Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3

Percentage Accurate: 96.2% → 96.8%

Time: 12.2s

Alternatives: 6

Speedup: 1.3×

• 24.2% 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: 96.2% 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: 96.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t\_s \cdot \left(y\_s \cdot \left(\left(\left(x - z\right) \cdot y\_m\right) \cdot t\_m\right)\right) \end{array} \]

FPCore

y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) y)
t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
(FPCore (t_s y_s x y_m z t_m)
 :precision binary64
 (* t_s (* y_s (* (* (- x z) y_m) t_m))))

C

y\_m = fabs(y);
y\_s = copysign(1.0, y);
t\_m = fabs(t);
t\_s = copysign(1.0, t);
assert(x < y_m && y_m < z && z < t_m);
double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	return t_s * (y_s * (((x - z) * y_m) * t_m));
}

Fortran

y\_m = abs(y)
y\_s = copysign(1.0d0, y)
t\_m = abs(t)
t\_s = copysign(1.0d0, t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
real(8) function code(t_s, y_s, x, y_m, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    code = t_s * (y_s * (((x - z) * y_m) * t_m))
end function

Java

y\_m = Math.abs(y);
y\_s = Math.copySign(1.0, y);
t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
assert x < y_m && y_m < z && z < t_m;
public static double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	return t_s * (y_s * (((x - z) * y_m) * t_m));
}

Python

y\_m = math.fabs(y)
y\_s = math.copysign(1.0, y)
t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
[x, y_m, z, t_m] = sort([x, y_m, z, t_m])
def code(t_s, y_s, x, y_m, z, t_m):
	return t_s * (y_s * (((x - z) * y_m) * t_m))

Julia

y\_m = abs(y)
y\_s = copysign(1.0, y)
t\_m = abs(t)
t\_s = copysign(1.0, t)
x, y_m, z, t_m = sort([x, y_m, z, t_m])
function code(t_s, y_s, x, y_m, z, t_m)
	return Float64(t_s * Float64(y_s * Float64(Float64(Float64(x - z) * y_m) * t_m)))
end

MATLAB

y\_m = abs(y);
y\_s = sign(y) * abs(1.0);
t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
x, y_m, z, t_m = num2cell(sort([x, y_m, z, t_m])){:}
function tmp = code(t_s, y_s, x, y_m, z, t_m)
	tmp = t_s * (y_s * (((x - z) * y_m) * t_m));
end

Wolfram

y\_m = N[Abs[y], $MachinePrecision]
y\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
code[t$95$s_, y$95$s_, x_, y$95$m_, z_, t$95$m_] := N[(t$95$s * N[(y$95$s * N[(N[(N[(x - z), $MachinePrecision] * y$95$m), $MachinePrecision] * t$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.8%

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

   1. *-commutative N/A

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

   2. distribute-rgt-out-- N/A

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

   3. associate-*r* N/A

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

   4. *-commutative N/A

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

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(x - z\right), \color{blue}{\left(t \cdot y\right)}\right) \]

   6. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, z\right), \left(\color{blue}{t} \cdot y\right)\right) \]

   7. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, z\right), \left(y \cdot \color{blue}{t}\right)\right) \]

   8. *-lowering-*.f64 93.6%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, z\right), \mathsf{*.f64}\left(y, \color{blue}{t}\right)\right) \]

3. Simplified 93.6%

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

   1. associate-*r* N/A

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

   2. *-commutative N/A

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

   3. distribute-rgt-out-- N/A

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

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(x \cdot y - z \cdot y\right), \color{blue}{t}\right) \]

   5. distribute-rgt-out-- N/A

      \[\leadsto \mathsf{*.f64}\left(\left(y \cdot \left(x - z\right)\right), t\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\left(x - z\right) \cdot y\right), t\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x - z\right), y\right), t\right) \]

   8. --lowering--.f64 92.7%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, z\right), y\right), t\right) \]

6. Applied egg-rr 92.7%

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

Alternative 2: 77.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ \begin{array}{l} t_2 := t\_m \cdot \left(z \cdot \left(0 - y\_m\right)\right)\\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(y\_m \cdot t\_m\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array}\right) \end{array} \end{array} \]

FPCore

y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) y)
t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
(FPCore (t_s y_s x y_m z t_m)
 :precision binary64
 (let* ((t_2 (* t_m (* z (- 0.0 y_m)))))
   (*
    t_s
    (*
     y_s
     (if (<= z -8.2e-25) t_2 (if (<= z 9.8e+20) (* x (* y_m t_m)) t_2))))))

C

y\_m = fabs(y);
y\_s = copysign(1.0, y);
t\_m = fabs(t);
t\_s = copysign(1.0, t);
assert(x < y_m && y_m < z && z < t_m);
double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	double t_2 = t_m * (z * (0.0 - y_m));
	double tmp;
	if (z <= -8.2e-25) {
		tmp = t_2;
	} else if (z <= 9.8e+20) {
		tmp = x * (y_m * t_m);
	} else {
		tmp = t_2;
	}
	return t_s * (y_s * tmp);
}

Fortran

y\_m = abs(y)
y\_s = copysign(1.0d0, y)
t\_m = abs(t)
t\_s = copysign(1.0d0, t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
real(8) function code(t_s, y_s, x, y_m, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: t_2
    real(8) :: tmp
    t_2 = t_m * (z * (0.0d0 - y_m))
    if (z <= (-8.2d-25)) then
        tmp = t_2
    else if (z <= 9.8d+20) then
        tmp = x * (y_m * t_m)
    else
        tmp = t_2
    end if
    code = t_s * (y_s * tmp)
end function

Java

y\_m = Math.abs(y);
y\_s = Math.copySign(1.0, y);
t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
assert x < y_m && y_m < z && z < t_m;
public static double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	double t_2 = t_m * (z * (0.0 - y_m));
	double tmp;
	if (z <= -8.2e-25) {
		tmp = t_2;
	} else if (z <= 9.8e+20) {
		tmp = x * (y_m * t_m);
	} else {
		tmp = t_2;
	}
	return t_s * (y_s * tmp);
}

Python

y\_m = math.fabs(y)
y\_s = math.copysign(1.0, y)
t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
[x, y_m, z, t_m] = sort([x, y_m, z, t_m])
def code(t_s, y_s, x, y_m, z, t_m):
	t_2 = t_m * (z * (0.0 - y_m))
	tmp = 0
	if z <= -8.2e-25:
		tmp = t_2
	elif z <= 9.8e+20:
		tmp = x * (y_m * t_m)
	else:
		tmp = t_2
	return t_s * (y_s * tmp)

Julia

y\_m = abs(y)
y\_s = copysign(1.0, y)
t\_m = abs(t)
t\_s = copysign(1.0, t)
x, y_m, z, t_m = sort([x, y_m, z, t_m])
function code(t_s, y_s, x, y_m, z, t_m)
	t_2 = Float64(t_m * Float64(z * Float64(0.0 - y_m)))
	tmp = 0.0
	if (z <= -8.2e-25)
		tmp = t_2;
	elseif (z <= 9.8e+20)
		tmp = Float64(x * Float64(y_m * t_m));
	else
		tmp = t_2;
	end
	return Float64(t_s * Float64(y_s * tmp))
end

MATLAB

y\_m = abs(y);
y\_s = sign(y) * abs(1.0);
t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
x, y_m, z, t_m = num2cell(sort([x, y_m, z, t_m])){:}
function tmp_2 = code(t_s, y_s, x, y_m, z, t_m)
	t_2 = t_m * (z * (0.0 - y_m));
	tmp = 0.0;
	if (z <= -8.2e-25)
		tmp = t_2;
	elseif (z <= 9.8e+20)
		tmp = x * (y_m * t_m);
	else
		tmp = t_2;
	end
	tmp_2 = t_s * (y_s * tmp);
end

Wolfram

y\_m = N[Abs[y], $MachinePrecision]
y\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
code[t$95$s_, y$95$s_, x_, y$95$m_, z_, t$95$m_] := Block[{t$95$2 = N[(t$95$m * N[(z * N[(0.0 - y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(t$95$s * N[(y$95$s * If[LessEqual[z, -8.2e-25], t$95$2, If[LessEqual[z, 9.8e+20], N[(x * N[(y$95$m * t$95$m), $MachinePrecision]), $MachinePrecision], t$95$2]]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.19999999999999974e-25 or 9.8e20 < z

   1. Initial program 89.7%

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

      1. *-commutative N/A

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

      2. distribute-rgt-out-- N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x - z\right), \color{blue}{\left(t \cdot y\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, z\right), \left(\color{blue}{t} \cdot y\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, z\right), \left(y \cdot \color{blue}{t}\right)\right) \]

      8. *-lowering-*.f64 93.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, z\right), \mathsf{*.f64}\left(y, \color{blue}{t}\right)\right) \]

   3. Simplified 93.1%

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

      1. *-commutative N/A

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

      2. flip-- N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot t\right), \color{blue}{\left(\frac{x + z}{x \cdot x - z \cdot z}\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, t\right), \left(\frac{\color{blue}{x + z}}{x \cdot x - z \cdot z}\right)\right) \]

      7. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, t\right), \left(\frac{1}{\color{blue}{\frac{x \cdot x - z \cdot z}{x + z}}}\right)\right) \]

      8. flip-- N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, t\right), \left(\frac{1}{x - \color{blue}{z}}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, t\right), \mathsf{/.f64}\left(1, \color{blue}{\left(x - z\right)}\right)\right) \]

      10. --lowering--.f64 93.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, t\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(x, \color{blue}{z}\right)\right)\right) \]

   6. Applied egg-rr 93.0%

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

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, t\right), \color{blue}{\left(\frac{-1}{z}\right)}\right) \]
   8. Step-by-step derivation

      1. /-lowering-/.f64 75.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, t\right), \mathsf{/.f64}\left(-1, \color{blue}{z}\right)\right) \]

   9. Simplified 75.4%

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

       1. clear-num N/A

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

       2. associate-/r/ N/A

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

       3. frac-2neg N/A

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

       4. metadata-eval N/A

          \[\leadsto \frac{1}{\frac{1}{\mathsf{neg}\left(z\right)}} \cdot \left(y \cdot t\right) \]

       5. remove-double-div N/A

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

       6. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{neg}\left(z \cdot \left(y \cdot t\right)\right) \]

       7. neg-lowering-neg.f64 N/A

          \[\leadsto \mathsf{neg.f64}\left(\left(z \cdot \left(y \cdot t\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot t\right)\right)\right) \]

       9. *-lowering-*.f64 75.6%

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, t\right)\right)\right) \]

   11. Applied egg-rr 75.6%

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

       1. associate-*r* N/A

          \[\leadsto \mathsf{neg.f64}\left(\left(\left(z \cdot y\right) \cdot t\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{neg.f64}\left(\left(\left(y \cdot z\right) \cdot t\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(y \cdot z\right), t\right)\right) \]

       4. *-lowering-*.f64 75.3%

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right)\right) \]

   13. Applied egg-rr 75.3%

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

   if -8.19999999999999974e-25 < z < 9.8e20

   1. Initial program 93.9%

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

      1. *-commutative N/A

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

      2. distribute-rgt-out-- N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x - z\right), \color{blue}{\left(t \cdot y\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, z\right), \left(\color{blue}{t} \cdot y\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, z\right), \left(y \cdot \color{blue}{t}\right)\right) \]

      8. *-lowering-*.f64 94.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, z\right), \mathsf{*.f64}\left(y, \color{blue}{t}\right)\right) \]

   3. Simplified 94.0%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(y, t\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 79.3%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \left(z \cdot \left(0 - y\right)\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(0 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ \begin{array}{l} t_2 := t\_m \cdot \left(x \cdot y\_m\right)\\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+115}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-10}:\\ \;\;\;\;0 - z \cdot \left(y\_m \cdot t\_m\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array}\right) \end{array} \end{array} \]

FPCore

y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) y)
t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
(FPCore (t_s y_s x y_m z t_m)
 :precision binary64
 (let* ((t_2 (* t_m (* x y_m))))
   (*
    t_s
    (*
     y_s
     (if (<= x -4.7e+115)
       t_2
       (if (<= x 1.1e-10) (- 0.0 (* z (* y_m t_m))) t_2))))))

C

y\_m = fabs(y);
y\_s = copysign(1.0, y);
t\_m = fabs(t);
t\_s = copysign(1.0, t);
assert(x < y_m && y_m < z && z < t_m);
double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	double t_2 = t_m * (x * y_m);
	double tmp;
	if (x <= -4.7e+115) {
		tmp = t_2;
	} else if (x <= 1.1e-10) {
		tmp = 0.0 - (z * (y_m * t_m));
	} else {
		tmp = t_2;
	}
	return t_s * (y_s * tmp);
}

Fortran

y\_m = abs(y)
y\_s = copysign(1.0d0, y)
t\_m = abs(t)
t\_s = copysign(1.0d0, t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
real(8) function code(t_s, y_s, x, y_m, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: t_2
    real(8) :: tmp
    t_2 = t_m * (x * y_m)
    if (x <= (-4.7d+115)) then
        tmp = t_2
    else if (x <= 1.1d-10) then
        tmp = 0.0d0 - (z * (y_m * t_m))
    else
        tmp = t_2
    end if
    code = t_s * (y_s * tmp)
end function

Java

y\_m = Math.abs(y);
y\_s = Math.copySign(1.0, y);
t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
assert x < y_m && y_m < z && z < t_m;
public static double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	double t_2 = t_m * (x * y_m);
	double tmp;
	if (x <= -4.7e+115) {
		tmp = t_2;
	} else if (x <= 1.1e-10) {
		tmp = 0.0 - (z * (y_m * t_m));
	} else {
		tmp = t_2;
	}
	return t_s * (y_s * tmp);
}

Python

y\_m = math.fabs(y)
y\_s = math.copysign(1.0, y)
t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
[x, y_m, z, t_m] = sort([x, y_m, z, t_m])
def code(t_s, y_s, x, y_m, z, t_m):
	t_2 = t_m * (x * y_m)
	tmp = 0
	if x <= -4.7e+115:
		tmp = t_2
	elif x <= 1.1e-10:
		tmp = 0.0 - (z * (y_m * t_m))
	else:
		tmp = t_2
	return t_s * (y_s * tmp)

Julia

y\_m = abs(y)
y\_s = copysign(1.0, y)
t\_m = abs(t)
t\_s = copysign(1.0, t)
x, y_m, z, t_m = sort([x, y_m, z, t_m])
function code(t_s, y_s, x, y_m, z, t_m)
	t_2 = Float64(t_m * Float64(x * y_m))
	tmp = 0.0
	if (x <= -4.7e+115)
		tmp = t_2;
	elseif (x <= 1.1e-10)
		tmp = Float64(0.0 - Float64(z * Float64(y_m * t_m)));
	else
		tmp = t_2;
	end
	return Float64(t_s * Float64(y_s * tmp))
end

MATLAB

y\_m = abs(y);
y\_s = sign(y) * abs(1.0);
t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
x, y_m, z, t_m = num2cell(sort([x, y_m, z, t_m])){:}
function tmp_2 = code(t_s, y_s, x, y_m, z, t_m)
	t_2 = t_m * (x * y_m);
	tmp = 0.0;
	if (x <= -4.7e+115)
		tmp = t_2;
	elseif (x <= 1.1e-10)
		tmp = 0.0 - (z * (y_m * t_m));
	else
		tmp = t_2;
	end
	tmp_2 = t_s * (y_s * tmp);
end

Wolfram

y\_m = N[Abs[y], $MachinePrecision]
y\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
code[t$95$s_, y$95$s_, x_, y$95$m_, z_, t$95$m_] := Block[{t$95$2 = N[(t$95$m * N[(x * y$95$m), $MachinePrecision]), $MachinePrecision]}, N[(t$95$s * N[(y$95$s * If[LessEqual[x, -4.7e+115], t$95$2, If[LessEqual[x, 1.1e-10], N[(0.0 - N[(z * N[(y$95$m * t$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.6999999999999996e115 or 1.09999999999999995e-10 < x

   1. Initial program 92.5%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(x \cdot y\right)}, t\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot x\right), t\right) \]

      2. *-lowering-*.f64 80.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, x\right), t\right) \]

   5. Simplified 80.1%

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

   if -4.6999999999999996e115 < x < 1.09999999999999995e-10

   1. Initial program 91.4%

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

      1. *-commutative N/A

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

      2. distribute-rgt-out-- N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x - z\right), \color{blue}{\left(t \cdot y\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, z\right), \left(\color{blue}{t} \cdot y\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, z\right), \left(y \cdot \color{blue}{t}\right)\right) \]

      8. *-lowering-*.f64 94.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, z\right), \mathsf{*.f64}\left(y, \color{blue}{t}\right)\right) \]

   3. Simplified 94.1%

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

      1. *-commutative N/A

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

      2. flip-- N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot t\right), \color{blue}{\left(\frac{x + z}{x \cdot x - z \cdot z}\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, t\right), \left(\frac{\color{blue}{x + z}}{x \cdot x - z \cdot z}\right)\right) \]

      7. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, t\right), \left(\frac{1}{\color{blue}{\frac{x \cdot x - z \cdot z}{x + z}}}\right)\right) \]

      8. flip-- N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, t\right), \left(\frac{1}{x - \color{blue}{z}}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, t\right), \mathsf{/.f64}\left(1, \color{blue}{\left(x - z\right)}\right)\right) \]

      10. --lowering--.f64 93.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, t\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(x, \color{blue}{z}\right)\right)\right) \]

   6. Applied egg-rr 93.9%

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

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, t\right), \color{blue}{\left(\frac{-1}{z}\right)}\right) \]
   8. Step-by-step derivation

      1. /-lowering-/.f64 75.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, t\right), \mathsf{/.f64}\left(-1, \color{blue}{z}\right)\right) \]

   9. Simplified 75.9%

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

       1. clear-num N/A

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

       2. associate-/r/ N/A

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

       3. frac-2neg N/A

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

       4. metadata-eval N/A

          \[\leadsto \frac{1}{\frac{1}{\mathsf{neg}\left(z\right)}} \cdot \left(y \cdot t\right) \]

       5. remove-double-div N/A

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

       6. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{neg}\left(z \cdot \left(y \cdot t\right)\right) \]

       7. neg-lowering-neg.f64 N/A

          \[\leadsto \mathsf{neg.f64}\left(\left(z \cdot \left(y \cdot t\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot t\right)\right)\right) \]

       9. *-lowering-*.f64 76.1%

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, t\right)\right)\right) \]

   11. Applied egg-rr 76.1%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+115}:\\ \;\;\;\;t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-10}:\\ \;\;\;\;0 - z \cdot \left(y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ \begin{array}{l} t_2 := t\_m \cdot \left(x \cdot y\_m\right)\\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+115}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{-11}:\\ \;\;\;\;0 - y\_m \cdot \left(z \cdot t\_m\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array}\right) \end{array} \end{array} \]

FPCore

y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) y)
t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
(FPCore (t_s y_s x y_m z t_m)
 :precision binary64
 (let* ((t_2 (* t_m (* x y_m))))
   (*
    t_s
    (*
     y_s
     (if (<= x -4.5e+115)
       t_2
       (if (<= x 1.18e-11) (- 0.0 (* y_m (* z t_m))) t_2))))))

C

y\_m = fabs(y);
y\_s = copysign(1.0, y);
t\_m = fabs(t);
t\_s = copysign(1.0, t);
assert(x < y_m && y_m < z && z < t_m);
double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	double t_2 = t_m * (x * y_m);
	double tmp;
	if (x <= -4.5e+115) {
		tmp = t_2;
	} else if (x <= 1.18e-11) {
		tmp = 0.0 - (y_m * (z * t_m));
	} else {
		tmp = t_2;
	}
	return t_s * (y_s * tmp);
}

Fortran

y\_m = abs(y)
y\_s = copysign(1.0d0, y)
t\_m = abs(t)
t\_s = copysign(1.0d0, t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
real(8) function code(t_s, y_s, x, y_m, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: t_2
    real(8) :: tmp
    t_2 = t_m * (x * y_m)
    if (x <= (-4.5d+115)) then
        tmp = t_2
    else if (x <= 1.18d-11) then
        tmp = 0.0d0 - (y_m * (z * t_m))
    else
        tmp = t_2
    end if
    code = t_s * (y_s * tmp)
end function

Java

y\_m = Math.abs(y);
y\_s = Math.copySign(1.0, y);
t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
assert x < y_m && y_m < z && z < t_m;
public static double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	double t_2 = t_m * (x * y_m);
	double tmp;
	if (x <= -4.5e+115) {
		tmp = t_2;
	} else if (x <= 1.18e-11) {
		tmp = 0.0 - (y_m * (z * t_m));
	} else {
		tmp = t_2;
	}
	return t_s * (y_s * tmp);
}

Python

y\_m = math.fabs(y)
y\_s = math.copysign(1.0, y)
t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
[x, y_m, z, t_m] = sort([x, y_m, z, t_m])
def code(t_s, y_s, x, y_m, z, t_m):
	t_2 = t_m * (x * y_m)
	tmp = 0
	if x <= -4.5e+115:
		tmp = t_2
	elif x <= 1.18e-11:
		tmp = 0.0 - (y_m * (z * t_m))
	else:
		tmp = t_2
	return t_s * (y_s * tmp)

Julia

y\_m = abs(y)
y\_s = copysign(1.0, y)
t\_m = abs(t)
t\_s = copysign(1.0, t)
x, y_m, z, t_m = sort([x, y_m, z, t_m])
function code(t_s, y_s, x, y_m, z, t_m)
	t_2 = Float64(t_m * Float64(x * y_m))
	tmp = 0.0
	if (x <= -4.5e+115)
		tmp = t_2;
	elseif (x <= 1.18e-11)
		tmp = Float64(0.0 - Float64(y_m * Float64(z * t_m)));
	else
		tmp = t_2;
	end
	return Float64(t_s * Float64(y_s * tmp))
end

MATLAB

y\_m = abs(y);
y\_s = sign(y) * abs(1.0);
t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
x, y_m, z, t_m = num2cell(sort([x, y_m, z, t_m])){:}
function tmp_2 = code(t_s, y_s, x, y_m, z, t_m)
	t_2 = t_m * (x * y_m);
	tmp = 0.0;
	if (x <= -4.5e+115)
		tmp = t_2;
	elseif (x <= 1.18e-11)
		tmp = 0.0 - (y_m * (z * t_m));
	else
		tmp = t_2;
	end
	tmp_2 = t_s * (y_s * tmp);
end

Wolfram

y\_m = N[Abs[y], $MachinePrecision]
y\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
code[t$95$s_, y$95$s_, x_, y$95$m_, z_, t$95$m_] := Block[{t$95$2 = N[(t$95$m * N[(x * y$95$m), $MachinePrecision]), $MachinePrecision]}, N[(t$95$s * N[(y$95$s * If[LessEqual[x, -4.5e+115], t$95$2, If[LessEqual[x, 1.18e-11], N[(0.0 - N[(y$95$m * N[(z * t$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.49999999999999963e115 or 1.18e-11 < x

   1. Initial program 92.5%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(x \cdot y\right)}, t\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot x\right), t\right) \]

      2. *-lowering-*.f64 80.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, x\right), t\right) \]

   5. Simplified 80.1%

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

   if -4.49999999999999963e115 < x < 1.18e-11

   1. Initial program 91.4%

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

      1. *-commutative N/A

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

      2. distribute-rgt-out-- N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x - z\right), \color{blue}{\left(t \cdot y\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, z\right), \left(\color{blue}{t} \cdot y\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, z\right), \left(y \cdot \color{blue}{t}\right)\right) \]

      8. *-lowering-*.f64 94.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, z\right), \mathsf{*.f64}\left(y, \color{blue}{t}\right)\right) \]

   3. Simplified 94.1%

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

      1. *-commutative N/A

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

      2. flip-- N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot t\right), \color{blue}{\left(\frac{x + z}{x \cdot x - z \cdot z}\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, t\right), \left(\frac{\color{blue}{x + z}}{x \cdot x - z \cdot z}\right)\right) \]

      7. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, t\right), \left(\frac{1}{\color{blue}{\frac{x \cdot x - z \cdot z}{x + z}}}\right)\right) \]

      8. flip-- N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, t\right), \left(\frac{1}{x - \color{blue}{z}}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, t\right), \mathsf{/.f64}\left(1, \color{blue}{\left(x - z\right)}\right)\right) \]

      10. --lowering--.f64 93.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, t\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(x, \color{blue}{z}\right)\right)\right) \]

   6. Applied egg-rr 93.9%

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

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, t\right), \color{blue}{\left(\frac{-1}{z}\right)}\right) \]
   8. Step-by-step derivation

      1. /-lowering-/.f64 75.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, t\right), \mathsf{/.f64}\left(-1, \color{blue}{z}\right)\right) \]

   9. Simplified 75.9%

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

       1. div-inv N/A

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

       2. mul-1-neg N/A

          \[\leadsto \frac{y \cdot t}{\mathsf{neg}\left(\frac{1}{z}\right)} \]

       3. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{neg}\left(\frac{y \cdot t}{\frac{1}{z}}\right) \]

       4. neg-lowering-neg.f64 N/A

          \[\leadsto \mathsf{neg.f64}\left(\left(\frac{y \cdot t}{\frac{1}{z}}\right)\right) \]

       5. div-inv N/A

          \[\leadsto \mathsf{neg.f64}\left(\left(\left(y \cdot t\right) \cdot \frac{1}{\frac{1}{z}}\right)\right) \]

       6. remove-double-div N/A

          \[\leadsto \mathsf{neg.f64}\left(\left(\left(y \cdot t\right) \cdot z\right)\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{neg.f64}\left(\left(y \cdot \left(t \cdot z\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(y, \left(t \cdot z\right)\right)\right) \]

       9. *-lowering-*.f64 74.8%

          \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, z\right)\right)\right) \]

   11. Applied egg-rr 74.8%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+115}:\\ \;\;\;\;t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{-11}:\\ \;\;\;\;0 - y \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+124}:\\ \;\;\;\;t\_m \cdot \left(x \cdot y\_m\right)\\ \mathbf{else}:\\ \;\;\;\;y\_m \cdot \left(\left(x - z\right) \cdot t\_m\right)\\ \end{array}\right) \end{array} \]

FPCore

y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) y)
t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
(FPCore (t_s y_s x y_m z t_m)
 :precision binary64
 (*
  t_s
  (* y_s (if (<= x -2.2e+124) (* t_m (* x y_m)) (* y_m (* (- x z) t_m))))))

C

y\_m = fabs(y);
y\_s = copysign(1.0, y);
t\_m = fabs(t);
t\_s = copysign(1.0, t);
assert(x < y_m && y_m < z && z < t_m);
double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	double tmp;
	if (x <= -2.2e+124) {
		tmp = t_m * (x * y_m);
	} else {
		tmp = y_m * ((x - z) * t_m);
	}
	return t_s * (y_s * tmp);
}

Fortran

y\_m = abs(y)
y\_s = copysign(1.0d0, y)
t\_m = abs(t)
t\_s = copysign(1.0d0, t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
real(8) function code(t_s, y_s, x, y_m, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if (x <= (-2.2d+124)) then
        tmp = t_m * (x * y_m)
    else
        tmp = y_m * ((x - z) * t_m)
    end if
    code = t_s * (y_s * tmp)
end function

Java

y\_m = Math.abs(y);
y\_s = Math.copySign(1.0, y);
t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
assert x < y_m && y_m < z && z < t_m;
public static double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	double tmp;
	if (x <= -2.2e+124) {
		tmp = t_m * (x * y_m);
	} else {
		tmp = y_m * ((x - z) * t_m);
	}
	return t_s * (y_s * tmp);
}

Python

y\_m = math.fabs(y)
y\_s = math.copysign(1.0, y)
t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
[x, y_m, z, t_m] = sort([x, y_m, z, t_m])
def code(t_s, y_s, x, y_m, z, t_m):
	tmp = 0
	if x <= -2.2e+124:
		tmp = t_m * (x * y_m)
	else:
		tmp = y_m * ((x - z) * t_m)
	return t_s * (y_s * tmp)

Julia

y\_m = abs(y)
y\_s = copysign(1.0, y)
t\_m = abs(t)
t\_s = copysign(1.0, t)
x, y_m, z, t_m = sort([x, y_m, z, t_m])
function code(t_s, y_s, x, y_m, z, t_m)
	tmp = 0.0
	if (x <= -2.2e+124)
		tmp = Float64(t_m * Float64(x * y_m));
	else
		tmp = Float64(y_m * Float64(Float64(x - z) * t_m));
	end
	return Float64(t_s * Float64(y_s * tmp))
end

MATLAB

y\_m = abs(y);
y\_s = sign(y) * abs(1.0);
t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
x, y_m, z, t_m = num2cell(sort([x, y_m, z, t_m])){:}
function tmp_2 = code(t_s, y_s, x, y_m, z, t_m)
	tmp = 0.0;
	if (x <= -2.2e+124)
		tmp = t_m * (x * y_m);
	else
		tmp = y_m * ((x - z) * t_m);
	end
	tmp_2 = t_s * (y_s * tmp);
end

Wolfram

y\_m = N[Abs[y], $MachinePrecision]
y\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
code[t$95$s_, y$95$s_, x_, y$95$m_, z_, t$95$m_] := N[(t$95$s * N[(y$95$s * If[LessEqual[x, -2.2e+124], N[(t$95$m * N[(x * y$95$m), $MachinePrecision]), $MachinePrecision], N[(y$95$m * N[(N[(x - z), $MachinePrecision] * t$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < -2.2000000000000001e124

   1. Initial program 89.2%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(x \cdot y\right)}, t\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot x\right), t\right) \]

      2. *-lowering-*.f64 84.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, x\right), t\right) \]

   5. Simplified 84.0%

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

   if -2.2000000000000001e124 < x

   1. Initial program 92.3%

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

      1. *-commutative N/A

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

      2. distribute-rgt-out-- N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x - z\right), \color{blue}{\left(t \cdot y\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, z\right), \left(\color{blue}{t} \cdot y\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, z\right), \left(y \cdot \color{blue}{t}\right)\right) \]

      8. *-lowering-*.f64 93.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, z\right), \mathsf{*.f64}\left(y, \color{blue}{t}\right)\right) \]

   3. Simplified 93.4%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(x - z\right) \cdot t\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x - z\right), t\right), y\right) \]

      5. --lowering--.f64 91.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, z\right), t\right), y\right) \]

   6. Applied egg-rr 91.7%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+124}:\\ \;\;\;\;t \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t\_s \cdot \left(y\_s \cdot \left(x \cdot \left(y\_m \cdot t\_m\right)\right)\right) \end{array} \]

FPCore

y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) y)
t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
(FPCore (t_s y_s x y_m z t_m)
 :precision binary64
 (* t_s (* y_s (* x (* y_m t_m)))))

C

y\_m = fabs(y);
y\_s = copysign(1.0, y);
t\_m = fabs(t);
t\_s = copysign(1.0, t);
assert(x < y_m && y_m < z && z < t_m);
double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	return t_s * (y_s * (x * (y_m * t_m)));
}

Fortran

y\_m = abs(y)
y\_s = copysign(1.0d0, y)
t\_m = abs(t)
t\_s = copysign(1.0d0, t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
real(8) function code(t_s, y_s, x, y_m, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    code = t_s * (y_s * (x * (y_m * t_m)))
end function

Java

y\_m = Math.abs(y);
y\_s = Math.copySign(1.0, y);
t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
assert x < y_m && y_m < z && z < t_m;
public static double code(double t_s, double y_s, double x, double y_m, double z, double t_m) {
	return t_s * (y_s * (x * (y_m * t_m)));
}

Python

y\_m = math.fabs(y)
y\_s = math.copysign(1.0, y)
t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
[x, y_m, z, t_m] = sort([x, y_m, z, t_m])
def code(t_s, y_s, x, y_m, z, t_m):
	return t_s * (y_s * (x * (y_m * t_m)))

Julia

y\_m = abs(y)
y\_s = copysign(1.0, y)
t\_m = abs(t)
t\_s = copysign(1.0, t)
x, y_m, z, t_m = sort([x, y_m, z, t_m])
function code(t_s, y_s, x, y_m, z, t_m)
	return Float64(t_s * Float64(y_s * Float64(x * Float64(y_m * t_m))))
end

MATLAB

y\_m = abs(y);
y\_s = sign(y) * abs(1.0);
t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
x, y_m, z, t_m = num2cell(sort([x, y_m, z, t_m])){:}
function tmp = code(t_s, y_s, x, y_m, z, t_m)
	tmp = t_s * (y_s * (x * (y_m * t_m)));
end

Wolfram

y\_m = N[Abs[y], $MachinePrecision]
y\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
code[t$95$s_, y$95$s_, x_, y$95$m_, z_, t$95$m_] := N[(t$95$s * N[(y$95$s * N[(x * N[(y$95$m * t$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.8%

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

   1. *-commutative N/A

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

   2. distribute-rgt-out-- N/A

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

   3. associate-*r* N/A

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

   4. *-commutative N/A

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

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(x - z\right), \color{blue}{\left(t \cdot y\right)}\right) \]

   6. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, z\right), \left(\color{blue}{t} \cdot y\right)\right) \]

   7. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, z\right), \left(y \cdot \color{blue}{t}\right)\right) \]

   8. *-lowering-*.f64 93.6%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, z\right), \mathsf{*.f64}\left(y, \color{blue}{t}\right)\right) \]

3. Simplified 93.6%

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

5. Taylor expanded in x around inf

   \[\leadsto \mathsf{*.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(y, t\right)\right) \]
6. Step-by-step derivation

7. Simplified 55.6%

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

Developer Target 1: 95.4% accurate, 0.5× 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 2024161 
(FPCore (x y z t)
  :name "Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -9231879582886777/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* (* y t) (- x z)) (if (< t 254306705156487700000000000000000000000000000000000000000000000000000000000000000000) (* y (* t (- x z))) (* (* y (- x z)) t))))

  (* (- (* x y) (* z y)) t))