Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3

Percentage Accurate: 90.6% → 97.2%

Time: 7.8s

Alternatives: 8

Speedup: 1.3×

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

• 24.6% 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: 90.6% 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

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1e+36) (* 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 <= -1e+36) {
		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 <= (-1d+36)) 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 <= -1e+36) {
		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 <= -1e+36:
		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 <= -1e+36)
		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 <= -1e+36)
		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, -1e+36], 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 < -1.00000000000000004e36

   1. Initial program 81.3%

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

      1. distribute-rgt-out-- 89.8%

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

      2. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   if -1.00000000000000004e36 < y

   1. Initial program 93.3%

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

      1. distribute-rgt-out-- 94.3%

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

   3. Simplified 94.3%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array} \]

Alternative 2: 73.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := t \cdot \left(y \cdot x\right)\\ t_2 := z \cdot \left(t \cdot \left(-y\right)\right)\\ \mathbf{if}\;x \leq -6.4 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (* y x))) (t_2 (* z (* t (- y)))))
   (if (<= x -6.4e+62)
     t_1
     (if (<= x 1.2e+37)
       t_2
       (if (<= x 8e+104) t_1 (if (<= x 4.3e+128) t_2 (* y (* x t))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = t * (y * x);
	double t_2 = z * (t * -y);
	double tmp;
	if (x <= -6.4e+62) {
		tmp = t_1;
	} else if (x <= 1.2e+37) {
		tmp = t_2;
	} else if (x <= 8e+104) {
		tmp = t_1;
	} else if (x <= 4.3e+128) {
		tmp = t_2;
	} else {
		tmp = y * (x * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (y * x)
    t_2 = z * (t * -y)
    if (x <= (-6.4d+62)) then
        tmp = t_1
    else if (x <= 1.2d+37) then
        tmp = t_2
    else if (x <= 8d+104) then
        tmp = t_1
    else if (x <= 4.3d+128) then
        tmp = t_2
    else
        tmp = y * (x * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y * x);
	double t_2 = z * (t * -y);
	double tmp;
	if (x <= -6.4e+62) {
		tmp = t_1;
	} else if (x <= 1.2e+37) {
		tmp = t_2;
	} else if (x <= 8e+104) {
		tmp = t_1;
	} else if (x <= 4.3e+128) {
		tmp = t_2;
	} else {
		tmp = y * (x * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = t * (y * x)
	t_2 = z * (t * -y)
	tmp = 0
	if x <= -6.4e+62:
		tmp = t_1
	elif x <= 1.2e+37:
		tmp = t_2
	elif x <= 8e+104:
		tmp = t_1
	elif x <= 4.3e+128:
		tmp = t_2
	else:
		tmp = y * (x * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(t * Float64(y * x))
	t_2 = Float64(z * Float64(t * Float64(-y)))
	tmp = 0.0
	if (x <= -6.4e+62)
		tmp = t_1;
	elseif (x <= 1.2e+37)
		tmp = t_2;
	elseif (x <= 8e+104)
		tmp = t_1;
	elseif (x <= 4.3e+128)
		tmp = t_2;
	else
		tmp = Float64(y * Float64(x * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = t * (y * x);
	t_2 = z * (t * -y);
	tmp = 0.0;
	if (x <= -6.4e+62)
		tmp = t_1;
	elseif (x <= 1.2e+37)
		tmp = t_2;
	elseif (x <= 8e+104)
		tmp = t_1;
	elseif (x <= 4.3e+128)
		tmp = t_2;
	else
		tmp = y * (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t * (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.4e+62], t$95$1, If[LessEqual[x, 1.2e+37], t$95$2, If[LessEqual[x, 8e+104], t$95$1, If[LessEqual[x, 4.3e+128], t$95$2, N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.39999999999999968e62 or 1.2e37 < x < 8e104

   1. Initial program 87.6%

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

      1. distribute-rgt-out-- 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in x around inf 81.7%

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

   if -6.39999999999999968e62 < x < 1.2e37 or 8e104 < x < 4.29999999999999975e128

   1. Initial program 95.8%

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

      1. distribute-rgt-out-- 95.8%

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

      2. associate-*l* 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in x around 0 76.4%

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

      1. associate-*r* 76.4%

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

      2. neg-mul-1 76.4%

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

   6. Simplified 76.4%

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

      1. distribute-lft-neg-out 76.4%

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

      2. add-sqr-sqrt 41.0%

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

      3. sqrt-unprod 41.7%

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

      4. sqr-neg 41.7%

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

      5. sqrt-unprod 7.4%

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

      6. add-sqr-sqrt 13.0%

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

      7. associate-*r* 13.8%

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

      8. *-commutative 13.8%

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

      9. *-commutative 13.8%

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

      10. add-sqr-sqrt 8.1%

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

      11. sqrt-unprod 40.3%

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

      12. sqr-neg 40.3%

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

      13. sqrt-unprod 40.8%

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

      14. add-sqr-sqrt 76.3%

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

   8. Applied egg-rr 76.3%

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

   if 4.29999999999999975e128 < x

   1. Initial program 78.0%

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

      1. distribute-rgt-out-- 84.7%

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

      2. associate-*l* 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in x around inf 72.7%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+37}:\\ \;\;\;\;z \cdot \left(t \cdot \left(-y\right)\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+104}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+128}:\\ \;\;\;\;z \cdot \left(t \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 3: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := t \cdot \left(y \cdot x\right)\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(t \cdot \left(-z\right)\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+134}:\\ \;\;\;\;z \cdot \left(t \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (* y x))))
   (if (<= x -1.35e+63)
     t_1
     (if (<= x 5.2e+37)
       (* y (* t (- z)))
       (if (<= x 3.2e+104)
         t_1
         (if (<= x 4.9e+134) (* z (* t (- y))) (* y (* x t))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = t * (y * x);
	double tmp;
	if (x <= -1.35e+63) {
		tmp = t_1;
	} else if (x <= 5.2e+37) {
		tmp = y * (t * -z);
	} else if (x <= 3.2e+104) {
		tmp = t_1;
	} else if (x <= 4.9e+134) {
		tmp = z * (t * -y);
	} else {
		tmp = y * (x * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y * x)
    if (x <= (-1.35d+63)) then
        tmp = t_1
    else if (x <= 5.2d+37) then
        tmp = y * (t * -z)
    else if (x <= 3.2d+104) then
        tmp = t_1
    else if (x <= 4.9d+134) then
        tmp = z * (t * -y)
    else
        tmp = y * (x * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y * x);
	double tmp;
	if (x <= -1.35e+63) {
		tmp = t_1;
	} else if (x <= 5.2e+37) {
		tmp = y * (t * -z);
	} else if (x <= 3.2e+104) {
		tmp = t_1;
	} else if (x <= 4.9e+134) {
		tmp = z * (t * -y);
	} else {
		tmp = y * (x * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = t * (y * x)
	tmp = 0
	if x <= -1.35e+63:
		tmp = t_1
	elif x <= 5.2e+37:
		tmp = y * (t * -z)
	elif x <= 3.2e+104:
		tmp = t_1
	elif x <= 4.9e+134:
		tmp = z * (t * -y)
	else:
		tmp = y * (x * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(t * Float64(y * x))
	tmp = 0.0
	if (x <= -1.35e+63)
		tmp = t_1;
	elseif (x <= 5.2e+37)
		tmp = Float64(y * Float64(t * Float64(-z)));
	elseif (x <= 3.2e+104)
		tmp = t_1;
	elseif (x <= 4.9e+134)
		tmp = Float64(z * Float64(t * Float64(-y)));
	else
		tmp = Float64(y * Float64(x * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = t * (y * x);
	tmp = 0.0;
	if (x <= -1.35e+63)
		tmp = t_1;
	elseif (x <= 5.2e+37)
		tmp = y * (t * -z);
	elseif (x <= 3.2e+104)
		tmp = t_1;
	elseif (x <= 4.9e+134)
		tmp = z * (t * -y);
	else
		tmp = y * (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.35e+63], t$95$1, If[LessEqual[x, 5.2e+37], N[(y * N[(t * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e+104], t$95$1, If[LessEqual[x, 4.9e+134], N[(z * N[(t * (-y)), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.35000000000000009e63 or 5.1999999999999998e37 < x < 3.2e104

   1. Initial program 87.6%

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

      1. distribute-rgt-out-- 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in x around inf 81.7%

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

   if -1.35000000000000009e63 < x < 5.1999999999999998e37

   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%

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

      2. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in x around 0 77.7%

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

      1. associate-*r* 77.7%

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

      2. neg-mul-1 77.7%

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

   6. Simplified 77.7%

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

   if 3.2e104 < x < 4.89999999999999996e134

   1. Initial program 99.6%

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

      1. distribute-rgt-out-- 99.6%

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

      2. associate-*l* 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in x around 0 51.3%

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

      1. associate-*r* 51.3%

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

      2. neg-mul-1 51.3%

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

   6. Simplified 51.3%

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

      1. distribute-lft-neg-out 51.3%

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

      2. add-sqr-sqrt 50.5%

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

      3. sqrt-unprod 35.5%

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

      4. sqr-neg 35.5%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 15.2%

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

      7. associate-*r* 15.2%

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

      8. *-commutative 15.2%

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

      9. *-commutative 15.2%

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

      10. add-sqr-sqrt 0.1%

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

      11. sqrt-unprod 36.1%

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

      12. sqr-neg 36.1%

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

      13. sqrt-unprod 63.7%

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

      14. add-sqr-sqrt 78.3%

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

   8. Applied egg-rr 78.3%

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

   if 4.89999999999999996e134 < x

   1. Initial program 78.0%

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

      1. distribute-rgt-out-- 84.7%

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

      2. associate-*l* 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in x around inf 72.7%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(t \cdot \left(-z\right)\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+104}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+134}:\\ \;\;\;\;z \cdot \left(t \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 4: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := t \cdot \left(y \cdot x\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+37}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+128}:\\ \;\;\;\;z \cdot \left(t \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (* y x))))
   (if (<= x -6e+62)
     t_1
     (if (<= x 2.7e+37)
       (* t (* y (- z)))
       (if (<= x 3.4e+105)
         t_1
         (if (<= x 5.8e+128) (* z (* t (- y))) (* y (* x t))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = t * (y * x);
	double tmp;
	if (x <= -6e+62) {
		tmp = t_1;
	} else if (x <= 2.7e+37) {
		tmp = t * (y * -z);
	} else if (x <= 3.4e+105) {
		tmp = t_1;
	} else if (x <= 5.8e+128) {
		tmp = z * (t * -y);
	} else {
		tmp = y * (x * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y * x)
    if (x <= (-6d+62)) then
        tmp = t_1
    else if (x <= 2.7d+37) then
        tmp = t * (y * -z)
    else if (x <= 3.4d+105) then
        tmp = t_1
    else if (x <= 5.8d+128) then
        tmp = z * (t * -y)
    else
        tmp = y * (x * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y * x);
	double tmp;
	if (x <= -6e+62) {
		tmp = t_1;
	} else if (x <= 2.7e+37) {
		tmp = t * (y * -z);
	} else if (x <= 3.4e+105) {
		tmp = t_1;
	} else if (x <= 5.8e+128) {
		tmp = z * (t * -y);
	} else {
		tmp = y * (x * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = t * (y * x)
	tmp = 0
	if x <= -6e+62:
		tmp = t_1
	elif x <= 2.7e+37:
		tmp = t * (y * -z)
	elif x <= 3.4e+105:
		tmp = t_1
	elif x <= 5.8e+128:
		tmp = z * (t * -y)
	else:
		tmp = y * (x * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(t * Float64(y * x))
	tmp = 0.0
	if (x <= -6e+62)
		tmp = t_1;
	elseif (x <= 2.7e+37)
		tmp = Float64(t * Float64(y * Float64(-z)));
	elseif (x <= 3.4e+105)
		tmp = t_1;
	elseif (x <= 5.8e+128)
		tmp = Float64(z * Float64(t * Float64(-y)));
	else
		tmp = Float64(y * Float64(x * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = t * (y * x);
	tmp = 0.0;
	if (x <= -6e+62)
		tmp = t_1;
	elseif (x <= 2.7e+37)
		tmp = t * (y * -z);
	elseif (x <= 3.4e+105)
		tmp = t_1;
	elseif (x <= 5.8e+128)
		tmp = z * (t * -y);
	else
		tmp = y * (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e+62], t$95$1, If[LessEqual[x, 2.7e+37], N[(t * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.4e+105], t$95$1, If[LessEqual[x, 5.8e+128], N[(z * N[(t * (-y)), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6e62 or 2.69999999999999986e37 < x < 3.3999999999999999e105

   1. Initial program 87.6%

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

      1. distribute-rgt-out-- 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in x around inf 81.7%

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

   if -6e62 < x < 2.69999999999999986e37

   1. Initial program 95.6%

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

      1. distribute-rgt-out-- 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in x around 0 79.6%

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

      1. neg-mul-1 79.6%

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

      2. distribute-lft-neg-in 79.6%

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

   6. Simplified 79.6%

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

   if 3.3999999999999999e105 < x < 5.8000000000000001e128

   1. Initial program 99.6%

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

      1. distribute-rgt-out-- 99.6%

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

      2. associate-*l* 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in x around 0 51.3%

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

      1. associate-*r* 51.3%

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

      2. neg-mul-1 51.3%

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

   6. Simplified 51.3%

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

      1. distribute-lft-neg-out 51.3%

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

      2. add-sqr-sqrt 50.5%

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

      3. sqrt-unprod 35.5%

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

      4. sqr-neg 35.5%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 15.2%

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

      7. associate-*r* 15.2%

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

      8. *-commutative 15.2%

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

      9. *-commutative 15.2%

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

      10. add-sqr-sqrt 0.1%

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

      11. sqrt-unprod 36.1%

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

      12. sqr-neg 36.1%

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

      13. sqrt-unprod 63.7%

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

      14. add-sqr-sqrt 78.3%

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

   8. Applied egg-rr 78.3%

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

   if 5.8000000000000001e128 < x

   1. Initial program 78.0%

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

      1. distribute-rgt-out-- 84.7%

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

      2. associate-*l* 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in x around inf 72.7%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+37}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+105}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+128}:\\ \;\;\;\;z \cdot \left(t \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 5: 97.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 3.1 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 3.1e+29) (* 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 <= 3.1e+29) {
		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 <= 3.1d+29) 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 <= 3.1e+29) {
		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 <= 3.1e+29:
		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 <= 3.1e+29)
		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 <= 3.1e+29)
		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, 3.1e+29], 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 < 3.0999999999999999e29

   1. Initial program 89.5%

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

      1. distribute-rgt-out-- 92.1%

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

      2. associate-*l* 94.5%

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

   3. Simplified 94.5%

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

   if 3.0999999999999999e29 < t

   1. Initial program 96.5%

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

      1. distribute-rgt-out-- 98.2%

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

      2. associate-*l* 80.7%

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

   3. Simplified 80.7%

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

      1. associate-*r* 98.2%

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

      2. distribute-rgt-out-- 96.5%

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

      3. *-commutative 96.5%

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

      4. sub-neg 96.5%

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

      5. distribute-rgt-in 89.8%

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

      6. *-commutative 89.8%

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

      7. *-commutative 89.8%

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

   5. Applied egg-rr 89.8%

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

   6. Taylor expanded in y around 0 75.3%

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

      1. +-commutative 75.3%

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

      2. mul-1-neg 75.3%

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

      3. distribute-rgt-neg-in 75.3%

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

      4. distribute-lft-in 80.7%

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

      5. sub-neg 80.7%

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

      6. associate-*r* 96.7%

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

   8. Simplified 96.7%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.1 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \end{array} \]

Alternative 6: 56.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -9e+39) (* y (* x t)) (* t (* y x))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9e+39) {
		tmp = y * (x * 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 (y <= (-9d+39)) then
        tmp = y * (x * 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 (y <= -9e+39) {
		tmp = y * (x * t);
	} else {
		tmp = t * (y * x);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -9e+39:
		tmp = y * (x * t)
	else:
		tmp = t * (y * x)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9e+39)
		tmp = Float64(y * Float64(x * 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 (y <= -9e+39)
		tmp = y * (x * 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[y, -9e+39], N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision], N[(t * N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.99999999999999991e39

   1. Initial program 80.9%

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

      1. distribute-rgt-out-- 89.6%

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

      2. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 70.0%

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

   if -8.99999999999999991e39 < y

   1. Initial program 93.3%

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

      1. distribute-rgt-out-- 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in x around inf 51.8%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 7: 92.5% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 91.1%

   \[\left(x \cdot y - z \cdot y\right) \cdot t \]
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* 91.3%

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

3. Simplified 91.3%

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

4. Final simplification 91.3%

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

Alternative 8: 54.1% 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 91.1%

   \[\left(x \cdot y - z \cdot y\right) \cdot t \]
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* 91.3%

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

3. Simplified 91.3%

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

4. Taylor expanded in x around inf 53.6%

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

5. Final simplification 53.6%

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

Developer target: 96.4% 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 2023171 
(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))