 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 <= (-1.22d+104)) .or. (.not. (x <= (-1.32d+69)) .or. (.not. (x <= (-2d-28))) .and. (x <= 6200000000000.0d0))) then
        tmp = (x * y_m) * t_m
    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 <= -1.22e+104) || !((x <= -1.32e+69) || (!(x <= -2e-28) && (x <= 6200000000000.0)))) {
		tmp = (x * y_m) * t_m;
	} 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 <= -1.22e+104) or not ((x <= -1.32e+69) or (not (x <= -2e-28) and (x <= 6200000000000.0))):
		tmp = (x * y_m) * t_m
	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 <= -1.22e+104) || !((x <= -1.32e+69) || (!(x <= -2e-28) && (x <= 6200000000000.0))))
		tmp = Float64(Float64(x * y_m) * t_m);
	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 <= -1.22e+104) || ~(((x <= -1.32e+69) || (~((x <= -2e-28)) && (x <= 6200000000000.0)))))
		tmp = (x * y_m) * t_m;
	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, -1.22e+104], N[Not[Or[LessEqual[x, -1.32e+69], And[N[Not[LessEqual[x, -2e-28]], $MachinePrecision], LessEqual[x, 6200000000000.0]]]], $MachinePrecision]], N[(N[(x * y$95$m), $MachinePrecision] * t$95$m), $MachinePrecision], N[(z * N[(y$95$m * (-t$95$m)), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < -1.22e104 or -1.32e69 < x < -1.99999999999999994e-28 or 6.2e12 < x

   1. Initial program 90.2%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 92.6%

         \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right)} \cdot t \]

   3. Simplified 92.6%

      \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right) \cdot t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 75.9%

      \[\leadsto \color{blue}{\left(x \cdot y\right)} \cdot t \]
   6. Step-by-step derivation

      1. *-commutative 75.9%

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot t \]

   7. Simplified 75.9%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot t \]

   if -1.22e104 < x < -1.32e69 or -1.99999999999999994e-28 < x < 6.2e12

   1. Initial program 91.7%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 92.5%

         \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right)} \cdot t \]

   3. Simplified 92.5%

      \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right) \cdot t} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. distribute-rgt-out-- 91.7%

         \[\leadsto \color{blue}{\left(x \cdot y - z \cdot y\right)} \cdot t \]

      2. add-cube-cbrt 90.8%

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{x \cdot y - z \cdot y} \cdot \sqrt[3]{x \cdot y - z \cdot y}\right) \cdot \sqrt[3]{x \cdot y - z \cdot y}\right)} \cdot t \]

      3. pow3 90.8%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot y - z \cdot y}\right)}^{3}} \cdot t \]

      4. distribute-rgt-out-- 91.6%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot \left(x - z\right)}}\right)}^{3} \cdot t \]

   6. Applied egg-rr 91.6%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{y \cdot \left(x - z\right)}\right)}^{3}} \cdot t \]

   7. Taylor expanded in x around 0 79.4%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 79.4%

         \[\leadsto \color{blue}{-t \cdot \left(y \cdot z\right)} \]

      2. *-commutative 79.4%

         \[\leadsto -\color{blue}{\left(y \cdot z\right) \cdot t} \]

      3. *-commutative 79.4%

         \[\leadsto -\color{blue}{\left(z \cdot y\right)} \cdot t \]

      4. associate-*r* 82.3%

         \[\leadsto -\color{blue}{z \cdot \left(y \cdot t\right)} \]

      5. distribute-rgt-neg-in 82.3%

         \[\leadsto \color{blue}{z \cdot \left(-y \cdot t\right)} \]

      6. *-commutative 82.3%

         \[\leadsto z \cdot \left(-\color{blue}{t \cdot y}\right) \]

      7. distribute-lft-neg-in 82.3%

         \[\leadsto z \cdot \color{blue}{\left(\left(-t\right) \cdot y\right)} \]

   9. Simplified 82.3%

      \[\leadsto \color{blue}{z \cdot \left(\left(-t\right) \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+104} \lor \neg \left(x \leq -1.32 \cdot 10^{+69} \lor \neg \left(x \leq -2 \cdot 10^{-28}\right) \land x \leq 6200000000000\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ \begin{array}{l} t_2 := y\_m \cdot \left(t\_m \cdot \left(-z\right)\right)\\ t_3 := \left(x \cdot y\_m\right) \cdot t\_m\\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+153}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+62}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(y\_m \cdot t\_m\right)\\ \mathbf{elif}\;x \leq 1420000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array}\right) \end{array} \end{array} \]

FPCore

y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) y)
t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) 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 (* t_m (- z)))) (t_3 (* (* x y_m) t_m)))
   (*
    t_s
    (*
     y_s
     (if (<= x -7.8e+153)
       t_3
       (if (<= x -1.6e+62)
         t_2
         (if (<= x -3.4e-41)
           (* x (* y_m t_m))
           (if (<= x 1420000.0) t_2 t_3))))))))

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 * (t_m * -z);
	double t_3 = (x * y_m) * t_m;
	double tmp;
	if (x <= -7.8e+153) {
		tmp = t_3;
	} else if (x <= -1.6e+62) {
		tmp = t_2;
	} else if (x <= -3.4e-41) {
		tmp = x * (y_m * t_m);
	} else if (x <= 1420000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_2 = y_m * (t_m * -z)
    t_3 = (x * y_m) * t_m
    if (x <= (-7.8d+153)) then
        tmp = t_3
    else if (x <= (-1.6d+62)) then
        tmp = t_2
    else if (x <= (-3.4d-41)) then
        tmp = x * (y_m * t_m)
    else if (x <= 1420000.0d0) then
        tmp = t_2
    else
        tmp = t_3
    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 * (t_m * -z);
	double t_3 = (x * y_m) * t_m;
	double tmp;
	if (x <= -7.8e+153) {
		tmp = t_3;
	} else if (x <= -1.6e+62) {
		tmp = t_2;
	} else if (x <= -3.4e-41) {
		tmp = x * (y_m * t_m);
	} else if (x <= 1420000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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 * (t_m * -z)
	t_3 = (x * y_m) * t_m
	tmp = 0
	if x <= -7.8e+153:
		tmp = t_3
	elif x <= -1.6e+62:
		tmp = t_2
	elif x <= -3.4e-41:
		tmp = x * (y_m * t_m)
	elif x <= 1420000.0:
		tmp = t_2
	else:
		tmp = t_3
	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(y_m * Float64(t_m * Float64(-z)))
	t_3 = Float64(Float64(x * y_m) * t_m)
	tmp = 0.0
	if (x <= -7.8e+153)
		tmp = t_3;
	elseif (x <= -1.6e+62)
		tmp = t_2;
	elseif (x <= -3.4e-41)
		tmp = Float64(x * Float64(y_m * t_m));
	elseif (x <= 1420000.0)
		tmp = t_2;
	else
		tmp = t_3;
	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 * (t_m * -z);
	t_3 = (x * y_m) * t_m;
	tmp = 0.0;
	if (x <= -7.8e+153)
		tmp = t_3;
	elseif (x <= -1.6e+62)
		tmp = t_2;
	elseif (x <= -3.4e-41)
		tmp = x * (y_m * t_m);
	elseif (x <= 1420000.0)
		tmp = t_2;
	else
		tmp = t_3;
	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[(y$95$m * N[(t$95$m * (-z)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y$95$m), $MachinePrecision] * t$95$m), $MachinePrecision]}, N[(t$95$s * N[(y$95$s * If[LessEqual[x, -7.8e+153], t$95$3, If[LessEqual[x, -1.6e+62], t$95$2, If[LessEqual[x, -3.4e-41], N[(x * N[(y$95$m * t$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1420000.0], t$95$2, t$95$3]]]]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.79999999999999966e153 or 1.42e6 < x

   1. Initial program 87.2%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 90.3%

         \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right)} \cdot t \]

   3. Simplified 90.3%

      \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right) \cdot t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 78.9%

      \[\leadsto \color{blue}{\left(x \cdot y\right)} \cdot t \]
   6. Step-by-step derivation

      1. *-commutative 78.9%

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot t \]

   7. Simplified 78.9%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot t \]

   if -7.79999999999999966e153 < x < -1.59999999999999992e62 or -3.3999999999999998e-41 < x < 1.42e6

   1. Initial program 93.4%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 94.1%

         \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right)} \cdot t \]

      2. associate-*l* 94.6%

         \[\leadsto \color{blue}{y \cdot \left(\left(x - z\right) \cdot t\right)} \]

      3. *-commutative 94.6%

         \[\leadsto y \cdot \color{blue}{\left(t \cdot \left(x - z\right)\right)} \]

   3. Simplified 94.6%

      \[\leadsto \color{blue}{y \cdot \left(t \cdot \left(x - z\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 77.9%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(t \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 77.9%

         \[\leadsto y \cdot \color{blue}{\left(-t \cdot z\right)} \]

      2. distribute-rgt-neg-out 77.9%

         \[\leadsto y \cdot \color{blue}{\left(t \cdot \left(-z\right)\right)} \]

   7. Simplified 77.9%

      \[\leadsto y \cdot \color{blue}{\left(t \cdot \left(-z\right)\right)} \]

   if -1.59999999999999992e62 < x < -3.3999999999999998e-41

   1. Initial program 92.3%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 92.3%

         \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right)} \cdot t \]

      2. associate-*l* 95.2%

         \[\leadsto \color{blue}{y \cdot \left(\left(x - z\right) \cdot t\right)} \]

      3. *-commutative 95.2%

         \[\leadsto y \cdot \color{blue}{\left(t \cdot \left(x - z\right)\right)} \]

   3. Simplified 95.2%

      \[\leadsto \color{blue}{y \cdot \left(t \cdot \left(x - z\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 99.6%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \frac{t \cdot \left(y \cdot z\right)}{x} + t \cdot y\right)} \]

   6. Taylor expanded in z around 0 72.7%

      \[\leadsto x \cdot \color{blue}{\left(t \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-commutative 72.7%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot t\right)} \]

   8. Simplified 72.7%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+153}:\\ \;\;\;\;\left(x \cdot y\right) \cdot t\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+62}:\\ \;\;\;\;y \cdot \left(t \cdot \left(-z\right)\right)\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;x \leq 1420000:\\ \;\;\;\;y \cdot \left(t \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+263} \lor \neg \left(x \leq 3.8 \cdot 10^{+189}\right):\\ \;\;\;\;\left(x \cdot y\_m\right) \cdot t\_m\\ \mathbf{else}:\\ \;\;\;\;y\_m \cdot \left(t\_m \cdot \left(x - z\right)\right)\\ \end{array}\right) \end{array} \]

FPCore

y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) y)
t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) 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 -1.3e+263) (not (<= x 3.8e+189)))
     (* (* x y_m) t_m)
     (* y_m (* t_m (- x z)))))))

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 <= -1.3e+263) || !(x <= 3.8e+189)) {
		tmp = (x * y_m) * t_m;
	} else {
		tmp = y_m * (t_m * (x - z));
	}
	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 <= (-1.3d+263)) .or. (.not. (x <= 3.8d+189))) then
        tmp = (x * y_m) * t_m
    else
        tmp = y_m * (t_m * (x - z))
    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 <= -1.3e+263) || !(x <= 3.8e+189)) {
		tmp = (x * y_m) * t_m;
	} else {
		tmp = y_m * (t_m * (x - z));
	}
	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 <= -1.3e+263) or not (x <= 3.8e+189):
		tmp = (x * y_m) * t_m
	else:
		tmp = y_m * (t_m * (x - z))
	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 <= -1.3e+263) || !(x <= 3.8e+189))
		tmp = Float64(Float64(x * y_m) * t_m);
	else
		tmp = Float64(y_m * Float64(t_m * Float64(x - z)));
	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 <= -1.3e+263) || ~((x <= 3.8e+189)))
		tmp = (x * y_m) * t_m;
	else
		tmp = y_m * (t_m * (x - z));
	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, -1.3e+263], N[Not[LessEqual[x, 3.8e+189]], $MachinePrecision]], N[(N[(x * y$95$m), $MachinePrecision] * t$95$m), $MachinePrecision], N[(y$95$m * N[(t$95$m * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < -1.3000000000000001e263 or 3.7999999999999998e189 < x

   1. Initial program 79.2%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 79.2%

         \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right)} \cdot t \]

   3. Simplified 79.2%

      \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right) \cdot t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 79.2%

      \[\leadsto \color{blue}{\left(x \cdot y\right)} \cdot t \]
   6. Step-by-step derivation

      1. *-commutative 79.2%

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot t \]

   7. Simplified 79.2%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot t \]

   if -1.3000000000000001e263 < x < 3.7999999999999998e189

   1. Initial program 92.4%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 94.1%

         \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right)} \cdot t \]

      2. associate-*l* 94.6%

         \[\leadsto \color{blue}{y \cdot \left(\left(x - z\right) \cdot t\right)} \]

      3. *-commutative 94.6%

         \[\leadsto y \cdot \color{blue}{\left(t \cdot \left(x - z\right)\right)} \]

   3. Simplified 94.6%

      \[\leadsto \color{blue}{y \cdot \left(t \cdot \left(x - z\right)\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+263} \lor \neg \left(x \leq 3.8 \cdot 10^{+189}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;t\_m \leq 5 \cdot 10^{-69}:\\ \;\;\;\;y\_m \cdot \left(t\_m \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y\_m \cdot t\_m\right)\\ \end{array}\right) \end{array} \]

FPCore

y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) y)
t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) 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-69) (* y_m (* t_m (- x z))) (* (- 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-69) {
		tmp = y_m * (t_m * (x - z));
	} 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-69) then
        tmp = y_m * (t_m * (x - z))
    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-69) {
		tmp = y_m * (t_m * (x - z));
	} 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-69:
		tmp = y_m * (t_m * (x - z))
	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-69)
		tmp = Float64(y_m * Float64(t_m * Float64(x - z)));
	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-69)
		tmp = y_m * (t_m * (x - z));
	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-69], N[(y$95$m * N[(t$95$m * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - z), $MachinePrecision] * N[(y$95$m * t$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < 5.00000000000000033e-69

   1. Initial program 90.2%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 91.9%

         \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right)} \cdot t \]

      2. associate-*l* 96.3%

         \[\leadsto \color{blue}{y \cdot \left(\left(x - z\right) \cdot t\right)} \]

      3. *-commutative 96.3%

         \[\leadsto y \cdot \color{blue}{\left(t \cdot \left(x - z\right)\right)} \]

   3. Simplified 96.3%

      \[\leadsto \color{blue}{y \cdot \left(t \cdot \left(x - z\right)\right)} \]
   4. Add Preprocessing

   if 5.00000000000000033e-69 < t

   1. Initial program 92.7%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 92.7%

         \[\leadsto \color{blue}{t \cdot \left(x \cdot y - z \cdot y\right)} \]

      2. distribute-rgt-out-- 94.0%

         \[\leadsto t \cdot \color{blue}{\left(y \cdot \left(x - z\right)\right)} \]

      3. associate-*r* 96.3%

         \[\leadsto \color{blue}{\left(t \cdot y\right) \cdot \left(x - z\right)} \]

      4. *-commutative 96.3%

         \[\leadsto \color{blue}{\left(y \cdot t\right)} \cdot \left(x - z\right) \]

   3. Simplified 96.3%

      \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(x - z\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;t\_m \leq 2.25 \cdot 10^{-53}:\\ \;\;\;\;\left(x \cdot y\_m\right) \cdot t\_m\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y\_m \cdot t\_m\right)\\ \end{array}\right) \end{array} \]

FPCore

y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) y)
t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) 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 2.25e-53) (* (* x y_m) 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 <= 2.25e-53) {
		tmp = (x * y_m) * 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 <= 2.25d-53) then
        tmp = (x * y_m) * 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 <= 2.25e-53) {
		tmp = (x * y_m) * 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 <= 2.25e-53:
		tmp = (x * y_m) * 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 <= 2.25e-53)
		tmp = Float64(Float64(x * y_m) * 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 <= 2.25e-53)
		tmp = (x * y_m) * 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, 2.25e-53], N[(N[(x * y$95$m), $MachinePrecision] * t$95$m), $MachinePrecision], N[(x * N[(y$95$m * t$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < 2.24999999999999992e-53

   1. Initial program 90.4%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 92.1%

         \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right)} \cdot t \]

   3. Simplified 92.1%

      \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right) \cdot t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 55.0%

      \[\leadsto \color{blue}{\left(x \cdot y\right)} \cdot t \]
   6. Step-by-step derivation

      1. *-commutative 55.0%

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot t \]

   7. Simplified 55.0%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot t \]

   if 2.24999999999999992e-53 < t

   1. Initial program 92.3%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 93.7%

         \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right)} \cdot t \]

      2. associate-*l* 87.0%

         \[\leadsto \color{blue}{y \cdot \left(\left(x - z\right) \cdot t\right)} \]

      3. *-commutative 87.0%

         \[\leadsto y \cdot \color{blue}{\left(t \cdot \left(x - z\right)\right)} \]

   3. Simplified 87.0%

      \[\leadsto \color{blue}{y \cdot \left(t \cdot \left(x - z\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 86.4%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \frac{t \cdot \left(y \cdot z\right)}{x} + t \cdot y\right)} \]

   6. Taylor expanded in z around 0 56.6%

      \[\leadsto x \cdot \color{blue}{\left(t \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-commutative 56.6%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot t\right)} \]

   8. Simplified 56.6%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.25 \cdot 10^{-53}:\\ \;\;\;\;\left(x \cdot y\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;t\_m \leq 5.8 \cdot 10^{-72}:\\ \;\;\;\;y\_m \cdot \left(x \cdot t\_m\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y\_m \cdot t\_m\right)\\ \end{array}\right) \end{array} \]

FPCore

y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) y)
t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) 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 5.8e-72) (* 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 <= 5.8e-72) {
		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 <= 5.8d-72) 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 <= 5.8e-72) {
		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 <= 5.8e-72:
		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 <= 5.8e-72)
		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 <= 5.8e-72)
		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, 5.8e-72], 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

1. Split input into 2 regimes

2. if t < 5.79999999999999995e-72

   1. Initial program 90.2%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 91.8%

         \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right)} \cdot t \]

      2. associate-*l* 96.2%

         \[\leadsto \color{blue}{y \cdot \left(\left(x - z\right) \cdot t\right)} \]

      3. *-commutative 96.2%

         \[\leadsto y \cdot \color{blue}{\left(t \cdot \left(x - z\right)\right)} \]

   3. Simplified 96.2%

      \[\leadsto \color{blue}{y \cdot \left(t \cdot \left(x - z\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 53.8%

      \[\leadsto \color{blue}{t \cdot \left(x \cdot y\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 56.4%

         \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot y} \]

      2. *-commutative 56.4%

         \[\leadsto \color{blue}{y \cdot \left(t \cdot x\right)} \]

   7. Simplified 56.4%

      \[\leadsto \color{blue}{y \cdot \left(t \cdot x\right)} \]

   if 5.79999999999999995e-72 < t

   1. Initial program 92.8%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 94.1%

         \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right)} \cdot t \]

      2. associate-*l* 87.8%

         \[\leadsto \color{blue}{y \cdot \left(\left(x - z\right) \cdot t\right)} \]

      3. *-commutative 87.8%

         \[\leadsto y \cdot \color{blue}{\left(t \cdot \left(x - z\right)\right)} \]

   3. Simplified 87.8%

      \[\leadsto \color{blue}{y \cdot \left(t \cdot \left(x - z\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 87.2%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \frac{t \cdot \left(y \cdot z\right)}{x} + t \cdot y\right)} \]

   6. Taylor expanded in z around 0 58.2%

      \[\leadsto x \cdot \color{blue}{\left(t \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-commutative 58.2%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot t\right)} \]

   8. Simplified 58.2%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.8 \cdot 10^{-72}:\\ \;\;\;\;y \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.0% accurate, 1.8× speedup

Math

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

FPCore

y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) y)
t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) 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 (* 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) {
	return t_s * (y_s * (x * (y_m * 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 * (x * (y_m * 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 * (x * (y_m * 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 * (x * (y_m * 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(x * Float64(y_m * 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 * (x * (y_m * 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[(x * N[(y$95$m * t$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.0%

   \[\left(x \cdot y - z \cdot y\right) \cdot t \]
2. Step-by-step derivation

   1. distribute-rgt-out-- 92.5%

      \[\leadsto \color{blue}{\left(y \cdot \left(x - z\right)\right)} \cdot t \]

   2. associate-*l* 93.6%

      \[\leadsto \color{blue}{y \cdot \left(\left(x - z\right) \cdot t\right)} \]

   3. *-commutative 93.6%

      \[\leadsto y \cdot \color{blue}{\left(t \cdot \left(x - z\right)\right)} \]

3. Simplified 93.6%

   \[\leadsto \color{blue}{y \cdot \left(t \cdot \left(x - z\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 83.1%

   \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \frac{t \cdot \left(y \cdot z\right)}{x} + t \cdot y\right)} \]

6. Taylor expanded in z around 0 55.4%

   \[\leadsto x \cdot \color{blue}{\left(t \cdot y\right)} \]
7. Step-by-step derivation

   1. *-commutative 55.4%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot t\right)} \]

8. Simplified 55.4%

   \[\leadsto x \cdot \color{blue}{\left(y \cdot t\right)} \]
9. Add Preprocessing

Developer target: 95.6% accurate, 0.5× 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 2024107 
(FPCore (x y z t)
  :name "Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3"
  :precision binary64

  :alt
  (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))