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

Percentage Accurate: 94.5% → 96.1%

Time: 6.6s

Alternatives: 13

Speedup: 0.9×

• 20.9% 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: 94.5% 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

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+287}:\\ \;\;\;\;x \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))))
   (if (<= t_1 2e+287) (* x t_1) (* (/ x z) y))))

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+287) {
		tmp = x * t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (y / z) - (t / (1.0d0 - z))
    if (t_1 <= 2d+287) then
        tmp = x * t_1
    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 t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= 2e+287) {
		tmp = x * t_1;
	} else {
		tmp = (x / z) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) - (t / (1.0 - z))
	tmp = 0
	if t_1 <= 2e+287:
		tmp = x * t_1
	else:
		tmp = (x / z) * y
	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+287)
		tmp = Float64(x * t_1);
	else
		tmp = Float64(Float64(x / z) * y);
	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+287)
		tmp = x * t_1;
	else
		tmp = (x / z) * y;
	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+287], N[(x * t$95$1), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < 2.0000000000000002e287

   1. Initial program 96.9%

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

   if 2.0000000000000002e287 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 66.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 66.2

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

   5. Applied rewrites 66.2%

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

   7. Applied rewrites 99.9%

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

Alternative 2: 77.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(t + y\right) \cdot x}{z}\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-103}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;z \leq 140000:\\ \;\;\;\;\frac{t \cdot x}{z - 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* (+ t y) x) z)))
   (if (<= z -4.3e-28)
     t_1
     (if (<= z 5.5e-103)
       (* (/ x z) y)
       (if (<= z 140000.0) (/ (* t x) (- z 1.0)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((t + y) * x) / z;
	double tmp;
	if (z <= -4.3e-28) {
		tmp = t_1;
	} else if (z <= 5.5e-103) {
		tmp = (x / z) * y;
	} else if (z <= 140000.0) {
		tmp = (t * x) / (z - 1.0);
	} 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) :: tmp
    t_1 = ((t + y) * x) / z
    if (z <= (-4.3d-28)) then
        tmp = t_1
    else if (z <= 5.5d-103) then
        tmp = (x / z) * y
    else if (z <= 140000.0d0) then
        tmp = (t * x) / (z - 1.0d0)
    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 = ((t + y) * x) / z;
	double tmp;
	if (z <= -4.3e-28) {
		tmp = t_1;
	} else if (z <= 5.5e-103) {
		tmp = (x / z) * y;
	} else if (z <= 140000.0) {
		tmp = (t * x) / (z - 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((t + y) * x) / z
	tmp = 0
	if z <= -4.3e-28:
		tmp = t_1
	elif z <= 5.5e-103:
		tmp = (x / z) * y
	elif z <= 140000.0:
		tmp = (t * x) / (z - 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(t + y) * x) / z)
	tmp = 0.0
	if (z <= -4.3e-28)
		tmp = t_1;
	elseif (z <= 5.5e-103)
		tmp = Float64(Float64(x / z) * y);
	elseif (z <= 140000.0)
		tmp = Float64(Float64(t * x) / Float64(z - 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((t + y) * x) / z;
	tmp = 0.0;
	if (z <= -4.3e-28)
		tmp = t_1;
	elseif (z <= 5.5e-103)
		tmp = (x / z) * y;
	elseif (z <= 140000.0)
		tmp = (t * x) / (z - 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -4.3e-28], t$95$1, If[LessEqual[z, 5.5e-103], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 140000.0], N[(N[(t * x), $MachinePrecision] / N[(z - 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.3e-28 or 1.4e5 < z

   1. Initial program 97.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 88.8

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

   5. Applied rewrites 88.8%

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

   if -4.3e-28 < z < 5.50000000000000032e-103

   1. Initial program 87.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 72.0

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

   5. Applied rewrites 72.0%

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

   7. Applied rewrites 83.9%

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

   if 5.50000000000000032e-103 < z < 1.4e5

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

      7. cancel-sign-sub N/A

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

      8. mul-1-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. remove-double-neg N/A

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

      12. metadata-eval N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval N/A

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

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

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

      16. metadata-eval N/A

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

      17. lower--.f64 70.3

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

   5. Applied rewrites 70.3%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z - 1}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 95.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -62000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - t \cdot z\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -62000000.0) (not (<= z 1.0)))
   (* x (/ (+ t y) z))
   (/ (* x (- y (* t z))) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -62000000.0) || !(z <= 1.0)) {
		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 <= (-62000000.0d0)) .or. (.not. (z <= 1.0d0))) 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 <= -62000000.0) || !(z <= 1.0)) {
		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 <= -62000000.0) or not (z <= 1.0):
		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 <= -62000000.0) || !(z <= 1.0))
		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 <= -62000000.0) || ~((z <= 1.0)))
		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, -62000000.0], N[Not[LessEqual[z, 1.0]], $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 < -6.2e7 or 1 < z

   1. Initial program 97.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 95.7

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

   5. Applied rewrites 95.7%

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

   if -6.2e7 < z < 1

   1. Initial program 91.1%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 95.1

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

   5. Applied rewrites 95.1%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -62000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - t \cdot z\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -62000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, x, \frac{x}{z} \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -62000000.0) (not (<= z 1.0)))
   (* x (/ (+ t y) z))
   (fma (- t) x (* (/ x z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -62000000.0) || !(z <= 1.0)) {
		tmp = x * ((t + y) / z);
	} else {
		tmp = fma(-t, x, ((x / z) * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -62000000.0) || !(z <= 1.0))
		tmp = Float64(x * Float64(Float64(t + y) / z));
	else
		tmp = fma(Float64(-t), x, Float64(Float64(x / z) * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -62000000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * N[(N[(t + y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[((-t) * x + N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2e7 or 1 < z

   1. Initial program 97.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 95.7

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

   5. Applied rewrites 95.7%

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

   if -6.2e7 < z < 1

   1. Initial program 91.1%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 90.2%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot \left(x \cdot z\right)\right) + x \cdot y}{z}} \]
   7. 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. associate-*r* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 92.7

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

   8. Applied rewrites 92.7%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 94.8%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -62000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, x, \frac{x}{z} \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -62000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -62000000.0) (not (<= z 1.0)))
   (* x (/ (+ t y) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -62000000.0) || !(z <= 1.0)) {
		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 <= (-62000000.0d0)) .or. (.not. (z <= 1.0d0))) 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 <= -62000000.0) || !(z <= 1.0)) {
		tmp = x * ((t + y) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -62000000.0) or not (z <= 1.0):
		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 <= -62000000.0) || !(z <= 1.0))
		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 <= -62000000.0) || ~((z <= 1.0)))
		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, -62000000.0], N[Not[LessEqual[z, 1.0]], $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 < -6.2e7 or 1 < z

   1. Initial program 97.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 95.7

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

   5. Applied rewrites 95.7%

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

   if -6.2e7 < z < 1

   1. Initial program 91.1%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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. div-add N/A

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. mul-1-neg N/A

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

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

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

      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 89.8

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

   5. Applied rewrites 89.8%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -62000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.86 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{\left(t + y\right) \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.86) (not (<= z 1.0)))
   (/ (* (+ t y) x) z)
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.86) || !(z <= 1.0)) {
		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 <= (-0.86d0)) .or. (.not. (z <= 1.0d0))) 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 <= -0.86) || !(z <= 1.0)) {
		tmp = ((t + y) * x) / z;
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.86) or not (z <= 1.0):
		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 <= -0.86) || !(z <= 1.0))
		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 <= -0.86) || ~((z <= 1.0)))
		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, -0.86], N[Not[LessEqual[z, 1.0]], $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 < -0.859999999999999987 or 1 < z

   1. Initial program 97.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 89.0

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

   5. Applied rewrites 89.0%

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

   if -0.859999999999999987 < z < 1

   1. Initial program 90.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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. div-add N/A

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. mul-1-neg N/A

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

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

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

      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 89.5

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

   5. Applied rewrites 89.5%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.86 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{\left(t + y\right) \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-88}:\\ \;\;\;\;\frac{t \cdot x}{z - 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.7e+53)
   (* (/ y z) x)
   (if (<= y 1.12e-88) (/ (* t x) (- z 1.0)) (* (/ x z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.7e+53) {
		tmp = (y / z) * x;
	} else if (y <= 1.12e-88) {
		tmp = (t * x) / (z - 1.0);
	} 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 (y <= (-3.7d+53)) then
        tmp = (y / z) * x
    else if (y <= 1.12d-88) then
        tmp = (t * x) / (z - 1.0d0)
    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 (y <= -3.7e+53) {
		tmp = (y / z) * x;
	} else if (y <= 1.12e-88) {
		tmp = (t * x) / (z - 1.0);
	} else {
		tmp = (x / z) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.7e+53:
		tmp = (y / z) * x
	elif y <= 1.12e-88:
		tmp = (t * x) / (z - 1.0)
	else:
		tmp = (x / z) * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.7e+53)
		tmp = Float64(Float64(y / z) * x);
	elseif (y <= 1.12e-88)
		tmp = Float64(Float64(t * x) / Float64(z - 1.0));
	else
		tmp = Float64(Float64(x / z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.7e+53)
		tmp = (y / z) * x;
	elseif (y <= 1.12e-88)
		tmp = (t * x) / (z - 1.0);
	else
		tmp = (x / z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.7e+53], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 1.12e-88], N[(N[(t * x), $MachinePrecision] / N[(z - 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7e53

   1. Initial program 95.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 85.7

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

   5. Applied rewrites 85.7%

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

   if -3.7e53 < y < 1.12e-88

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

      7. cancel-sign-sub N/A

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

      8. mul-1-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. remove-double-neg N/A

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

      12. metadata-eval N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval N/A

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

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

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

      16. metadata-eval N/A

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

      17. lower--.f64 78.8

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

   5. Applied rewrites 78.8%

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

   if 1.12e-88 < y

   1. Initial program 86.9%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   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 73.3

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

   5. Applied rewrites 73.3%

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

   7. Applied rewrites 82.3%

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

Alternative 8: 70.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-85}:\\ \;\;\;\;\frac{x}{z - 1} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.7e+53)
   (* (/ y z) x)
   (if (<= y 1.3e-85) (* (/ x (- z 1.0)) t) (* (/ x z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.7e+53) {
		tmp = (y / z) * x;
	} else if (y <= 1.3e-85) {
		tmp = (x / (z - 1.0)) * 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 (y <= (-3.7d+53)) then
        tmp = (y / z) * x
    else if (y <= 1.3d-85) then
        tmp = (x / (z - 1.0d0)) * 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 (y <= -3.7e+53) {
		tmp = (y / z) * x;
	} else if (y <= 1.3e-85) {
		tmp = (x / (z - 1.0)) * t;
	} else {
		tmp = (x / z) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.7e+53:
		tmp = (y / z) * x
	elif y <= 1.3e-85:
		tmp = (x / (z - 1.0)) * t
	else:
		tmp = (x / z) * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.7e+53)
		tmp = Float64(Float64(y / z) * x);
	elseif (y <= 1.3e-85)
		tmp = Float64(Float64(x / Float64(z - 1.0)) * 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 (y <= -3.7e+53)
		tmp = (y / z) * x;
	elseif (y <= 1.3e-85)
		tmp = (x / (z - 1.0)) * t;
	else
		tmp = (x / z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.7e+53], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 1.3e-85], N[(N[(x / N[(z - 1.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7e53

   1. Initial program 95.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 85.7

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

   5. Applied rewrites 85.7%

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

   if -3.7e53 < y < 1.30000000000000006e-85

   1. Initial program 98.1%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 89.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 75.7%

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

   if 1.30000000000000006e-85 < y

   1. Initial program 86.9%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   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 73.3

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

   5. Applied rewrites 73.3%

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

   7. Applied rewrites 82.3%

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

Alternative 9: 64.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-80} \lor \neg \left(y \leq 5.2 \cdot 10^{-96}\right):\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.2e-80) (not (<= y 5.2e-96))) (* (/ x z) y) (/ (* t x) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.2e-80) || !(y <= 5.2e-96)) {
		tmp = (x / z) * y;
	} else {
		tmp = (t * 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 ((y <= (-1.2d-80)) .or. (.not. (y <= 5.2d-96))) then
        tmp = (x / z) * y
    else
        tmp = (t * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.2e-80) || !(y <= 5.2e-96)) {
		tmp = (x / z) * y;
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.2e-80) or not (y <= 5.2e-96):
		tmp = (x / z) * y
	else:
		tmp = (t * x) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.2e-80) || !(y <= 5.2e-96))
		tmp = Float64(Float64(x / z) * y);
	else
		tmp = Float64(Float64(t * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.2e-80) || ~((y <= 5.2e-96)))
		tmp = (x / z) * y;
	else
		tmp = (t * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.2e-80], N[Not[LessEqual[y, 5.2e-96]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2e-80 or 5.2000000000000003e-96 < y

   1. Initial program 92.5%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   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 73.5

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

   5. Applied rewrites 73.5%

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

   7. Applied rewrites 76.1%

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

   if -1.2e-80 < y < 5.2000000000000003e-96

   1. Initial program 97.5%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 61.5

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

   5. Applied rewrites 61.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 64.1%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-80} \lor \neg \left(y \leq 5.2 \cdot 10^{-96}\right):\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 38.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 4 \cdot 10^{-267} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(-\mathsf{fma}\left(z, x, x\right)\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z 4e-267) (not (<= z 1.0))) (/ (* t x) z) (* (- (fma z x x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= 4e-267) || !(z <= 1.0)) {
		tmp = (t * x) / z;
	} else {
		tmp = -fma(z, x, x) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= 4e-267) || !(z <= 1.0))
		tmp = Float64(Float64(t * x) / z);
	else
		tmp = Float64(Float64(-fma(z, x, x)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, 4e-267], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], N[((-N[(z * x + x), $MachinePrecision]) * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.9999999999999999e-267 or 1 < z

   1. Initial program 94.2%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 78.9

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

   5. Applied rewrites 78.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 48.4%

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

   if 3.9999999999999999e-267 < z < 1

   1. Initial program 94.7%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 89.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 39.7%

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

   9. Taylor expanded in z around 0

      \[\leadsto \left(-1 \cdot x + -1 \cdot \left(x \cdot z\right)\right) \cdot t \]
   10. Step-by-step derivation

   11. Applied rewrites 39.3%

       \[\leadsto \left(-\mathsf{fma}\left(z, x, x\right)\right) \cdot t \]
3. Recombined 2 regimes into one program.

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4 \cdot 10^{-267} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(-\mathsf{fma}\left(z, x, x\right)\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-80}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-96}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.2e-80)
   (* (/ y z) x)
   (if (<= y 5.2e-96) (/ (* t x) z) (* (/ x z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.2e-80) {
		tmp = (y / z) * x;
	} else if (y <= 5.2e-96) {
		tmp = (t * x) / z;
	} 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 (y <= (-1.2d-80)) then
        tmp = (y / z) * x
    else if (y <= 5.2d-96) then
        tmp = (t * x) / z
    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 (y <= -1.2e-80) {
		tmp = (y / z) * x;
	} else if (y <= 5.2e-96) {
		tmp = (t * x) / z;
	} else {
		tmp = (x / z) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.2e-80:
		tmp = (y / z) * x
	elif y <= 5.2e-96:
		tmp = (t * x) / z
	else:
		tmp = (x / z) * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.2e-80)
		tmp = Float64(Float64(y / z) * x);
	elseif (y <= 5.2e-96)
		tmp = Float64(Float64(t * x) / z);
	else
		tmp = Float64(Float64(x / z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.2e-80)
		tmp = (y / z) * x;
	elseif (y <= 5.2e-96)
		tmp = (t * x) / z;
	else
		tmp = (x / z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.2e-80], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 5.2e-96], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2e-80

   1. Initial program 96.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 73.7

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

   5. Applied rewrites 73.7%

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

   if -1.2e-80 < y < 5.2000000000000003e-96

   1. Initial program 97.5%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 61.5

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

   5. Applied rewrites 61.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 64.1%

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

   if 5.2000000000000003e-96 < y

   1. Initial program 86.9%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   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 73.3

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

   5. Applied rewrites 73.3%

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

   7. Applied rewrites 82.3%

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

Alternative 12: 39.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.65 \cdot 10^{-196}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\left(-\mathsf{fma}\left(z, x, x\right)\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 1.65e-196)
   (* (/ x z) t)
   (if (<= z 1.0) (* (- (fma z x x)) t) (/ (* t x) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.65e-196) {
		tmp = (x / z) * t;
	} else if (z <= 1.0) {
		tmp = -fma(z, x, x) * t;
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 1.65e-196)
		tmp = Float64(Float64(x / z) * t);
	elseif (z <= 1.0)
		tmp = Float64(Float64(-fma(z, x, x)) * t);
	else
		tmp = Float64(Float64(t * x) / z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 1.65e-196], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 1.0], N[((-N[(z * x + x), $MachinePrecision]) * t), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < 1.64999999999999999e-196

   1. Initial program 91.6%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 85.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 38.9%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 41.5%

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

   if 1.64999999999999999e-196 < z < 1

   1. Initial program 97.6%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 92.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 49.3%

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

   9. Taylor expanded in z around 0

      \[\leadsto \left(-1 \cdot x + -1 \cdot \left(x \cdot z\right)\right) \cdot t \]
   10. Step-by-step derivation

   11. Applied rewrites 48.7%

       \[\leadsto \left(-\mathsf{fma}\left(z, x, x\right)\right) \cdot t \]

   if 1 < z

   1. Initial program 98.2%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 82.3

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

   5. Applied rewrites 82.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 57.4%

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

Alternative 13: 22.9% 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 94.3%

   \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
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. div-add N/A

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

   2. associate-*r* N/A

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

   3. associate-/l* N/A

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

   4. mul-1-neg N/A

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

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

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

   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 62.6

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

5. Applied rewrites 62.6%

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

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 22.7%

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

Developer Target 1: 95.1% 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 2025015 
(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)))))