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

Percentage Accurate: 94.3% → 94.3%

Time: 6.7s

Alternatives: 15

Speedup: 1.0×

• 20.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) - (t / (1.0d0 - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) - (t / (1.0d0 - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) - (t / (1.0d0 - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

Alternative 2: 92.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -16500 \lor \neg \left(z \leq 3.3 \cdot 10^{-18}\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \mathsf{fma}\left(t, z, t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -16500.0) (not (<= z 3.3e-18)))
   (* x (/ (+ t y) z))
   (* x (- (/ y z) (fma t z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -16500.0) || !(z <= 3.3e-18)) {
		tmp = x * ((t + y) / z);
	} else {
		tmp = x * ((y / z) - fma(t, z, t));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -16500.0) || !(z <= 3.3e-18))
		tmp = Float64(x * Float64(Float64(t + y) / z));
	else
		tmp = Float64(x * Float64(Float64(y / z) - fma(t, z, t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -16500.0], N[Not[LessEqual[z, 3.3e-18]], $MachinePrecision]], N[(x * N[(N[(t + y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - N[(t * z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -16500 or 3.3000000000000002e-18 < z

   1. Initial program 97.6%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 97.3

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

   5. Applied rewrites 97.3%

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

   if -16500 < z < 3.3000000000000002e-18

   1. Initial program 95.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 95.7

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

   5. Applied rewrites 95.7%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -16500 \lor \neg \left(z \leq 3.3 \cdot 10^{-18}\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \mathsf{fma}\left(t, z, t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z - 1}\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-158}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+116}:\\ \;\;\;\;\left(t + y\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t (- z 1.0)))))
   (if (<= t -3.8e+67)
     t_1
     (if (<= t 2.1e-158)
       (* x (/ y z))
       (if (<= t 7.5e+116) (* (+ t y) (/ x z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / (z - 1.0));
	double tmp;
	if (t <= -3.8e+67) {
		tmp = t_1;
	} else if (t <= 2.1e-158) {
		tmp = x * (y / z);
	} else if (t <= 7.5e+116) {
		tmp = (t + y) * (x / 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) :: tmp
    t_1 = x * (t / (z - 1.0d0))
    if (t <= (-3.8d+67)) then
        tmp = t_1
    else if (t <= 2.1d-158) then
        tmp = x * (y / z)
    else if (t <= 7.5d+116) then
        tmp = (t + y) * (x / 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 * (t / (z - 1.0));
	double tmp;
	if (t <= -3.8e+67) {
		tmp = t_1;
	} else if (t <= 2.1e-158) {
		tmp = x * (y / z);
	} else if (t <= 7.5e+116) {
		tmp = (t + y) * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / (z - 1.0))
	tmp = 0
	if t <= -3.8e+67:
		tmp = t_1
	elif t <= 2.1e-158:
		tmp = x * (y / z)
	elif t <= 7.5e+116:
		tmp = (t + y) * (x / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / Float64(z - 1.0)))
	tmp = 0.0
	if (t <= -3.8e+67)
		tmp = t_1;
	elseif (t <= 2.1e-158)
		tmp = Float64(x * Float64(y / z));
	elseif (t <= 7.5e+116)
		tmp = Float64(Float64(t + y) * Float64(x / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / (z - 1.0));
	tmp = 0.0;
	if (t <= -3.8e+67)
		tmp = t_1;
	elseif (t <= 2.1e-158)
		tmp = x * (y / z);
	elseif (t <= 7.5e+116)
		tmp = (t + y) * (x / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / N[(z - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.8e+67], t$95$1, If[LessEqual[t, 2.1e-158], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e+116], N[(N[(t + y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.8000000000000002e67 or 7.5e116 < t

   1. Initial program 96.9%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

      6. cancel-sign-sub N/A

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

      7. mul-1-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. remove-double-neg N/A

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

      11. metadata-eval N/A

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

      12. metadata-eval N/A

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

      13. metadata-eval N/A

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

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

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

      15. metadata-eval N/A

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

      16. lower--.f64 77.5

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

   5. Applied rewrites 77.5%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 55.7%

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

   9. Taylor expanded in z around 0

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

       1. lower--.f64 77.5

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

   11. Applied rewrites 77.5%

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

   if -3.8000000000000002e67 < t < 2.09999999999999991e-158

   1. Initial program 95.1%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 88.4

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

   5. Applied rewrites 88.4%

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

   if 2.09999999999999991e-158 < t < 7.5e116

   1. Initial program 99.7%

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

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 87.4

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

   5. Applied rewrites 87.4%

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

   6. Taylor expanded in y around 0

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

      1. lower-+.f64 87.4

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

   8. Applied rewrites 87.4%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \frac{t}{z - 1}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-158}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+116}:\\ \;\;\;\;\left(t + y\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -16500:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \mathsf{fma}\left(t, z, t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -16500.0)
   (* x (+ (/ y z) (/ t z)))
   (if (<= z 3.3e-18) (* x (- (/ y z) (fma t z t))) (* x (/ (+ t y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -16500.0) {
		tmp = x * ((y / z) + (t / z));
	} else if (z <= 3.3e-18) {
		tmp = x * ((y / z) - fma(t, z, t));
	} else {
		tmp = x * ((t + y) / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -16500.0)
		tmp = Float64(x * Float64(Float64(y / z) + Float64(t / z)));
	elseif (z <= 3.3e-18)
		tmp = Float64(x * Float64(Float64(y / z) - fma(t, z, t)));
	else
		tmp = Float64(x * Float64(Float64(t + y) / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -16500.0], N[(x * N[(N[(y / z), $MachinePrecision] + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e-18], N[(x * N[(N[(y / z), $MachinePrecision] - N[(t * z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(t + y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -16500

   1. Initial program 96.0%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 95.4

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

   5. Applied rewrites 95.4%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. lift-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 95.4

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

   7. Applied rewrites 95.4%

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

   if -16500 < z < 3.3000000000000002e-18

   1. Initial program 95.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 95.7

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

   5. Applied rewrites 95.7%

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

   if 3.3000000000000002e-18 < z

   1. Initial program 99.7%

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

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

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

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 99.6

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

   5. Applied rewrites 99.6%

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

Alternative 5: 92.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -16500 \lor \neg \left(z \leq 3.3 \cdot 10^{-18}\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -16500.0) (not (<= z 3.3e-18)))
   (* x (/ (+ t y) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -16500.0) || !(z <= 3.3e-18)) {
		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 <= (-16500.0d0)) .or. (.not. (z <= 3.3d-18))) 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 <= -16500.0) || !(z <= 3.3e-18)) {
		tmp = x * ((t + y) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -16500.0) or not (z <= 3.3e-18):
		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 <= -16500.0) || !(z <= 3.3e-18))
		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 <= -16500.0) || ~((z <= 3.3e-18)))
		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, -16500.0], N[Not[LessEqual[z, 3.3e-18]], $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 < -16500 or 3.3000000000000002e-18 < z

   1. Initial program 97.6%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 97.3

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

   5. Applied rewrites 97.3%

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

   if -16500 < z < 3.3000000000000002e-18

   1. Initial program 95.8%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 95.1%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -16500 \lor \neg \left(z \leq 3.3 \cdot 10^{-18}\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-123} \lor \neg \left(z \leq 3.3 \cdot 10^{-18}\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.8e-123) (not (<= z 3.3e-18)))
   (* x (/ (+ t y) z))
   (* x (/ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.8e-123) || !(z <= 3.3e-18)) {
		tmp = x * ((t + y) / z);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4.8d-123)) .or. (.not. (z <= 3.3d-18))) then
        tmp = x * ((t + y) / z)
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.8e-123) || !(z <= 3.3e-18)) {
		tmp = x * ((t + y) / z);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.8e-123) or not (z <= 3.3e-18):
		tmp = x * ((t + y) / z)
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.8e-123) || !(z <= 3.3e-18))
		tmp = Float64(x * Float64(Float64(t + y) / z));
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.8e-123) || ~((z <= 3.3e-18)))
		tmp = x * ((t + y) / z);
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.8e-123], N[Not[LessEqual[z, 3.3e-18]], $MachinePrecision]], N[(x * N[(N[(t + y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e-123 or 3.3000000000000002e-18 < z

   1. Initial program 98.0%

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

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

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

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 92.6

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

   5. Applied rewrites 92.6%

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

   if -4.8e-123 < z < 3.3000000000000002e-18

   1. Initial program 94.6%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 71.2

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

   5. Applied rewrites 71.2%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-123} \lor \neg \left(z \leq 3.3 \cdot 10^{-18}\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+67} \lor \neg \left(t \leq 1.05 \cdot 10^{+115}\right):\\ \;\;\;\;\frac{x}{z - 1} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.8e+67) (not (<= t 1.05e+115)))
   (* (/ x (- z 1.0)) t)
   (* x (/ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.8e+67) || !(t <= 1.05e+115)) {
		tmp = (x / (z - 1.0)) * t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.8d+67)) .or. (.not. (t <= 1.05d+115))) then
        tmp = (x / (z - 1.0d0)) * t
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.8e+67) || !(t <= 1.05e+115)) {
		tmp = (x / (z - 1.0)) * t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.8e+67) or not (t <= 1.05e+115):
		tmp = (x / (z - 1.0)) * t
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.8e+67) || !(t <= 1.05e+115))
		tmp = Float64(Float64(x / Float64(z - 1.0)) * t);
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.8e+67) || ~((t <= 1.05e+115)))
		tmp = (x / (z - 1.0)) * t;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.8e+67], N[Not[LessEqual[t, 1.05e+115]], $MachinePrecision]], N[(N[(x / N[(z - 1.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.8000000000000002e67 or 1.05000000000000002e115 < t

   1. Initial program 96.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. associate-*l/ N/A

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

      7. distribute-lft-neg-out N/A

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

      8. metadata-eval N/A

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

      9. *-lft-identity N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. mul-1-neg N/A

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

      14. distribute-neg-frac2 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. *-lft-identity N/A

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

      18. metadata-eval N/A

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

   5. Applied rewrites 75.7%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 69.3

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

   8. Applied rewrites 69.3%

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

   if -3.8000000000000002e67 < t < 1.05000000000000002e115

   1. Initial program 96.7%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 82.4

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

   5. Applied rewrites 82.4%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+67} \lor \neg \left(t \leq 1.05 \cdot 10^{+115}\right):\\ \;\;\;\;\frac{x}{z - 1} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-57}:\\ \;\;\;\;\left(t + y\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(t + y\right) \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.8e-57)
   (* (+ t y) (/ x z))
   (if (<= z 3.3e-18) (* x (/ y z)) (/ (* (+ t y) x) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.8e-57) {
		tmp = (t + y) * (x / z);
	} else if (z <= 3.3e-18) {
		tmp = x * (y / z);
	} else {
		tmp = ((t + y) * x) / z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-7.8d-57)) then
        tmp = (t + y) * (x / z)
    else if (z <= 3.3d-18) then
        tmp = x * (y / z)
    else
        tmp = ((t + y) * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.8e-57) {
		tmp = (t + y) * (x / z);
	} else if (z <= 3.3e-18) {
		tmp = x * (y / z);
	} else {
		tmp = ((t + y) * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.8e-57:
		tmp = (t + y) * (x / z)
	elif z <= 3.3e-18:
		tmp = x * (y / z)
	else:
		tmp = ((t + y) * x) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.8e-57)
		tmp = Float64(Float64(t + y) * Float64(x / z));
	elseif (z <= 3.3e-18)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(Float64(Float64(t + y) * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.8e-57)
		tmp = (t + y) * (x / z);
	elseif (z <= 3.3e-18)
		tmp = x * (y / z);
	else
		tmp = ((t + y) * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.8e-57], N[(N[(t + y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e-18], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t + y), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.80000000000000013e-57

   1. Initial program 96.6%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 84.4

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

   5. Applied rewrites 84.4%

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

   6. Taylor expanded in y around 0

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

      1. lower-+.f64 84.4

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

   8. Applied rewrites 84.4%

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

   if -7.80000000000000013e-57 < z < 3.3000000000000002e-18

   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

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

      1. lower-/.f64 71.5

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

   5. Applied rewrites 71.5%

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

   if 3.3000000000000002e-18 < z

   1. Initial program 99.7%

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

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 90.5

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

   5. Applied rewrites 90.5%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-57}:\\ \;\;\;\;\left(t + y\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(t + y\right) \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{z - 1} \cdot t\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-158}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(t + y\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.8e+67)
   (* (/ x (- z 1.0)) t)
   (if (<= t 2.1e-158) (* x (/ y z)) (* (+ t y) (/ x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.8e+67) {
		tmp = (x / (z - 1.0)) * t;
	} else if (t <= 2.1e-158) {
		tmp = x * (y / z);
	} else {
		tmp = (t + y) * (x / z);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-3.8d+67)) then
        tmp = (x / (z - 1.0d0)) * t
    else if (t <= 2.1d-158) then
        tmp = x * (y / z)
    else
        tmp = (t + y) * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.8e+67) {
		tmp = (x / (z - 1.0)) * t;
	} else if (t <= 2.1e-158) {
		tmp = x * (y / z);
	} else {
		tmp = (t + y) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.8e+67:
		tmp = (x / (z - 1.0)) * t
	elif t <= 2.1e-158:
		tmp = x * (y / z)
	else:
		tmp = (t + y) * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.8e+67)
		tmp = Float64(Float64(x / Float64(z - 1.0)) * t);
	elseif (t <= 2.1e-158)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(Float64(t + y) * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.8e+67)
		tmp = (x / (z - 1.0)) * t;
	elseif (t <= 2.1e-158)
		tmp = x * (y / z);
	else
		tmp = (t + y) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.8e+67], N[(N[(x / N[(z - 1.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, 2.1e-158], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(N[(t + y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.8000000000000002e67

   1. Initial program 96.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. associate-*l/ N/A

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

      7. distribute-lft-neg-out N/A

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

      8. metadata-eval N/A

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

      9. *-lft-identity N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. mul-1-neg N/A

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

      14. distribute-neg-frac2 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. *-lft-identity N/A

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

      18. metadata-eval N/A

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

   5. Applied rewrites 78.4%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 75.4

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

   8. Applied rewrites 75.4%

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

   if -3.8000000000000002e67 < t < 2.09999999999999991e-158

   1. Initial program 95.1%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 88.4

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

   5. Applied rewrites 88.4%

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

   if 2.09999999999999991e-158 < t

   1. Initial program 98.8%

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

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 72.8

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

   5. Applied rewrites 72.8%

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

   6. Taylor expanded in y around 0

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

      1. lower-+.f64 72.8

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

   8. Applied rewrites 72.8%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{z - 1} \cdot t\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-158}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(t + y\right) \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+67} \lor \neg \left(t \leq 3.9 \cdot 10^{+127}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.8e+67) (not (<= t 3.9e+127))) (* x (/ t z)) (* x (/ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.8e+67) || !(t <= 3.9e+127)) {
		tmp = x * (t / z);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-5.8d+67)) .or. (.not. (t <= 3.9d+127))) then
        tmp = x * (t / z)
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.8e+67) || !(t <= 3.9e+127)) {
		tmp = x * (t / z);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5.8e+67) or not (t <= 3.9e+127):
		tmp = x * (t / z)
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5.8e+67) || !(t <= 3.9e+127))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5.8e+67) || ~((t <= 3.9e+127)))
		tmp = x * (t / z);
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5.8e+67], N[Not[LessEqual[t, 3.9e+127]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.80000000000000047e67 or 3.89999999999999981e127 < t

   1. Initial program 97.8%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

      6. cancel-sign-sub N/A

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

      7. mul-1-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. remove-double-neg N/A

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

      11. metadata-eval N/A

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

      12. metadata-eval N/A

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

      13. metadata-eval N/A

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

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

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

      15. metadata-eval N/A

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

      16. lower--.f64 78.1

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

   5. Applied rewrites 78.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 56.8%

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

   if -5.80000000000000047e67 < t < 3.89999999999999981e127

   1. Initial program 96.2%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 81.4

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

   5. Applied rewrites 81.4%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+67} \lor \neg \left(t \leq 3.9 \cdot 10^{+127}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+67} \lor \neg \left(t \leq 8 \cdot 10^{+128}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.8e+67) (not (<= t 8e+128))) (* x (/ t z)) (/ (* x y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.8e+67) || !(t <= 8e+128)) {
		tmp = x * (t / z);
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-5.8d+67)) .or. (.not. (t <= 8d+128))) then
        tmp = x * (t / z)
    else
        tmp = (x * y) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.8e+67) || !(t <= 8e+128)) {
		tmp = x * (t / z);
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5.8e+67) or not (t <= 8e+128):
		tmp = x * (t / z)
	else:
		tmp = (x * y) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5.8e+67) || !(t <= 8e+128))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(Float64(x * y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5.8e+67) || ~((t <= 8e+128)))
		tmp = x * (t / z);
	else
		tmp = (x * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5.8e+67], N[Not[LessEqual[t, 8e+128]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.80000000000000047e67 or 8.0000000000000006e128 < t

   1. Initial program 97.8%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

      6. cancel-sign-sub N/A

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

      7. mul-1-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. remove-double-neg N/A

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

      11. metadata-eval N/A

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

      12. metadata-eval N/A

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

      13. metadata-eval N/A

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

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

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

      15. metadata-eval N/A

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

      16. lower--.f64 78.1

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

   5. Applied rewrites 78.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 56.8%

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

   if -5.80000000000000047e67 < t < 8.0000000000000006e128

   1. Initial program 96.2%

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

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

      2. +-commutative N/A

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

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

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

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

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

      11. mul-1-neg N/A

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

      12. associate-*r* N/A

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

      13. lower-*.f64 N/A

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

      14. associate-*r* N/A

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

      15. mul-1-neg N/A

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

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

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

      17. lower--.f64 N/A

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

      18. lower-*.f64 67.2

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

   5. Applied rewrites 67.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 76.1%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+67} \lor \neg \left(t \leq 8 \cdot 10^{+128}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+68} \lor \neg \left(t \leq 1.3 \cdot 10^{+129}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.5e+68) (not (<= t 1.3e+129))) (* t (/ x z)) (/ (* x y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.5e+68) || !(t <= 1.3e+129)) {
		tmp = t * (x / z);
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-5.5d+68)) .or. (.not. (t <= 1.3d+129))) then
        tmp = t * (x / z)
    else
        tmp = (x * y) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.5e+68) || !(t <= 1.3e+129)) {
		tmp = t * (x / z);
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5.5e+68) or not (t <= 1.3e+129):
		tmp = t * (x / z)
	else:
		tmp = (x * y) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5.5e+68) || !(t <= 1.3e+129))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(Float64(x * y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5.5e+68) || ~((t <= 1.3e+129)))
		tmp = t * (x / z);
	else
		tmp = (x * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5.5e+68], N[Not[LessEqual[t, 1.3e+129]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.5000000000000004e68 or 1.30000000000000006e129 < t

   1. Initial program 97.8%

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

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 56.6

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

   5. Applied rewrites 56.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 48.6%

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

   if -5.5000000000000004e68 < t < 1.30000000000000006e129

   1. Initial program 96.2%

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

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

      2. +-commutative N/A

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

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

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

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

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

      11. mul-1-neg N/A

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

      12. associate-*r* N/A

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

      13. lower-*.f64 N/A

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

      14. associate-*r* N/A

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

      15. mul-1-neg N/A

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

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

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

      17. lower--.f64 N/A

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

      18. lower-*.f64 67.2

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

   5. Applied rewrites 67.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 76.1%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+68} \lor \neg \left(t \leq 1.3 \cdot 10^{+129}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 64.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+141} \lor \neg \left(t \leq 1.3 \cdot 10^{+129}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.2e+141) (not (<= t 1.3e+129))) (* t (/ x z)) (* (/ x z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.2e+141) || !(t <= 1.3e+129)) {
		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 ((t <= (-2.2d+141)) .or. (.not. (t <= 1.3d+129))) 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 ((t <= -2.2e+141) || !(t <= 1.3e+129)) {
		tmp = t * (x / z);
	} else {
		tmp = (x / z) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.2e+141) or not (t <= 1.3e+129):
		tmp = t * (x / z)
	else:
		tmp = (x / z) * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.2e+141) || !(t <= 1.3e+129))
		tmp = Float64(t * Float64(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 ((t <= -2.2e+141) || ~((t <= 1.3e+129)))
		tmp = t * (x / z);
	else
		tmp = (x / z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.2e+141], N[Not[LessEqual[t, 1.3e+129]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2e141 or 1.30000000000000006e129 < t

   1. Initial program 98.6%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 56.3

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

   5. Applied rewrites 56.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 50.5%

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

   if -2.2e141 < t < 1.30000000000000006e129

   1. Initial program 96.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. associate-*l/ N/A

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

      7. distribute-lft-neg-out N/A

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

      8. metadata-eval N/A

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

      9. *-lft-identity N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. mul-1-neg N/A

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

      14. distribute-neg-frac2 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. *-lft-identity N/A

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

      18. metadata-eval N/A

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

   5. Applied rewrites 84.7%

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

   6. Taylor expanded in y around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 69.5

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

   8. Applied rewrites 69.5%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+141} \lor \neg \left(t \leq 1.3 \cdot 10^{+129}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 43.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.75 \lor \neg \left(z \leq 3.3 \cdot 10^{-18}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-\mathsf{fma}\left(t, z, t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.75) (not (<= z 3.3e-18)))
   (* t (/ x z))
   (* x (- (fma t z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.75) || !(z <= 3.3e-18)) {
		tmp = t * (x / z);
	} else {
		tmp = x * -fma(t, z, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.75) || !(z <= 3.3e-18))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(x * Float64(-fma(t, z, t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.75], N[Not[LessEqual[z, 3.3e-18]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * (-N[(t * z + t), $MachinePrecision])), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.75 or 3.3000000000000002e-18 < z

   1. Initial program 97.6%

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

   3. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 86.1

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

   5. Applied rewrites 86.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 47.9%

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

   if -0.75 < z < 3.3000000000000002e-18

   1. Initial program 95.8%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

      6. cancel-sign-sub N/A

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

      7. mul-1-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. remove-double-neg N/A

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

      11. metadata-eval N/A

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

      12. metadata-eval N/A

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

      13. metadata-eval N/A

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

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

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

      15. metadata-eval N/A

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

      16. lower--.f64 33.2

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

   5. Applied rewrites 33.2%

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

   6. Taylor expanded in z around 0

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

      1. distribute-lft-out N/A

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

      2. mul-1-neg N/A

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

      3. +-commutative N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

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

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

      7. lower-neg.f64 N/A

         \[\leadsto x \cdot \left(-\left(t \cdot z - -1 \cdot t\right)\right) \]

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

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

      9. metadata-eval N/A

         \[\leadsto x \cdot \left(-\left(t \cdot z + 1 \cdot t\right)\right) \]

      10. *-lft-identity N/A

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

      11. lower-fma.f64 33.1

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

   8. Applied rewrites 33.1%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.75 \lor \neg \left(z \leq 3.3 \cdot 10^{-18}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-\mathsf{fma}\left(t, z, t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 23.4% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

3. Taylor expanded in y around 0

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

   1. mul-1-neg N/A

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

   2. distribute-neg-frac2 N/A

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

   3. lower-/.f64 N/A

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

   4. *-lft-identity N/A

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

   5. metadata-eval N/A

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

   6. cancel-sign-sub N/A

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

   7. mul-1-neg N/A

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

   8. +-commutative N/A

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

   9. distribute-neg-in N/A

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

   10. remove-double-neg N/A

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

   11. metadata-eval N/A

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

   12. metadata-eval N/A

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

   13. metadata-eval N/A

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

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

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

   15. metadata-eval N/A

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

   16. lower--.f64 43.3

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

5. Applied rewrites 43.3%

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

6. Taylor expanded in z around 0

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

   1. mul-1-neg N/A

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

   2. lower-neg.f64 19.7

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

8. Applied rewrites 19.7%

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

Developer Target 1: 94.8% 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 2025026 
(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)))))