Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3

Percentage Accurate: 90.8% → 95.2%

Time: 5.6s

Alternatives: 5

Speedup: 1.0×

• 25.3% 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: 95.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;\left(x \cdot y - y \cdot z\right) \cdot t \leq 4 \cdot 10^{+256}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= (* (- (* x y) (* y z)) t) 4e+256)
   (* t (* y (- x z)))
   (* (- x z) (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((((x * y) - (y * z)) * t) <= 4e+256) {
		tmp = t * (y * (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 ((((x * y) - (y * z)) * t) <= 4d+256) then
        tmp = t * (y * (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 ((((x * y) - (y * z)) * t) <= 4e+256) {
		tmp = t * (y * (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 (((x * y) - (y * z)) * t) <= 4e+256:
		tmp = t * (y * (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 (Float64(Float64(Float64(x * y) - Float64(y * z)) * t) <= 4e+256)
		tmp = Float64(t * Float64(y * 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 ((((x * y) - (y * z)) * t) <= 4e+256)
		tmp = t * (y * (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[N[(N[(N[(x * y), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], 4e+256], N[(t * N[(y * 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 (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t) < 4.0000000000000001e256

   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%

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

   if 4.0000000000000001e256 < (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t)

   1. Initial program 82.7%

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

      1. *-commutative 82.7%

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

      2. distribute-rgt-out-- 84.7%

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

      3. associate-*r* 99.9%

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

      4. *-commutative 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y - y \cdot z\right) \cdot t \leq 4 \cdot 10^{+256}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \end{array} \]

Alternative 2: 73.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4700 \lor \neg \left(z \leq 1.9 \cdot 10^{-51}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4700.0) (not (<= z 1.9e-51))) (* (* y z) (- t)) (* (* x y) t)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4700.0) || !(z <= 1.9e-51)) {
		tmp = (y * z) * -t;
	} else {
		tmp = (x * 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 ((z <= (-4700.0d0)) .or. (.not. (z <= 1.9d-51))) then
        tmp = (y * z) * -t
    else
        tmp = (x * 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 ((z <= -4700.0) || !(z <= 1.9e-51)) {
		tmp = (y * z) * -t;
	} else {
		tmp = (x * y) * t;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -4700.0) or not (z <= 1.9e-51):
		tmp = (y * z) * -t
	else:
		tmp = (x * y) * t
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4700.0) || !(z <= 1.9e-51))
		tmp = Float64(Float64(y * z) * Float64(-t));
	else
		tmp = Float64(Float64(x * 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 ((z <= -4700.0) || ~((z <= 1.9e-51)))
		tmp = (y * z) * -t;
	else
		tmp = (x * 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[Or[LessEqual[z, -4700.0], N[Not[LessEqual[z, 1.9e-51]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * (-t)), $MachinePrecision], N[(N[(x * y), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4700 or 1.90000000000000001e-51 < z

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

      2. distribute-rgt-out-- 91.1%

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

      3. associate-*r* 90.4%

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

      4. *-commutative 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in x around 0 77.0%

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

      1. mul-1-neg 77.0%

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

      2. distribute-rgt-neg-in 77.0%

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

      3. *-commutative 77.0%

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

      4. distribute-lft-neg-out 77.0%

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

      5. *-commutative 77.0%

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

   6. Simplified 77.0%

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

   if -4700 < z < 1.90000000000000001e-51

   1. Initial program 95.8%

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

      1. *-commutative 95.8%

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

      2. distribute-rgt-out-- 95.8%

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

      3. associate-*r* 89.9%

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

      4. *-commutative 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in x around inf 78.5%

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

      1. *-commutative 78.5%

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

   6. Simplified 78.5%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4700 \lor \neg \left(z \leq 1.9 \cdot 10^{-51}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot t\\ \end{array} \]

Alternative 3: 92.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 2.4 \cdot 10^{+237}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z 2.4e+237) (* (- x z) (* y t)) (* (* y z) (- t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 2.4e+237) {
		tmp = (x - z) * (y * t);
	} else {
		tmp = (y * z) * -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 (z <= 2.4d+237) then
        tmp = (x - z) * (y * t)
    else
        tmp = (y * z) * -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 (z <= 2.4e+237) {
		tmp = (x - z) * (y * t);
	} else {
		tmp = (y * z) * -t;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= 2.4e+237:
		tmp = (x - z) * (y * t)
	else:
		tmp = (y * z) * -t
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= 2.4e+237)
		tmp = Float64(Float64(x - z) * Float64(y * t));
	else
		tmp = Float64(Float64(y * z) * Float64(-t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 2.4e+237)
		tmp = (x - z) * (y * t);
	else
		tmp = (y * z) * -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[z, 2.4e+237], N[(N[(x - z), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.3999999999999999e237

   1. Initial program 93.5%

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

      1. *-commutative 93.5%

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

      2. distribute-rgt-out-- 93.5%

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

      3. associate-*r* 91.6%

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

      4. *-commutative 91.6%

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

   3. Simplified 91.6%

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

   if 2.3999999999999999e237 < z

   1. Initial program 83.3%

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

      1. *-commutative 83.3%

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

      2. distribute-rgt-out-- 89.2%

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

      3. associate-*r* 69.9%

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

      4. *-commutative 69.9%

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

   3. Simplified 69.9%

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

   4. Taylor expanded in x around 0 89.2%

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

      1. mul-1-neg 89.2%

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

      2. distribute-rgt-neg-in 89.2%

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

      3. *-commutative 89.2%

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

      4. distribute-lft-neg-out 89.2%

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

      5. *-commutative 89.2%

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

   6. Simplified 89.2%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.4 \cdot 10^{+237}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-t\right)\\ \end{array} \]

Alternative 4: 52.9% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

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 = (x * y) * t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.8%

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

   1. *-commutative 92.8%

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

   2. distribute-rgt-out-- 93.2%

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

   3. associate-*r* 90.1%

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

   4. *-commutative 90.1%

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

3. Simplified 90.1%

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

4. Taylor expanded in x around inf 48.9%

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

   1. *-commutative 48.9%

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

6. Simplified 48.9%

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

7. Final simplification 48.9%

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

Alternative 5: 52.7% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

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 * (x * t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.8%

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

   1. *-commutative 92.8%

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

   2. distribute-rgt-out-- 93.2%

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

   3. associate-*r* 90.1%

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

   4. *-commutative 90.1%

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

3. Simplified 90.1%

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

4. Taylor expanded in x around inf 48.9%

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

   1. associate-*r* 50.8%

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

   2. *-commutative 50.8%

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

6. Simplified 50.8%

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

7. Final simplification 50.8%

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

Developer target: 96.0% 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 2023290 
(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))