Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3

Percentage Accurate: 90.5% → 97.2%

Time: 5.4s

Alternatives: 7

Speedup: 1.0×

• Unsound rule application detected in e-graph. Results may not be sound.

• 25.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.5% 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: 97.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -4e-65) (* y (* (- x z) t)) (* t (* y (- x z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4e-65) {
		tmp = y * ((x - z) * t);
	} 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 <= (-4d-65)) then
        tmp = y * ((x - z) * t)
    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 <= -4e-65) {
		tmp = y * ((x - z) * 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 <= -4e-65:
		tmp = y * ((x - z) * 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 (y <= -4e-65)
		tmp = Float64(y * Float64(Float64(x - z) * 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 <= -4e-65)
		tmp = y * ((x - z) * 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[y, -4e-65], N[(y * N[(N[(x - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(t * N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.99999999999999969e-65

   1. Initial program 89.9%

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

      1. distribute-rgt-out-- 94.3%

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

      2. associate-*l* 98.4%

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

   3. Simplified 98.4%

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

   if -3.99999999999999969e-65 < y

   1. Initial program 90.9%

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

      1. distribute-rgt-out-- 92.0%

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

   3. Simplified 92.0%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array} \]

Alternative 2: 73.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;x \leq 820000:\\ \;\;\;\;z \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.15e-23)
   (* x (* y t))
   (if (<= x 820000.0) (* z (* y (- t))) (* t (* y x)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.15e-23) {
		tmp = x * (y * t);
	} else if (x <= 820000.0) {
		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 (x <= (-1.15d-23)) then
        tmp = x * (y * t)
    else if (x <= 820000.0d0) 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 (x <= -1.15e-23) {
		tmp = x * (y * t);
	} else if (x <= 820000.0) {
		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 x <= -1.15e-23:
		tmp = x * (y * t)
	elif x <= 820000.0:
		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 (x <= -1.15e-23)
		tmp = Float64(x * Float64(y * t));
	elseif (x <= 820000.0)
		tmp = Float64(z * Float64(y * Float64(-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 (x <= -1.15e-23)
		tmp = x * (y * t);
	elseif (x <= 820000.0)
		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[LessEqual[x, -1.15e-23], N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 820000.0], N[(z * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], N[(t * N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.15000000000000005e-23

   1. Initial program 83.8%

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

      1. distribute-rgt-out-- 88.9%

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

      2. associate-*l* 91.8%

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

   3. Simplified 91.8%

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

      1. add-cube-cbrt 90.8%

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

      2. pow3 90.9%

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

   5. Applied egg-rr 90.9%

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

   6. Taylor expanded in z around 0 78.1%

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

      1. pow-base-1 78.1%

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

      2. *-lft-identity 78.1%

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

      3. associate-*r* 81.2%

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

   8. Simplified 81.2%

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

   if -1.15000000000000005e-23 < x < 8.2e5

   1. Initial program 93.5%

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

      1. distribute-rgt-out-- 93.5%

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

      2. associate-*l* 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in x around 0 80.6%

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

      1. mul-1-neg 80.6%

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

      2. associate-*r* 79.6%

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

   6. Simplified 79.6%

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

   if 8.2e5 < x

   1. Initial program 91.0%

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

      1. distribute-rgt-out-- 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in x around inf 81.4%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;x \leq 820000:\\ \;\;\;\;z \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 3: 73.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;x \leq 135000000:\\ \;\;\;\;y \cdot \left(z \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.15e-23)
   (* x (* y t))
   (if (<= x 135000000.0) (* y (* z (- t))) (* t (* y x)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.15e-23) {
		tmp = x * (y * t);
	} else if (x <= 135000000.0) {
		tmp = y * (z * -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 (x <= (-1.15d-23)) then
        tmp = x * (y * t)
    else if (x <= 135000000.0d0) then
        tmp = y * (z * -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 (x <= -1.15e-23) {
		tmp = x * (y * t);
	} else if (x <= 135000000.0) {
		tmp = y * (z * -t);
	} else {
		tmp = t * (y * x);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if x <= -1.15e-23:
		tmp = x * (y * t)
	elif x <= 135000000.0:
		tmp = y * (z * -t)
	else:
		tmp = t * (y * x)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.15e-23)
		tmp = Float64(x * Float64(y * t));
	elseif (x <= 135000000.0)
		tmp = Float64(y * Float64(z * Float64(-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 (x <= -1.15e-23)
		tmp = x * (y * t);
	elseif (x <= 135000000.0)
		tmp = y * (z * -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[LessEqual[x, -1.15e-23], N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 135000000.0], N[(y * N[(z * (-t)), $MachinePrecision]), $MachinePrecision], N[(t * N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.15000000000000005e-23

   1. Initial program 83.8%

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

      1. distribute-rgt-out-- 88.9%

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

      2. associate-*l* 91.8%

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

   3. Simplified 91.8%

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

      1. add-cube-cbrt 90.8%

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

      2. pow3 90.9%

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

   5. Applied egg-rr 90.9%

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

   6. Taylor expanded in z around 0 78.1%

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

      1. pow-base-1 78.1%

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

      2. *-lft-identity 78.1%

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

      3. associate-*r* 81.2%

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

   8. Simplified 81.2%

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

   if -1.15000000000000005e-23 < x < 1.35e8

   1. Initial program 93.5%

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

      1. distribute-rgt-out-- 93.5%

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

      2. associate-*l* 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in x around 0 80.6%

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

      1. mul-1-neg 80.6%

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

      2. distribute-rgt-neg-in 80.6%

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

      3. distribute-rgt-neg-in 80.6%

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

   6. Simplified 80.6%

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

   if 1.35e8 < x

   1. Initial program 91.0%

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

      1. distribute-rgt-out-- 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in x around inf 81.4%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;x \leq 135000000:\\ \;\;\;\;y \cdot \left(z \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 4: 91.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 2.1 \cdot 10^{+196}:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= x 2.1e+196) (* y (* (- x z) t)) (* t (* y x))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 2.1e+196) {
		tmp = y * ((x - z) * 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 (x <= 2.1d+196) then
        tmp = y * ((x - z) * 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 (x <= 2.1e+196) {
		tmp = y * ((x - z) * t);
	} else {
		tmp = t * (y * x);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if x <= 2.1e+196:
		tmp = y * ((x - z) * t)
	else:
		tmp = t * (y * x)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (x <= 2.1e+196)
		tmp = Float64(y * Float64(Float64(x - z) * 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 (x <= 2.1e+196)
		tmp = y * ((x - z) * 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[LessEqual[x, 2.1e+196], N[(y * N[(N[(x - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(t * N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.10000000000000015e196

   1. Initial program 91.0%

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

      1. distribute-rgt-out-- 92.8%

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

      2. associate-*l* 93.5%

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

   3. Simplified 93.5%

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

   if 2.10000000000000015e196 < x

   1. Initial program 87.5%

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

      1. distribute-rgt-out-- 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in x around inf 90.9%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.1 \cdot 10^{+196}:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 5: 97.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 6.5 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 6.5e+71) (* y (* (- x z) t)) (* (- x z) (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 6.5e+71) {
		tmp = y * ((x - z) * t);
	} 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 <= 6.5d+71) then
        tmp = y * ((x - z) * t)
    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 <= 6.5e+71) {
		tmp = y * ((x - z) * t);
	} else {
		tmp = (x - z) * (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 6.5e+71:
		tmp = y * ((x - z) * t)
	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 <= 6.5e+71)
		tmp = Float64(y * Float64(Float64(x - z) * t));
	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 <= 6.5e+71)
		tmp = y * ((x - z) * t);
	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, 6.5e+71], N[(y * N[(N[(x - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x - z), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 6.49999999999999954e71

   1. Initial program 89.5%

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

      1. distribute-rgt-out-- 92.0%

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

      2. associate-*l* 93.6%

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

   3. Simplified 93.6%

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

   if 6.49999999999999954e71 < t

   1. Initial program 94.8%

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

      1. distribute-rgt-out-- 94.8%

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

      2. associate-*l* 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in y around 0 89.8%

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

      1. associate-*r* 89.8%

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

   6. Simplified 89.8%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 6.5 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \end{array} \]

Alternative 6: 56.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 5 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 5e+49) (* y (* x t)) (* x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 5e+49) {
		tmp = y * (x * 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 (t <= 5d+49) then
        tmp = y * (x * 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 (t <= 5e+49) {
		tmp = y * (x * t);
	} else {
		tmp = x * (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 5e+49:
		tmp = y * (x * t)
	else:
		tmp = x * (y * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 5e+49)
		tmp = Float64(y * Float64(x * t));
	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 <= 5e+49)
		tmp = y * (x * 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[LessEqual[t, 5e+49], N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 5.0000000000000004e49

   1. Initial program 89.3%

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

      1. distribute-rgt-out-- 91.9%

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

      2. associate-*l* 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in x around inf 53.1%

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

   if 5.0000000000000004e49 < t

   1. Initial program 95.0%

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

      1. distribute-rgt-out-- 95.0%

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

      2. associate-*l* 90.3%

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

   3. Simplified 90.3%

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

      1. add-cube-cbrt 89.6%

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

      2. pow3 89.6%

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

   5. Applied egg-rr 89.6%

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

   6. Taylor expanded in z around 0 46.2%

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

      1. pow-base-1 46.2%

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

      2. *-lft-identity 46.2%

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

      3. associate-*r* 57.3%

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

   8. Simplified 57.3%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \end{array} \]

Alternative 7: 53.5% 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 90.6%

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

   1. distribute-rgt-out-- 92.6%

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

   2. associate-*l* 92.8%

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

3. Simplified 92.8%

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

4. Taylor expanded in x around inf 51.5%

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

5. Final simplification 51.5%

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

Developer target: 96.6% 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 2023176 
(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))