Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 58.1% → 62.6%

Time: 5.4s

Alternatives: 9

Speedup: 1.2×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot 2}{y \cdot z - t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (* x 2.0) (- (* y z) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x * 2.0) / ((y * z) - (t * z));
}

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 * 2.0d0) / ((y * z) - (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * 2.0) / ((y * z) - (t * z));
}

Python

def code(x, y, z, t):
	return (x * 2.0) / ((y * z) - (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x * 2.0) / Float64(Float64(y * z) - Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * 2.0) / ((y * z) - (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * 2.0), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 58.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot 2}{y \cdot z - t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (* x 2.0) (- (* y z) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x * 2.0) / ((y * z) - (t * z));
}

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 * 2.0d0) / ((y * z) - (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * 2.0) / ((y * z) - (t * z));
}

Python

def code(x, y, z, t):
	return (x * 2.0) / ((y * z) - (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x * 2.0) / Float64(Float64(y * z) - Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * 2.0) / ((y * z) - (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * 2.0), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 62.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ [x, y, z_m, t] = \mathsf{sort}([x, y, z_m, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z\_m - t \cdot z\_m \leq -5 \cdot 10^{+306}:\\ \;\;\;\;\frac{2}{y - t} \cdot \frac{x}{z\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\left(y - t\right) \cdot z\_m}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
NOTE: x, y, z_m, and t should be sorted in increasing order before calling this function.
(FPCore (x y z_m t)
 :precision binary64
 (if (<= (- (* y z_m) (* t z_m)) -5e+306)
   (* (/ 2.0 (- y t)) (/ x z_m))
   (/ (* x 2.0) (* (- y t) z_m))))

C

z_m = fabs(z);
assert(x < y && y < z_m && z_m < t);
double code(double x, double y, double z_m, double t) {
	double tmp;
	if (((y * z_m) - (t * z_m)) <= -5e+306) {
		tmp = (2.0 / (y - t)) * (x / z_m);
	} else {
		tmp = (x * 2.0) / ((y - t) * z_m);
	}
	return tmp;
}

Fortran

z_m =     private
NOTE: x, y, z_m, 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(x, y, z_m, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((y * z_m) - (t * z_m)) <= (-5d+306)) then
        tmp = (2.0d0 / (y - t)) * (x / z_m)
    else
        tmp = (x * 2.0d0) / ((y - t) * z_m)
    end if
    code = tmp
end function

Java

z_m = Math.abs(z);
assert x < y && y < z_m && z_m < t;
public static double code(double x, double y, double z_m, double t) {
	double tmp;
	if (((y * z_m) - (t * z_m)) <= -5e+306) {
		tmp = (2.0 / (y - t)) * (x / z_m);
	} else {
		tmp = (x * 2.0) / ((y - t) * z_m);
	}
	return tmp;
}

Python

z_m = math.fabs(z)
[x, y, z_m, t] = sort([x, y, z_m, t])
def code(x, y, z_m, t):
	tmp = 0
	if ((y * z_m) - (t * z_m)) <= -5e+306:
		tmp = (2.0 / (y - t)) * (x / z_m)
	else:
		tmp = (x * 2.0) / ((y - t) * z_m)
	return tmp

Julia

z_m = abs(z)
x, y, z_m, t = sort([x, y, z_m, t])
function code(x, y, z_m, t)
	tmp = 0.0
	if (Float64(Float64(y * z_m) - Float64(t * z_m)) <= -5e+306)
		tmp = Float64(Float64(2.0 / Float64(y - t)) * Float64(x / z_m));
	else
		tmp = Float64(Float64(x * 2.0) / Float64(Float64(y - t) * z_m));
	end
	return tmp
end

MATLAB

z_m = abs(z);
x, y, z_m, t = num2cell(sort([x, y, z_m, t])){:}
function tmp_2 = code(x, y, z_m, t)
	tmp = 0.0;
	if (((y * z_m) - (t * z_m)) <= -5e+306)
		tmp = (2.0 / (y - t)) * (x / z_m);
	else
		tmp = (x * 2.0) / ((y - t) * z_m);
	end
	tmp_2 = tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
NOTE: x, y, z_m, and t should be sorted in increasing order before calling this function.
code[x_, y_, z$95$m_, t_] := If[LessEqual[N[(N[(y * z$95$m), $MachinePrecision] - N[(t * z$95$m), $MachinePrecision]), $MachinePrecision], -5e+306], N[(N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision] * N[(x / z$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] / N[(N[(y - t), $MachinePrecision] * z$95$m), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 y z) (*.f64 t z)) < -4.99999999999999993e306

   1. Initial program 58.1%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]

   3. Applied rewrites 60.0%

      \[\leadsto \color{blue}{\frac{2}{y - t} \cdot \frac{x}{z}} \]

   if -4.99999999999999993e306 < (-.f64 (*.f64 y z) (*.f64 t z))

   1. Initial program 58.1%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]

   3. Applied rewrites 59.7%

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

Alternative 2: 59.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ [x, y, z_m, t] = \mathsf{sort}([x, y, z_m, t])\\ \\ \frac{x}{y - t} \cdot \frac{2}{z\_m} \end{array} \]

FPCore

z_m = (fabs.f64 z)
NOTE: x, y, z_m, and t should be sorted in increasing order before calling this function.
(FPCore (x y z_m t) :precision binary64 (* (/ x (- y t)) (/ 2.0 z_m)))

C

z_m = fabs(z);
assert(x < y && y < z_m && z_m < t);
double code(double x, double y, double z_m, double t) {
	return (x / (y - t)) * (2.0 / z_m);
}

Fortran

z_m =     private
NOTE: x, y, z_m, 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(x, y, z_m, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    code = (x / (y - t)) * (2.0d0 / z_m)
end function

Java

z_m = Math.abs(z);
assert x < y && y < z_m && z_m < t;
public static double code(double x, double y, double z_m, double t) {
	return (x / (y - t)) * (2.0 / z_m);
}

Python

z_m = math.fabs(z)
[x, y, z_m, t] = sort([x, y, z_m, t])
def code(x, y, z_m, t):
	return (x / (y - t)) * (2.0 / z_m)

Julia

z_m = abs(z)
x, y, z_m, t = sort([x, y, z_m, t])
function code(x, y, z_m, t)
	return Float64(Float64(x / Float64(y - t)) * Float64(2.0 / z_m))
end

MATLAB

z_m = abs(z);
x, y, z_m, t = num2cell(sort([x, y, z_m, t])){:}
function tmp = code(x, y, z_m, t)
	tmp = (x / (y - t)) * (2.0 / z_m);
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
NOTE: x, y, z_m, and t should be sorted in increasing order before calling this function.
code[x_, y_, z$95$m_, t_] := N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] * N[(2.0 / z$95$m), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 58.1%

   \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]

3. Applied rewrites 59.8%

   \[\leadsto \color{blue}{\frac{x}{y - t} \cdot \frac{2}{z}} \]
4. Add Preprocessing

Alternative 3: 58.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ [x, y, z_m, t] = \mathsf{sort}([x, y, z_m, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 8 \cdot 10^{+169}:\\ \;\;\;\;\frac{x \cdot 2}{\left(y - t\right) \cdot z\_m}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y}}{z\_m}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
NOTE: x, y, z_m, and t should be sorted in increasing order before calling this function.
(FPCore (x y z_m t)
 :precision binary64
 (if (<= x 8e+169) (/ (* x 2.0) (* (- y t) z_m)) (* 2.0 (/ (/ x y) z_m))))

C

z_m = fabs(z);
assert(x < y && y < z_m && z_m < t);
double code(double x, double y, double z_m, double t) {
	double tmp;
	if (x <= 8e+169) {
		tmp = (x * 2.0) / ((y - t) * z_m);
	} else {
		tmp = 2.0 * ((x / y) / z_m);
	}
	return tmp;
}

Fortran

z_m =     private
NOTE: x, y, z_m, 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(x, y, z_m, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= 8d+169) then
        tmp = (x * 2.0d0) / ((y - t) * z_m)
    else
        tmp = 2.0d0 * ((x / y) / z_m)
    end if
    code = tmp
end function

Java

z_m = Math.abs(z);
assert x < y && y < z_m && z_m < t;
public static double code(double x, double y, double z_m, double t) {
	double tmp;
	if (x <= 8e+169) {
		tmp = (x * 2.0) / ((y - t) * z_m);
	} else {
		tmp = 2.0 * ((x / y) / z_m);
	}
	return tmp;
}

Python

z_m = math.fabs(z)
[x, y, z_m, t] = sort([x, y, z_m, t])
def code(x, y, z_m, t):
	tmp = 0
	if x <= 8e+169:
		tmp = (x * 2.0) / ((y - t) * z_m)
	else:
		tmp = 2.0 * ((x / y) / z_m)
	return tmp

Julia

z_m = abs(z)
x, y, z_m, t = sort([x, y, z_m, t])
function code(x, y, z_m, t)
	tmp = 0.0
	if (x <= 8e+169)
		tmp = Float64(Float64(x * 2.0) / Float64(Float64(y - t) * z_m));
	else
		tmp = Float64(2.0 * Float64(Float64(x / y) / z_m));
	end
	return tmp
end

MATLAB

z_m = abs(z);
x, y, z_m, t = num2cell(sort([x, y, z_m, t])){:}
function tmp_2 = code(x, y, z_m, t)
	tmp = 0.0;
	if (x <= 8e+169)
		tmp = (x * 2.0) / ((y - t) * z_m);
	else
		tmp = 2.0 * ((x / y) / z_m);
	end
	tmp_2 = tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
NOTE: x, y, z_m, and t should be sorted in increasing order before calling this function.
code[x_, y_, z$95$m_, t_] := If[LessEqual[x, 8e+169], N[(N[(x * 2.0), $MachinePrecision] / N[(N[(y - t), $MachinePrecision] * z$95$m), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x / y), $MachinePrecision] / z$95$m), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 7.99999999999999947e169

   1. Initial program 58.1%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]

   3. Applied rewrites 59.7%

      \[\leadsto \frac{x \cdot 2}{\color{blue}{\left(y - t\right) \cdot z}} \]

   if 7.99999999999999947e169 < x

   1. Initial program 58.1%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]

   4. Applied rewrites 37.6%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]

   6. Applied rewrites 37.6%

      \[\leadsto 2 \cdot \frac{\frac{x}{y}}{\color{blue}{z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 58.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ [x, y, z_m, t] = \mathsf{sort}([x, y, z_m, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 8 \cdot 10^{+169}:\\ \;\;\;\;\frac{2}{\left(y - t\right) \cdot z\_m} \cdot x\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y}}{z\_m}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
NOTE: x, y, z_m, and t should be sorted in increasing order before calling this function.
(FPCore (x y z_m t)
 :precision binary64
 (if (<= x 8e+169) (* (/ 2.0 (* (- y t) z_m)) x) (* 2.0 (/ (/ x y) z_m))))

C

z_m = fabs(z);
assert(x < y && y < z_m && z_m < t);
double code(double x, double y, double z_m, double t) {
	double tmp;
	if (x <= 8e+169) {
		tmp = (2.0 / ((y - t) * z_m)) * x;
	} else {
		tmp = 2.0 * ((x / y) / z_m);
	}
	return tmp;
}

Fortran

z_m =     private
NOTE: x, y, z_m, 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(x, y, z_m, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= 8d+169) then
        tmp = (2.0d0 / ((y - t) * z_m)) * x
    else
        tmp = 2.0d0 * ((x / y) / z_m)
    end if
    code = tmp
end function

Java

z_m = Math.abs(z);
assert x < y && y < z_m && z_m < t;
public static double code(double x, double y, double z_m, double t) {
	double tmp;
	if (x <= 8e+169) {
		tmp = (2.0 / ((y - t) * z_m)) * x;
	} else {
		tmp = 2.0 * ((x / y) / z_m);
	}
	return tmp;
}

Python

z_m = math.fabs(z)
[x, y, z_m, t] = sort([x, y, z_m, t])
def code(x, y, z_m, t):
	tmp = 0
	if x <= 8e+169:
		tmp = (2.0 / ((y - t) * z_m)) * x
	else:
		tmp = 2.0 * ((x / y) / z_m)
	return tmp

Julia

z_m = abs(z)
x, y, z_m, t = sort([x, y, z_m, t])
function code(x, y, z_m, t)
	tmp = 0.0
	if (x <= 8e+169)
		tmp = Float64(Float64(2.0 / Float64(Float64(y - t) * z_m)) * x);
	else
		tmp = Float64(2.0 * Float64(Float64(x / y) / z_m));
	end
	return tmp
end

MATLAB

z_m = abs(z);
x, y, z_m, t = num2cell(sort([x, y, z_m, t])){:}
function tmp_2 = code(x, y, z_m, t)
	tmp = 0.0;
	if (x <= 8e+169)
		tmp = (2.0 / ((y - t) * z_m)) * x;
	else
		tmp = 2.0 * ((x / y) / z_m);
	end
	tmp_2 = tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
NOTE: x, y, z_m, and t should be sorted in increasing order before calling this function.
code[x_, y_, z$95$m_, t_] := If[LessEqual[x, 8e+169], N[(N[(2.0 / N[(N[(y - t), $MachinePrecision] * z$95$m), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(2.0 * N[(N[(x / y), $MachinePrecision] / z$95$m), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 7.99999999999999947e169

   1. Initial program 58.1%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]

   3. Applied rewrites 59.6%

      \[\leadsto \color{blue}{\frac{2}{\left(y - t\right) \cdot z} \cdot x} \]

   if 7.99999999999999947e169 < x

   1. Initial program 58.1%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]

   4. Applied rewrites 37.6%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]

   6. Applied rewrites 37.6%

      \[\leadsto 2 \cdot \frac{\frac{x}{y}}{\color{blue}{z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 53.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ [x, y, z_m, t] = \mathsf{sort}([x, y, z_m, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 9.5 \cdot 10^{-135}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y}}{z\_m}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z\_m}}{t}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
NOTE: x, y, z_m, and t should be sorted in increasing order before calling this function.
(FPCore (x y z_m t)
 :precision binary64
 (if (<= t 9.5e-135) (* 2.0 (/ (/ x y) z_m)) (* -2.0 (/ (/ x z_m) t))))

C

z_m = fabs(z);
assert(x < y && y < z_m && z_m < t);
double code(double x, double y, double z_m, double t) {
	double tmp;
	if (t <= 9.5e-135) {
		tmp = 2.0 * ((x / y) / z_m);
	} else {
		tmp = -2.0 * ((x / z_m) / t);
	}
	return tmp;
}

Fortran

z_m =     private
NOTE: x, y, z_m, 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(x, y, z_m, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 9.5d-135) then
        tmp = 2.0d0 * ((x / y) / z_m)
    else
        tmp = (-2.0d0) * ((x / z_m) / t)
    end if
    code = tmp
end function

Java

z_m = Math.abs(z);
assert x < y && y < z_m && z_m < t;
public static double code(double x, double y, double z_m, double t) {
	double tmp;
	if (t <= 9.5e-135) {
		tmp = 2.0 * ((x / y) / z_m);
	} else {
		tmp = -2.0 * ((x / z_m) / t);
	}
	return tmp;
}

Python

z_m = math.fabs(z)
[x, y, z_m, t] = sort([x, y, z_m, t])
def code(x, y, z_m, t):
	tmp = 0
	if t <= 9.5e-135:
		tmp = 2.0 * ((x / y) / z_m)
	else:
		tmp = -2.0 * ((x / z_m) / t)
	return tmp

Julia

z_m = abs(z)
x, y, z_m, t = sort([x, y, z_m, t])
function code(x, y, z_m, t)
	tmp = 0.0
	if (t <= 9.5e-135)
		tmp = Float64(2.0 * Float64(Float64(x / y) / z_m));
	else
		tmp = Float64(-2.0 * Float64(Float64(x / z_m) / t));
	end
	return tmp
end

MATLAB

z_m = abs(z);
x, y, z_m, t = num2cell(sort([x, y, z_m, t])){:}
function tmp_2 = code(x, y, z_m, t)
	tmp = 0.0;
	if (t <= 9.5e-135)
		tmp = 2.0 * ((x / y) / z_m);
	else
		tmp = -2.0 * ((x / z_m) / t);
	end
	tmp_2 = tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
NOTE: x, y, z_m, and t should be sorted in increasing order before calling this function.
code[x_, y_, z$95$m_, t_] := If[LessEqual[t, 9.5e-135], N[(2.0 * N[(N[(x / y), $MachinePrecision] / z$95$m), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(N[(x / z$95$m), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 9.50000000000000007e-135

   1. Initial program 58.1%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]

   4. Applied rewrites 37.6%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]

   6. Applied rewrites 37.6%

      \[\leadsto 2 \cdot \frac{\frac{x}{y}}{\color{blue}{z}} \]

   if 9.50000000000000007e-135 < t

   1. Initial program 58.1%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]

   4. Applied rewrites 37.4%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]

   6. Applied rewrites 39.5%

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

Alternative 6: 53.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ [x, y, z_m, t] = \mathsf{sort}([x, y, z_m, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 7.2 \cdot 10^{-135}:\\ \;\;\;\;2 \cdot \frac{x}{y \cdot z\_m}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z\_m}}{t}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
NOTE: x, y, z_m, and t should be sorted in increasing order before calling this function.
(FPCore (x y z_m t)
 :precision binary64
 (if (<= t 7.2e-135) (* 2.0 (/ x (* y z_m))) (* -2.0 (/ (/ x z_m) t))))

C

z_m = fabs(z);
assert(x < y && y < z_m && z_m < t);
double code(double x, double y, double z_m, double t) {
	double tmp;
	if (t <= 7.2e-135) {
		tmp = 2.0 * (x / (y * z_m));
	} else {
		tmp = -2.0 * ((x / z_m) / t);
	}
	return tmp;
}

Fortran

z_m =     private
NOTE: x, y, z_m, 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(x, y, z_m, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 7.2d-135) then
        tmp = 2.0d0 * (x / (y * z_m))
    else
        tmp = (-2.0d0) * ((x / z_m) / t)
    end if
    code = tmp
end function

Java

z_m = Math.abs(z);
assert x < y && y < z_m && z_m < t;
public static double code(double x, double y, double z_m, double t) {
	double tmp;
	if (t <= 7.2e-135) {
		tmp = 2.0 * (x / (y * z_m));
	} else {
		tmp = -2.0 * ((x / z_m) / t);
	}
	return tmp;
}

Python

z_m = math.fabs(z)
[x, y, z_m, t] = sort([x, y, z_m, t])
def code(x, y, z_m, t):
	tmp = 0
	if t <= 7.2e-135:
		tmp = 2.0 * (x / (y * z_m))
	else:
		tmp = -2.0 * ((x / z_m) / t)
	return tmp

Julia

z_m = abs(z)
x, y, z_m, t = sort([x, y, z_m, t])
function code(x, y, z_m, t)
	tmp = 0.0
	if (t <= 7.2e-135)
		tmp = Float64(2.0 * Float64(x / Float64(y * z_m)));
	else
		tmp = Float64(-2.0 * Float64(Float64(x / z_m) / t));
	end
	return tmp
end

MATLAB

z_m = abs(z);
x, y, z_m, t = num2cell(sort([x, y, z_m, t])){:}
function tmp_2 = code(x, y, z_m, t)
	tmp = 0.0;
	if (t <= 7.2e-135)
		tmp = 2.0 * (x / (y * z_m));
	else
		tmp = -2.0 * ((x / z_m) / t);
	end
	tmp_2 = tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
NOTE: x, y, z_m, and t should be sorted in increasing order before calling this function.
code[x_, y_, z$95$m_, t_] := If[LessEqual[t, 7.2e-135], N[(2.0 * N[(x / N[(y * z$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(N[(x / z$95$m), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 7.19999999999999955e-135

   1. Initial program 58.1%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]

   4. Applied rewrites 37.6%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]

   if 7.19999999999999955e-135 < t

   1. Initial program 58.1%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]

   4. Applied rewrites 37.4%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]

   6. Applied rewrites 39.5%

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

Alternative 7: 52.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ [x, y, z_m, t] = \mathsf{sort}([x, y, z_m, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 7.2 \cdot 10^{-135}:\\ \;\;\;\;2 \cdot \frac{x}{y \cdot z\_m}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{x}{t \cdot z\_m}\\ \end{array} \end{array} \]

FPCore

z_m = (fabs.f64 z)
NOTE: x, y, z_m, and t should be sorted in increasing order before calling this function.
(FPCore (x y z_m t)
 :precision binary64
 (if (<= t 7.2e-135) (* 2.0 (/ x (* y z_m))) (* -2.0 (/ x (* t z_m)))))

C

z_m = fabs(z);
assert(x < y && y < z_m && z_m < t);
double code(double x, double y, double z_m, double t) {
	double tmp;
	if (t <= 7.2e-135) {
		tmp = 2.0 * (x / (y * z_m));
	} else {
		tmp = -2.0 * (x / (t * z_m));
	}
	return tmp;
}

Fortran

z_m =     private
NOTE: x, y, z_m, 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(x, y, z_m, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 7.2d-135) then
        tmp = 2.0d0 * (x / (y * z_m))
    else
        tmp = (-2.0d0) * (x / (t * z_m))
    end if
    code = tmp
end function

Java

z_m = Math.abs(z);
assert x < y && y < z_m && z_m < t;
public static double code(double x, double y, double z_m, double t) {
	double tmp;
	if (t <= 7.2e-135) {
		tmp = 2.0 * (x / (y * z_m));
	} else {
		tmp = -2.0 * (x / (t * z_m));
	}
	return tmp;
}

Python

z_m = math.fabs(z)
[x, y, z_m, t] = sort([x, y, z_m, t])
def code(x, y, z_m, t):
	tmp = 0
	if t <= 7.2e-135:
		tmp = 2.0 * (x / (y * z_m))
	else:
		tmp = -2.0 * (x / (t * z_m))
	return tmp

Julia

z_m = abs(z)
x, y, z_m, t = sort([x, y, z_m, t])
function code(x, y, z_m, t)
	tmp = 0.0
	if (t <= 7.2e-135)
		tmp = Float64(2.0 * Float64(x / Float64(y * z_m)));
	else
		tmp = Float64(-2.0 * Float64(x / Float64(t * z_m)));
	end
	return tmp
end

MATLAB

z_m = abs(z);
x, y, z_m, t = num2cell(sort([x, y, z_m, t])){:}
function tmp_2 = code(x, y, z_m, t)
	tmp = 0.0;
	if (t <= 7.2e-135)
		tmp = 2.0 * (x / (y * z_m));
	else
		tmp = -2.0 * (x / (t * z_m));
	end
	tmp_2 = tmp;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
NOTE: x, y, z_m, and t should be sorted in increasing order before calling this function.
code[x_, y_, z$95$m_, t_] := If[LessEqual[t, 7.2e-135], N[(2.0 * N[(x / N[(y * z$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(x / N[(t * z$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 7.19999999999999955e-135

   1. Initial program 58.1%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]

   4. Applied rewrites 37.6%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]

   if 7.19999999999999955e-135 < t

   1. Initial program 58.1%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]

   4. Applied rewrites 37.4%

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

Alternative 8: 37.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ [x, y, z_m, t] = \mathsf{sort}([x, y, z_m, t])\\ \\ -2 \cdot \frac{x}{t \cdot z\_m} \end{array} \]

FPCore

z_m = (fabs.f64 z)
NOTE: x, y, z_m, and t should be sorted in increasing order before calling this function.
(FPCore (x y z_m t) :precision binary64 (* -2.0 (/ x (* t z_m))))

C

z_m = fabs(z);
assert(x < y && y < z_m && z_m < t);
double code(double x, double y, double z_m, double t) {
	return -2.0 * (x / (t * z_m));
}

Fortran

z_m =     private
NOTE: x, y, z_m, 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(x, y, z_m, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    code = (-2.0d0) * (x / (t * z_m))
end function

Java

z_m = Math.abs(z);
assert x < y && y < z_m && z_m < t;
public static double code(double x, double y, double z_m, double t) {
	return -2.0 * (x / (t * z_m));
}

Python

z_m = math.fabs(z)
[x, y, z_m, t] = sort([x, y, z_m, t])
def code(x, y, z_m, t):
	return -2.0 * (x / (t * z_m))

Julia

z_m = abs(z)
x, y, z_m, t = sort([x, y, z_m, t])
function code(x, y, z_m, t)
	return Float64(-2.0 * Float64(x / Float64(t * z_m)))
end

MATLAB

z_m = abs(z);
x, y, z_m, t = num2cell(sort([x, y, z_m, t])){:}
function tmp = code(x, y, z_m, t)
	tmp = -2.0 * (x / (t * z_m));
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
NOTE: x, y, z_m, and t should be sorted in increasing order before calling this function.
code[x_, y_, z$95$m_, t_] := N[(-2.0 * N[(x / N[(t * z$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 58.1%

   \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]

2. Taylor expanded in y around 0

   \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]

4. Applied rewrites 37.4%

   \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]
5. Add Preprocessing

Alternative 9: 3.4% accurate, 15.8× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ [x, y, z_m, t] = \mathsf{sort}([x, y, z_m, t])\\ \\ 2 \end{array} \]

FPCore

z_m = (fabs.f64 z)
NOTE: x, y, z_m, and t should be sorted in increasing order before calling this function.
(FPCore (x y z_m t) :precision binary64 2.0)

C

z_m = fabs(z);
assert(x < y && y < z_m && z_m < t);
double code(double x, double y, double z_m, double t) {
	return 2.0;
}

Fortran

z_m =     private
NOTE: x, y, z_m, 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(x, y, z_m, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z_m
    real(8), intent (in) :: t
    code = 2.0d0
end function

Java

z_m = Math.abs(z);
assert x < y && y < z_m && z_m < t;
public static double code(double x, double y, double z_m, double t) {
	return 2.0;
}

Python

z_m = math.fabs(z)
[x, y, z_m, t] = sort([x, y, z_m, t])
def code(x, y, z_m, t):
	return 2.0

Julia

z_m = abs(z)
x, y, z_m, t = sort([x, y, z_m, t])
function code(x, y, z_m, t)
	return 2.0
end

MATLAB

z_m = abs(z);
x, y, z_m, t = num2cell(sort([x, y, z_m, t])){:}
function tmp = code(x, y, z_m, t)
	tmp = 2.0;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
NOTE: x, y, z_m, and t should be sorted in increasing order before calling this function.
code[x_, y_, z$95$m_, t_] := 2.0

Derivation

1. Initial program 58.1%

   \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]

2. Taylor expanded in y around inf

   \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]

4. Applied rewrites 37.6%

   \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]

6. Applied rewrites 3.4%

   \[\leadsto \color{blue}{2} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2025159 
(FPCore (x y z t)
  :name "Linear.Projection:infinitePerspective from linear-1.19.1.3, A"
  :precision binary64
  (/ (* x 2.0) (- (* y z) (* t z))))