Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3

Percentage Accurate: 96.4% → 98.2%

Time: 10.4s

Alternatives: 7

Speedup: 0.7×

• 24.8% 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: 96.4% 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: 98.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;t\_m \leq 7.5 \cdot 10^{-29}:\\ \;\;\;\;y\_m \cdot \left(t\_m \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(t\_m \cdot y\_m\right)\\ \end{array}\right) \end{array} \]

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 (<= t_m 7.5e-29) (* y_m (* t_m (- x z))) (* (- x z) (* t_m y_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 (t_m <= 7.5e-29) {
		tmp = y_m * (t_m * (x - z));
	} else {
		tmp = (x - z) * (t_m * y_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 (t_m <= 7.5d-29) then
        tmp = y_m * (t_m * (x - z))
    else
        tmp = (x - z) * (t_m * y_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 (t_m <= 7.5e-29) {
		tmp = y_m * (t_m * (x - z));
	} else {
		tmp = (x - z) * (t_m * y_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 t_m <= 7.5e-29:
		tmp = y_m * (t_m * (x - z))
	else:
		tmp = (x - z) * (t_m * y_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 (t_m <= 7.5e-29)
		tmp = Float64(y_m * Float64(t_m * Float64(x - z)));
	else
		tmp = Float64(Float64(x - z) * Float64(t_m * y_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 (t_m <= 7.5e-29)
		tmp = y_m * (t_m * (x - z));
	else
		tmp = (x - z) * (t_m * y_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[t$95$m, 7.5e-29], N[(y$95$m * N[(t$95$m * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - z), $MachinePrecision] * N[(t$95$m * y$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < 7.50000000000000006e-29

   1. Initial program 88.6%

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

      1. distribute-rgt-out-- 90.3%

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

      2. associate-*l* 96.1%

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

      3. *-commutative 96.1%

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

   3. Simplified 96.1%

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

   if 7.50000000000000006e-29 < t

   1. Initial program 97.1%

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

      1. *-commutative 97.1%

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

      2. distribute-rgt-out-- 98.5%

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

      3. associate-*r* 99.7%

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

      4. *-commutative 99.7%

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

   3. Simplified 99.7%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 7.5 \cdot 10^{-29}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(t \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+214}:\\ \;\;\;\;t\_m \cdot \left(y\_m \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+248}:\\ \;\;\;\;y\_m \cdot \left(t\_m \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t\_m \cdot \left(-y\_m\right)\right)\\ \end{array}\right) \end{array} \]

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 (<= z -4.8e+214)
     (* t_m (* y_m (- z)))
     (if (<= z 1.35e+248) (* y_m (* t_m (- x z))) (* z (* t_m (- y_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 (z <= -4.8e+214) {
		tmp = t_m * (y_m * -z);
	} else if (z <= 1.35e+248) {
		tmp = y_m * (t_m * (x - z));
	} else {
		tmp = z * (t_m * -y_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 (z <= (-4.8d+214)) then
        tmp = t_m * (y_m * -z)
    else if (z <= 1.35d+248) then
        tmp = y_m * (t_m * (x - z))
    else
        tmp = z * (t_m * -y_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 (z <= -4.8e+214) {
		tmp = t_m * (y_m * -z);
	} else if (z <= 1.35e+248) {
		tmp = y_m * (t_m * (x - z));
	} else {
		tmp = z * (t_m * -y_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 z <= -4.8e+214:
		tmp = t_m * (y_m * -z)
	elif z <= 1.35e+248:
		tmp = y_m * (t_m * (x - z))
	else:
		tmp = z * (t_m * -y_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 (z <= -4.8e+214)
		tmp = Float64(t_m * Float64(y_m * Float64(-z)));
	elseif (z <= 1.35e+248)
		tmp = Float64(y_m * Float64(t_m * Float64(x - z)));
	else
		tmp = Float64(z * Float64(t_m * Float64(-y_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 (z <= -4.8e+214)
		tmp = t_m * (y_m * -z);
	elseif (z <= 1.35e+248)
		tmp = y_m * (t_m * (x - z));
	else
		tmp = z * (t_m * -y_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[z, -4.8e+214], N[(t$95$m * N[(y$95$m * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+248], N[(y$95$m * N[(t$95$m * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(t$95$m * (-y$95$m)), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -4.8000000000000002e214

   1. Initial program 99.6%

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

      1. distribute-rgt-out-- 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 95.0%

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

      1. mul-1-neg 95.0%

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

      2. distribute-rgt-neg-out 95.0%

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

   7. Simplified 95.0%

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

   if -4.8000000000000002e214 < z < 1.34999999999999994e248

   1. Initial program 92.5%

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

      1. distribute-rgt-out-- 93.5%

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

      2. associate-*l* 96.2%

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

      3. *-commutative 96.2%

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

   3. Simplified 96.2%

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

   if 1.34999999999999994e248 < z

   1. Initial program 64.4%

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

      1. distribute-rgt-out-- 74.9%

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

   3. Simplified 74.9%

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

   5. Taylor expanded in x around inf 59.5%

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

      1. mul-1-neg 59.5%

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

      2. unsub-neg 59.5%

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

      3. associate-/l* 59.7%

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

   7. Simplified 59.7%

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

   8. Taylor expanded in z around inf 54.7%

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

      1. mul-1-neg 54.7%

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

      2. associate-*r/ 49.6%

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

      3. distribute-rgt-neg-in 49.6%

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

      4. mul-1-neg 49.6%

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

      5. associate-*r/ 49.6%

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

      6. mul-1-neg 49.6%

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

   10. Simplified 49.6%

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

   11. Taylor expanded in x around 0 64.8%

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

       1. associate-*r* 64.8%

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

       2. neg-mul-1 64.8%

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

       3. associate-*r* 89.8%

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

   13. Simplified 89.8%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+214}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+248}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(-y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-23} \lor \neg \left(z \leq 1.08 \cdot 10^{-73}\right):\\ \;\;\;\;y\_m \cdot \left(t\_m \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_m \cdot \left(y\_m \cdot x\right)\\ \end{array}\right) \end{array} \]

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 (or (<= z -3.2e-23) (not (<= z 1.08e-73)))
     (* y_m (* t_m (- z)))
     (* t_m (* y_m x))))))

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 ((z <= -3.2e-23) || !(z <= 1.08e-73)) {
		tmp = y_m * (t_m * -z);
	} else {
		tmp = t_m * (y_m * x);
	}
	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 ((z <= (-3.2d-23)) .or. (.not. (z <= 1.08d-73))) then
        tmp = y_m * (t_m * -z)
    else
        tmp = t_m * (y_m * x)
    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 ((z <= -3.2e-23) || !(z <= 1.08e-73)) {
		tmp = y_m * (t_m * -z);
	} else {
		tmp = t_m * (y_m * x);
	}
	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 (z <= -3.2e-23) or not (z <= 1.08e-73):
		tmp = y_m * (t_m * -z)
	else:
		tmp = t_m * (y_m * x)
	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 ((z <= -3.2e-23) || !(z <= 1.08e-73))
		tmp = Float64(y_m * Float64(t_m * Float64(-z)));
	else
		tmp = Float64(t_m * Float64(y_m * x));
	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 ((z <= -3.2e-23) || ~((z <= 1.08e-73)))
		tmp = y_m * (t_m * -z);
	else
		tmp = t_m * (y_m * x);
	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[Or[LessEqual[z, -3.2e-23], N[Not[LessEqual[z, 1.08e-73]], $MachinePrecision]], N[(y$95$m * N[(t$95$m * (-z)), $MachinePrecision]), $MachinePrecision], N[(t$95$m * N[(y$95$m * x), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -3.19999999999999976e-23 or 1.08000000000000007e-73 < z

   1. Initial program 89.2%

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

      1. distribute-rgt-out-- 92.0%

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

      2. associate-*l* 91.3%

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

      3. *-commutative 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in x around 0 75.3%

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

      1. mul-1-neg 75.3%

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

      2. distribute-rgt-neg-out 75.3%

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

   7. Simplified 75.3%

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

   if -3.19999999999999976e-23 < z < 1.08000000000000007e-73

   1. Initial program 93.4%

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

      1. distribute-rgt-out-- 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in x around inf 83.8%

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

      1. *-commutative 83.8%

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

   7. Simplified 83.8%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-23} \lor \neg \left(z \leq 1.08 \cdot 10^{-73}\right):\\ \;\;\;\;y \cdot \left(t \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -7.3 \cdot 10^{-25} \lor \neg \left(z \leq 1.4 \cdot 10^{-74}\right):\\ \;\;\;\;t\_m \cdot \left(y\_m \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_m \cdot \left(y\_m \cdot x\right)\\ \end{array}\right) \end{array} \]

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 (or (<= z -7.3e-25) (not (<= z 1.4e-74)))
     (* t_m (* y_m (- z)))
     (* t_m (* y_m x))))))

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 ((z <= -7.3e-25) || !(z <= 1.4e-74)) {
		tmp = t_m * (y_m * -z);
	} else {
		tmp = t_m * (y_m * x);
	}
	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 ((z <= (-7.3d-25)) .or. (.not. (z <= 1.4d-74))) then
        tmp = t_m * (y_m * -z)
    else
        tmp = t_m * (y_m * x)
    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 ((z <= -7.3e-25) || !(z <= 1.4e-74)) {
		tmp = t_m * (y_m * -z);
	} else {
		tmp = t_m * (y_m * x);
	}
	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 (z <= -7.3e-25) or not (z <= 1.4e-74):
		tmp = t_m * (y_m * -z)
	else:
		tmp = t_m * (y_m * x)
	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 ((z <= -7.3e-25) || !(z <= 1.4e-74))
		tmp = Float64(t_m * Float64(y_m * Float64(-z)));
	else
		tmp = Float64(t_m * Float64(y_m * x));
	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 ((z <= -7.3e-25) || ~((z <= 1.4e-74)))
		tmp = t_m * (y_m * -z);
	else
		tmp = t_m * (y_m * x);
	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[Or[LessEqual[z, -7.3e-25], N[Not[LessEqual[z, 1.4e-74]], $MachinePrecision]], N[(t$95$m * N[(y$95$m * (-z)), $MachinePrecision]), $MachinePrecision], N[(t$95$m * N[(y$95$m * x), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -7.30000000000000045e-25 or 1.39999999999999994e-74 < z

   1. Initial program 89.2%

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

      1. distribute-rgt-out-- 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in x around 0 75.4%

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

      1. mul-1-neg 75.4%

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

      2. distribute-rgt-neg-out 75.4%

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

   7. Simplified 75.4%

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

   if -7.30000000000000045e-25 < z < 1.39999999999999994e-74

   1. Initial program 93.4%

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

      1. distribute-rgt-out-- 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in x around inf 83.8%

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

      1. *-commutative 83.8%

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

   7. Simplified 83.8%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.3 \cdot 10^{-25} \lor \neg \left(z \leq 1.4 \cdot 10^{-74}\right):\\ \;\;\;\;t \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-24}:\\ \;\;\;\;t\_m \cdot \left(y\_m \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-73}:\\ \;\;\;\;t\_m \cdot \left(y\_m \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t\_m \cdot \left(-y\_m\right)\right)\\ \end{array}\right) \end{array} \]

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 (<= z -6.2e-24)
     (* t_m (* y_m (- z)))
     (if (<= z 1.22e-73) (* t_m (* y_m x)) (* z (* t_m (- y_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 (z <= -6.2e-24) {
		tmp = t_m * (y_m * -z);
	} else if (z <= 1.22e-73) {
		tmp = t_m * (y_m * x);
	} else {
		tmp = z * (t_m * -y_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 (z <= (-6.2d-24)) then
        tmp = t_m * (y_m * -z)
    else if (z <= 1.22d-73) then
        tmp = t_m * (y_m * x)
    else
        tmp = z * (t_m * -y_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 (z <= -6.2e-24) {
		tmp = t_m * (y_m * -z);
	} else if (z <= 1.22e-73) {
		tmp = t_m * (y_m * x);
	} else {
		tmp = z * (t_m * -y_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 z <= -6.2e-24:
		tmp = t_m * (y_m * -z)
	elif z <= 1.22e-73:
		tmp = t_m * (y_m * x)
	else:
		tmp = z * (t_m * -y_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 (z <= -6.2e-24)
		tmp = Float64(t_m * Float64(y_m * Float64(-z)));
	elseif (z <= 1.22e-73)
		tmp = Float64(t_m * Float64(y_m * x));
	else
		tmp = Float64(z * Float64(t_m * Float64(-y_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 (z <= -6.2e-24)
		tmp = t_m * (y_m * -z);
	elseif (z <= 1.22e-73)
		tmp = t_m * (y_m * x);
	else
		tmp = z * (t_m * -y_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[z, -6.2e-24], N[(t$95$m * N[(y$95$m * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.22e-73], N[(t$95$m * N[(y$95$m * x), $MachinePrecision]), $MachinePrecision], N[(z * N[(t$95$m * (-y$95$m)), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -6.2000000000000001e-24

   1. Initial program 93.9%

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

      1. distribute-rgt-out-- 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in x around 0 83.5%

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

      1. mul-1-neg 83.5%

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

      2. distribute-rgt-neg-out 83.5%

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

   7. Simplified 83.5%

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

   if -6.2000000000000001e-24 < z < 1.22e-73

   1. Initial program 93.4%

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

      1. distribute-rgt-out-- 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in x around inf 83.8%

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

      1. *-commutative 83.8%

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

   7. Simplified 83.8%

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

   if 1.22e-73 < z

   1. Initial program 85.1%

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

      1. distribute-rgt-out-- 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in x around inf 80.2%

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

      1. mul-1-neg 80.2%

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

      2. unsub-neg 80.2%

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

      3. associate-/l* 76.5%

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

   7. Simplified 76.5%

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

   8. Taylor expanded in z around inf 62.3%

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

      1. mul-1-neg 62.3%

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

      2. associate-*r/ 57.2%

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

      3. distribute-rgt-neg-in 57.2%

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

      4. mul-1-neg 57.2%

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

      5. associate-*r/ 57.2%

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

      6. mul-1-neg 57.2%

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

   10. Simplified 57.2%

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

   11. Taylor expanded in x around 0 68.4%

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

       1. associate-*r* 68.4%

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

       2. neg-mul-1 68.4%

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

       3. associate-*r* 78.5%

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

   13. Simplified 78.5%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-24}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-73}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(-y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;t\_m \leq 1.2 \cdot 10^{-30}:\\ \;\;\;\;y\_m \cdot \left(t\_m \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t\_m \cdot y\_m\right)\\ \end{array}\right) \end{array} \]

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 (<= t_m 1.2e-30) (* y_m (* t_m x)) (* x (* t_m y_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 (t_m <= 1.2e-30) {
		tmp = y_m * (t_m * x);
	} else {
		tmp = x * (t_m * y_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 (t_m <= 1.2d-30) then
        tmp = y_m * (t_m * x)
    else
        tmp = x * (t_m * y_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 (t_m <= 1.2e-30) {
		tmp = y_m * (t_m * x);
	} else {
		tmp = x * (t_m * y_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 t_m <= 1.2e-30:
		tmp = y_m * (t_m * x)
	else:
		tmp = x * (t_m * y_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 (t_m <= 1.2e-30)
		tmp = Float64(y_m * Float64(t_m * x));
	else
		tmp = Float64(x * Float64(t_m * y_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 (t_m <= 1.2e-30)
		tmp = y_m * (t_m * x);
	else
		tmp = x * (t_m * y_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[t$95$m, 1.2e-30], N[(y$95$m * N[(t$95$m * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(t$95$m * y$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < 1.19999999999999992e-30

   1. Initial program 88.6%

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

      1. distribute-rgt-out-- 90.3%

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

      2. associate-*l* 96.1%

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

      3. *-commutative 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in x around inf 55.7%

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

      1. associate-*r* 58.6%

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

      2. *-commutative 58.6%

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

   7. Simplified 58.6%

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

   if 1.19999999999999992e-30 < t

   1. Initial program 97.1%

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

      1. distribute-rgt-out-- 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in z around inf 97.2%

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

      1. neg-mul-1 97.2%

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

      2. +-commutative 97.2%

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

      3. sub-neg 97.2%

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

      4. *-commutative 97.2%

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

      5. associate-/l* 94.6%

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

   7. Simplified 94.6%

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

   8. Taylor expanded in z around 0 53.1%

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

      1. associate-*r* 50.8%

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

      2. *-commutative 50.8%

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

      3. associate-*r* 54.9%

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

      4. *-commutative 54.9%

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

   10. Simplified 54.9%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.2 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \left(t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.1% accurate, 1.8× speedup

Math

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

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 (* t_m y_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 * (t_m * y_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 * (t_m * y_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 * (t_m * y_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 * (t_m * y_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(t_m * y_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 * (t_m * y_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[(t$95$m * y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.0%

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

   1. distribute-rgt-out-- 92.6%

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

3. Simplified 92.6%

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

5. Taylor expanded in z around inf 85.1%

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

   1. neg-mul-1 85.1%

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

   2. +-commutative 85.1%

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

   3. sub-neg 85.1%

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

   4. *-commutative 85.1%

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

   5. associate-/l* 80.6%

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

7. Simplified 80.6%

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

8. Taylor expanded in z around 0 55.0%

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

   1. associate-*r* 56.4%

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

   2. *-commutative 56.4%

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

   3. associate-*r* 55.7%

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

   4. *-commutative 55.7%

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

10. Simplified 55.7%

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

11. Final simplification 55.7%

    \[\leadsto x \cdot \left(t \cdot y\right) \]
12. Add Preprocessing

Developer target: 95.8% 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 2024082 
(FPCore (x y z t)
  :name "Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3"
  :precision binary64

  :alt
  (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))