Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3

Percentage Accurate: 91.1% → 95.1%

Time: 8.8s

Alternatives: 8

Speedup: 0.6×

• 25.6% 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: 91.1% 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: 95.1% accurate, 0.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-188}:\\ \;\;\;\;{\left(\sqrt[3]{y \cdot \left(t \cdot \left(x - z\right)\right)}\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.7e-188)
   (pow (cbrt (* y (* t (- x z)))) 3.0)
   (* t (* y (- x z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.7e-188) {
		tmp = pow(cbrt((y * (t * (x - z)))), 3.0);
	} else {
		tmp = t * (y * (x - z));
	}
	return tmp;
}

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.7e-188) {
		tmp = Math.pow(Math.cbrt((y * (t * (x - z)))), 3.0);
	} 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 <= -3.7e-188)
		tmp = cbrt(Float64(y * Float64(t * Float64(x - z)))) ^ 3.0;
	else
		tmp = Float64(t * Float64(y * Float64(x - z)));
	end
	return 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, -3.7e-188], N[Power[N[Power[N[(y * N[(t * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision], N[(t * N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.69999999999999972e-188

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. distribute-rgt-out-- 92.6%

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

      3. associate-*r* 95.4%

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

      4. *-commutative 95.4%

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

   3. Simplified 95.4%

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

      1. add-cube-cbrt 94.3%

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

      2. pow3 94.3%

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

      3. associate-*l* 97.7%

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

   5. Applied egg-rr 97.7%

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

   if -3.69999999999999972e-188 < y

   1. Initial program 93.9%

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

      1. distribute-rgt-out-- 95.9%

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

   3. Simplified 95.9%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-188}:\\ \;\;\;\;{\left(\sqrt[3]{y \cdot \left(t \cdot \left(x - z\right)\right)}\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array} \]

Alternative 2: 95.2% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((y * x) - (y * z)) <= -Double.POSITIVE_INFINITY) {
		tmp = (x - z) * (y * t);
	} else {
		tmp = t * (y * (x - z));
	}
	return tmp;
}

Python

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

Julia

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

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z y)) < -inf.0

   1. Initial program 73.4%

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

      1. *-commutative 73.4%

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

      2. distribute-rgt-out-- 73.4%

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

      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%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z y))

   1. Initial program 93.9%

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

      1. distribute-rgt-out-- 96.5%

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

   3. Simplified 96.5%

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

4. Final simplification 96.7%

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

Alternative 3: 74.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -0.038 \lor \neg \left(z \leq 1.06 \cdot 10^{-10}\right):\\ \;\;\;\;-z \cdot \left(y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.038) (not (<= z 1.06e-10))) (- (* z (* y t))) (* t (* y x))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.038) || !(z <= 1.06e-10)) {
		tmp = -(z * (y * t));
	} 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 ((z <= (-0.038d0)) .or. (.not. (z <= 1.06d-10))) then
        tmp = -(z * (y * t))
    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 ((z <= -0.038) || !(z <= 1.06e-10)) {
		tmp = -(z * (y * t));
	} else {
		tmp = t * (y * x);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -0.038) or not (z <= 1.06e-10):
		tmp = -(z * (y * t))
	else:
		tmp = t * (y * x)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.038) || !(z <= 1.06e-10))
		tmp = Float64(-Float64(z * Float64(y * t)));
	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 ((z <= -0.038) || ~((z <= 1.06e-10)))
		tmp = -(z * (y * t));
	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[Or[LessEqual[z, -0.038], N[Not[LessEqual[z, 1.06e-10]], $MachinePrecision]], (-N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), N[(t * N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0379999999999999991 or 1.06e-10 < z

   1. Initial program 90.2%

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

      1. *-commutative 90.2%

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

      2. distribute-rgt-out-- 94.4%

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

      3. associate-*r* 88.1%

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

      4. *-commutative 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in x around 0 78.4%

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

      1. mul-1-neg 78.4%

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

      2. associate-*r* 73.5%

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

      3. distribute-rgt-neg-out 73.5%

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

      4. *-commutative 73.5%

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

      5. distribute-lft-neg-out 73.5%

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

   6. Simplified 73.5%

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

   if -0.0379999999999999991 < z < 1.06e-10

   1. Initial program 94.7%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   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 82.4%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.038 \lor \neg \left(z \leq 1.06 \cdot 10^{-10}\right):\\ \;\;\;\;-z \cdot \left(y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 4: 74.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00098 \lor \neg \left(z \leq 3.5 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot \left(t \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.00098) (not (<= z 3.5e-12)))
   (* y (* t (- z)))
   (* t (* y x))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.00098) || !(z <= 3.5e-12)) {
		tmp = y * (t * -z);
	} 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 ((z <= (-0.00098d0)) .or. (.not. (z <= 3.5d-12))) then
        tmp = y * (t * -z)
    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 ((z <= -0.00098) || !(z <= 3.5e-12)) {
		tmp = y * (t * -z);
	} else {
		tmp = t * (y * x);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -0.00098) or not (z <= 3.5e-12):
		tmp = y * (t * -z)
	else:
		tmp = t * (y * x)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.00098) || !(z <= 3.5e-12))
		tmp = Float64(y * Float64(t * Float64(-z)));
	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 ((z <= -0.00098) || ~((z <= 3.5e-12)))
		tmp = y * (t * -z);
	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[Or[LessEqual[z, -0.00098], N[Not[LessEqual[z, 3.5e-12]], $MachinePrecision]], N[(y * N[(t * (-z)), $MachinePrecision]), $MachinePrecision], N[(t * N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.7999999999999997e-4 or 3.5e-12 < z

   1. Initial program 90.2%

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

      1. *-commutative 90.2%

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

      2. distribute-rgt-out-- 94.4%

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

      3. associate-*r* 88.1%

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

      4. *-commutative 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in x around 0 78.4%

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

      1. mul-1-neg 78.4%

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

      2. distribute-rgt-neg-in 78.4%

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

      3. distribute-rgt-neg-out 78.4%

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

   6. Simplified 78.4%

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

   if -9.7999999999999997e-4 < z < 3.5e-12

   1. Initial program 94.7%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   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 82.4%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00098 \lor \neg \left(z \leq 3.5 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot \left(t \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 5: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -0.037:\\ \;\;\;\;y \cdot \left(t \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-22}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.037)
   (* y (* t (- z)))
   (if (<= z 2.1e-22) (* t (* y x)) (* t (* z (- y))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.037) {
		tmp = y * (t * -z);
	} else if (z <= 2.1e-22) {
		tmp = t * (y * x);
	} else {
		tmp = t * (z * -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 (z <= (-0.037d0)) then
        tmp = y * (t * -z)
    else if (z <= 2.1d-22) then
        tmp = t * (y * x)
    else
        tmp = t * (z * -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 (z <= -0.037) {
		tmp = y * (t * -z);
	} else if (z <= 2.1e-22) {
		tmp = t * (y * x);
	} else {
		tmp = t * (z * -y);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -0.037:
		tmp = y * (t * -z)
	elif z <= 2.1e-22:
		tmp = t * (y * x)
	else:
		tmp = t * (z * -y)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.037)
		tmp = Float64(y * Float64(t * Float64(-z)));
	elseif (z <= 2.1e-22)
		tmp = Float64(t * Float64(y * x));
	else
		tmp = Float64(t * Float64(z * Float64(-y)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -0.037)
		tmp = y * (t * -z);
	elseif (z <= 2.1e-22)
		tmp = t * (y * x);
	else
		tmp = t * (z * -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[z, -0.037], N[(y * N[(t * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-22], N[(t * N[(y * x), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0369999999999999982

   1. Initial program 90.0%

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

      1. *-commutative 90.0%

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

      2. distribute-rgt-out-- 93.8%

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

      3. associate-*r* 89.1%

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

      4. *-commutative 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in x around 0 80.5%

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

      1. mul-1-neg 80.5%

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

      2. distribute-rgt-neg-in 80.5%

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

      3. distribute-rgt-neg-out 80.5%

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

   6. Simplified 80.5%

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

   if -0.0369999999999999982 < z < 2.10000000000000008e-22

   1. Initial program 94.6%

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

      1. distribute-rgt-out-- 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in x around inf 82.9%

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

   if 2.10000000000000008e-22 < z

   1. Initial program 90.8%

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

      1. distribute-rgt-out-- 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in x around 0 75.0%

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

      1. mul-1-neg 75.0%

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

      2. distribute-rgt-neg-out 75.0%

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

   6. Simplified 75.0%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.037:\\ \;\;\;\;y \cdot \left(t \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-22}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(-y\right)\right)\\ \end{array} \]

Alternative 6: 90.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+142}:\\ \;\;\;\;y \cdot \left(t \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.7e+142) (* y (* t (- z))) (* (- x z) (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e+142) {
		tmp = y * (t * -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 (z <= (-2.7d+142)) then
        tmp = y * (t * -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 (z <= -2.7e+142) {
		tmp = y * (t * -z);
	} else {
		tmp = (x - z) * (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2.7e+142:
		tmp = y * (t * -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 (z <= -2.7e+142)
		tmp = Float64(y * Float64(t * Float64(-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 (z <= -2.7e+142)
		tmp = y * (t * -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[z, -2.7e+142], N[(y * N[(t * (-z)), $MachinePrecision]), $MachinePrecision], N[(N[(x - z), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.69999999999999983e142

   1. Initial program 86.1%

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

      1. *-commutative 86.1%

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

      2. distribute-rgt-out-- 90.9%

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

      3. associate-*r* 79.8%

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

      4. *-commutative 79.8%

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

   3. Simplified 79.8%

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

   4. Taylor expanded in x around 0 83.5%

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

      1. mul-1-neg 83.5%

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

      2. distribute-rgt-neg-in 83.5%

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

      3. distribute-rgt-neg-out 83.5%

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

   6. Simplified 83.5%

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

   if -2.69999999999999983e142 < z

   1. Initial program 93.4%

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

      1. *-commutative 93.4%

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

      2. distribute-rgt-out-- 95.3%

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

      3. associate-*r* 92.5%

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

      4. *-commutative 92.5%

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

   3. Simplified 92.5%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+142}:\\ \;\;\;\;y \cdot \left(t \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \end{array} \]

Alternative 7: 56.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 2.05 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \left(t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 2.05e-52) (* y (* t x)) (* x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.05e-52) {
		tmp = y * (t * x);
	} 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 (t <= 2.05d-52) then
        tmp = y * (t * x)
    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 (t <= 2.05e-52) {
		tmp = y * (t * x);
	} else {
		tmp = x * (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 2.05e-52:
		tmp = y * (t * x)
	else:
		tmp = x * (y * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 2.05e-52)
		tmp = Float64(y * Float64(t * x));
	else
		tmp = Float64(x * 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 <= 2.05e-52)
		tmp = y * (t * x);
	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[LessEqual[t, 2.05e-52], N[(y * N[(t * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.04999999999999994e-52

   1. Initial program 91.5%

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

      1. *-commutative 91.5%

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

      2. distribute-rgt-out-- 93.1%

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

      3. associate-*r* 87.3%

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

      4. *-commutative 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in x around inf 56.5%

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

   if 2.04999999999999994e-52 < t

   1. Initial program 94.1%

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

      1. *-commutative 94.1%

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

      2. distribute-rgt-out-- 98.4%

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

      3. associate-*r* 98.5%

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

      4. *-commutative 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in x around inf 35.8%

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

      1. associate-*r* 46.5%

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

      2. *-commutative 46.5%

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

   6. Simplified 46.5%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.05 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \left(t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \end{array} \]

Alternative 8: 54.7% accurate, 1.8× speedup

Math

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

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (* 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(x * Float64(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[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.2%

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

   1. *-commutative 92.2%

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

   2. distribute-rgt-out-- 94.6%

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

   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 inf 50.9%

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

   1. associate-*r* 52.4%

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

   2. *-commutative 52.4%

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

6. Simplified 52.4%

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

7. Final simplification 52.4%

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

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 2023279 
(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))