Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3

Percentage Accurate: 93.4% → 97.5%

Time: 3.6s

Alternatives: 8

Speedup: 0.9×

• 24.7% 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: 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

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: 97.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ [x, y_m, z, t] = \mathsf{sort}([x, y_m, z, t])\\ \\ y\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq 6 \cdot 10^{-13}:\\ \;\;\;\;\left(t \cdot \left(x - z\right)\right) \cdot y\_m\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(t \cdot y\_m\right)\\ \end{array} \end{array} \]

FPCore

y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) 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 6e-13) (* (* t (- x z)) y_m) (* (- x z) (* t 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 (t <= 6e-13) {
		tmp = (t * (x - z)) * y_m;
	} else {
		tmp = (x - z) * (t * y_m);
	}
	return y_s * tmp;
}

Fortran

y\_m =     private
y\_s =     private
NOTE: x, y_m, z, and t 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(y_s, x, y_m, z, t)
use fmin_fmax_functions
    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 <= 6d-13) then
        tmp = (t * (x - z)) * y_m
    else
        tmp = (x - z) * (t * 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 (t <= 6e-13) {
		tmp = (t * (x - z)) * y_m;
	} else {
		tmp = (x - z) * (t * 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 t <= 6e-13:
		tmp = (t * (x - z)) * y_m
	else:
		tmp = (x - z) * (t * 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 (t <= 6e-13)
		tmp = Float64(Float64(t * Float64(x - z)) * y_m);
	else
		tmp = Float64(Float64(x - z) * Float64(t * 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 (t <= 6e-13)
		tmp = (t * (x - z)) * y_m;
	else
		tmp = (x - z) * (t * 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[t, 6e-13], N[(N[(t * N[(x - z), $MachinePrecision]), $MachinePrecision] * y$95$m), $MachinePrecision], N[(N[(x - z), $MachinePrecision] * N[(t * y$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < 5.99999999999999968e-13

   1. Initial program 93.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower--.f64 89.5

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

   3. Applied rewrites 89.5%

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

   if 5.99999999999999968e-13 < t

   1. Initial program 93.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 92.3

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

   3. Applied rewrites 92.3%

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

Alternative 2: 94.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ [x, y_m, z, t] = \mathsf{sort}([x, y_m, z, t])\\ \\ y\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq 2.4 \cdot 10^{-40}:\\ \;\;\;\;\left(x \cdot y\_m - z \cdot y\_m\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(t \cdot y\_m\right)\\ \end{array} \end{array} \]

FPCore

y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) 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 2.4e-40) (* (- (* x y_m) (* z y_m)) t) (* (- x z) (* t 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 (t <= 2.4e-40) {
		tmp = ((x * y_m) - (z * y_m)) * t;
	} else {
		tmp = (x - z) * (t * y_m);
	}
	return y_s * tmp;
}

Fortran

y\_m =     private
y\_s =     private
NOTE: x, y_m, z, and t 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(y_s, x, y_m, z, t)
use fmin_fmax_functions
    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 <= 2.4d-40) then
        tmp = ((x * y_m) - (z * y_m)) * t
    else
        tmp = (x - z) * (t * 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 (t <= 2.4e-40) {
		tmp = ((x * y_m) - (z * y_m)) * t;
	} else {
		tmp = (x - z) * (t * 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 t <= 2.4e-40:
		tmp = ((x * y_m) - (z * y_m)) * t
	else:
		tmp = (x - z) * (t * 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 (t <= 2.4e-40)
		tmp = Float64(Float64(Float64(x * y_m) - Float64(z * y_m)) * t);
	else
		tmp = Float64(Float64(x - z) * Float64(t * 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 (t <= 2.4e-40)
		tmp = ((x * y_m) - (z * y_m)) * t;
	else
		tmp = (x - z) * (t * 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[t, 2.4e-40], N[(N[(N[(x * y$95$m), $MachinePrecision] - N[(z * y$95$m), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(x - z), $MachinePrecision] * N[(t * y$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < 2.39999999999999991e-40

   1. Initial program 93.4%

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

   if 2.39999999999999991e-40 < t

   1. Initial program 93.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 92.3

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

   3. Applied rewrites 92.3%

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

Alternative 3: 89.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ [x, y_m, z, t] = \mathsf{sort}([x, y_m, z, t])\\ \\ \begin{array}{l} t_1 := \left(\left(-z\right) \cdot y\_m\right) \cdot t\\ y\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+158}:\\ \;\;\;\;\left(t \cdot \left(x - z\right)\right) \cdot y\_m\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) 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
 (let* ((t_1 (* (* (- z) y_m) t)))
   (*
    y_s
    (if (<= z -1.15e+124)
      t_1
      (if (<= z 2.5e+158) (* (* t (- x z)) y_m) t_1)))))

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 t_1 = (-z * y_m) * t;
	double tmp;
	if (z <= -1.15e+124) {
		tmp = t_1;
	} else if (z <= 2.5e+158) {
		tmp = (t * (x - z)) * y_m;
	} else {
		tmp = t_1;
	}
	return y_s * tmp;
}

Fortran

y\_m =     private
y\_s =     private
NOTE: x, y_m, z, and t 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(y_s, x, y_m, z, t)
use fmin_fmax_functions
    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) :: t_1
    real(8) :: tmp
    t_1 = (-z * y_m) * t
    if (z <= (-1.15d+124)) then
        tmp = t_1
    else if (z <= 2.5d+158) then
        tmp = (t * (x - z)) * y_m
    else
        tmp = t_1
    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 t_1 = (-z * y_m) * t;
	double tmp;
	if (z <= -1.15e+124) {
		tmp = t_1;
	} else if (z <= 2.5e+158) {
		tmp = (t * (x - z)) * y_m;
	} else {
		tmp = t_1;
	}
	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):
	t_1 = (-z * y_m) * t
	tmp = 0
	if z <= -1.15e+124:
		tmp = t_1
	elif z <= 2.5e+158:
		tmp = (t * (x - z)) * y_m
	else:
		tmp = t_1
	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)
	t_1 = Float64(Float64(Float64(-z) * y_m) * t)
	tmp = 0.0
	if (z <= -1.15e+124)
		tmp = t_1;
	elseif (z <= 2.5e+158)
		tmp = Float64(Float64(t * Float64(x - z)) * y_m);
	else
		tmp = t_1;
	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)
	t_1 = (-z * y_m) * t;
	tmp = 0.0;
	if (z <= -1.15e+124)
		tmp = t_1;
	elseif (z <= 2.5e+158)
		tmp = (t * (x - z)) * y_m;
	else
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(N[((-z) * y$95$m), $MachinePrecision] * t), $MachinePrecision]}, N[(y$95$s * If[LessEqual[z, -1.15e+124], t$95$1, If[LessEqual[z, 2.5e+158], N[(N[(t * N[(x - z), $MachinePrecision]), $MachinePrecision] * y$95$m), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.14999999999999992e124 or 2.4999999999999998e158 < z

   1. Initial program 93.4%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 53.0

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

   4. Applied rewrites 53.0%

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

   if -1.14999999999999992e124 < z < 2.4999999999999998e158

   1. Initial program 93.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower--.f64 89.5

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

   3. Applied rewrites 89.5%

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

Alternative 4: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ [x, y_m, z, t] = \mathsf{sort}([x, y_m, z, t])\\ \\ \begin{array}{l} t_1 := \left(y\_m \cdot x\right) \cdot t\\ y\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-65}:\\ \;\;\;\;\left(\left(-z\right) \cdot y\_m\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) 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
 (let* ((t_1 (* (* y_m x) t)))
   (*
    y_s
    (if (<= x -6.8e+36) t_1 (if (<= x 2.55e-65) (* (* (- z) y_m) t) t_1)))))

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 t_1 = (y_m * x) * t;
	double tmp;
	if (x <= -6.8e+36) {
		tmp = t_1;
	} else if (x <= 2.55e-65) {
		tmp = (-z * y_m) * t;
	} else {
		tmp = t_1;
	}
	return y_s * tmp;
}

Fortran

y\_m =     private
y\_s =     private
NOTE: x, y_m, z, and t 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(y_s, x, y_m, z, t)
use fmin_fmax_functions
    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) :: t_1
    real(8) :: tmp
    t_1 = (y_m * x) * t
    if (x <= (-6.8d+36)) then
        tmp = t_1
    else if (x <= 2.55d-65) then
        tmp = (-z * y_m) * t
    else
        tmp = t_1
    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 t_1 = (y_m * x) * t;
	double tmp;
	if (x <= -6.8e+36) {
		tmp = t_1;
	} else if (x <= 2.55e-65) {
		tmp = (-z * y_m) * t;
	} else {
		tmp = t_1;
	}
	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):
	t_1 = (y_m * x) * t
	tmp = 0
	if x <= -6.8e+36:
		tmp = t_1
	elif x <= 2.55e-65:
		tmp = (-z * y_m) * t
	else:
		tmp = t_1
	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)
	t_1 = Float64(Float64(y_m * x) * t)
	tmp = 0.0
	if (x <= -6.8e+36)
		tmp = t_1;
	elseif (x <= 2.55e-65)
		tmp = Float64(Float64(Float64(-z) * y_m) * t);
	else
		tmp = t_1;
	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)
	t_1 = (y_m * x) * t;
	tmp = 0.0;
	if (x <= -6.8e+36)
		tmp = t_1;
	elseif (x <= 2.55e-65)
		tmp = (-z * y_m) * t;
	else
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(N[(y$95$m * x), $MachinePrecision] * t), $MachinePrecision]}, N[(y$95$s * If[LessEqual[x, -6.8e+36], t$95$1, If[LessEqual[x, 2.55e-65], N[(N[((-z) * y$95$m), $MachinePrecision] * t), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.7999999999999996e36 or 2.55e-65 < x

   1. Initial program 93.4%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 55.3

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

   4. Applied rewrites 55.3%

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

   if -6.7999999999999996e36 < x < 2.55e-65

   1. Initial program 93.4%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 53.0

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

   4. Applied rewrites 53.0%

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

Alternative 5: 74.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ [x, y_m, z, t] = \mathsf{sort}([x, y_m, z, t])\\ \\ \begin{array}{l} t_1 := \left(y\_m \cdot x\right) \cdot t\\ y\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-65}:\\ \;\;\;\;\left(-z\right) \cdot \left(t \cdot y\_m\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) 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
 (let* ((t_1 (* (* y_m x) t)))
   (*
    y_s
    (if (<= x -6.8e+36) t_1 (if (<= x 2.55e-65) (* (- z) (* t y_m)) t_1)))))

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 t_1 = (y_m * x) * t;
	double tmp;
	if (x <= -6.8e+36) {
		tmp = t_1;
	} else if (x <= 2.55e-65) {
		tmp = -z * (t * y_m);
	} else {
		tmp = t_1;
	}
	return y_s * tmp;
}

Fortran

y\_m =     private
y\_s =     private
NOTE: x, y_m, z, and t 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(y_s, x, y_m, z, t)
use fmin_fmax_functions
    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) :: t_1
    real(8) :: tmp
    t_1 = (y_m * x) * t
    if (x <= (-6.8d+36)) then
        tmp = t_1
    else if (x <= 2.55d-65) then
        tmp = -z * (t * y_m)
    else
        tmp = t_1
    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 t_1 = (y_m * x) * t;
	double tmp;
	if (x <= -6.8e+36) {
		tmp = t_1;
	} else if (x <= 2.55e-65) {
		tmp = -z * (t * y_m);
	} else {
		tmp = t_1;
	}
	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):
	t_1 = (y_m * x) * t
	tmp = 0
	if x <= -6.8e+36:
		tmp = t_1
	elif x <= 2.55e-65:
		tmp = -z * (t * y_m)
	else:
		tmp = t_1
	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)
	t_1 = Float64(Float64(y_m * x) * t)
	tmp = 0.0
	if (x <= -6.8e+36)
		tmp = t_1;
	elseif (x <= 2.55e-65)
		tmp = Float64(Float64(-z) * Float64(t * y_m));
	else
		tmp = t_1;
	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)
	t_1 = (y_m * x) * t;
	tmp = 0.0;
	if (x <= -6.8e+36)
		tmp = t_1;
	elseif (x <= 2.55e-65)
		tmp = -z * (t * y_m);
	else
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(N[(y$95$m * x), $MachinePrecision] * t), $MachinePrecision]}, N[(y$95$s * If[LessEqual[x, -6.8e+36], t$95$1, If[LessEqual[x, 2.55e-65], N[((-z) * N[(t * y$95$m), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.7999999999999996e36 or 2.55e-65 < x

   1. Initial program 93.4%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 55.3

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

   4. Applied rewrites 55.3%

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

   if -6.7999999999999996e36 < x < 2.55e-65

   1. Initial program 93.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 92.3

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

   3. Applied rewrites 92.3%

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

   4. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 53.2

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

   6. Applied rewrites 53.2%

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

Alternative 6: 73.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ [x, y_m, z, t] = \mathsf{sort}([x, y_m, z, t])\\ \\ \begin{array}{l} t_1 := \left(y\_m \cdot x\right) \cdot t\\ y\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-65}:\\ \;\;\;\;\left(\left(-t\right) \cdot z\right) \cdot y\_m\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) 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
 (let* ((t_1 (* (* y_m x) t)))
   (*
    y_s
    (if (<= x -7.8e+15) t_1 (if (<= x 2.55e-65) (* (* (- t) z) y_m) t_1)))))

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 t_1 = (y_m * x) * t;
	double tmp;
	if (x <= -7.8e+15) {
		tmp = t_1;
	} else if (x <= 2.55e-65) {
		tmp = (-t * z) * y_m;
	} else {
		tmp = t_1;
	}
	return y_s * tmp;
}

Fortran

y\_m =     private
y\_s =     private
NOTE: x, y_m, z, and t 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(y_s, x, y_m, z, t)
use fmin_fmax_functions
    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) :: t_1
    real(8) :: tmp
    t_1 = (y_m * x) * t
    if (x <= (-7.8d+15)) then
        tmp = t_1
    else if (x <= 2.55d-65) then
        tmp = (-t * z) * y_m
    else
        tmp = t_1
    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 t_1 = (y_m * x) * t;
	double tmp;
	if (x <= -7.8e+15) {
		tmp = t_1;
	} else if (x <= 2.55e-65) {
		tmp = (-t * z) * y_m;
	} else {
		tmp = t_1;
	}
	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):
	t_1 = (y_m * x) * t
	tmp = 0
	if x <= -7.8e+15:
		tmp = t_1
	elif x <= 2.55e-65:
		tmp = (-t * z) * y_m
	else:
		tmp = t_1
	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)
	t_1 = Float64(Float64(y_m * x) * t)
	tmp = 0.0
	if (x <= -7.8e+15)
		tmp = t_1;
	elseif (x <= 2.55e-65)
		tmp = Float64(Float64(Float64(-t) * z) * y_m);
	else
		tmp = t_1;
	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)
	t_1 = (y_m * x) * t;
	tmp = 0.0;
	if (x <= -7.8e+15)
		tmp = t_1;
	elseif (x <= 2.55e-65)
		tmp = (-t * z) * y_m;
	else
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(N[(y$95$m * x), $MachinePrecision] * t), $MachinePrecision]}, N[(y$95$s * If[LessEqual[x, -7.8e+15], t$95$1, If[LessEqual[x, 2.55e-65], N[(N[((-t) * z), $MachinePrecision] * y$95$m), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.8e15 or 2.55e-65 < x

   1. Initial program 93.4%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 55.3

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

   4. Applied rewrites 55.3%

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

   if -7.8e15 < x < 2.55e-65

   1. Initial program 93.4%

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

   2. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-lft-neg-in N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-neg.f64 50.6

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

   4. Applied rewrites 50.6%

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

Alternative 7: 55.3% accurate, 1.8× speedup

Math

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

FPCore

y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) 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 =     private
y\_s =     private
NOTE: x, y_m, z, and t 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(y_s, x, y_m, z, t)
use fmin_fmax_functions
    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(Float64(y_m * 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[(N[(y$95$m * x), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.4%

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

2. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. *-commutative N/A

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

   4. lower-*.f64 55.3

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

4. Applied rewrites 55.3%

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

Alternative 8: 52.9% accurate, 1.8× speedup

Math

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

FPCore

y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) 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 x) 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) {
	return y_s * ((t * x) * y_m);
}

Fortran

y\_m =     private
y\_s =     private
NOTE: x, y_m, z, and t 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(y_s, x, y_m, z, t)
use fmin_fmax_functions
    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 * x) * y_m)
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 * x) * y_m);
}

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 * x) * y_m)

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(t * x) * y_m))
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 * x) * 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]
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[(t * x), $MachinePrecision] * y$95$m), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.4%

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

2. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. *-commutative N/A

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

   4. lower-*.f64 55.3

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

4. Applied rewrites 55.3%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. *-commutative N/A

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

   5. associate-*r* N/A

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

   6. lower-*.f64 N/A

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

   7. lower-*.f64 52.9

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

6. Applied rewrites 52.9%

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

Reproduce

herbie shell --seed 2025139 
(FPCore (x y z t)
  :name "Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3"
  :precision binary64
  (* (- (* x y) (* z y)) t))