Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3

Percentage Accurate: 96.3% → 98.0%

Time: 10.3s

Alternatives: 9

Speedup: 0.7×

• 26.2% 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: 96.3% 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: 98.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;t\_m \leq 5.2 \cdot 10^{+63}:\\ \;\;\;\;t\_m \cdot \left(y\_m \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(t\_m \cdot y\_m\right)\\ \end{array}\right) \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 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 5.2e+63) (* t_m (* y_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 <= 5.2e+63) {
		tmp = t_m * (y_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 <= 5.2d+63) then
        tmp = t_m * (y_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 <= 5.2e+63) {
		tmp = t_m * (y_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 <= 5.2e+63:
		tmp = t_m * (y_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 <= 5.2e+63)
		tmp = Float64(t_m * Float64(y_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 <= 5.2e+63)
		tmp = t_m * (y_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, 5.2e+63], N[(t$95$m * N[(y$95$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 < 5.2000000000000002e63

   1. Initial program 88.7%

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

      1. distribute-rgt-out-- 89.3%

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

   3. Simplified 89.3%

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

   if 5.2000000000000002e63 < t

   1. Initial program 92.6%

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

      1. *-commutative 92.6%

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

      2. distribute-rgt-out-- 94.8%

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

      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 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.2 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(t \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{-53} \lor \neg \left(x \leq 1.4 \cdot 10^{+125}\right):\\ \;\;\;\;t\_m \cdot \left(y\_m \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;y\_m \cdot \left(t\_m \cdot \left(-z\right)\right)\\ \end{array}\right) \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 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 (<= x -2.15e-53) (not (<= x 1.4e+125)))
     (* t_m (* y_m x))
     (* y_m (* t_m (- z)))))))

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 <= -2.15e-53) || !(x <= 1.4e+125)) {
		tmp = t_m * (y_m * x);
	} else {
		tmp = y_m * (t_m * -z);
	}
	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 <= (-2.15d-53)) .or. (.not. (x <= 1.4d+125))) then
        tmp = t_m * (y_m * x)
    else
        tmp = y_m * (t_m * -z)
    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 <= -2.15e-53) || !(x <= 1.4e+125)) {
		tmp = t_m * (y_m * x);
	} else {
		tmp = y_m * (t_m * -z);
	}
	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 <= -2.15e-53) or not (x <= 1.4e+125):
		tmp = t_m * (y_m * x)
	else:
		tmp = y_m * (t_m * -z)
	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 <= -2.15e-53) || !(x <= 1.4e+125))
		tmp = Float64(t_m * Float64(y_m * x));
	else
		tmp = Float64(y_m * Float64(t_m * Float64(-z)));
	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 <= -2.15e-53) || ~((x <= 1.4e+125)))
		tmp = t_m * (y_m * x);
	else
		tmp = y_m * (t_m * -z);
	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[x, -2.15e-53], N[Not[LessEqual[x, 1.4e+125]], $MachinePrecision]], N[(t$95$m * N[(y$95$m * x), $MachinePrecision]), $MachinePrecision], N[(y$95$m * N[(t$95$m * (-z)), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < -2.15e-53 or 1.4e125 < x

   1. Initial program 84.7%

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

      1. distribute-rgt-out-- 85.8%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in x around inf 73.1%

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

      1. *-commutative 73.1%

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

   7. Simplified 73.1%

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

   if -2.15e-53 < x < 1.4e125

   1. Initial program 93.3%

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

      1. distribute-rgt-out-- 94.1%

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

      2. associate-*l* 93.1%

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

      3. *-commutative 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in x around 0 78.6%

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

      1. mul-1-neg 78.6%

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

      2. distribute-rgt-neg-out 78.6%

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

   7. Simplified 78.6%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{-53} \lor \neg \left(x \leq 1.4 \cdot 10^{+125}\right):\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-63} \lor \neg \left(x \leq 1.9 \cdot 10^{-25}\right):\\ \;\;\;\;t\_m \cdot \left(y\_m \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t\_m \cdot \left(-y\_m\right)\right)\\ \end{array}\right) \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 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 (<= x -5.4e-63) (not (<= x 1.9e-25)))
     (* 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 ((x <= -5.4e-63) || !(x <= 1.9e-25)) {
		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 ((x <= (-5.4d-63)) .or. (.not. (x <= 1.9d-25))) 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 ((x <= -5.4e-63) || !(x <= 1.9e-25)) {
		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 (x <= -5.4e-63) or not (x <= 1.9e-25):
		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 ((x <= -5.4e-63) || !(x <= 1.9e-25))
		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 ((x <= -5.4e-63) || ~((x <= 1.9e-25)))
		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[Or[LessEqual[x, -5.4e-63], N[Not[LessEqual[x, 1.9e-25]], $MachinePrecision]], 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 2 regimes

2. if x < -5.4000000000000004e-63 or 1.8999999999999999e-25 < x

   1. Initial program 86.6%

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

      1. distribute-rgt-out-- 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in x around inf 68.4%

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

      1. *-commutative 68.4%

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

   7. Simplified 68.4%

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

   if -5.4000000000000004e-63 < x < 1.8999999999999999e-25

   1. Initial program 93.3%

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

      1. distribute-rgt-out-- 93.3%

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

      2. associate-*l* 92.0%

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

      3. *-commutative 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in x around 0 84.5%

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

      1. mul-1-neg 84.5%

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

      2. distribute-rgt-neg-in 84.5%

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

      3. distribute-rgt-neg-out 84.5%

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

      4. associate-*l* 85.7%

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

   7. Simplified 85.7%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-63} \lor \neg \left(x \leq 1.9 \cdot 10^{-25}\right):\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(-y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-52} \lor \neg \left(x \leq 1.45 \cdot 10^{+125}\right):\\ \;\;\;\;t\_m \cdot \left(y\_m \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_m \cdot \left(y\_m \cdot \left(-z\right)\right)\\ \end{array}\right) \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 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 (<= x -1.15e-52) (not (<= x 1.45e+125)))
     (* t_m (* y_m x))
     (* t_m (* y_m (- z)))))))

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 <= -1.15e-52) || !(x <= 1.45e+125)) {
		tmp = t_m * (y_m * x);
	} else {
		tmp = t_m * (y_m * -z);
	}
	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 <= (-1.15d-52)) .or. (.not. (x <= 1.45d+125))) then
        tmp = t_m * (y_m * x)
    else
        tmp = t_m * (y_m * -z)
    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 <= -1.15e-52) || !(x <= 1.45e+125)) {
		tmp = t_m * (y_m * x);
	} else {
		tmp = t_m * (y_m * -z);
	}
	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 <= -1.15e-52) or not (x <= 1.45e+125):
		tmp = t_m * (y_m * x)
	else:
		tmp = t_m * (y_m * -z)
	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 <= -1.15e-52) || !(x <= 1.45e+125))
		tmp = Float64(t_m * Float64(y_m * x));
	else
		tmp = Float64(t_m * Float64(y_m * Float64(-z)));
	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 <= -1.15e-52) || ~((x <= 1.45e+125)))
		tmp = t_m * (y_m * x);
	else
		tmp = t_m * (y_m * -z);
	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[x, -1.15e-52], N[Not[LessEqual[x, 1.45e+125]], $MachinePrecision]], N[(t$95$m * N[(y$95$m * x), $MachinePrecision]), $MachinePrecision], N[(t$95$m * N[(y$95$m * (-z)), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < -1.14999999999999997e-52 or 1.44999999999999997e125 < x

   1. Initial program 84.7%

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

      1. distribute-rgt-out-- 85.8%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in x around inf 73.1%

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

      1. *-commutative 73.1%

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

   7. Simplified 73.1%

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

   if -1.14999999999999997e-52 < x < 1.44999999999999997e125

   1. Initial program 93.3%

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

      1. distribute-rgt-out-- 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in x around 0 78.9%

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

      1. associate-*r* 78.9%

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

      2. *-commutative 78.9%

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

      3. mul-1-neg 78.9%

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

   7. Simplified 78.9%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-52} \lor \neg \left(x \leq 1.45 \cdot 10^{+125}\right):\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq 3.5 \cdot 10^{+134}:\\ \;\;\;\;y\_m \cdot \left(t\_m \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_m \cdot \left(y\_m \cdot x\right)\\ \end{array}\right) \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 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 3.5e+134) (* y_m (* t_m (- x 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 (x <= 3.5e+134) {
		tmp = y_m * (t_m * (x - 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 (x <= 3.5d+134) then
        tmp = y_m * (t_m * (x - 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 (x <= 3.5e+134) {
		tmp = y_m * (t_m * (x - 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 x <= 3.5e+134:
		tmp = y_m * (t_m * (x - 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 (x <= 3.5e+134)
		tmp = Float64(y_m * Float64(t_m * Float64(x - 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 (x <= 3.5e+134)
		tmp = y_m * (t_m * (x - 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[LessEqual[x, 3.5e+134], N[(y$95$m * N[(t$95$m * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$m * N[(y$95$m * x), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 3.50000000000000003e134

   1. Initial program 91.9%

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

      1. distribute-rgt-out-- 92.9%

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

      2. associate-*l* 94.6%

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

      3. *-commutative 94.6%

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

   3. Simplified 94.6%

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

   if 3.50000000000000003e134 < x

   1. Initial program 75.8%

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

      1. distribute-rgt-out-- 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in x around inf 71.3%

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

      1. *-commutative 71.3%

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

   7. Simplified 71.3%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.5 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;t\_m \leq 3.2 \cdot 10^{-33}:\\ \;\;\;\;y\_m \cdot \left(t\_m \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(t\_m \cdot y\_m\right)\\ \end{array}\right) \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 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 3.2e-33) (* 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 <= 3.2e-33) {
		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 <= 3.2d-33) 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 <= 3.2e-33) {
		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 <= 3.2e-33:
		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 <= 3.2e-33)
		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 <= 3.2e-33)
		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, 3.2e-33], 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 < 3.19999999999999977e-33

   1. Initial program 88.3%

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

      1. distribute-rgt-out-- 89.0%

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

      2. associate-*l* 94.1%

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

      3. *-commutative 94.1%

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

   3. Simplified 94.1%

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

   if 3.19999999999999977e-33 < t

   1. Initial program 92.9%

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

      1. *-commutative 92.9%

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

      2. distribute-rgt-out-- 94.6%

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

      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 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.2 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(t \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;t\_m \leq 10^{-65}:\\ \;\;\;\;y\_m \cdot \left(t\_m \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t\_m \cdot y\_m\right)\\ \end{array}\right) \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 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 1e-65) (* 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 <= 1e-65) {
		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 <= 1d-65) 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 <= 1e-65) {
		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 <= 1e-65:
		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 <= 1e-65)
		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 <= 1e-65)
		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, 1e-65], 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 < 9.99999999999999923e-66

   1. Initial program 87.9%

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

      1. distribute-rgt-out-- 88.6%

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

      2. associate-*l* 93.9%

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

      3. *-commutative 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in x around inf 49.8%

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

      1. associate-*r* 54.3%

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

      2. *-commutative 54.3%

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

   7. Simplified 54.3%

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

   if 9.99999999999999923e-66 < t

   1. Initial program 93.6%

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

      1. distribute-rgt-out-- 95.1%

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

   3. Simplified 95.1%

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

      1. add-cube-cbrt 93.9%

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

      2. pow3 93.9%

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

   6. Applied egg-rr 93.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{y \cdot \left(x - z\right)}\right)}^{3}} \cdot t \]
   7. Step-by-step derivation

      1. add-cube-cbrt 93.9%

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

      2. pow3 93.9%

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

   8. Applied egg-rr 93.7%

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

   9. Taylor expanded in x around inf 49.2%

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

       1. *-commutative 49.2%

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

       2. associate-*l* 56.6%

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

   11. Simplified 56.6%

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

4. Final simplification 54.9%

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

Alternative 8: 57.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ t\_s \cdot \left(y\_s \cdot \begin{array}{l} \mathbf{if}\;t\_m \leq 6 \cdot 10^{+63}:\\ \;\;\;\;t\_m \cdot \left(y\_m \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t\_m \cdot y\_m\right)\\ \end{array}\right) \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 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 6e+63) (* t_m (* y_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 <= 6e+63) {
		tmp = t_m * (y_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 <= 6d+63) then
        tmp = t_m * (y_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 <= 6e+63) {
		tmp = t_m * (y_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 <= 6e+63:
		tmp = t_m * (y_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 <= 6e+63)
		tmp = Float64(t_m * Float64(y_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 <= 6e+63)
		tmp = t_m * (y_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, 6e+63], N[(t$95$m * N[(y$95$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 < 5.99999999999999998e63

   1. Initial program 88.7%

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

      1. distribute-rgt-out-- 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in x around inf 48.7%

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

      1. *-commutative 48.7%

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

   7. Simplified 48.7%

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

   if 5.99999999999999998e63 < t

   1. Initial program 92.6%

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

      1. distribute-rgt-out-- 94.8%

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

   3. Simplified 94.8%

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

      1. add-cube-cbrt 93.6%

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

      2. pow3 93.6%

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

   6. Applied egg-rr 93.6%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{y \cdot \left(x - z\right)}\right)}^{3}} \cdot t \]
   7. Step-by-step derivation

      1. add-cube-cbrt 93.6%

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

      2. pow3 93.6%

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

   8. Applied egg-rr 93.5%

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

   9. Taylor expanded in x around inf 54.2%

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

       1. *-commutative 54.2%

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

       2. associate-*l* 65.3%

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

   11. Simplified 65.3%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 6 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.7% 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 1 y)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 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 89.4%

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

   1. distribute-rgt-out-- 90.3%

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

3. Simplified 90.3%

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

   1. add-cube-cbrt 89.3%

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

   2. pow3 89.2%

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

6. Applied egg-rr 89.2%

   \[\leadsto \color{blue}{{\left(\sqrt[3]{y \cdot \left(x - z\right)}\right)}^{3}} \cdot t \]
7. Step-by-step derivation

   1. add-cube-cbrt 89.3%

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

   2. pow3 89.2%

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

8. Applied egg-rr 89.0%

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

9. Taylor expanded in x around inf 49.6%

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

    1. *-commutative 49.6%

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

    2. associate-*l* 55.4%

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

11. Simplified 55.4%

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

12. Final simplification 55.4%

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

Developer target: 95.7% 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 2024043 
(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))