Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3

Percentage Accurate: 90.2% → 96.4%

Time: 10.6s

Alternatives: 8

Speedup: 1.3×

• 24.4% 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: 90.2% 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: 96.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.02 \cdot 10^{-104}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(t \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.02e-104) (* y (* t (- x z))) (* (- x z) (* t y))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.02e-104) {
		tmp = y * (t * (x - z));
	} else {
		tmp = (x - z) * (t * 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 (t <= 1.02d-104) then
        tmp = y * (t * (x - z))
    else
        tmp = (x - z) * (t * 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 (t <= 1.02e-104) {
		tmp = y * (t * (x - z));
	} else {
		tmp = (x - z) * (t * y);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 1.02e-104:
		tmp = y * (t * (x - z))
	else:
		tmp = (x - z) * (t * y)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.02e-104)
		tmp = Float64(y * Float64(t * Float64(x - z)));
	else
		tmp = Float64(Float64(x - z) * Float64(t * y));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.02e-104)
		tmp = y * (t * (x - z));
	else
		tmp = (x - z) * (t * 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[t, 1.02e-104], N[(y * N[(t * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - z), $MachinePrecision] * N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.02000000000000001e-104

   1. Initial program 88.3%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   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* 92.5%

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

      3. *-commutative 92.5%

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

   3. Simplified 92.5%

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

   if 1.02000000000000001e-104 < t

   1. Initial program 95.3%

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

      1. distribute-rgt-out-- 97.6%

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

      2. associate-*l* 93.3%

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

      3. *-commutative 93.3%

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

   3. Simplified 93.3%

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

      1. associate-*r* 97.3%

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

      2. flip3-- 49.0%

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

      3. associate-*r/ 44.6%

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

      4. associate-/l* 48.9%

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

      5. *-un-lft-identity 48.9%

         \[\leadsto \frac{y \cdot t}{\frac{\color{blue}{1 \cdot \left(x \cdot x + \left(z \cdot z + x \cdot z\right)\right)}}{{x}^{3} - {z}^{3}}} \]

      6. associate-/l* 48.9%

         \[\leadsto \frac{y \cdot t}{\color{blue}{\frac{1}{\frac{{x}^{3} - {z}^{3}}{x \cdot x + \left(z \cdot z + x \cdot z\right)}}}} \]

      7. flip3-- 97.2%

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

   5. Applied egg-rr 97.2%

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

      1. frac-2neg 97.2%

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

      2. clear-num 97.2%

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

      3. associate-/r/ 97.3%

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

      4. distribute-neg-frac 97.3%

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

      5. metadata-eval 97.3%

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

      6. associate-/r/ 97.3%

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

      7. metadata-eval 97.3%

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

      8. neg-mul-1 97.3%

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

      9. neg-sub0 97.3%

         \[\leadsto \color{blue}{\left(0 - \left(x - z\right)\right)} \cdot \left(-y \cdot t\right) \]

      10. sub-neg 97.3%

          \[\leadsto \left(0 - \color{blue}{\left(x + \left(-z\right)\right)}\right) \cdot \left(-y \cdot t\right) \]

      11. +-commutative 97.3%

          \[\leadsto \left(0 - \color{blue}{\left(\left(-z\right) + x\right)}\right) \cdot \left(-y \cdot t\right) \]

      12. associate--r+ 97.3%

          \[\leadsto \color{blue}{\left(\left(0 - \left(-z\right)\right) - x\right)} \cdot \left(-y \cdot t\right) \]

      13. add-sqr-sqrt 55.6%

          \[\leadsto \left(\left(0 - \color{blue}{\sqrt{-z} \cdot \sqrt{-z}}\right) - x\right) \cdot \left(-y \cdot t\right) \]

      14. sqrt-unprod 76.1%

          \[\leadsto \left(\left(0 - \color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}\right) - x\right) \cdot \left(-y \cdot t\right) \]

      15. sqr-neg 76.1%

          \[\leadsto \left(\left(0 - \sqrt{\color{blue}{z \cdot z}}\right) - x\right) \cdot \left(-y \cdot t\right) \]

      16. sqrt-unprod 24.2%

          \[\leadsto \left(\left(0 - \color{blue}{\sqrt{z} \cdot \sqrt{z}}\right) - x\right) \cdot \left(-y \cdot t\right) \]

      17. add-sqr-sqrt 51.8%

          \[\leadsto \left(\left(0 - \color{blue}{z}\right) - x\right) \cdot \left(-y \cdot t\right) \]

      18. neg-sub0 51.8%

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

      19. add-sqr-sqrt 27.7%

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

      20. sqrt-unprod 63.8%

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

      21. sqr-neg 63.8%

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

      22. sqrt-unprod 41.7%

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

      23. add-sqr-sqrt 97.3%

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

      24. distribute-rgt-neg-in 97.3%

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

   7. Applied egg-rr 97.3%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.02 \cdot 10^{-104}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(t \cdot y\right)\\ \end{array} \]

Alternative 2: 73.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+61} \lor \neg \left(z \leq 7.2 \cdot 10^{-24}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot y\right)\\ \end{array} \end{array} \]

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 -2.15e+61) (not (<= z 7.2e-24)))
   (* y (* z (- t)))
   (* x (* t y))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.15e+61) || !(z <= 7.2e-24)) {
		tmp = y * (z * -t);
	} else {
		tmp = x * (t * 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 <= (-2.15d+61)) .or. (.not. (z <= 7.2d-24))) then
        tmp = y * (z * -t)
    else
        tmp = x * (t * 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 <= -2.15e+61) || !(z <= 7.2e-24)) {
		tmp = y * (z * -t);
	} else {
		tmp = x * (t * y);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -2.15e+61) or not (z <= 7.2e-24):
		tmp = y * (z * -t)
	else:
		tmp = x * (t * y)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.15e+61) || !(z <= 7.2e-24))
		tmp = Float64(y * Float64(z * Float64(-t)));
	else
		tmp = Float64(x * Float64(t * 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 <= -2.15e+61) || ~((z <= 7.2e-24)))
		tmp = y * (z * -t);
	else
		tmp = x * (t * 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[Or[LessEqual[z, -2.15e+61], N[Not[LessEqual[z, 7.2e-24]], $MachinePrecision]], N[(y * N[(z * (-t)), $MachinePrecision]), $MachinePrecision], N[(x * N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1500000000000001e61 or 7.2000000000000002e-24 < z

   1. Initial program 88.1%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   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* 94.6%

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

      3. *-commutative 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in x around 0 79.2%

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

      1. mul-1-neg 79.2%

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

      2. distribute-rgt-neg-out 79.2%

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

   6. Simplified 79.2%

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

   if -2.1500000000000001e61 < z < 7.2000000000000002e-24

   1. Initial program 93.5%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   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* 90.9%

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

      3. *-commutative 90.9%

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

   3. Simplified 90.9%

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

      1. associate-*r* 95.1%

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

      2. flip3-- 47.3%

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

      3. associate-*r/ 42.4%

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

      4. associate-/l* 47.3%

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

      5. *-un-lft-identity 47.3%

         \[\leadsto \frac{y \cdot t}{\frac{\color{blue}{1 \cdot \left(x \cdot x + \left(z \cdot z + x \cdot z\right)\right)}}{{x}^{3} - {z}^{3}}} \]

      6. associate-/l* 47.3%

         \[\leadsto \frac{y \cdot t}{\color{blue}{\frac{1}{\frac{{x}^{3} - {z}^{3}}{x \cdot x + \left(z \cdot z + x \cdot z\right)}}}} \]

      7. flip3-- 95.0%

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

   5. Applied egg-rr 95.0%

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

   6. Taylor expanded in x around inf 79.4%

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

      1. associate-/r/ 79.5%

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

      2. /-rgt-identity 79.5%

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

   8. Applied egg-rr 79.5%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+61} \lor \neg \left(z \leq 7.2 \cdot 10^{-24}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot y\right)\\ \end{array} \]

Alternative 3: 73.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(t \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.45e+63)
   (* z (* y (- t)))
   (if (<= z 2.55e-24) (* x (* t y)) (* y (* z (- t))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.45e+63) {
		tmp = z * (y * -t);
	} else if (z <= 2.55e-24) {
		tmp = x * (t * y);
	} else {
		tmp = y * (z * -t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.45d+63)) then
        tmp = z * (y * -t)
    else if (z <= 2.55d-24) then
        tmp = x * (t * y)
    else
        tmp = y * (z * -t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.45e+63) {
		tmp = z * (y * -t);
	} else if (z <= 2.55e-24) {
		tmp = x * (t * y);
	} else {
		tmp = y * (z * -t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.45e+63:
		tmp = z * (y * -t)
	elif z <= 2.55e-24:
		tmp = x * (t * y)
	else:
		tmp = y * (z * -t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.45e+63)
		tmp = Float64(z * Float64(y * Float64(-t)));
	elseif (z <= 2.55e-24)
		tmp = Float64(x * Float64(t * y));
	else
		tmp = Float64(y * Float64(z * Float64(-t)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.45e+63)
		tmp = z * (y * -t);
	elseif (z <= 2.55e-24)
		tmp = x * (t * y);
	else
		tmp = y * (z * -t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -1.45e+63], N[(z * N[(y * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.55e-24], N[(x * N[(t * y), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * (-t)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45e63

   1. Initial program 82.9%

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

      1. distribute-rgt-out-- 86.4%

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

      2. associate-*l* 93.0%

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

      3. *-commutative 93.0%

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

   3. Simplified 93.0%

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

      1. associate-*r* 90.6%

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

      2. flip3-- 23.1%

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

      3. associate-*r/ 19.9%

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

      4. associate-/l* 23.1%

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

      5. *-un-lft-identity 23.1%

         \[\leadsto \frac{y \cdot t}{\frac{\color{blue}{1 \cdot \left(x \cdot x + \left(z \cdot z + x \cdot z\right)\right)}}{{x}^{3} - {z}^{3}}} \]

      6. associate-/l* 23.1%

         \[\leadsto \frac{y \cdot t}{\color{blue}{\frac{1}{\frac{{x}^{3} - {z}^{3}}{x \cdot x + \left(z \cdot z + x \cdot z\right)}}}} \]

      7. flip3-- 90.5%

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

   5. Applied egg-rr 90.5%

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

   6. Taylor expanded in x around 0 76.9%

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

      1. div-inv 76.9%

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

      2. associate-/r/ 77.0%

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

      3. metadata-eval 77.0%

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

      4. neg-mul-1 77.0%

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

   8. Applied egg-rr 77.0%

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

   if -1.45e63 < z < 2.55000000000000013e-24

   1. Initial program 93.5%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   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* 90.9%

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

      3. *-commutative 90.9%

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

   3. Simplified 90.9%

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

      1. associate-*r* 95.1%

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

      2. flip3-- 47.3%

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

      3. associate-*r/ 42.4%

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

      4. associate-/l* 47.3%

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

      5. *-un-lft-identity 47.3%

         \[\leadsto \frac{y \cdot t}{\frac{\color{blue}{1 \cdot \left(x \cdot x + \left(z \cdot z + x \cdot z\right)\right)}}{{x}^{3} - {z}^{3}}} \]

      6. associate-/l* 47.3%

         \[\leadsto \frac{y \cdot t}{\color{blue}{\frac{1}{\frac{{x}^{3} - {z}^{3}}{x \cdot x + \left(z \cdot z + x \cdot z\right)}}}} \]

      7. flip3-- 95.0%

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

   5. Applied egg-rr 95.0%

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

   6. Taylor expanded in x around inf 79.4%

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

      1. associate-/r/ 79.5%

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

      2. /-rgt-identity 79.5%

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

   8. Applied egg-rr 79.5%

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

   if 2.55000000000000013e-24 < z

   1. Initial program 92.1%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   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* 95.9%

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

      3. *-commutative 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in x around 0 78.3%

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

      1. mul-1-neg 78.3%

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

      2. distribute-rgt-neg-out 78.3%

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

   6. Simplified 78.3%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-t\right)\right)\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(t \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 4: 73.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(t \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.12e+61)
   (* t (* y (- z)))
   (if (<= z 1.4e-25) (* x (* t y)) (* y (* t (- z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.12e+61) {
		tmp = t * (y * -z);
	} else if (z <= 1.4e-25) {
		tmp = x * (t * y);
	} else {
		tmp = y * (t * -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 (z <= (-1.12d+61)) then
        tmp = t * (y * -z)
    else if (z <= 1.4d-25) then
        tmp = x * (t * y)
    else
        tmp = y * (t * -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 (z <= -1.12e+61) {
		tmp = t * (y * -z);
	} else if (z <= 1.4e-25) {
		tmp = x * (t * y);
	} else {
		tmp = y * (t * -z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.12e+61:
		tmp = t * (y * -z)
	elif z <= 1.4e-25:
		tmp = x * (t * y)
	else:
		tmp = y * (t * -z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.12e+61)
		tmp = Float64(t * Float64(y * Float64(-z)));
	elseif (z <= 1.4e-25)
		tmp = Float64(x * Float64(t * y));
	else
		tmp = Float64(y * Float64(t * Float64(-z)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.12e+61)
		tmp = t * (y * -z);
	elseif (z <= 1.4e-25)
		tmp = x * (t * y);
	else
		tmp = y * (t * -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[z, -1.12e+61], N[(t * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-25], N[(x * N[(t * y), $MachinePrecision]), $MachinePrecision], N[(y * N[(t * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.12e61

   1. Initial program 82.9%

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

      1. distribute-rgt-out-- 86.4%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in x around 0 73.0%

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

      1. associate-*r* 73.0%

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

      2. neg-mul-1 73.0%

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

      3. *-commutative 73.0%

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

   6. Simplified 73.0%

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

   if -1.12e61 < z < 1.39999999999999994e-25

   1. Initial program 93.5%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   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* 90.9%

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

      3. *-commutative 90.9%

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

   3. Simplified 90.9%

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

      1. associate-*r* 95.1%

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

      2. flip3-- 47.3%

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

      3. associate-*r/ 42.4%

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

      4. associate-/l* 47.3%

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

      5. *-un-lft-identity 47.3%

         \[\leadsto \frac{y \cdot t}{\frac{\color{blue}{1 \cdot \left(x \cdot x + \left(z \cdot z + x \cdot z\right)\right)}}{{x}^{3} - {z}^{3}}} \]

      6. associate-/l* 47.3%

         \[\leadsto \frac{y \cdot t}{\color{blue}{\frac{1}{\frac{{x}^{3} - {z}^{3}}{x \cdot x + \left(z \cdot z + x \cdot z\right)}}}} \]

      7. flip3-- 95.0%

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

   5. Applied egg-rr 95.0%

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

   6. Taylor expanded in x around inf 79.4%

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

      1. associate-/r/ 79.5%

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

      2. /-rgt-identity 79.5%

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

   8. Applied egg-rr 79.5%

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

   if 1.39999999999999994e-25 < z

   1. Initial program 92.1%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   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* 95.9%

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

      3. *-commutative 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in x around 0 78.3%

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

      1. mul-1-neg 78.3%

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

      2. distribute-rgt-neg-out 78.3%

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

   6. Simplified 78.3%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(t \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 5: 96.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.35 \cdot 10^{-105}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.35e-105) (* y (* t (- x z))) (* t (* y (- x z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.35e-105) {
		tmp = y * (t * (x - z));
	} else {
		tmp = t * (y * (x - z));
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 1.35d-105) then
        tmp = y * (t * (x - z))
    else
        tmp = t * (y * (x - z))
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.35e-105) {
		tmp = y * (t * (x - z));
	} else {
		tmp = t * (y * (x - z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 1.35e-105:
		tmp = y * (t * (x - z))
	else:
		tmp = t * (y * (x - z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.35e-105)
		tmp = Float64(y * Float64(t * Float64(x - z)));
	else
		tmp = Float64(t * Float64(y * Float64(x - z)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.35e-105)
		tmp = y * (t * (x - z));
	else
		tmp = t * (y * (x - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 1.35e-105], N[(y * N[(t * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.34999999999999996e-105

   1. Initial program 88.3%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   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* 92.5%

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

      3. *-commutative 92.5%

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

   3. Simplified 92.5%

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

   if 1.34999999999999996e-105 < t

   1. Initial program 95.3%

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

      1. distribute-rgt-out-- 97.6%

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

   3. Simplified 97.6%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.35 \cdot 10^{-105}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array} \]

Alternative 6: 55.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 3 \cdot 10^{-106}:\\ \;\;\;\;y \cdot \left(t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 3e-106) (* y (* t x)) (* x (* t y))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 3e-106) {
		tmp = y * (t * x);
	} else {
		tmp = x * (t * 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 (t <= 3d-106) then
        tmp = y * (t * x)
    else
        tmp = x * (t * 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 (t <= 3e-106) {
		tmp = y * (t * x);
	} else {
		tmp = x * (t * y);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 3e-106:
		tmp = y * (t * x)
	else:
		tmp = x * (t * y)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 3e-106)
		tmp = Float64(y * Float64(t * x));
	else
		tmp = Float64(x * Float64(t * y));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 3e-106)
		tmp = y * (t * x);
	else
		tmp = x * (t * 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[t, 3e-106], N[(y * N[(t * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 3.00000000000000019e-106

   1. Initial program 88.8%

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

      1. distribute-rgt-out-- 89.4%

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

      2. associate-*l* 92.5%

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

      3. *-commutative 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in x around inf 49.8%

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

   if 3.00000000000000019e-106 < t

   1. Initial program 94.4%

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

      1. distribute-rgt-out-- 96.7%

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

      2. associate-*l* 93.4%

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

      3. *-commutative 93.4%

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

   3. Simplified 93.4%

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

      1. associate-*r* 97.4%

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

      2. flip3-- 48.5%

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

      3. associate-*r/ 44.1%

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

      4. associate-/l* 48.4%

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

      5. *-un-lft-identity 48.4%

         \[\leadsto \frac{y \cdot t}{\frac{\color{blue}{1 \cdot \left(x \cdot x + \left(z \cdot z + x \cdot z\right)\right)}}{{x}^{3} - {z}^{3}}} \]

      6. associate-/l* 48.3%

         \[\leadsto \frac{y \cdot t}{\color{blue}{\frac{1}{\frac{{x}^{3} - {z}^{3}}{x \cdot x + \left(z \cdot z + x \cdot z\right)}}}} \]

      7. flip3-- 97.2%

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

   5. Applied egg-rr 97.2%

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

   6. Taylor expanded in x around inf 57.8%

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

      1. associate-/r/ 57.9%

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

      2. /-rgt-identity 57.9%

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

   8. Applied egg-rr 57.9%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3 \cdot 10^{-106}:\\ \;\;\;\;y \cdot \left(t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot y\right)\\ \end{array} \]

Alternative 7: 91.6% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = y * (t * (x - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.7%

   \[\left(x \cdot y - z \cdot y\right) \cdot t \]
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* 92.8%

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

   3. *-commutative 92.8%

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

3. Simplified 92.8%

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

4. Final simplification 92.8%

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

Alternative 8: 52.3% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = y * (t * x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.7%

   \[\left(x \cdot y - z \cdot y\right) \cdot t \]
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* 92.8%

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

   3. *-commutative 92.8%

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

3. Simplified 92.8%

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

4. Taylor expanded in x around inf 50.2%

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

5. Final simplification 50.2%

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

Developer target: 96.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t < -9.231879582886777 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t < 2.543067051564877 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (< t -9.231879582886777e-80)
   (* (* y t) (- x z))
   (if (< t 2.543067051564877e+83) (* y (* t (- x z))) (* (* y (- x z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t < -9.231879582886777e-80) {
		tmp = (y * t) * (x - z);
	} else if (t < 2.543067051564877e+83) {
		tmp = y * (t * (x - z));
	} else {
		tmp = (y * (x - z)) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t < (-9.231879582886777d-80)) then
        tmp = (y * t) * (x - z)
    else if (t < 2.543067051564877d+83) then
        tmp = y * (t * (x - z))
    else
        tmp = (y * (x - z)) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t < -9.231879582886777e-80) {
		tmp = (y * t) * (x - z);
	} else if (t < 2.543067051564877e+83) {
		tmp = y * (t * (x - z));
	} else {
		tmp = (y * (x - z)) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t < -9.231879582886777e-80:
		tmp = (y * t) * (x - z)
	elif t < 2.543067051564877e+83:
		tmp = y * (t * (x - z))
	else:
		tmp = (y * (x - z)) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t < -9.231879582886777e-80)
		tmp = Float64(Float64(y * t) * Float64(x - z));
	elseif (t < 2.543067051564877e+83)
		tmp = Float64(y * Float64(t * Float64(x - z)));
	else
		tmp = Float64(Float64(y * Float64(x - z)) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t < -9.231879582886777e-80)
		tmp = (y * t) * (x - z);
	elseif (t < 2.543067051564877e+83)
		tmp = y * (t * (x - z));
	else
		tmp = (y * (x - z)) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Less[t, -9.231879582886777e-80], N[(N[(y * t), $MachinePrecision] * N[(x - z), $MachinePrecision]), $MachinePrecision], If[Less[t, 2.543067051564877e+83], N[(y * N[(t * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023301 
(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))