Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3

Percentage Accurate: 90.8% → 97.1%

Time: 7.6s

Alternatives: 8

Speedup: 1.3×

• 25.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.8% 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

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -16600000000000:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot x - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -16600000000000.0) (* y (* t (- x z))) (* t (- (* y x) (* y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -16600000000000.0) {
		tmp = y * (t * (x - z));
	} else {
		tmp = t * ((y * x) - (y * 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 <= (-16600000000000.0d0)) then
        tmp = y * (t * (x - z))
    else
        tmp = t * ((y * x) - (y * 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 <= -16600000000000.0) {
		tmp = y * (t * (x - z));
	} else {
		tmp = t * ((y * x) - (y * z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -16600000000000.0:
		tmp = y * (t * (x - z))
	else:
		tmp = t * ((y * x) - (y * z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -16600000000000.0)
		tmp = Float64(y * Float64(t * Float64(x - z)));
	else
		tmp = Float64(t * Float64(Float64(y * x) - Float64(y * 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 <= -16600000000000.0)
		tmp = y * (t * (x - z));
	else
		tmp = t * ((y * x) - (y * 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, -16600000000000.0], N[(y * N[(t * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y * x), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.66e13

   1. Initial program 69.4%

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

      1. distribute-rgt-out-- 73.1%

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

      2. associate-*l* 96.4%

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

      3. *-commutative 96.4%

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

   3. Simplified 96.4%

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

   if -1.66e13 < y

   1. Initial program 94.2%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -16600000000000:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot x - y \cdot z\right)\\ \end{array} \]

Alternative 2: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := t \cdot \left(y \cdot x\right)\\ t_2 := y \cdot \left(z \cdot \left(-t\right)\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{-94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-237}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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))) (t_2 (* y (* z (- t)))))
   (if (<= z -2.1e-94)
     t_2
     (if (<= z 3.8e-237)
       t_1
       (if (<= z 3.45e+18) (* x (* y t)) (if (<= z 5e+28) t_1 t_2))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = t * (y * x);
	double t_2 = y * (z * -t);
	double tmp;
	if (z <= -2.1e-94) {
		tmp = t_2;
	} else if (z <= 3.8e-237) {
		tmp = t_1;
	} else if (z <= 3.45e+18) {
		tmp = x * (y * t);
	} else if (z <= 5e+28) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = t * (y * x)
    t_2 = y * (z * -t)
    if (z <= (-2.1d-94)) then
        tmp = t_2
    else if (z <= 3.8d-237) then
        tmp = t_1
    else if (z <= 3.45d+18) then
        tmp = x * (y * t)
    else if (z <= 5d+28) then
        tmp = t_1
    else
        tmp = t_2
    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 t_2 = y * (z * -t);
	double tmp;
	if (z <= -2.1e-94) {
		tmp = t_2;
	} else if (z <= 3.8e-237) {
		tmp = t_1;
	} else if (z <= 3.45e+18) {
		tmp = x * (y * t);
	} else if (z <= 5e+28) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = t * (y * x)
	t_2 = y * (z * -t)
	tmp = 0
	if z <= -2.1e-94:
		tmp = t_2
	elif z <= 3.8e-237:
		tmp = t_1
	elif z <= 3.45e+18:
		tmp = x * (y * t)
	elif z <= 5e+28:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(t * Float64(y * x))
	t_2 = Float64(y * Float64(z * Float64(-t)))
	tmp = 0.0
	if (z <= -2.1e-94)
		tmp = t_2;
	elseif (z <= 3.8e-237)
		tmp = t_1;
	elseif (z <= 3.45e+18)
		tmp = Float64(x * Float64(y * t));
	elseif (z <= 5e+28)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = t * (y * x);
	t_2 = y * (z * -t);
	tmp = 0.0;
	if (z <= -2.1e-94)
		tmp = t_2;
	elseif (z <= 3.8e-237)
		tmp = t_1;
	elseif (z <= 3.45e+18)
		tmp = x * (y * t);
	elseif (z <= 5e+28)
		tmp = t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(y * N[(z * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e-94], t$95$2, If[LessEqual[z, 3.8e-237], t$95$1, If[LessEqual[z, 3.45e+18], N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+28], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1000000000000001e-94 or 4.99999999999999957e28 < z

   1. Initial program 83.9%

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

      1. distribute-rgt-out-- 86.2%

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

      2. associate-*l* 90.9%

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

      3. *-commutative 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in x around 0 76.4%

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

      1. associate-*r* 76.4%

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

      2. neg-mul-1 76.4%

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

   6. Simplified 76.4%

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

   if -2.1000000000000001e-94 < z < 3.80000000000000024e-237 or 3.45e18 < z < 4.99999999999999957e28

   1. Initial program 95.6%

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

      1. distribute-rgt-out-- 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in x around inf 88.2%

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

      1. *-commutative 88.2%

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

   6. Simplified 88.2%

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

   if 3.80000000000000024e-237 < z < 3.45e18

   1. Initial program 93.2%

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

      1. distribute-rgt-out-- 93.2%

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

      2. associate-*l* 88.1%

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

      3. *-commutative 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in x around inf 70.5%

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

      1. *-commutative 70.5%

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

      2. associate-*r* 75.5%

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

   6. Simplified 75.5%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-t\right)\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-237}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 3: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := t \cdot \left(y \cdot x\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-t\right)\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-237}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (* y x))))
   (if (<= z -2.1e-94)
     (* y (* z (- t)))
     (if (<= z 7.5e-237)
       t_1
       (if (<= z 8.8e+18)
         (* x (* y t))
         (if (<= z 3e+31) t_1 (* z (* y (- t)))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = t * (y * x);
	double tmp;
	if (z <= -2.1e-94) {
		tmp = y * (z * -t);
	} else if (z <= 7.5e-237) {
		tmp = t_1;
	} else if (z <= 8.8e+18) {
		tmp = x * (y * t);
	} else if (z <= 3e+31) {
		tmp = t_1;
	} else {
		tmp = z * (y * -t);
	}
	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 (z <= (-2.1d-94)) then
        tmp = y * (z * -t)
    else if (z <= 7.5d-237) then
        tmp = t_1
    else if (z <= 8.8d+18) then
        tmp = x * (y * t)
    else if (z <= 3d+31) then
        tmp = t_1
    else
        tmp = z * (y * -t)
    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 (z <= -2.1e-94) {
		tmp = y * (z * -t);
	} else if (z <= 7.5e-237) {
		tmp = t_1;
	} else if (z <= 8.8e+18) {
		tmp = x * (y * t);
	} else if (z <= 3e+31) {
		tmp = t_1;
	} else {
		tmp = z * (y * -t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = t * (y * x)
	tmp = 0
	if z <= -2.1e-94:
		tmp = y * (z * -t)
	elif z <= 7.5e-237:
		tmp = t_1
	elif z <= 8.8e+18:
		tmp = x * (y * t)
	elif z <= 3e+31:
		tmp = t_1
	else:
		tmp = z * (y * -t)
	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 (z <= -2.1e-94)
		tmp = Float64(y * Float64(z * Float64(-t)));
	elseif (z <= 7.5e-237)
		tmp = t_1;
	elseif (z <= 8.8e+18)
		tmp = Float64(x * Float64(y * t));
	elseif (z <= 3e+31)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(y * Float64(-t)));
	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 (z <= -2.1e-94)
		tmp = y * (z * -t);
	elseif (z <= 7.5e-237)
		tmp = t_1;
	elseif (z <= 8.8e+18)
		tmp = x * (y * t);
	elseif (z <= 3e+31)
		tmp = t_1;
	else
		tmp = z * (y * -t);
	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[z, -2.1e-94], N[(y * N[(z * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e-237], t$95$1, If[LessEqual[z, 8.8e+18], N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+31], t$95$1, N[(z * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.1000000000000001e-94

   1. Initial program 85.0%

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

      1. distribute-rgt-out-- 86.5%

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

      2. associate-*l* 95.8%

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

      3. *-commutative 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in x around 0 79.7%

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

      1. associate-*r* 79.7%

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

      2. neg-mul-1 79.7%

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

   6. Simplified 79.7%

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

   if -2.1000000000000001e-94 < z < 7.50000000000000034e-237 or 8.8e18 < z < 2.99999999999999989e31

   1. Initial program 95.6%

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

      1. distribute-rgt-out-- 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in x around inf 88.2%

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

      1. *-commutative 88.2%

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

   6. Simplified 88.2%

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

   if 7.50000000000000034e-237 < z < 8.8e18

   1. Initial program 93.2%

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

      1. distribute-rgt-out-- 93.2%

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

      2. associate-*l* 88.1%

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

      3. *-commutative 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in x around inf 70.5%

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

      1. *-commutative 70.5%

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

      2. associate-*r* 75.5%

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

   6. Simplified 75.5%

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

   if 2.99999999999999989e31 < z

   1. Initial program 82.8%

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

      1. distribute-rgt-out-- 85.8%

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

      2. associate-*l* 85.7%

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

      3. *-commutative 85.7%

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

   3. Simplified 85.7%

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

      1. flip-- 43.3%

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

      2. associate-*r/ 40.4%

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

      3. clear-num 40.4%

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

      4. un-div-inv 40.4%

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

      5. clear-num 40.4%

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

      6. associate-*r/ 43.3%

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

      7. flip-- 85.6%

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

   5. Applied egg-rr 85.6%

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

   6. Taylor expanded in x around 0 72.8%

      \[\leadsto \frac{y}{\color{blue}{\frac{-1}{t \cdot z}}} \]
   7. Step-by-step derivation

      1. div-inv 72.8%

         \[\leadsto \color{blue}{y \cdot \frac{1}{\frac{-1}{t \cdot z}}} \]

      2. frac-2neg 72.8%

         \[\leadsto y \cdot \frac{1}{\color{blue}{\frac{--1}{-t \cdot z}}} \]

      3. metadata-eval 72.8%

         \[\leadsto y \cdot \frac{1}{\frac{\color{blue}{1}}{-t \cdot z}} \]

      4. remove-double-div 72.9%

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

      5. distribute-lft-neg-in 72.9%

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

      6. associate-*r* 78.7%

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

   8. Applied egg-rr 78.7%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-t\right)\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-237}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 4: 97.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 200000:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 200000.0) (* y (* t (- x z))) (* (- x z) (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 200000.0) {
		tmp = y * (t * (x - z));
	} else {
		tmp = (x - z) * (y * t);
	}
	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 <= 200000.0d0) then
        tmp = y * (t * (x - z))
    else
        tmp = (x - z) * (y * t)
    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 <= 200000.0) {
		tmp = y * (t * (x - z));
	} else {
		tmp = (x - z) * (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 200000.0:
		tmp = y * (t * (x - z))
	else:
		tmp = (x - z) * (y * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 200000.0)
		tmp = Float64(y * Float64(t * Float64(x - z)));
	else
		tmp = Float64(Float64(x - z) * Float64(y * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 200000.0)
		tmp = y * (t * (x - z));
	else
		tmp = (x - z) * (y * t);
	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, 200000.0], N[(y * N[(t * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - z), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2e5

   1. Initial program 86.6%

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

      1. distribute-rgt-out-- 87.7%

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

      2. associate-*l* 92.8%

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

      3. *-commutative 92.8%

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

   3. Simplified 92.8%

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

   if 2e5 < t

   1. Initial program 94.7%

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

      1. *-commutative 94.7%

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

      2. distribute-rgt-out-- 96.1%

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

      3. associate-*r* 94.3%

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

      4. *-commutative 94.3%

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

   3. Simplified 94.3%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 200000:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \end{array} \]

Alternative 5: 97.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -21500000000000:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -21500000000000.0) (* 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 <= -21500000000000.0) {
		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 <= (-21500000000000.0d0)) 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 <= -21500000000000.0) {
		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 <= -21500000000000.0:
		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 <= -21500000000000.0)
		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 <= -21500000000000.0)
		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, -21500000000000.0], 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 < -2.15e13

   1. Initial program 69.4%

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

      1. distribute-rgt-out-- 73.1%

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

      2. associate-*l* 96.4%

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

      3. *-commutative 96.4%

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

   3. Simplified 96.4%

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

   if -2.15e13 < y

   1. Initial program 94.2%

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

      1. distribute-rgt-out-- 94.7%

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

   3. Simplified 94.7%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -21500000000000:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array} \]

Alternative 6: 55.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -17000000000000:\\ \;\;\;\;y \cdot \left(t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -17000000000000.0) (* y (* t x)) (* t (* y x))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -17000000000000.0) {
		tmp = y * (t * x);
	} else {
		tmp = t * (y * x);
	}
	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 <= (-17000000000000.0d0)) then
        tmp = y * (t * x)
    else
        tmp = t * (y * x)
    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 <= -17000000000000.0) {
		tmp = y * (t * x);
	} else {
		tmp = t * (y * x);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -17000000000000.0:
		tmp = y * (t * x)
	else:
		tmp = t * (y * x)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -17000000000000.0)
		tmp = Float64(y * Float64(t * x));
	else
		tmp = Float64(t * Float64(y * x));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -17000000000000.0)
		tmp = y * (t * x);
	else
		tmp = t * (y * x);
	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, -17000000000000.0], N[(y * N[(t * x), $MachinePrecision]), $MachinePrecision], N[(t * N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7e13

   1. Initial program 69.4%

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

      1. distribute-rgt-out-- 73.1%

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

      2. associate-*l* 96.4%

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

      3. *-commutative 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in x around inf 48.1%

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

   if -1.7e13 < y

   1. Initial program 94.2%

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

      1. distribute-rgt-out-- 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in x around inf 52.4%

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

      1. *-commutative 52.4%

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

   6. Simplified 52.4%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -17000000000000:\\ \;\;\;\;y \cdot \left(t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 7: 92.3% 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 88.8%

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

   1. distribute-rgt-out-- 90.0%

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

   2. associate-*l* 90.9%

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

   3. *-commutative 90.9%

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

3. Simplified 90.9%

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

4. Final simplification 90.9%

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

Alternative 8: 53.3% 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 88.8%

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

   1. distribute-rgt-out-- 90.0%

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

   2. associate-*l* 90.9%

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

   3. *-commutative 90.9%

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

3. Simplified 90.9%

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

4. Taylor expanded in x around inf 49.6%

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

5. Final simplification 49.6%

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

Developer target: 96.2% 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 2023297 
(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))