Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3

Percentage Accurate: 90.7% → 97.1%

Time: 7.4s

Alternatives: 8

Speedup: 1.3×

• 25.0% 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: 90.7% 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: 97.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.08 \cdot 10^{-17}:\\ \;\;\;\;y \cdot \left(t \cdot x - t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(t \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.08e-17) (* y (- (* t x) (* t z))) (* (- x z) (* t y))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.08e-17) {
		tmp = y * ((t * x) - (t * z));
	} else {
		tmp = (x - z) * (t * y);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 <= 1.08d-17) then
        tmp = y * ((t * x) - (t * z))
    else
        tmp = (x - z) * (t * y)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.08e-17) {
		tmp = y * ((t * x) - (t * z));
	} else {
		tmp = (x - z) * (t * y);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 1.08e-17:
		tmp = y * ((t * x) - (t * z))
	else:
		tmp = (x - z) * (t * y)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.08e-17)
		tmp = Float64(y * Float64(Float64(t * x) - Float64(t * z)));
	else
		tmp = Float64(Float64(x - z) * Float64(t * y));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.08e-17)
		tmp = y * ((t * x) - (t * z));
	else
		tmp = (x - z) * (t * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 1.08e-17], N[(y * N[(N[(t * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - z), $MachinePrecision] * N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.07999999999999995e-17

   1. Initial program 86.1%

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

      1. distribute-rgt-out-- 87.3%

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

      2. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

      1. *-commutative 92.9%

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

      2. sub-neg 92.9%

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

      3. distribute-rgt-in 91.7%

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

   5. Applied egg-rr 91.7%

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

   if 1.07999999999999995e-17 < t

   1. Initial program 92.1%

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

      1. distribute-rgt-out-- 98.0%

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

   3. Simplified 98.0%

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

      1. *-commutative 98.0%

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

      2. flip-- 73.7%

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

      3. associate-*l/ 70.3%

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

   5. Applied egg-rr 70.3%

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

   6. Taylor expanded in x around inf 46.1%

      \[\leadsto \frac{\color{blue}{{x}^{2}} \cdot y}{x + z} \cdot t \]
   7. Step-by-step derivation

      1. unpow2 46.1%

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

   8. Simplified 46.1%

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

   9. Taylor expanded in x around inf 79.6%

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

       1. +-commutative 79.6%

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

       2. associate-*r* 82.2%

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

       3. mul-1-neg 82.2%

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

       4. associate-*r* 82.1%

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

       5. distribute-rgt-neg-in 82.1%

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

       6. distribute-lft-in 98.4%

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

       7. sub-neg 98.4%

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

       8. *-commutative 98.4%

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

   11. Simplified 98.4%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.08 \cdot 10^{-17}:\\ \;\;\;\;y \cdot \left(t \cdot x - t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(t \cdot y\right)\\ \end{array} \]

Alternative 2: 73.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := t \cdot \left(y \cdot x\right)\\ \mathbf{if}\;x \leq -4.3 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-289}:\\ \;\;\;\;y \cdot \left(t \cdot \left(-z\right)\right)\\ \mathbf{elif}\;x \leq 3200000000000:\\ \;\;\;\;t \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (* y x))))
   (if (<= x -4.3e+83)
     t_1
     (if (<= x 5.2e-289)
       (* y (* t (- z)))
       (if (<= x 3200000000000.0) (* t (* y (- z))) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = t * (y * x);
	double tmp;
	if (x <= -4.3e+83) {
		tmp = t_1;
	} else if (x <= 5.2e-289) {
		tmp = y * (t * -z);
	} else if (x <= 3200000000000.0) {
		tmp = t * (y * -z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y * x)
    if (x <= (-4.3d+83)) then
        tmp = t_1
    else if (x <= 5.2d-289) then
        tmp = y * (t * -z)
    else if (x <= 3200000000000.0d0) then
        tmp = t * (y * -z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y * x);
	double tmp;
	if (x <= -4.3e+83) {
		tmp = t_1;
	} else if (x <= 5.2e-289) {
		tmp = y * (t * -z);
	} else if (x <= 3200000000000.0) {
		tmp = t * (y * -z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = t * (y * x)
	tmp = 0
	if x <= -4.3e+83:
		tmp = t_1
	elif x <= 5.2e-289:
		tmp = y * (t * -z)
	elif x <= 3200000000000.0:
		tmp = t * (y * -z)
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(t * Float64(y * x))
	tmp = 0.0
	if (x <= -4.3e+83)
		tmp = t_1;
	elseif (x <= 5.2e-289)
		tmp = Float64(y * Float64(t * Float64(-z)));
	elseif (x <= 3200000000000.0)
		tmp = Float64(t * Float64(y * Float64(-z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = t * (y * x);
	tmp = 0.0;
	if (x <= -4.3e+83)
		tmp = t_1;
	elseif (x <= 5.2e-289)
		tmp = y * (t * -z);
	elseif (x <= 3200000000000.0)
		tmp = t * (y * -z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.3e+83], t$95$1, If[LessEqual[x, 5.2e-289], N[(y * N[(t * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3200000000000.0], N[(t * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.3e83 or 3.2e12 < x

   1. Initial program 82.5%

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

      1. distribute-rgt-out-- 87.7%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in x around inf 75.1%

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

   if -4.3e83 < x < 5.1999999999999998e-289

   1. Initial program 94.3%

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

      1. distribute-rgt-out-- 94.3%

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

      2. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in x around 0 80.2%

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

      1. mul-1-neg 80.2%

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

      2. *-commutative 80.2%

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

      3. distribute-rgt-neg-in 80.2%

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

   6. Simplified 80.2%

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

   if 5.1999999999999998e-289 < x < 3.2e12

   1. Initial program 90.2%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   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. Taylor expanded in x around 0 69.2%

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

      1. mul-1-neg 69.2%

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

      2. distribute-rgt-neg-out 69.2%

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

   6. Simplified 69.2%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+83}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-289}:\\ \;\;\;\;y \cdot \left(t \cdot \left(-z\right)\right)\\ \mathbf{elif}\;x \leq 3200000000000:\\ \;\;\;\;t \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 3: 73.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+82} \lor \neg \left(x \leq 2500000000000\right):\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.6e+82) (not (<= x 2500000000000.0)))
   (* t (* y x))
   (* y (* t (- z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.6e+82) || !(x <= 2500000000000.0)) {
		tmp = t * (y * x);
	} else {
		tmp = y * (t * -z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 ((x <= (-1.6d+82)) .or. (.not. (x <= 2500000000000.0d0))) then
        tmp = t * (y * x)
    else
        tmp = y * (t * -z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.6e+82) || !(x <= 2500000000000.0)) {
		tmp = t * (y * x);
	} else {
		tmp = y * (t * -z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (x <= -1.6e+82) or not (x <= 2500000000000.0):
		tmp = t * (y * x)
	else:
		tmp = y * (t * -z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.6e+82) || !(x <= 2500000000000.0))
		tmp = Float64(t * Float64(y * x));
	else
		tmp = Float64(y * Float64(t * Float64(-z)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.6e+82) || ~((x <= 2500000000000.0)))
		tmp = t * (y * x);
	else
		tmp = y * (t * -z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.6e+82], N[Not[LessEqual[x, 2500000000000.0]], $MachinePrecision]], N[(t * N[(y * x), $MachinePrecision]), $MachinePrecision], N[(y * N[(t * (-z)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.59999999999999987e82 or 2.5e12 < x

   1. Initial program 82.5%

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

      1. distribute-rgt-out-- 87.7%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in x around inf 75.1%

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

   if -1.59999999999999987e82 < x < 2.5e12

   1. Initial program 92.5%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   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* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in x around 0 78.2%

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

      1. mul-1-neg 78.2%

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

      2. *-commutative 78.2%

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

      3. distribute-rgt-neg-in 78.2%

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

   6. Simplified 78.2%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+82} \lor \neg \left(x \leq 2500000000000\right):\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 4: 97.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.4e-65) (* y (* t (- x z))) (* t (* y (- x z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.4e-65) {
		tmp = y * (t * (x - z));
	} else {
		tmp = t * (y * (x - z));
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 (y <= (-4.4d-65)) then
        tmp = y * (t * (x - z))
    else
        tmp = t * (y * (x - z))
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.4e-65) {
		tmp = y * (t * (x - z));
	} else {
		tmp = t * (y * (x - z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -4.4e-65:
		tmp = y * (t * (x - z))
	else:
		tmp = t * (y * (x - z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.4e-65)
		tmp = Float64(y * Float64(t * Float64(x - z)));
	else
		tmp = Float64(t * Float64(y * Float64(x - z)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.4e-65)
		tmp = y * (t * (x - z));
	else
		tmp = t * (y * (x - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -4.4e-65], N[(y * N[(t * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.40000000000000042e-65

   1. Initial program 86.4%

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

      1. distribute-rgt-out-- 91.1%

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

      2. associate-*l* 98.3%

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

   3. Simplified 98.3%

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

   if -4.40000000000000042e-65 < y

   1. Initial program 88.1%

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

      1. distribute-rgt-out-- 89.8%

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

   3. Simplified 89.8%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array} \]

Alternative 5: 97.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.18 \cdot 10^{-17}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(t \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.18e-17) (* y (* t (- x z))) (* (- x z) (* t y))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.18e-17) {
		tmp = y * (t * (x - z));
	} else {
		tmp = (x - z) * (t * y);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 <= 1.18d-17) then
        tmp = y * (t * (x - z))
    else
        tmp = (x - z) * (t * y)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.18e-17) {
		tmp = y * (t * (x - z));
	} else {
		tmp = (x - z) * (t * y);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 1.18e-17:
		tmp = y * (t * (x - z))
	else:
		tmp = (x - z) * (t * y)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.18e-17)
		tmp = Float64(y * Float64(t * Float64(x - z)));
	else
		tmp = Float64(Float64(x - z) * Float64(t * y));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.18e-17)
		tmp = y * (t * (x - z));
	else
		tmp = (x - z) * (t * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 1.18e-17], N[(y * N[(t * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - z), $MachinePrecision] * N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.18000000000000004e-17

   1. Initial program 86.1%

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

      1. distribute-rgt-out-- 87.3%

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

      2. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

   if 1.18000000000000004e-17 < t

   1. Initial program 92.1%

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

      1. distribute-rgt-out-- 98.0%

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

   3. Simplified 98.0%

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

      1. *-commutative 98.0%

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

      2. flip-- 73.7%

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

      3. associate-*l/ 70.3%

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

   5. Applied egg-rr 70.3%

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

   6. Taylor expanded in x around inf 46.1%

      \[\leadsto \frac{\color{blue}{{x}^{2}} \cdot y}{x + z} \cdot t \]
   7. Step-by-step derivation

      1. unpow2 46.1%

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

   8. Simplified 46.1%

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

   9. Taylor expanded in x around inf 79.6%

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

       1. +-commutative 79.6%

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

       2. associate-*r* 82.2%

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

       3. mul-1-neg 82.2%

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

       4. associate-*r* 82.1%

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

       5. distribute-rgt-neg-in 82.1%

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

       6. distribute-lft-in 98.4%

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

       7. sub-neg 98.4%

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

       8. *-commutative 98.4%

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

   11. Simplified 98.4%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.18 \cdot 10^{-17}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(t \cdot y\right)\\ \end{array} \]

Alternative 6: 56.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 10^{-11}:\\ \;\;\;\;y \cdot \left(t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 1e-11) (* y (* t x)) (* x (* t y))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1e-11) {
		tmp = y * (t * x);
	} else {
		tmp = x * (t * y);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 <= 1d-11) then
        tmp = y * (t * x)
    else
        tmp = x * (t * y)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1e-11) {
		tmp = y * (t * x);
	} else {
		tmp = x * (t * y);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 1e-11:
		tmp = y * (t * x)
	else:
		tmp = x * (t * y)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1e-11)
		tmp = Float64(y * Float64(t * x));
	else
		tmp = Float64(x * Float64(t * y));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1e-11)
		tmp = y * (t * x);
	else
		tmp = x * (t * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 1e-11], N[(y * N[(t * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 9.99999999999999939e-12

   1. Initial program 86.2%

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

      1. distribute-rgt-out-- 87.4%

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

      2. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in x around inf 53.5%

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

   if 9.99999999999999939e-12 < t

   1. Initial program 91.9%

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

      1. distribute-rgt-out-- 98.0%

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

      2. associate-*l* 91.1%

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

   3. Simplified 91.1%

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

      1. add-cube-cbrt 90.2%

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

      2. pow3 90.2%

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

   5. Applied egg-rr 90.2%

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

   6. Taylor expanded in z around 0 54.4%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(y \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. pow-base-1 54.4%

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

      2. *-lft-identity 54.4%

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

      3. associate-*r* 64.4%

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

   8. Simplified 64.4%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 10^{-11}:\\ \;\;\;\;y \cdot \left(t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot y\right)\\ \end{array} \]

Alternative 7: 92.4% accurate, 1.3× speedup

Math

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

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (* y (* t (- x z))))

C

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

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 = y * (t * (x - z))
end function

Java

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

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	return y * (t * (x - z))

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	return Float64(y * Float64(t * Float64(x - z)))
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp = code(x, y, z, t)
	tmp = y * (t * (x - z));
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(y * N[(t * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.7%

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

   1. distribute-rgt-out-- 90.2%

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

   2. associate-*l* 92.5%

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

3. Simplified 92.5%

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

4. Final simplification 92.5%

   \[\leadsto y \cdot \left(t \cdot \left(x - z\right)\right) \]

Alternative 8: 52.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ y \cdot \left(t \cdot x\right) \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (* y (* t x)))

C

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

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 = y * (t * x)
end function

Java

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

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	return y * (t * x)

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	return Float64(y * Float64(t * x))
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp = code(x, y, z, t)
	tmp = y * (t * x);
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(y * N[(t * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.7%

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

   1. distribute-rgt-out-- 90.2%

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

   2. associate-*l* 92.5%

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

3. Simplified 92.5%

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

4. Taylor expanded in x around inf 53.7%

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

5. Final simplification 53.7%

   \[\leadsto y \cdot \left(t \cdot x\right) \]

Developer target: 96.5% 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 2023182 
(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))