Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3

Percentage Accurate: 52.7% → 52.9%

Time: 4.1s

Alternatives: 4

Speedup: 1.3×

• 25.0% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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: 52.7% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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: 52.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ t_m = \left|t\right| \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y\_m - z \cdot y\_m \leq -4 \cdot 10^{+272}:\\ \;\;\;\;\left(\left(\left(z + x\right) \cdot \left(x - z\right)\right) \cdot \frac{t\_m}{z}\right) \cdot y\_m\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x - z\right) \cdot y\_m\right) \cdot t\_m\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
t_m = (fabs.f64 t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
(FPCore (x y_m z t_m)
 :precision binary64
 (if (<= (- (* x y_m) (* z y_m)) -4e+272)
   (* (* (* (+ z x) (- x z)) (/ t_m z)) y_m)
   (* (* (- x z) y_m) t_m)))

C

y_m = fabs(y);
t_m = fabs(t);
assert(x < y_m && y_m < z && z < t_m);
double code(double x, double y_m, double z, double t_m) {
	double tmp;
	if (((x * y_m) - (z * y_m)) <= -4e+272) {
		tmp = (((z + x) * (x - z)) * (t_m / z)) * y_m;
	} else {
		tmp = ((x - z) * y_m) * t_m;
	}
	return tmp;
}

Fortran

y_m =     private
t_m =     private
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y_m, z, t_m)
use fmin_fmax_functions
    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 * y_m) - (z * y_m)) <= (-4d+272)) then
        tmp = (((z + x) * (x - z)) * (t_m / z)) * y_m
    else
        tmp = ((x - z) * y_m) * t_m
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
t_m = Math.abs(t);
assert x < y_m && y_m < z && z < t_m;
public static double code(double x, double y_m, double z, double t_m) {
	double tmp;
	if (((x * y_m) - (z * y_m)) <= -4e+272) {
		tmp = (((z + x) * (x - z)) * (t_m / z)) * y_m;
	} else {
		tmp = ((x - z) * y_m) * t_m;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
t_m = math.fabs(t)
[x, y_m, z, t_m] = sort([x, y_m, z, t_m])
def code(x, y_m, z, t_m):
	tmp = 0
	if ((x * y_m) - (z * y_m)) <= -4e+272:
		tmp = (((z + x) * (x - z)) * (t_m / z)) * y_m
	else:
		tmp = ((x - z) * y_m) * t_m
	return tmp

Julia

y_m = abs(y)
t_m = abs(t)
x, y_m, z, t_m = sort([x, y_m, z, t_m])
function code(x, y_m, z, t_m)
	tmp = 0.0
	if (Float64(Float64(x * y_m) - Float64(z * y_m)) <= -4e+272)
		tmp = Float64(Float64(Float64(Float64(z + x) * Float64(x - z)) * Float64(t_m / z)) * y_m);
	else
		tmp = Float64(Float64(Float64(x - z) * y_m) * t_m);
	end
	return tmp
end

MATLAB

y_m = abs(y);
t_m = abs(t);
x, y_m, z, t_m = num2cell(sort([x, y_m, z, t_m])){:}
function tmp_2 = code(x, y_m, z, t_m)
	tmp = 0.0;
	if (((x * y_m) - (z * y_m)) <= -4e+272)
		tmp = (((z + x) * (x - z)) * (t_m / z)) * y_m;
	else
		tmp = ((x - z) * y_m) * t_m;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
t_m = N[Abs[t], $MachinePrecision]
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
code[x_, y$95$m_, z_, t$95$m_] := If[LessEqual[N[(N[(x * y$95$m), $MachinePrecision] - N[(z * y$95$m), $MachinePrecision]), $MachinePrecision], -4e+272], N[(N[(N[(N[(z + x), $MachinePrecision] * N[(x - z), $MachinePrecision]), $MachinePrecision] * N[(t$95$m / z), $MachinePrecision]), $MachinePrecision] * y$95$m), $MachinePrecision], N[(N[(N[(x - z), $MachinePrecision] * y$95$m), $MachinePrecision] * t$95$m), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z y)) < -4.0000000000000003e272

   1. Initial program 52.7%

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

   3. Applied rewrites 47.6%

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

   5. Applied rewrites 36.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 26.6%

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

   if -4.0000000000000003e272 < (-.f64 (*.f64 x y) (*.f64 z y))

   1. Initial program 52.7%

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

   3. Applied rewrites 52.9%

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

Alternative 2: 52.7% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

y_m =     private
t_m =     private
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y_m, z, t_m)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    code = ((x - z) * y_m) * t_m
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

y_m = N[Abs[y], $MachinePrecision]
t_m = N[Abs[t], $MachinePrecision]
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
code[x_, y$95$m_, z_, t$95$m_] := N[(N[(N[(x - z), $MachinePrecision] * y$95$m), $MachinePrecision] * t$95$m), $MachinePrecision]

Derivation

1. Initial program 52.7%

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

3. Applied rewrites 52.9%

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

Alternative 3: 48.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ t_m = \left|t\right| \\ [x, y_m, z, t_m] = \mathsf{sort}([x, y_m, z, t_m])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{+116}:\\ \;\;\;\;t\_m \cdot \left(x \cdot y\_m\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x - z\right) \cdot t\_m\right) \cdot y\_m\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
t_m = (fabs.f64 t)
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
(FPCore (x y_m z t_m)
 :precision binary64
 (if (<= x -1.26e+116) (* t_m (* x y_m)) (* (* (- x z) t_m) y_m)))

C

y_m = fabs(y);
t_m = fabs(t);
assert(x < y_m && y_m < z && z < t_m);
double code(double x, double y_m, double z, double t_m) {
	double tmp;
	if (x <= -1.26e+116) {
		tmp = t_m * (x * y_m);
	} else {
		tmp = ((x - z) * t_m) * y_m;
	}
	return tmp;
}

Fortran

y_m =     private
t_m =     private
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y_m, z, t_m)
use fmin_fmax_functions
    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 <= (-1.26d+116)) then
        tmp = t_m * (x * y_m)
    else
        tmp = ((x - z) * t_m) * y_m
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
t_m = Math.abs(t);
assert x < y_m && y_m < z && z < t_m;
public static double code(double x, double y_m, double z, double t_m) {
	double tmp;
	if (x <= -1.26e+116) {
		tmp = t_m * (x * y_m);
	} else {
		tmp = ((x - z) * t_m) * y_m;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
t_m = math.fabs(t)
[x, y_m, z, t_m] = sort([x, y_m, z, t_m])
def code(x, y_m, z, t_m):
	tmp = 0
	if x <= -1.26e+116:
		tmp = t_m * (x * y_m)
	else:
		tmp = ((x - z) * t_m) * y_m
	return tmp

Julia

y_m = abs(y)
t_m = abs(t)
x, y_m, z, t_m = sort([x, y_m, z, t_m])
function code(x, y_m, z, t_m)
	tmp = 0.0
	if (x <= -1.26e+116)
		tmp = Float64(t_m * Float64(x * y_m));
	else
		tmp = Float64(Float64(Float64(x - z) * t_m) * y_m);
	end
	return tmp
end

MATLAB

y_m = abs(y);
t_m = abs(t);
x, y_m, z, t_m = num2cell(sort([x, y_m, z, t_m])){:}
function tmp_2 = code(x, y_m, z, t_m)
	tmp = 0.0;
	if (x <= -1.26e+116)
		tmp = t_m * (x * y_m);
	else
		tmp = ((x - z) * t_m) * y_m;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
t_m = N[Abs[t], $MachinePrecision]
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
code[x_, y$95$m_, z_, t$95$m_] := If[LessEqual[x, -1.26e+116], N[(t$95$m * N[(x * y$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - z), $MachinePrecision] * t$95$m), $MachinePrecision] * y$95$m), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2599999999999999e116

   1. Initial program 52.7%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 34.2%

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

   if -1.2599999999999999e116 < x

   1. Initial program 52.7%

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

   3. Applied rewrites 47.6%

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

Alternative 4: 34.2% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

y_m =     private
t_m =     private
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y_m, z, t_m)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    code = t_m * (x * y_m)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

y_m = N[Abs[y], $MachinePrecision]
t_m = N[Abs[t], $MachinePrecision]
NOTE: x, y_m, z, and t_m should be sorted in increasing order before calling this function.
code[x_, y$95$m_, z_, t$95$m_] := N[(t$95$m * N[(x * y$95$m), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 52.7%

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

2. Taylor expanded in x around inf

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

4. Applied rewrites 34.2%

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

Reproduce

herbie shell --seed 2025159 
(FPCore (x y z t)
  :name "Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3"
  :precision binary64
  (* (- (* x y) (* z y)) t))