Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3

Percentage Accurate: 93.4% → 97.7%

Time: 8.9s

Alternatives: 8

Speedup: 1.3×

• 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: 93.4% 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: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ [x, y_m, z, t] = \mathsf{sort}([x, y_m, z, t])\\ \\ y\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq 1.5 \cdot 10^{+30}:\\ \;\;\;\;y\_m \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y\_m \cdot t\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
NOTE: x, y_m, z, and t should be sorted in increasing order before calling this function.
(FPCore (y_s x y_m z t)
 :precision binary64
 (* y_s (if (<= t 1.5e+30) (* y_m (* (- x z) t)) (* (- x z) (* y_m t)))))

C

y_m = fabs(y);
y_s = copysign(1.0, y);
assert(x < y_m && y_m < z && z < t);
double code(double y_s, double x, double y_m, double z, double t) {
	double tmp;
	if (t <= 1.5e+30) {
		tmp = y_m * ((x - z) * t);
	} else {
		tmp = (x - z) * (y_m * t);
	}
	return y_s * tmp;
}

Fortran

y_m = abs(y)
y_s = copysign(1.0d0, y)
NOTE: x, y_m, z, and t should be sorted in increasing order before calling this function.
real(8) function code(y_s, x, y_m, z, t)
    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
    real(8) :: tmp
    if (t <= 1.5d+30) then
        tmp = y_m * ((x - z) * t)
    else
        tmp = (x - z) * (y_m * t)
    end if
    code = y_s * tmp
end function

Java

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
assert x < y_m && y_m < z && z < t;
public static double code(double y_s, double x, double y_m, double z, double t) {
	double tmp;
	if (t <= 1.5e+30) {
		tmp = y_m * ((x - z) * t);
	} else {
		tmp = (x - z) * (y_m * t);
	}
	return y_s * tmp;
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
[x, y_m, z, t] = sort([x, y_m, z, t])
def code(y_s, x, y_m, z, t):
	tmp = 0
	if t <= 1.5e+30:
		tmp = y_m * ((x - z) * t)
	else:
		tmp = (x - z) * (y_m * t)
	return y_s * tmp

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
x, y_m, z, t = sort([x, y_m, z, t])
function code(y_s, x, y_m, z, t)
	tmp = 0.0
	if (t <= 1.5e+30)
		tmp = Float64(y_m * Float64(Float64(x - z) * t));
	else
		tmp = Float64(Float64(x - z) * Float64(y_m * t));
	end
	return Float64(y_s * tmp)
end

MATLAB

y_m = abs(y);
y_s = sign(y) * abs(1.0);
x, y_m, z, t = num2cell(sort([x, y_m, z, t])){:}
function tmp_2 = code(y_s, x, y_m, z, t)
	tmp = 0.0;
	if (t <= 1.5e+30)
		tmp = y_m * ((x - z) * t);
	else
		tmp = (x - z) * (y_m * t);
	end
	tmp_2 = 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]
NOTE: x, y_m, z, and t should be sorted in increasing order before calling this function.
code[y$95$s_, x_, y$95$m_, z_, t_] := N[(y$95$s * If[LessEqual[t, 1.5e+30], N[(y$95$m * N[(N[(x - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x - z), $MachinePrecision] * N[(y$95$m * t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < 1.49999999999999989e30

   1. Initial program 90.0%

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

      1. distribute-rgt-out-- 91.9%

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

      2. associate-*l* 93.7%

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

      3. *-commutative 93.7%

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

   3. Simplified 93.7%

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

   if 1.49999999999999989e30 < t

   1. Initial program 96.1%

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

      1. *-commutative 96.1%

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

      2. distribute-rgt-out-- 98.0%

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

      3. associate-*r* 98.0%

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

      4. *-commutative 98.0%

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

   3. Simplified 98.0%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.5 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ [x, y_m, z, t] = \mathsf{sort}([x, y_m, z, t])\\ \\ y\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-48} \lor \neg \left(x \leq 0.11\right):\\ \;\;\;\;t \cdot \left(y\_m \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;y\_m \cdot \left(-z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
NOTE: x, y_m, z, and t should be sorted in increasing order before calling this function.
(FPCore (y_s x y_m z t)
 :precision binary64
 (*
  y_s
  (if (or (<= x -1.9e-48) (not (<= x 0.11)))
    (* t (* y_m x))
    (* y_m (- (* z t))))))

C

y_m = fabs(y);
y_s = copysign(1.0, y);
assert(x < y_m && y_m < z && z < t);
double code(double y_s, double x, double y_m, double z, double t) {
	double tmp;
	if ((x <= -1.9e-48) || !(x <= 0.11)) {
		tmp = t * (y_m * x);
	} else {
		tmp = y_m * -(z * t);
	}
	return y_s * tmp;
}

Fortran

y_m = abs(y)
y_s = copysign(1.0d0, y)
NOTE: x, y_m, z, and t should be sorted in increasing order before calling this function.
real(8) function code(y_s, x, y_m, z, t)
    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
    real(8) :: tmp
    if ((x <= (-1.9d-48)) .or. (.not. (x <= 0.11d0))) then
        tmp = t * (y_m * x)
    else
        tmp = y_m * -(z * t)
    end if
    code = y_s * tmp
end function

Java

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
assert x < y_m && y_m < z && z < t;
public static double code(double y_s, double x, double y_m, double z, double t) {
	double tmp;
	if ((x <= -1.9e-48) || !(x <= 0.11)) {
		tmp = t * (y_m * x);
	} else {
		tmp = y_m * -(z * t);
	}
	return y_s * tmp;
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
[x, y_m, z, t] = sort([x, y_m, z, t])
def code(y_s, x, y_m, z, t):
	tmp = 0
	if (x <= -1.9e-48) or not (x <= 0.11):
		tmp = t * (y_m * x)
	else:
		tmp = y_m * -(z * t)
	return y_s * tmp

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
x, y_m, z, t = sort([x, y_m, z, t])
function code(y_s, x, y_m, z, t)
	tmp = 0.0
	if ((x <= -1.9e-48) || !(x <= 0.11))
		tmp = Float64(t * Float64(y_m * x));
	else
		tmp = Float64(y_m * Float64(-Float64(z * t)));
	end
	return Float64(y_s * tmp)
end

MATLAB

y_m = abs(y);
y_s = sign(y) * abs(1.0);
x, y_m, z, t = num2cell(sort([x, y_m, z, t])){:}
function tmp_2 = code(y_s, x, y_m, z, t)
	tmp = 0.0;
	if ((x <= -1.9e-48) || ~((x <= 0.11)))
		tmp = t * (y_m * x);
	else
		tmp = y_m * -(z * t);
	end
	tmp_2 = 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]
NOTE: x, y_m, z, and t should be sorted in increasing order before calling this function.
code[y$95$s_, x_, y$95$m_, z_, t_] := N[(y$95$s * If[Or[LessEqual[x, -1.9e-48], N[Not[LessEqual[x, 0.11]], $MachinePrecision]], N[(t * N[(y$95$m * x), $MachinePrecision]), $MachinePrecision], N[(y$95$m * (-N[(z * t), $MachinePrecision])), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < -1.90000000000000001e-48 or 0.110000000000000001 < x

   1. Initial program 88.4%

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

      1. distribute-rgt-out-- 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in x around inf 74.2%

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

      1. *-commutative 74.2%

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

   7. Simplified 74.2%

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

   if -1.90000000000000001e-48 < x < 0.110000000000000001

   1. Initial program 94.3%

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

      1. distribute-rgt-out-- 94.3%

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

      2. associate-*l* 91.1%

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

      3. *-commutative 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in x around 0 82.2%

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

      1. mul-1-neg 82.2%

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

      2. distribute-rgt-neg-out 82.2%

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

   7. Simplified 82.2%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-48} \lor \neg \left(x \leq 0.11\right):\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ [x, y_m, z, t] = \mathsf{sort}([x, y_m, z, t])\\ \\ y\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-50} \lor \neg \left(x \leq 0.6\right):\\ \;\;\;\;t \cdot \left(y\_m \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\_m \cdot t\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
NOTE: x, y_m, z, and t should be sorted in increasing order before calling this function.
(FPCore (y_s x y_m z t)
 :precision binary64
 (*
  y_s
  (if (or (<= x -2.5e-50) (not (<= x 0.6)))
    (* t (* y_m x))
    (* z (- (* y_m t))))))

C

y_m = fabs(y);
y_s = copysign(1.0, y);
assert(x < y_m && y_m < z && z < t);
double code(double y_s, double x, double y_m, double z, double t) {
	double tmp;
	if ((x <= -2.5e-50) || !(x <= 0.6)) {
		tmp = t * (y_m * x);
	} else {
		tmp = z * -(y_m * t);
	}
	return y_s * tmp;
}

Fortran

y_m = abs(y)
y_s = copysign(1.0d0, y)
NOTE: x, y_m, z, and t should be sorted in increasing order before calling this function.
real(8) function code(y_s, x, y_m, z, t)
    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
    real(8) :: tmp
    if ((x <= (-2.5d-50)) .or. (.not. (x <= 0.6d0))) then
        tmp = t * (y_m * x)
    else
        tmp = z * -(y_m * t)
    end if
    code = y_s * tmp
end function

Java

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
assert x < y_m && y_m < z && z < t;
public static double code(double y_s, double x, double y_m, double z, double t) {
	double tmp;
	if ((x <= -2.5e-50) || !(x <= 0.6)) {
		tmp = t * (y_m * x);
	} else {
		tmp = z * -(y_m * t);
	}
	return y_s * tmp;
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
[x, y_m, z, t] = sort([x, y_m, z, t])
def code(y_s, x, y_m, z, t):
	tmp = 0
	if (x <= -2.5e-50) or not (x <= 0.6):
		tmp = t * (y_m * x)
	else:
		tmp = z * -(y_m * t)
	return y_s * tmp

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
x, y_m, z, t = sort([x, y_m, z, t])
function code(y_s, x, y_m, z, t)
	tmp = 0.0
	if ((x <= -2.5e-50) || !(x <= 0.6))
		tmp = Float64(t * Float64(y_m * x));
	else
		tmp = Float64(z * Float64(-Float64(y_m * t)));
	end
	return Float64(y_s * tmp)
end

MATLAB

y_m = abs(y);
y_s = sign(y) * abs(1.0);
x, y_m, z, t = num2cell(sort([x, y_m, z, t])){:}
function tmp_2 = code(y_s, x, y_m, z, t)
	tmp = 0.0;
	if ((x <= -2.5e-50) || ~((x <= 0.6)))
		tmp = t * (y_m * x);
	else
		tmp = z * -(y_m * t);
	end
	tmp_2 = 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]
NOTE: x, y_m, z, and t should be sorted in increasing order before calling this function.
code[y$95$s_, x_, y$95$m_, z_, t_] := N[(y$95$s * If[Or[LessEqual[x, -2.5e-50], N[Not[LessEqual[x, 0.6]], $MachinePrecision]], N[(t * N[(y$95$m * x), $MachinePrecision]), $MachinePrecision], N[(z * (-N[(y$95$m * t), $MachinePrecision])), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < -2.49999999999999984e-50 or 0.599999999999999978 < x

   1. Initial program 88.4%

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

      1. distribute-rgt-out-- 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in x around inf 74.2%

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

      1. *-commutative 74.2%

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

   7. Simplified 74.2%

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

   if -2.49999999999999984e-50 < x < 0.599999999999999978

   1. Initial program 94.3%

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

      1. distribute-rgt-out-- 94.3%

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

      2. associate-*l* 91.1%

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

      3. *-commutative 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in x around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. distribute-rgt-neg-in 84.6%

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

      3. distribute-rgt-neg-out 84.6%

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

      4. associate-*l* 86.4%

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

   7. Simplified 86.4%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-50} \lor \neg \left(x \leq 0.6\right):\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ [x, y_m, z, t] = \mathsf{sort}([x, y_m, z, t])\\ \\ y\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-50} \lor \neg \left(x \leq 1.6\right):\\ \;\;\;\;t \cdot \left(y\_m \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(-y\_m\right)\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
NOTE: x, y_m, z, and t should be sorted in increasing order before calling this function.
(FPCore (y_s x y_m z t)
 :precision binary64
 (*
  y_s
  (if (or (<= x -8.5e-50) (not (<= x 1.6)))
    (* t (* y_m x))
    (* t (* z (- y_m))))))

C

y_m = fabs(y);
y_s = copysign(1.0, y);
assert(x < y_m && y_m < z && z < t);
double code(double y_s, double x, double y_m, double z, double t) {
	double tmp;
	if ((x <= -8.5e-50) || !(x <= 1.6)) {
		tmp = t * (y_m * x);
	} else {
		tmp = t * (z * -y_m);
	}
	return y_s * tmp;
}

Fortran

y_m = abs(y)
y_s = copysign(1.0d0, y)
NOTE: x, y_m, z, and t should be sorted in increasing order before calling this function.
real(8) function code(y_s, x, y_m, z, t)
    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
    real(8) :: tmp
    if ((x <= (-8.5d-50)) .or. (.not. (x <= 1.6d0))) then
        tmp = t * (y_m * x)
    else
        tmp = t * (z * -y_m)
    end if
    code = y_s * tmp
end function

Java

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
assert x < y_m && y_m < z && z < t;
public static double code(double y_s, double x, double y_m, double z, double t) {
	double tmp;
	if ((x <= -8.5e-50) || !(x <= 1.6)) {
		tmp = t * (y_m * x);
	} else {
		tmp = t * (z * -y_m);
	}
	return y_s * tmp;
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
[x, y_m, z, t] = sort([x, y_m, z, t])
def code(y_s, x, y_m, z, t):
	tmp = 0
	if (x <= -8.5e-50) or not (x <= 1.6):
		tmp = t * (y_m * x)
	else:
		tmp = t * (z * -y_m)
	return y_s * tmp

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
x, y_m, z, t = sort([x, y_m, z, t])
function code(y_s, x, y_m, z, t)
	tmp = 0.0
	if ((x <= -8.5e-50) || !(x <= 1.6))
		tmp = Float64(t * Float64(y_m * x));
	else
		tmp = Float64(t * Float64(z * Float64(-y_m)));
	end
	return Float64(y_s * tmp)
end

MATLAB

y_m = abs(y);
y_s = sign(y) * abs(1.0);
x, y_m, z, t = num2cell(sort([x, y_m, z, t])){:}
function tmp_2 = code(y_s, x, y_m, z, t)
	tmp = 0.0;
	if ((x <= -8.5e-50) || ~((x <= 1.6)))
		tmp = t * (y_m * x);
	else
		tmp = t * (z * -y_m);
	end
	tmp_2 = 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]
NOTE: x, y_m, z, and t should be sorted in increasing order before calling this function.
code[y$95$s_, x_, y$95$m_, z_, t_] := N[(y$95$s * If[Or[LessEqual[x, -8.5e-50], N[Not[LessEqual[x, 1.6]], $MachinePrecision]], N[(t * N[(y$95$m * x), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * (-y$95$m)), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < -8.50000000000000012e-50 or 1.6000000000000001 < x

   1. Initial program 88.4%

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

      1. distribute-rgt-out-- 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in x around inf 74.2%

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

      1. *-commutative 74.2%

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

   7. Simplified 74.2%

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

   if -8.50000000000000012e-50 < x < 1.6000000000000001

   1. Initial program 94.3%

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

      1. distribute-rgt-out-- 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in x around 0 84.6%

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

      1. associate-*r* 84.6%

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

      2. *-commutative 84.6%

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

      3. mul-1-neg 84.6%

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

   7. Simplified 84.6%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-50} \lor \neg \left(x \leq 1.6\right):\\ \;\;\;\;t \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(-y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ [x, y_m, z, t] = \mathsf{sort}([x, y_m, z, t])\\ \\ y\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq 3.5 \cdot 10^{+100}:\\ \;\;\;\;y\_m \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(-y\_m\right)\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
NOTE: x, y_m, z, and t should be sorted in increasing order before calling this function.
(FPCore (y_s x y_m z t)
 :precision binary64
 (* y_s (if (<= z 3.5e+100) (* y_m (* (- x z) t)) (* t (* z (- y_m))))))

C

y_m = fabs(y);
y_s = copysign(1.0, y);
assert(x < y_m && y_m < z && z < t);
double code(double y_s, double x, double y_m, double z, double t) {
	double tmp;
	if (z <= 3.5e+100) {
		tmp = y_m * ((x - z) * t);
	} else {
		tmp = t * (z * -y_m);
	}
	return y_s * tmp;
}

Fortran

y_m = abs(y)
y_s = copysign(1.0d0, y)
NOTE: x, y_m, z, and t should be sorted in increasing order before calling this function.
real(8) function code(y_s, x, y_m, z, t)
    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
    real(8) :: tmp
    if (z <= 3.5d+100) then
        tmp = y_m * ((x - z) * t)
    else
        tmp = t * (z * -y_m)
    end if
    code = y_s * tmp
end function

Java

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
assert x < y_m && y_m < z && z < t;
public static double code(double y_s, double x, double y_m, double z, double t) {
	double tmp;
	if (z <= 3.5e+100) {
		tmp = y_m * ((x - z) * t);
	} else {
		tmp = t * (z * -y_m);
	}
	return y_s * tmp;
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
[x, y_m, z, t] = sort([x, y_m, z, t])
def code(y_s, x, y_m, z, t):
	tmp = 0
	if z <= 3.5e+100:
		tmp = y_m * ((x - z) * t)
	else:
		tmp = t * (z * -y_m)
	return y_s * tmp

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
x, y_m, z, t = sort([x, y_m, z, t])
function code(y_s, x, y_m, z, t)
	tmp = 0.0
	if (z <= 3.5e+100)
		tmp = Float64(y_m * Float64(Float64(x - z) * t));
	else
		tmp = Float64(t * Float64(z * Float64(-y_m)));
	end
	return Float64(y_s * tmp)
end

MATLAB

y_m = abs(y);
y_s = sign(y) * abs(1.0);
x, y_m, z, t = num2cell(sort([x, y_m, z, t])){:}
function tmp_2 = code(y_s, x, y_m, z, t)
	tmp = 0.0;
	if (z <= 3.5e+100)
		tmp = y_m * ((x - z) * t);
	else
		tmp = t * (z * -y_m);
	end
	tmp_2 = 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]
NOTE: x, y_m, z, and t should be sorted in increasing order before calling this function.
code[y$95$s_, x_, y$95$m_, z_, t_] := N[(y$95$s * If[LessEqual[z, 3.5e+100], N[(y$95$m * N[(N[(x - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * (-y$95$m)), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < 3.49999999999999976e100

   1. Initial program 93.0%

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

      1. distribute-rgt-out-- 94.8%

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

      2. associate-*l* 94.7%

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

      3. *-commutative 94.7%

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

   3. Simplified 94.7%

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

   if 3.49999999999999976e100 < z

   1. Initial program 77.5%

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

      1. distribute-rgt-out-- 80.9%

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

   3. Simplified 80.9%

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

   5. Taylor expanded in x around 0 70.9%

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

      1. associate-*r* 70.9%

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

      2. *-commutative 70.9%

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

      3. mul-1-neg 70.9%

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

   7. Simplified 70.9%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.5 \cdot 10^{+100}:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(-y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.5% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

y_m = abs(y);
y_s = sign(y) * abs(1.0);
x, y_m, z, t = num2cell(sort([x, y_m, z, t])){:}
function tmp = code(y_s, x, y_m, z, t)
	tmp = y_s * ((y_m * (x - z)) * t);
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]
NOTE: x, y_m, z, and t should be sorted in increasing order before calling this function.
code[y$95$s_, x_, y$95$m_, z_, t_] := N[(y$95$s * N[(N[(y$95$m * N[(x - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.2%

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

   1. distribute-rgt-out-- 93.2%

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

3. Simplified 93.2%

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

5. Final simplification 93.2%

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

Alternative 7: 52.3% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

y_m = abs(y);
y_s = sign(y) * abs(1.0);
x, y_m, z, t = num2cell(sort([x, y_m, z, t])){:}
function tmp = code(y_s, x, y_m, z, t)
	tmp = y_s * (y_m * (x * t));
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]
NOTE: x, y_m, z, and t should be sorted in increasing order before calling this function.
code[y$95$s_, x_, y$95$m_, z_, t_] := N[(y$95$s * N[(y$95$m * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.2%

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

   1. distribute-rgt-out-- 93.2%

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

   2. associate-*l* 93.5%

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

   3. *-commutative 93.5%

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

3. Simplified 93.5%

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

5. Taylor expanded in x around inf 52.8%

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

   1. associate-*r* 54.1%

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

   2. *-commutative 54.1%

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

7. Simplified 54.1%

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

8. Final simplification 54.1%

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

Alternative 8: 54.9% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

y_m = abs(y);
y_s = sign(y) * abs(1.0);
x, y_m, z, t = num2cell(sort([x, y_m, z, t])){:}
function tmp = code(y_s, x, y_m, z, t)
	tmp = y_s * (t * (y_m * x));
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]
NOTE: x, y_m, z, and t should be sorted in increasing order before calling this function.
code[y$95$s_, x_, y$95$m_, z_, t_] := N[(y$95$s * N[(t * N[(y$95$m * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.2%

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

   1. distribute-rgt-out-- 93.2%

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

3. Simplified 93.2%

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

5. Taylor expanded in x around inf 52.8%

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

   1. *-commutative 52.8%

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

7. Simplified 52.8%

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

8. Final simplification 52.8%

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

Developer target: 96.2% 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 2024027 
(FPCore (x y z t)
  :name "Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -9.231879582886777e-80) (* (* y t) (- x z)) (if (< t 2.543067051564877e+83) (* y (* t (- x z))) (* (* y (- x z)) t)))

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