Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C

Percentage Accurate: 94.3% → 96.1%

Time: 7.0s

Alternatives: 11

Speedup: 0.9×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - 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 * ((y / z) - (t / (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 94.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - 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 * ((y / z) - (t / (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;x \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))))
   (if (<= t_1 2e+304) (* x t_1) (/ (* y x) z))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= 2e+304) {
		tmp = x * t_1;
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / z) - (t / (1.0d0 - z))
    if (t_1 <= 2d+304) then
        tmp = x * t_1
    else
        tmp = (y * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= 2e+304) {
		tmp = x * t_1;
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) - (t / (1.0 - z))
	tmp = 0
	if t_1 <= 2e+304:
		tmp = x * t_1
	else:
		tmp = (y * x) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) - Float64(t / Float64(1.0 - z)))
	tmp = 0.0
	if (t_1 <= 2e+304)
		tmp = Float64(x * t_1);
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) - (t / (1.0 - z));
	tmp = 0.0;
	if (t_1 <= 2e+304)
		tmp = x * t_1;
	else
		tmp = (y * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+304], N[(x * t$95$1), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < 1.9999999999999999e304

   1. Initial program 96.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   if 1.9999999999999999e304 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 68.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 68.7

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

   5. Applied rewrites 68.7%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x} \]
   6. Step-by-step derivation

   7. Applied rewrites 99.9%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq 2 \cdot 10^{+304}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.4 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - t \cdot z\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.4e-13)))
   (* x (/ (+ t y) z))
   (/ (* x (- y (* t z))) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.4e-13)) {
		tmp = x * ((t + y) / z);
	} else {
		tmp = (x * (y - (t * z))) / z;
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 1.4d-13))) then
        tmp = x * ((t + y) / z)
    else
        tmp = (x * (y - (t * z))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.4e-13)) {
		tmp = x * ((t + y) / z);
	} else {
		tmp = (x * (y - (t * z))) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.4e-13):
		tmp = x * ((t + y) / z)
	else:
		tmp = (x * (y - (t * z))) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.4e-13))
		tmp = Float64(x * Float64(Float64(t + y) / z));
	else
		tmp = Float64(Float64(x * Float64(y - Float64(t * z))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 1.4e-13)))
		tmp = x * ((t + y) / z);
	else
		tmp = (x * (y - (t * z))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.4e-13]], $MachinePrecision]], N[(x * N[(N[(t + y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1.4000000000000001e-13 < z

   1. Initial program 95.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto x \cdot \color{blue}{\frac{y - -1 \cdot t}{z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x \cdot \color{blue}{\frac{y - -1 \cdot t}{z}} \]

      2. fp-cancel-sub-sign-inv N/A

         \[\leadsto x \cdot \frac{\color{blue}{y + \left(\mathsf{neg}\left(-1\right)\right) \cdot t}}{z} \]

      3. metadata-eval N/A

         \[\leadsto x \cdot \frac{y + \color{blue}{1} \cdot t}{z} \]

      4. *-lft-identity N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 94.9

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

   5. Applied rewrites 94.9%

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

   if -1 < z < 1.4000000000000001e-13

   1. Initial program 92.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out-- N/A

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

      10. fp-cancel-sub-sign N/A

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

      11. mul-1-neg N/A

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

      12. associate-*r* N/A

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

      13. lower-*.f64 N/A

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

      14. associate-*r* N/A

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

      15. mul-1-neg N/A

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

      16. fp-cancel-sub-sign N/A

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

      17. lower--.f64 N/A

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

      18. lower-*.f64 96.5

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

   5. Applied rewrites 96.5%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.4 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - t \cdot z\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.4 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.4e-13)))
   (* x (/ (+ t y) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.4e-13)) {
		tmp = x * ((t + y) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 1.4d-13))) then
        tmp = x * ((t + y) / z)
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.4e-13)) {
		tmp = x * ((t + y) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.4e-13):
		tmp = x * ((t + y) / z)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.4e-13))
		tmp = Float64(x * Float64(Float64(t + y) / z));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 1.4e-13)))
		tmp = x * ((t + y) / z);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.4e-13]], $MachinePrecision]], N[(x * N[(N[(t + y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1.4000000000000001e-13 < z

   1. Initial program 95.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto x \cdot \color{blue}{\frac{y - -1 \cdot t}{z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x \cdot \color{blue}{\frac{y - -1 \cdot t}{z}} \]

      2. fp-cancel-sub-sign-inv N/A

         \[\leadsto x \cdot \frac{\color{blue}{y + \left(\mathsf{neg}\left(-1\right)\right) \cdot t}}{z} \]

      3. metadata-eval N/A

         \[\leadsto x \cdot \frac{y + \color{blue}{1} \cdot t}{z} \]

      4. *-lft-identity N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 94.9

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

   5. Applied rewrites 94.9%

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

   if -1 < z < 1.4000000000000001e-13

   1. Initial program 92.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. fp-cancel-sub-sign N/A

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

      4. div-sub N/A

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

      5. associate-/l* N/A

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

      6. *-inverses N/A

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

      7. *-rgt-identity N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 91.9

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

   5. Applied rewrites 91.9%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.4 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.95 \lor \neg \left(z \leq 1.4 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{\left(t + y\right) \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.95) (not (<= z 1.4e-13)))
   (/ (* (+ t y) x) z)
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.95) || !(z <= 1.4e-13)) {
		tmp = ((t + y) * x) / z;
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((z <= (-0.95d0)) .or. (.not. (z <= 1.4d-13))) then
        tmp = ((t + y) * x) / z
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.95) || !(z <= 1.4e-13)) {
		tmp = ((t + y) * x) / z;
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.95) or not (z <= 1.4e-13):
		tmp = ((t + y) * x) / z
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.95) || !(z <= 1.4e-13))
		tmp = Float64(Float64(Float64(t + y) * x) / z);
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -0.95) || ~((z <= 1.4e-13)))
		tmp = ((t + y) * x) / z;
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.95], N[Not[LessEqual[z, 1.4e-13]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.94999999999999996 or 1.4000000000000001e-13 < z

   1. Initial program 95.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. fp-cancel-sub-sign-inv N/A

         \[\leadsto \frac{\color{blue}{\left(y + \left(\mathsf{neg}\left(-1\right)\right) \cdot t\right)} \cdot x}{z} \]

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 85.9

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

   5. Applied rewrites 85.9%

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

   if -0.94999999999999996 < z < 1.4000000000000001e-13

   1. Initial program 92.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. fp-cancel-sub-sign N/A

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

      4. div-sub N/A

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

      5. associate-/l* N/A

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

      6. *-inverses N/A

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

      7. *-rgt-identity N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 91.9

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

   5. Applied rewrites 91.9%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.95 \lor \neg \left(z \leq 1.4 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{\left(t + y\right) \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-56} \lor \neg \left(z \leq 1.4 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{\left(t + y\right) \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.3e-56) (not (<= z 1.4e-13)))
   (/ (* (+ t y) x) z)
   (/ (* y x) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.3e-56) || !(z <= 1.4e-13)) {
		tmp = ((t + y) * x) / z;
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((z <= (-4.3d-56)) .or. (.not. (z <= 1.4d-13))) then
        tmp = ((t + y) * x) / z
    else
        tmp = (y * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.3e-56) || !(z <= 1.4e-13)) {
		tmp = ((t + y) * x) / z;
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.3e-56) or not (z <= 1.4e-13):
		tmp = ((t + y) * x) / z
	else:
		tmp = (y * x) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.3e-56) || !(z <= 1.4e-13))
		tmp = Float64(Float64(Float64(t + y) * x) / z);
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.3e-56) || ~((z <= 1.4e-13)))
		tmp = ((t + y) * x) / z;
	else
		tmp = (y * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.3e-56], N[Not[LessEqual[z, 1.4e-13]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.3000000000000001e-56 or 1.4000000000000001e-13 < z

   1. Initial program 96.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. fp-cancel-sub-sign-inv N/A

         \[\leadsto \frac{\color{blue}{\left(y + \left(\mathsf{neg}\left(-1\right)\right) \cdot t\right)} \cdot x}{z} \]

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 82.3

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

   5. Applied rewrites 82.3%

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

   if -4.3000000000000001e-56 < z < 1.4000000000000001e-13

   1. Initial program 91.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 76.9

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

   5. Applied rewrites 76.9%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x} \]
   6. Step-by-step derivation

   7. Applied rewrites 82.1%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-56} \lor \neg \left(z \leq 1.4 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{\left(t + y\right) \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+232} \lor \neg \left(t \leq 7 \cdot 10^{+128}\right):\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.6e+232) (not (<= t 7e+128))) (* (/ x z) t) (* (/ y z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.6e+232) || !(t <= 7e+128)) {
		tmp = (x / z) * t;
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((t <= (-1.6d+232)) .or. (.not. (t <= 7d+128))) then
        tmp = (x / z) * t
    else
        tmp = (y / z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.6e+232) || !(t <= 7e+128)) {
		tmp = (x / z) * t;
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.6e+232) or not (t <= 7e+128):
		tmp = (x / z) * t
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.6e+232) || !(t <= 7e+128))
		tmp = Float64(Float64(x / z) * t);
	else
		tmp = Float64(Float64(y / z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.6e+232) || ~((t <= 7e+128)))
		tmp = (x / z) * t;
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.6e+232], N[Not[LessEqual[t, 7e+128]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6000000000000001e232 or 6.99999999999999937e128 < t

   1. Initial program 91.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 70.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\frac{x}{y}}{-1 + z}, t, \frac{x}{z}\right) \cdot y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \frac{t \cdot x}{\color{blue}{z - 1}} \]
   7. Step-by-step derivation

   8. Applied rewrites 67.0%

      \[\leadsto \frac{x}{z - 1} \cdot \color{blue}{t} \]

   9. Taylor expanded in z around inf

      \[\leadsto \frac{x}{z} \cdot t \]
   10. Step-by-step derivation

   11. Applied rewrites 53.5%

       \[\leadsto \frac{x}{z} \cdot t \]

   if -1.6000000000000001e232 < t < 6.99999999999999937e128

   1. Initial program 94.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 76.4

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

   5. Applied rewrites 76.4%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+232} \lor \neg \left(t \leq 7 \cdot 10^{+128}\right):\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+232} \lor \neg \left(t \leq 2.2 \cdot 10^{+129}\right):\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.8e+232) (not (<= t 2.2e+129))) (* (/ x z) t) (* (/ x z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.8e+232) || !(t <= 2.2e+129)) {
		tmp = (x / z) * t;
	} else {
		tmp = (x / z) * y;
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((t <= (-1.8d+232)) .or. (.not. (t <= 2.2d+129))) then
        tmp = (x / z) * t
    else
        tmp = (x / z) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.8e+232) || !(t <= 2.2e+129)) {
		tmp = (x / z) * t;
	} else {
		tmp = (x / z) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.8e+232) or not (t <= 2.2e+129):
		tmp = (x / z) * t
	else:
		tmp = (x / z) * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.8e+232) || !(t <= 2.2e+129))
		tmp = Float64(Float64(x / z) * t);
	else
		tmp = Float64(Float64(x / z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.8e+232) || ~((t <= 2.2e+129)))
		tmp = (x / z) * t;
	else
		tmp = (x / z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.8e+232], N[Not[LessEqual[t, 2.2e+129]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.79999999999999996e232 or 2.1999999999999999e129 < t

   1. Initial program 91.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 70.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\frac{x}{y}}{-1 + z}, t, \frac{x}{z}\right) \cdot y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \frac{t \cdot x}{\color{blue}{z - 1}} \]
   7. Step-by-step derivation

   8. Applied rewrites 67.0%

      \[\leadsto \frac{x}{z - 1} \cdot \color{blue}{t} \]

   9. Taylor expanded in z around inf

      \[\leadsto \frac{x}{z} \cdot t \]
   10. Step-by-step derivation

   11. Applied rewrites 53.5%

       \[\leadsto \frac{x}{z} \cdot t \]

   if -1.79999999999999996e232 < t < 2.1999999999999999e129

   1. Initial program 94.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 80.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\frac{x}{y}}{-1 + z}, t, \frac{x}{z}\right) \cdot y} \]

   6. Taylor expanded in y around inf

      \[\leadsto \frac{x}{z} \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 74.2%

      \[\leadsto \frac{x}{z} \cdot y \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+232} \lor \neg \left(t \leq 2.2 \cdot 10^{+129}\right):\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 42.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00115 \lor \neg \left(z \leq 2.05 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-1 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.00115) (not (<= z 2.05e-6)))
   (* (/ x z) t)
   (* x (* t (- -1.0 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.00115) || !(z <= 2.05e-6)) {
		tmp = (x / z) * t;
	} else {
		tmp = x * (t * (-1.0 - z));
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((z <= (-0.00115d0)) .or. (.not. (z <= 2.05d-6))) then
        tmp = (x / z) * t
    else
        tmp = x * (t * ((-1.0d0) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.00115) || !(z <= 2.05e-6)) {
		tmp = (x / z) * t;
	} else {
		tmp = x * (t * (-1.0 - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.00115) or not (z <= 2.05e-6):
		tmp = (x / z) * t
	else:
		tmp = x * (t * (-1.0 - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.00115) || !(z <= 2.05e-6))
		tmp = Float64(Float64(x / z) * t);
	else
		tmp = Float64(x * Float64(t * Float64(-1.0 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -0.00115) || ~((z <= 2.05e-6)))
		tmp = (x / z) * t;
	else
		tmp = x * (t * (-1.0 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.00115], N[Not[LessEqual[z, 2.05e-6]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(t * N[(-1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.00115 or 2.0499999999999999e-6 < z

   1. Initial program 95.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 76.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\frac{x}{y}}{-1 + z}, t, \frac{x}{z}\right) \cdot y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \frac{t \cdot x}{\color{blue}{z - 1}} \]
   7. Step-by-step derivation

   8. Applied rewrites 51.4%

      \[\leadsto \frac{x}{z - 1} \cdot \color{blue}{t} \]

   9. Taylor expanded in z around inf

      \[\leadsto \frac{x}{z} \cdot t \]
   10. Step-by-step derivation

   11. Applied rewrites 50.7%

       \[\leadsto \frac{x}{z} \cdot t \]

   if -0.00115 < z < 2.0499999999999999e-6

   1. Initial program 92.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

         \[\leadsto x \cdot \color{blue}{\left(\mathsf{neg}\left(\frac{t}{1 - z}\right)\right)} \]

      2. distribute-neg-frac2 N/A

         \[\leadsto x \cdot \color{blue}{\frac{t}{\mathsf{neg}\left(\left(1 - z\right)\right)}} \]

      3. lower-/.f64 N/A

         \[\leadsto x \cdot \color{blue}{\frac{t}{\mathsf{neg}\left(\left(1 - z\right)\right)}} \]

      4. *-lft-identity N/A

         \[\leadsto x \cdot \frac{t}{\mathsf{neg}\left(\left(1 - \color{blue}{1 \cdot z}\right)\right)} \]

      5. metadata-eval N/A

         \[\leadsto x \cdot \frac{t}{\mathsf{neg}\left(\left(1 - \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot z\right)\right)} \]

      6. fp-cancel-sign-sub-inv N/A

         \[\leadsto x \cdot \frac{t}{\mathsf{neg}\left(\color{blue}{\left(1 + -1 \cdot z\right)}\right)} \]

      7. mul-1-neg N/A

         \[\leadsto x \cdot \frac{t}{\mathsf{neg}\left(\left(1 + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)} \]

      8. distribute-neg-in N/A

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(\mathsf{neg}\left(1\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)}} \]

      9. metadata-eval N/A

         \[\leadsto x \cdot \frac{t}{\color{blue}{-1} + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)} \]

      10. remove-double-neg N/A

          \[\leadsto x \cdot \frac{t}{-1 + \color{blue}{z}} \]

      11. lower-+.f64 23.2

          \[\leadsto x \cdot \frac{t}{\color{blue}{-1 + z}} \]

   5. Applied rewrites 23.2%

      \[\leadsto x \cdot \color{blue}{\frac{t}{-1 + z}} \]

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 23.1%

      \[\leadsto x \cdot \left(t \cdot \color{blue}{\left(-1 - z\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00115 \lor \neg \left(z \leq 2.05 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-1 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+191}:\\ \;\;\;\;\frac{x}{z - 1} \cdot t\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+125}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.7e+191)
   (* (/ x (- z 1.0)) t)
   (if (<= t 6.8e+125) (/ (* y x) z) (* x (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.7e+191) {
		tmp = (x / (z - 1.0)) * t;
	} else if (t <= 6.8e+125) {
		tmp = (y * x) / z;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (t <= (-2.7d+191)) then
        tmp = (x / (z - 1.0d0)) * t
    else if (t <= 6.8d+125) then
        tmp = (y * x) / z
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.7e+191) {
		tmp = (x / (z - 1.0)) * t;
	} else if (t <= 6.8e+125) {
		tmp = (y * x) / z;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.7e+191:
		tmp = (x / (z - 1.0)) * t
	elif t <= 6.8e+125:
		tmp = (y * x) / z
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.7e+191)
		tmp = Float64(Float64(x / Float64(z - 1.0)) * t);
	elseif (t <= 6.8e+125)
		tmp = Float64(Float64(y * x) / z);
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.7e+191)
		tmp = (x / (z - 1.0)) * t;
	elseif (t <= 6.8e+125)
		tmp = (y * x) / z;
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.7e+191], N[(N[(x / N[(z - 1.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, 6.8e+125], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.69999999999999996e191

   1. Initial program 99.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 68.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\frac{x}{y}}{-1 + z}, t, \frac{x}{z}\right) \cdot y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \frac{t \cdot x}{\color{blue}{z - 1}} \]
   7. Step-by-step derivation

   8. Applied rewrites 78.4%

      \[\leadsto \frac{x}{z - 1} \cdot \color{blue}{t} \]

   if -2.69999999999999996e191 < t < 6.7999999999999998e125

   1. Initial program 94.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 78.2

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

   5. Applied rewrites 78.2%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x} \]
   6. Step-by-step derivation

   7. Applied rewrites 78.3%

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

   if 6.7999999999999998e125 < t

   1. Initial program 87.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto x \cdot \color{blue}{\frac{y - -1 \cdot t}{z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x \cdot \color{blue}{\frac{y - -1 \cdot t}{z}} \]

      2. fp-cancel-sub-sign-inv N/A

         \[\leadsto x \cdot \frac{\color{blue}{y + \left(\mathsf{neg}\left(-1\right)\right) \cdot t}}{z} \]

      3. metadata-eval N/A

         \[\leadsto x \cdot \frac{y + \color{blue}{1} \cdot t}{z} \]

      4. *-lft-identity N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 71.2

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

   5. Applied rewrites 71.2%

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

   6. Taylor expanded in y around 0

      \[\leadsto x \cdot \frac{t}{\color{blue}{z}} \]
   7. Step-by-step derivation

   8. Applied rewrites 64.8%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+191}:\\ \;\;\;\;\frac{x}{z - 1} \cdot t\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+125}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+232}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+125}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.6e+232)
   (* (/ x z) t)
   (if (<= t 6.8e+125) (* (/ y z) x) (* x (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.6e+232) {
		tmp = (x / z) * t;
	} else if (t <= 6.8e+125) {
		tmp = (y / z) * x;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (t <= (-1.6d+232)) then
        tmp = (x / z) * t
    else if (t <= 6.8d+125) then
        tmp = (y / z) * x
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.6e+232) {
		tmp = (x / z) * t;
	} else if (t <= 6.8e+125) {
		tmp = (y / z) * x;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.6e+232:
		tmp = (x / z) * t
	elif t <= 6.8e+125:
		tmp = (y / z) * x
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.6e+232)
		tmp = Float64(Float64(x / z) * t);
	elseif (t <= 6.8e+125)
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.6e+232)
		tmp = (x / z) * t;
	elseif (t <= 6.8e+125)
		tmp = (y / z) * x;
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.6e+232], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, 6.8e+125], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6000000000000001e232

   1. Initial program 99.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 60.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\frac{x}{y}}{-1 + z}, t, \frac{x}{z}\right) \cdot y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \frac{t \cdot x}{\color{blue}{z - 1}} \]
   7. Step-by-step derivation

   8. Applied rewrites 91.5%

      \[\leadsto \frac{x}{z - 1} \cdot \color{blue}{t} \]

   9. Taylor expanded in z around inf

      \[\leadsto \frac{x}{z} \cdot t \]
   10. Step-by-step derivation

   11. Applied rewrites 68.1%

       \[\leadsto \frac{x}{z} \cdot t \]

   if -1.6000000000000001e232 < t < 6.7999999999999998e125

   1. Initial program 94.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 76.4

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

   5. Applied rewrites 76.4%

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

   if 6.7999999999999998e125 < t

   1. Initial program 87.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto x \cdot \color{blue}{\frac{y - -1 \cdot t}{z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x \cdot \color{blue}{\frac{y - -1 \cdot t}{z}} \]

      2. fp-cancel-sub-sign-inv N/A

         \[\leadsto x \cdot \frac{\color{blue}{y + \left(\mathsf{neg}\left(-1\right)\right) \cdot t}}{z} \]

      3. metadata-eval N/A

         \[\leadsto x \cdot \frac{y + \color{blue}{1} \cdot t}{z} \]

      4. *-lft-identity N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 71.2

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

   5. Applied rewrites 71.2%

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

   6. Taylor expanded in y around 0

      \[\leadsto x \cdot \frac{t}{\color{blue}{z}} \]
   7. Step-by-step derivation

   8. Applied rewrites 64.8%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+232}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+125}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 23.4% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(-t\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x * -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 * -t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.1%

   \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
2. Add Preprocessing

3. Taylor expanded in z around 0

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

   1. associate-*r* N/A

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

   2. mul-1-neg N/A

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

   3. fp-cancel-sub-sign N/A

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

   4. div-sub N/A

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

   5. associate-/l* N/A

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

   6. *-inverses N/A

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

   7. *-rgt-identity N/A

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

   8. lower--.f64 N/A

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

   9. lower-/.f64 67.1

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

5. Applied rewrites 67.1%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 18.0%

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

Developer Target 1: 95.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ t_2 := x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{if}\;t\_2 < -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))))
        (t_2 (* x (- (/ y z) (/ t (- 1.0 z))))))
   (if (< t_2 -7.623226303312042e-196)
     t_1
     (if (< t_2 1.4133944927702302e-211)
       (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z))))
       t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y / z) - (t * (1.0d0 / (1.0d0 - z))))
    t_2 = x * ((y / z) - (t / (1.0d0 - z)))
    if (t_2 < (-7.623226303312042d-196)) then
        tmp = t_1
    else if (t_2 < 1.4133944927702302d-211) then
        tmp = ((y * x) / z) + -((t * x) / (1.0d0 - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))))
	t_2 = x * ((y / z) - (t / (1.0 - z)))
	tmp = 0
	if t_2 < -7.623226303312042e-196:
		tmp = t_1
	elif t_2 < 1.4133944927702302e-211:
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - Float64(t * Float64(1.0 / Float64(1.0 - z)))))
	t_2 = Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
	tmp = 0.0
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = Float64(Float64(Float64(y * x) / z) + Float64(-Float64(Float64(t * x) / Float64(1.0 - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	t_2 = x * ((y / z) - (t / (1.0 - z)));
	tmp = 0.0;
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t * N[(1.0 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -7.623226303312042e-196], t$95$1, If[Less[t$95$2, 1.4133944927702302e-211], N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] + (-N[(N[(t * x), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024352 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (* x (- (/ y z) (/ t (- 1 z)))) -3811613151656021/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* x (- (/ y z) (* t (/ 1 (- 1 z))))) (if (< (* x (- (/ y z) (/ t (- 1 z)))) 7066972463851151/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (/ (* y x) z) (- (/ (* t x) (- 1 z)))) (* x (- (/ y z) (* t (/ 1 (- 1 z))))))))

  (* x (- (/ y z) (/ t (- 1.0 z)))))