Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2

Percentage Accurate: 86.1% → 99.0%

Time: 7.8s

Alternatives: 16

Speedup: 1.1×

• 23.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / y) + ((2.0d0 + ((z * 2.0d0) * (1.0d0 - t))) / (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Python

def code(x, y, z, t):
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 86.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / y) + ((2.0d0 + ((z * 2.0d0) * (1.0d0 - t))) / (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Python

def code(x, y, z, t):
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_1 \leq 10^{+299}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\frac{\frac{2}{z} - -2}{t} - 2}{x} + \frac{1}{y}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z)))))
   (if (<= t_1 1e+299)
     t_1
     (* (+ (/ (- (/ (- (/ 2.0 z) -2.0) t) 2.0) x) (/ 1.0 y)) x))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
	double tmp;
	if (t_1 <= 1e+299) {
		tmp = t_1;
	} else {
		tmp = ((((((2.0 / z) - -2.0) / t) - 2.0) / x) + (1.0 / y)) * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + ((2.0d0 + ((z * 2.0d0) * (1.0d0 - t))) / (t * z))
    if (t_1 <= 1d+299) then
        tmp = t_1
    else
        tmp = ((((((2.0d0 / z) - (-2.0d0)) / t) - 2.0d0) / x) + (1.0d0 / y)) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
	double tmp;
	if (t_1 <= 1e+299) {
		tmp = t_1;
	} else {
		tmp = ((((((2.0 / z) - -2.0) / t) - 2.0) / x) + (1.0 / y)) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))
	tmp = 0
	if t_1 <= 1e+299:
		tmp = t_1
	else:
		tmp = ((((((2.0 / z) - -2.0) / t) - 2.0) / x) + (1.0 / y)) * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z)))
	tmp = 0.0
	if (t_1 <= 1e+299)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(2.0 / z) - -2.0) / t) - 2.0) / x) + Float64(1.0 / y)) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
	tmp = 0.0;
	if (t_1 <= 1e+299)
		tmp = t_1;
	else
		tmp = ((((((2.0 / z) - -2.0) / t) - 2.0) / x) + (1.0 / y)) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+299], t$95$1, N[(N[(N[(N[(N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision] / x), $MachinePrecision] + N[(1.0 / y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 x y) (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))) < 1.0000000000000001e299

   1. Initial program 99.8%

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

   if 1.0000000000000001e299 < (+.f64 (/.f64 x y) (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)))

   1. Initial program 52.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{1 - t}{t \cdot x} + \left(\frac{1}{y} + \frac{2}{t \cdot \left(x \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 99.9%

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

Alternative 2: 68.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+250}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{+32}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+164} \lor \neg \left(t\_2 \leq \infty\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z)))
        (t_2 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
   (if (<= t_2 -5e+250)
     t_1
     (if (<= t_2 -1e+32)
       (- (/ 2.0 t) 2.0)
       (if (or (<= t_2 5e+164) (not (<= t_2 INFINITY)))
         (+ (/ x y) -2.0)
         t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_2 <= -5e+250) {
		tmp = t_1;
	} else if (t_2 <= -1e+32) {
		tmp = (2.0 / t) - 2.0;
	} else if ((t_2 <= 5e+164) || !(t_2 <= ((double) INFINITY))) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_2 <= -5e+250) {
		tmp = t_1;
	} else if (t_2 <= -1e+32) {
		tmp = (2.0 / t) - 2.0;
	} else if ((t_2 <= 5e+164) || !(t_2 <= Double.POSITIVE_INFINITY)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	tmp = 0
	if t_2 <= -5e+250:
		tmp = t_1
	elif t_2 <= -1e+32:
		tmp = (2.0 / t) - 2.0
	elif (t_2 <= 5e+164) or not (t_2 <= math.inf):
		tmp = (x / y) + -2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if (t_2 <= -5e+250)
		tmp = t_1;
	elseif (t_2 <= -1e+32)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	elseif ((t_2 <= 5e+164) || !(t_2 <= Inf))
		tmp = Float64(Float64(x / y) + -2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (t * z);
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	tmp = 0.0;
	if (t_2 <= -5e+250)
		tmp = t_1;
	elseif (t_2 <= -1e+32)
		tmp = (2.0 / t) - 2.0;
	elseif ((t_2 <= 5e+164) || ~((t_2 <= Inf)))
		tmp = (x / y) + -2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+250], t$95$1, If[LessEqual[t$95$2, -1e+32], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], If[Or[LessEqual[t$95$2, 5e+164], N[Not[LessEqual[t$95$2, Infinity]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -5.0000000000000002e250 or 4.9999999999999995e164 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 97.2%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]

   5. Applied rewrites 97.2%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{x}{y} - 2, t, \frac{2}{z} - -2\right)}{t}} \]
   6. Step-by-step derivation

   7. Applied rewrites 97.2%

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

   8. Taylor expanded in x around inf

      \[\leadsto \frac{x \cdot \left(-2 \cdot \frac{t}{x} + \left(2 \cdot \frac{1}{x} + \left(\frac{2}{x \cdot z} + \frac{t}{y}\right)\right)\right)}{t} \]

   10. Applied rewrites 94.0%

       \[\leadsto \frac{\left(\frac{t}{y} - \frac{\mathsf{fma}\left(-2, 1 - t, \frac{-2}{z}\right)}{x}\right) \cdot x}{t} \]

   11. Taylor expanded in z around 0

       \[\leadsto \color{blue}{\frac{2}{t \cdot z}} \]
   12. Step-by-step derivation

       1. lower-/.f64 N/A

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

       2. lower-*.f64 77.1

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

   13. Applied rewrites 77.1%

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

   if -5.0000000000000002e250 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.00000000000000005e32

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

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

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 69.3%

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

   6. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \frac{1}{t} - \color{blue}{2} \]
   7. Step-by-step derivation

   8. Applied rewrites 43.9%

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

   if -1.00000000000000005e32 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 4.9999999999999995e164 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 82.7%

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

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Applied rewrites 81.5%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -5 \cdot 10^{+250}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -1 \cdot 10^{+32}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq 5 \cdot 10^{+164} \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq \infty\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+32} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+15} \lor \neg \left(t\_1 \leq \infty\right)\right):\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
   (if (or (<= t_1 -1e+32) (not (or (<= t_1 2e+15) (not (<= t_1 INFINITY)))))
     (/ (- (/ 2.0 z) -2.0) t)
     (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if ((t_1 <= -1e+32) || !((t_1 <= 2e+15) || !(t_1 <= ((double) INFINITY)))) {
		tmp = ((2.0 / z) - -2.0) / t;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if ((t_1 <= -1e+32) || !((t_1 <= 2e+15) || !(t_1 <= Double.POSITIVE_INFINITY))) {
		tmp = ((2.0 / z) - -2.0) / t;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	tmp = 0
	if (t_1 <= -1e+32) or not ((t_1 <= 2e+15) or not (t_1 <= math.inf)):
		tmp = ((2.0 / z) - -2.0) / t
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if ((t_1 <= -1e+32) || !((t_1 <= 2e+15) || !(t_1 <= Inf)))
		tmp = Float64(Float64(Float64(2.0 / z) - -2.0) / t);
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	tmp = 0.0;
	if ((t_1 <= -1e+32) || ~(((t_1 <= 2e+15) || ~((t_1 <= Inf)))))
		tmp = ((2.0 / z) - -2.0) / t;
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+32], N[Not[Or[LessEqual[t$95$1, 2e+15], N[Not[LessEqual[t$95$1, Infinity]], $MachinePrecision]]], $MachinePrecision]], N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.00000000000000005e32 or 2e15 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 98.5%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} + 2}}{t} \]

      3. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} + \color{blue}{2 \cdot 1}}{t} \]

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

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} - \left(\mathsf{neg}\left(2\right)\right) \cdot 1}}{t} \]

      5. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} - \color{blue}{-2} \cdot 1}{t} \]

      6. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} - \color{blue}{-2}}{t} \]

      7. lower--.f64 N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} - -2}}{t} \]

      8. associate-*r/ N/A

         \[\leadsto \frac{\color{blue}{\frac{2 \cdot 1}{z}} - -2}{t} \]

      9. metadata-eval N/A

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

      10. lower-/.f64 79.1

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

   5. Applied rewrites 79.1%

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

   if -1.00000000000000005e32 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 2e15 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 76.3%

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

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Applied rewrites 94.6%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -1 \cdot 10^{+32} \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq 2 \cdot 10^{+15} \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq \infty\right)\right):\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_1 \leq -2.00000000001:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(-2, t, 2\right), z, 2\right)}{t \cdot z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+15} \lor \neg \left(t\_1 \leq \infty\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
   (if (<= t_1 -2.00000000001)
     (/ (fma (fma -2.0 t 2.0) z 2.0) (* t z))
     (if (or (<= t_1 2e+15) (not (<= t_1 INFINITY)))
       (+ (/ x y) -2.0)
       (/ (- (/ 2.0 z) -2.0) t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_1 <= -2.00000000001) {
		tmp = fma(fma(-2.0, t, 2.0), z, 2.0) / (t * z);
	} else if ((t_1 <= 2e+15) || !(t_1 <= ((double) INFINITY))) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = ((2.0 / z) - -2.0) / t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if (t_1 <= -2.00000000001)
		tmp = Float64(fma(fma(-2.0, t, 2.0), z, 2.0) / Float64(t * z));
	elseif ((t_1 <= 2e+15) || !(t_1 <= Inf))
		tmp = Float64(Float64(x / y) + -2.0);
	else
		tmp = Float64(Float64(Float64(2.0 / z) - -2.0) / t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2.00000000001], N[(N[(N[(-2.0 * t + 2.0), $MachinePrecision] * z + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, 2e+15], N[Not[LessEqual[t$95$1, Infinity]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -2.00000000001

   1. Initial program 98.6%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

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

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 79.3%

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

   6. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \frac{1}{t} - \color{blue}{2} \]
   7. Step-by-step derivation

   8. Applied rewrites 33.6%

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

   9. Taylor expanded in z around 0

      \[\leadsto \frac{z \cdot \left(2 \cdot \frac{1}{t} - 2\right) + 2 \cdot \frac{1}{t}}{\color{blue}{z}} \]

   11. Applied rewrites 79.1%

       \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(-2, t, 2\right), z, 2\right)}{\color{blue}{t \cdot z}} \]

   if -2.00000000001 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 2e15 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 74.4%

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

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Applied rewrites 97.6%

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]

   if 2e15 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 98.6%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} + 2}}{t} \]

      3. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} + \color{blue}{2 \cdot 1}}{t} \]

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

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} - \left(\mathsf{neg}\left(2\right)\right) \cdot 1}}{t} \]

      5. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} - \color{blue}{-2} \cdot 1}{t} \]

      6. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} - \color{blue}{-2}}{t} \]

      7. lower--.f64 N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} - -2}}{t} \]

      8. associate-*r/ N/A

         \[\leadsto \frac{\color{blue}{\frac{2 \cdot 1}{z}} - -2}{t} \]

      9. metadata-eval N/A

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

      10. lower-/.f64 78.3

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

   5. Applied rewrites 78.3%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -2.00000000001:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(-2, t, 2\right), z, 2\right)}{t \cdot z}\\ \mathbf{elif}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq 2 \cdot 10^{+15} \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq \infty\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+32} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+15} \lor \neg \left(t\_1 \leq \infty\right)\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
   (if (or (<= t_1 -1e+32) (not (or (<= t_1 2e+15) (not (<= t_1 INFINITY)))))
     (/ (fma z 2.0 2.0) (* t z))
     (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if ((t_1 <= -1e+32) || !((t_1 <= 2e+15) || !(t_1 <= ((double) INFINITY)))) {
		tmp = fma(z, 2.0, 2.0) / (t * z);
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if ((t_1 <= -1e+32) || !((t_1 <= 2e+15) || !(t_1 <= Inf)))
		tmp = Float64(fma(z, 2.0, 2.0) / Float64(t * z));
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+32], N[Not[Or[LessEqual[t$95$1, 2e+15], N[Not[LessEqual[t$95$1, Infinity]], $MachinePrecision]]], $MachinePrecision]], N[(N[(z * 2.0 + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.00000000000000005e32 or 2e15 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 98.5%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

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

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 79.1%

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

   6. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \frac{1}{t} - \color{blue}{2} \]
   7. Step-by-step derivation

   8. Applied rewrites 29.8%

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

   9. Taylor expanded in z around 0

      \[\leadsto \frac{z \cdot \left(2 \cdot \frac{1}{t} - 2\right) + 2 \cdot \frac{1}{t}}{\color{blue}{z}} \]

   11. Applied rewrites 79.0%

       \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(-2, t, 2\right), z, 2\right)}{\color{blue}{t \cdot z}} \]

   12. Taylor expanded in t around 0

       \[\leadsto \frac{2 + 2 \cdot z}{t \cdot z} \]
   13. Step-by-step derivation

   14. Applied rewrites 79.0%

       \[\leadsto \frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z} \]

   if -1.00000000000000005e32 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 2e15 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 76.3%

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

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Applied rewrites 94.6%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -1 \cdot 10^{+32} \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq 2 \cdot 10^{+15} \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq \infty\right)\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z)))))
   (if (<= t_1 INFINITY) t_1 (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 x y) (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))) < +inf.0

   1. Initial program 99.8%

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

   if +inf.0 < (+.f64 (/.f64 x y) (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)))

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Applied rewrites 91.7%

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

Alternative 7: 50.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1.7 \cdot 10^{-177}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 8.5 \cdot 10^{-79}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2.0)
   (/ x y)
   (if (<= (/ x y) -1.7e-177)
     -2.0
     (if (<= (/ x y) 8.5e-79) (/ 2.0 t) (if (<= (/ x y) 2.0) -2.0 (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2.0) {
		tmp = x / y;
	} else if ((x / y) <= -1.7e-177) {
		tmp = -2.0;
	} else if ((x / y) <= 8.5e-79) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 2.0) {
		tmp = -2.0;
	} else {
		tmp = x / 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 ((x / y) <= (-2.0d0)) then
        tmp = x / y
    else if ((x / y) <= (-1.7d-177)) then
        tmp = -2.0d0
    else if ((x / y) <= 8.5d-79) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 2.0d0) then
        tmp = -2.0d0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2.0) {
		tmp = x / y;
	} else if ((x / y) <= -1.7e-177) {
		tmp = -2.0;
	} else if ((x / y) <= 8.5e-79) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 2.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2.0:
		tmp = x / y
	elif (x / y) <= -1.7e-177:
		tmp = -2.0
	elif (x / y) <= 8.5e-79:
		tmp = 2.0 / t
	elif (x / y) <= 2.0:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -1.7e-177)
		tmp = -2.0;
	elseif (Float64(x / y) <= 8.5e-79)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 2.0)
		tmp = -2.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2.0)
		tmp = x / y;
	elseif ((x / y) <= -1.7e-177)
		tmp = -2.0;
	elseif ((x / y) <= 8.5e-79)
		tmp = 2.0 / t;
	elseif ((x / y) <= 2.0)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -1.7e-177], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 8.5e-79], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.0], -2.0, N[(x / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2 or 2 < (/.f64 x y)

   1. Initial program 89.9%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]

   5. Applied rewrites 81.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{x}{y} - 2, t, \frac{2}{z} - -2\right)}{t}} \]
   6. Step-by-step derivation

   7. Applied rewrites 81.7%

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

   8. Taylor expanded in x around inf

      \[\leadsto \frac{x \cdot \left(-2 \cdot \frac{t}{x} + \left(2 \cdot \frac{1}{x} + \left(\frac{2}{x \cdot z} + \frac{t}{y}\right)\right)\right)}{t} \]

   10. Applied rewrites 77.9%

       \[\leadsto \frac{\left(\frac{t}{y} - \frac{\mathsf{fma}\left(-2, 1 - t, \frac{-2}{z}\right)}{x}\right) \cdot x}{t} \]

   11. Taylor expanded in x around inf

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

       1. lower-/.f64 66.9

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

   13. Applied rewrites 66.9%

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

   if -2 < (/.f64 x y) < -1.7e-177 or 8.50000000000000029e-79 < (/.f64 x y) < 2

   1. Initial program 83.5%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

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

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 98.9%

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

   6. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \frac{1}{t} - \color{blue}{2} \]
   7. Step-by-step derivation

   8. Applied rewrites 60.2%

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

   9. Taylor expanded in t around inf

      \[\leadsto -2 \]
   10. Step-by-step derivation

   11. Applied rewrites 49.6%

       \[\leadsto -2 \]

   if -1.7e-177 < (/.f64 x y) < 8.50000000000000029e-79

   1. Initial program 94.9%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} + 2}}{t} \]

      3. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} + \color{blue}{2 \cdot 1}}{t} \]

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

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} - \left(\mathsf{neg}\left(2\right)\right) \cdot 1}}{t} \]

      5. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} - \color{blue}{-2} \cdot 1}{t} \]

      6. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} - \color{blue}{-2}}{t} \]

      7. lower--.f64 N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} - -2}}{t} \]

      8. associate-*r/ N/A

         \[\leadsto \frac{\color{blue}{\frac{2 \cdot 1}{z}} - -2}{t} \]

      9. metadata-eval N/A

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

      10. lower-/.f64 78.6

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

   5. Applied rewrites 78.6%

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

   6. Taylor expanded in z around inf

      \[\leadsto \frac{2}{\color{blue}{t}} \]
   7. Step-by-step derivation

   8. Applied rewrites 37.6%

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

Alternative 8: 98.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -10000000000000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+58}\right):\\ \;\;\;\;\frac{x}{y} + \frac{\mathsf{fma}\left(2, z, 2\right)}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{x}{y} - 2, t, \frac{2}{z} - -2\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -10000000000000.0) (not (<= (/ x y) 5e+58)))
   (+ (/ x y) (/ (fma 2.0 z 2.0) (* t z)))
   (/ (fma (- (/ x y) 2.0) t (- (/ 2.0 z) -2.0)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -10000000000000.0) || !((x / y) <= 5e+58)) {
		tmp = (x / y) + (fma(2.0, z, 2.0) / (t * z));
	} else {
		tmp = fma(((x / y) - 2.0), t, ((2.0 / z) - -2.0)) / t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -10000000000000.0) || !(Float64(x / y) <= 5e+58))
		tmp = Float64(Float64(x / y) + Float64(fma(2.0, z, 2.0) / Float64(t * z)));
	else
		tmp = Float64(fma(Float64(Float64(x / y) - 2.0), t, Float64(Float64(2.0 / z) - -2.0)) / t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -10000000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e+58]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 * z + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision] * t + N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e13 or 4.99999999999999986e58 < (/.f64 x y)

   1. Initial program 89.7%

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

   3. Taylor expanded in t around 0

      \[\leadsto \frac{x}{y} + \frac{\color{blue}{2 + 2 \cdot z}}{t \cdot z} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. lower-fma.f64 98.0

         \[\leadsto \frac{x}{y} + \frac{\color{blue}{\mathsf{fma}\left(2, z, 2\right)}}{t \cdot z} \]

   5. Applied rewrites 98.0%

      \[\leadsto \frac{x}{y} + \frac{\color{blue}{\mathsf{fma}\left(2, z, 2\right)}}{t \cdot z} \]

   if -1e13 < (/.f64 x y) < 4.99999999999999986e58

   1. Initial program 91.1%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]

   5. Applied rewrites 99.9%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -10000000000000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+58}\right):\\ \;\;\;\;\frac{x}{y} + \frac{\mathsf{fma}\left(2, z, 2\right)}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{x}{y} - 2, t, \frac{2}{z} - -2\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -10000000000000 \lor \neg \left(\frac{x}{y} \leq 10000\right):\\ \;\;\;\;\frac{x}{y} + \frac{\mathsf{fma}\left(2, z, 2\right)}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -10000000000000.0) (not (<= (/ x y) 10000.0)))
   (+ (/ x y) (/ (fma 2.0 z 2.0) (* t z)))
   (- (/ (- (/ 2.0 z) -2.0) t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -10000000000000.0) || !((x / y) <= 10000.0)) {
		tmp = (x / y) + (fma(2.0, z, 2.0) / (t * z));
	} else {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -10000000000000.0) || !(Float64(x / y) <= 10000.0))
		tmp = Float64(Float64(x / y) + Float64(fma(2.0, z, 2.0) / Float64(t * z)));
	else
		tmp = Float64(Float64(Float64(Float64(2.0 / z) - -2.0) / t) - 2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -10000000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 10000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 * z + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e13 or 1e4 < (/.f64 x y)

   1. Initial program 89.8%

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

   3. Taylor expanded in t around 0

      \[\leadsto \frac{x}{y} + \frac{\color{blue}{2 + 2 \cdot z}}{t \cdot z} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. lower-fma.f64 97.4

         \[\leadsto \frac{x}{y} + \frac{\color{blue}{\mathsf{fma}\left(2, z, 2\right)}}{t \cdot z} \]

   5. Applied rewrites 97.4%

      \[\leadsto \frac{x}{y} + \frac{\color{blue}{\mathsf{fma}\left(2, z, 2\right)}}{t \cdot z} \]

   if -1e13 < (/.f64 x y) < 1e4

   1. Initial program 91.1%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

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

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 99.6%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -10000000000000 \lor \neg \left(\frac{x}{y} \leq 10000\right):\\ \;\;\;\;\frac{x}{y} + \frac{\mathsf{fma}\left(2, z, 2\right)}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+148} \lor \neg \left(\frac{x}{y} \leq 10^{-14}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 - \frac{-2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+148) (not (<= (/ x y) 1e-14)))
   (+ (/ x y) (- -2.0 (/ -2.0 t)))
   (- (/ (- (/ 2.0 z) -2.0) t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+148) || !((x / y) <= 1e-14)) {
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	} else {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	}
	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 (((x / y) <= (-2d+148)) .or. (.not. ((x / y) <= 1d-14))) then
        tmp = (x / y) + ((-2.0d0) - ((-2.0d0) / t))
    else
        tmp = (((2.0d0 / z) - (-2.0d0)) / t) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+148) || !((x / y) <= 1e-14)) {
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	} else {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e+148) or not ((x / y) <= 1e-14):
		tmp = (x / y) + (-2.0 - (-2.0 / t))
	else:
		tmp = (((2.0 / z) - -2.0) / t) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e+148) || !(Float64(x / y) <= 1e-14))
		tmp = Float64(Float64(x / y) + Float64(-2.0 - Float64(-2.0 / t)));
	else
		tmp = Float64(Float64(Float64(Float64(2.0 / z) - -2.0) / t) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e+148) || ~(((x / y) <= 1e-14)))
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	else
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e+148], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e-14]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.0000000000000001e148 or 9.99999999999999999e-15 < (/.f64 x y)

   1. Initial program 89.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \frac{x}{y} + \color{blue}{2 \cdot \frac{1 - t}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{x}{y} + \color{blue}{\frac{2 \cdot \left(1 - t\right)}{t}} \]

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

         \[\leadsto \frac{x}{y} + \frac{\color{blue}{2 \cdot 1 - 2 \cdot t}}{t} \]

      3. metadata-eval N/A

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

      4. metadata-eval N/A

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

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

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

      6. +-commutative N/A

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

      7. metadata-eval N/A

         \[\leadsto \frac{x}{y} + \frac{-2 \cdot t + \color{blue}{2 \cdot 1}}{t} \]

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

         \[\leadsto \frac{x}{y} + \frac{\color{blue}{-2 \cdot t - \left(\mathsf{neg}\left(2\right)\right) \cdot 1}}{t} \]

      9. metadata-eval N/A

         \[\leadsto \frac{x}{y} + \frac{-2 \cdot t - \color{blue}{-2} \cdot 1}{t} \]

      10. metadata-eval N/A

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

      11. div-sub N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. *-inverses N/A

          \[\leadsto \frac{x}{y} + \left(\left(\mathsf{neg}\left(2\right)\right) \cdot \color{blue}{1} - \frac{-2}{t}\right) \]

      15. metadata-eval N/A

          \[\leadsto \frac{x}{y} + \left(\color{blue}{-2} \cdot 1 - \frac{-2}{t}\right) \]

      16. metadata-eval N/A

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

      17. metadata-eval N/A

          \[\leadsto \frac{x}{y} + \left(-2 - \frac{\color{blue}{-2 \cdot 1}}{t}\right) \]

      18. associate-*r/ N/A

          \[\leadsto \frac{x}{y} + \left(-2 - \color{blue}{-2 \cdot \frac{1}{t}}\right) \]

      19. metadata-eval N/A

          \[\leadsto \frac{x}{y} + \left(-2 - \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot \frac{1}{t}\right) \]

      20. lower--.f64 N/A

          \[\leadsto \frac{x}{y} + \color{blue}{\left(-2 - \left(\mathsf{neg}\left(2\right)\right) \cdot \frac{1}{t}\right)} \]

      21. metadata-eval N/A

          \[\leadsto \frac{x}{y} + \left(-2 - \color{blue}{-2} \cdot \frac{1}{t}\right) \]

      22. associate-*r/ N/A

          \[\leadsto \frac{x}{y} + \left(-2 - \color{blue}{\frac{-2 \cdot 1}{t}}\right) \]

      23. metadata-eval N/A

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

      24. lower-/.f64 82.5

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

   5. Applied rewrites 82.5%

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

   if -2.0000000000000001e148 < (/.f64 x y) < 9.99999999999999999e-15

   1. Initial program 91.5%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

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

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 95.5%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+148} \lor \neg \left(\frac{x}{y} \leq 10^{-14}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 - \frac{-2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 84.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+173}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10000:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e+173)
   (/ x y)
   (if (<= (/ x y) 10000.0)
     (- (/ (- (/ 2.0 z) -2.0) t) 2.0)
     (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+173) {
		tmp = x / y;
	} else if ((x / y) <= 10000.0) {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	} else {
		tmp = (x / y) + -2.0;
	}
	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 ((x / y) <= (-2d+173)) then
        tmp = x / y
    else if ((x / y) <= 10000.0d0) then
        tmp = (((2.0d0 / z) - (-2.0d0)) / t) - 2.0d0
    else
        tmp = (x / y) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+173) {
		tmp = x / y;
	} else if ((x / y) <= 10000.0) {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2e+173:
		tmp = x / y
	elif (x / y) <= 10000.0:
		tmp = (((2.0 / z) - -2.0) / t) - 2.0
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e+173)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 10000.0)
		tmp = Float64(Float64(Float64(Float64(2.0 / z) - -2.0) / t) - 2.0);
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2e+173)
		tmp = x / y;
	elseif ((x / y) <= 10000.0)
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e+173], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 10000.0], N[(N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2e173

   1. Initial program 91.6%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]

   5. Applied rewrites 76.4%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{x}{y} - 2, t, \frac{2}{z} - -2\right)}{t}} \]
   6. Step-by-step derivation

   7. Applied rewrites 76.4%

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

   8. Taylor expanded in x around inf

      \[\leadsto \frac{x \cdot \left(-2 \cdot \frac{t}{x} + \left(2 \cdot \frac{1}{x} + \left(\frac{2}{x \cdot z} + \frac{t}{y}\right)\right)\right)}{t} \]

   10. Applied rewrites 79.2%

       \[\leadsto \frac{\left(\frac{t}{y} - \frac{\mathsf{fma}\left(-2, 1 - t, \frac{-2}{z}\right)}{x}\right) \cdot x}{t} \]

   11. Taylor expanded in x around inf

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

       1. lower-/.f64 86.5

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

   13. Applied rewrites 86.5%

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

   if -2e173 < (/.f64 x y) < 1e4

   1. Initial program 91.1%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

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

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 94.7%

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

   if 1e4 < (/.f64 x y)

   1. Initial program 88.4%

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

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Applied rewrites 69.2%

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

Alternative 12: 65.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3400 \lor \neg \left(\frac{x}{y} \leq 22500\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -3400.0) (not (<= (/ x y) 22500.0)))
   (+ (/ x y) -2.0)
   (- (/ 2.0 t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -3400.0) || !((x / y) <= 22500.0)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = (2.0 / t) - 2.0;
	}
	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 (((x / y) <= (-3400.0d0)) .or. (.not. ((x / y) <= 22500.0d0))) then
        tmp = (x / y) + (-2.0d0)
    else
        tmp = (2.0d0 / t) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -3400.0) || !((x / y) <= 22500.0)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = (2.0 / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -3400.0) or not ((x / y) <= 22500.0):
		tmp = (x / y) + -2.0
	else:
		tmp = (2.0 / t) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -3400.0) || !(Float64(x / y) <= 22500.0))
		tmp = Float64(Float64(x / y) + -2.0);
	else
		tmp = Float64(Float64(2.0 / t) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -3400.0) || ~(((x / y) <= 22500.0)))
		tmp = (x / y) + -2.0;
	else
		tmp = (2.0 / t) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -3400.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 22500.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -3400 or 22500 < (/.f64 x y)

   1. Initial program 89.8%

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

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Applied rewrites 68.3%

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]

   if -3400 < (/.f64 x y) < 22500

   1. Initial program 91.1%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

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

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 99.6%

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

   6. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \frac{1}{t} - \color{blue}{2} \]
   7. Step-by-step derivation

   8. Applied rewrites 59.2%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3400 \lor \neg \left(\frac{x}{y} \leq 22500\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -11000000 \lor \neg \left(\frac{x}{y} \leq 9 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -11000000.0) (not (<= (/ x y) 9e+14)))
   (/ x y)
   (- (/ 2.0 t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -11000000.0) || !((x / y) <= 9e+14)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) - 2.0;
	}
	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 (((x / y) <= (-11000000.0d0)) .or. (.not. ((x / y) <= 9d+14))) then
        tmp = x / y
    else
        tmp = (2.0d0 / t) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -11000000.0) || !((x / y) <= 9e+14)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -11000000.0) or not ((x / y) <= 9e+14):
		tmp = x / y
	else:
		tmp = (2.0 / t) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -11000000.0) || !(Float64(x / y) <= 9e+14))
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(2.0 / t) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -11000000.0) || ~(((x / y) <= 9e+14)))
		tmp = x / y;
	else
		tmp = (2.0 / t) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -11000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 9e+14]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.1e7 or 9e14 < (/.f64 x y)

   1. Initial program 89.6%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]

   5. Applied rewrites 81.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{x}{y} - 2, t, \frac{2}{z} - -2\right)}{t}} \]
   6. Step-by-step derivation

   7. Applied rewrites 81.1%

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

   8. Taylor expanded in x around inf

      \[\leadsto \frac{x \cdot \left(-2 \cdot \frac{t}{x} + \left(2 \cdot \frac{1}{x} + \left(\frac{2}{x \cdot z} + \frac{t}{y}\right)\right)\right)}{t} \]

   10. Applied rewrites 78.0%

       \[\leadsto \frac{\left(\frac{t}{y} - \frac{\mathsf{fma}\left(-2, 1 - t, \frac{-2}{z}\right)}{x}\right) \cdot x}{t} \]

   11. Taylor expanded in x around inf

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

       1. lower-/.f64 68.1

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

   13. Applied rewrites 68.1%

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

   if -1.1e7 < (/.f64 x y) < 9e14

   1. Initial program 91.3%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

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

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 98.1%

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

   6. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \frac{1}{t} - \color{blue}{2} \]
   7. Step-by-step derivation

   8. Applied rewrites 58.6%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -11000000 \lor \neg \left(\frac{x}{y} \leq 9 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 92.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-25} \lor \neg \left(z \leq 9.5 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 - \frac{-2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.5e-25) (not (<= z 9.5e-9)))
   (+ (/ x y) (- -2.0 (/ -2.0 t)))
   (+ (/ x y) (/ 2.0 (* t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.5e-25) || !(z <= 9.5e-9)) {
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	} else {
		tmp = (x / y) + (2.0 / (t * z));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-7.5d-25)) .or. (.not. (z <= 9.5d-9))) then
        tmp = (x / y) + ((-2.0d0) - ((-2.0d0) / t))
    else
        tmp = (x / y) + (2.0d0 / (t * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.5e-25) || !(z <= 9.5e-9)) {
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	} else {
		tmp = (x / y) + (2.0 / (t * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.5e-25) or not (z <= 9.5e-9):
		tmp = (x / y) + (-2.0 - (-2.0 / t))
	else:
		tmp = (x / y) + (2.0 / (t * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.5e-25) || !(z <= 9.5e-9))
		tmp = Float64(Float64(x / y) + Float64(-2.0 - Float64(-2.0 / t)));
	else
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.5e-25) || ~((z <= 9.5e-9)))
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	else
		tmp = (x / y) + (2.0 / (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.5e-25], N[Not[LessEqual[z, 9.5e-9]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.49999999999999989e-25 or 9.5000000000000007e-9 < z

   1. Initial program 83.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \frac{x}{y} + \color{blue}{2 \cdot \frac{1 - t}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{x}{y} + \color{blue}{\frac{2 \cdot \left(1 - t\right)}{t}} \]

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

         \[\leadsto \frac{x}{y} + \frac{\color{blue}{2 \cdot 1 - 2 \cdot t}}{t} \]

      3. metadata-eval N/A

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

      4. metadata-eval N/A

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

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

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

      6. +-commutative N/A

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

      7. metadata-eval N/A

         \[\leadsto \frac{x}{y} + \frac{-2 \cdot t + \color{blue}{2 \cdot 1}}{t} \]

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

         \[\leadsto \frac{x}{y} + \frac{\color{blue}{-2 \cdot t - \left(\mathsf{neg}\left(2\right)\right) \cdot 1}}{t} \]

      9. metadata-eval N/A

         \[\leadsto \frac{x}{y} + \frac{-2 \cdot t - \color{blue}{-2} \cdot 1}{t} \]

      10. metadata-eval N/A

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

      11. div-sub N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. *-inverses N/A

          \[\leadsto \frac{x}{y} + \left(\left(\mathsf{neg}\left(2\right)\right) \cdot \color{blue}{1} - \frac{-2}{t}\right) \]

      15. metadata-eval N/A

          \[\leadsto \frac{x}{y} + \left(\color{blue}{-2} \cdot 1 - \frac{-2}{t}\right) \]

      16. metadata-eval N/A

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

      17. metadata-eval N/A

          \[\leadsto \frac{x}{y} + \left(-2 - \frac{\color{blue}{-2 \cdot 1}}{t}\right) \]

      18. associate-*r/ N/A

          \[\leadsto \frac{x}{y} + \left(-2 - \color{blue}{-2 \cdot \frac{1}{t}}\right) \]

      19. metadata-eval N/A

          \[\leadsto \frac{x}{y} + \left(-2 - \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot \frac{1}{t}\right) \]

      20. lower--.f64 N/A

          \[\leadsto \frac{x}{y} + \color{blue}{\left(-2 - \left(\mathsf{neg}\left(2\right)\right) \cdot \frac{1}{t}\right)} \]

      21. metadata-eval N/A

          \[\leadsto \frac{x}{y} + \left(-2 - \color{blue}{-2} \cdot \frac{1}{t}\right) \]

      22. associate-*r/ N/A

          \[\leadsto \frac{x}{y} + \left(-2 - \color{blue}{\frac{-2 \cdot 1}{t}}\right) \]

      23. metadata-eval N/A

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

      24. lower-/.f64 98.1

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

   5. Applied rewrites 98.1%

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

   if -7.49999999999999989e-25 < z < 9.5000000000000007e-9

   1. Initial program 98.2%

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

   3. Taylor expanded in z around 0

      \[\leadsto \frac{x}{y} + \frac{\color{blue}{2}}{t \cdot z} \]
   4. Step-by-step derivation

   5. Applied rewrites 90.8%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-25} \lor \neg \left(z \leq 9.5 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 - \frac{-2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 36.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \lor \neg \left(t \leq 1.95\right):\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.0) (not (<= t 1.95))) -2.0 (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.0) || !(t <= 1.95)) {
		tmp = -2.0;
	} else {
		tmp = 2.0 / 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 ((t <= (-1.0d0)) .or. (.not. (t <= 1.95d0))) then
        tmp = -2.0d0
    else
        tmp = 2.0d0 / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.0) || !(t <= 1.95)) {
		tmp = -2.0;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.0) or not (t <= 1.95):
		tmp = -2.0
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.0) || !(t <= 1.95))
		tmp = -2.0;
	else
		tmp = Float64(2.0 / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.0) || ~((t <= 1.95)))
		tmp = -2.0;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.0], N[Not[LessEqual[t, 1.95]], $MachinePrecision]], -2.0, N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1 or 1.94999999999999996 < t

   1. Initial program 81.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

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

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 54.5%

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

   6. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \frac{1}{t} - \color{blue}{2} \]
   7. Step-by-step derivation

   8. Applied rewrites 35.7%

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

   9. Taylor expanded in t around inf

      \[\leadsto -2 \]
   10. Step-by-step derivation

   11. Applied rewrites 34.3%

       \[\leadsto -2 \]

   if -1 < t < 1.94999999999999996

   1. Initial program 98.3%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} + 2}}{t} \]

      3. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} + \color{blue}{2 \cdot 1}}{t} \]

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

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} - \left(\mathsf{neg}\left(2\right)\right) \cdot 1}}{t} \]

      5. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} - \color{blue}{-2} \cdot 1}{t} \]

      6. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} - \color{blue}{-2}}{t} \]

      7. lower--.f64 N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} - -2}}{t} \]

      8. associate-*r/ N/A

         \[\leadsto \frac{\color{blue}{\frac{2 \cdot 1}{z}} - -2}{t} \]

      9. metadata-eval N/A

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

      10. lower-/.f64 77.7

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

   5. Applied rewrites 77.7%

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

   6. Taylor expanded in z around inf

      \[\leadsto \frac{2}{\color{blue}{t}} \]
   7. Step-by-step derivation

   8. Applied rewrites 34.7%

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

4. Final simplification 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \lor \neg \left(t \leq 1.95\right):\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 20.0% accurate, 47.0× speedup

Math

\[\begin{array}{l} \\ -2 \end{array} \]

FPCore

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

C

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

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 = -2.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := -2.0

Derivation

1. Initial program 90.4%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

   2. div-sub N/A

      \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

   3. *-inverses N/A

      \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

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

      \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

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

      \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

   6. metadata-eval N/A

      \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

   7. metadata-eval N/A

      \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

   8. associate-+l+ N/A

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

   9. +-commutative N/A

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

   10. associate-*r/ N/A

       \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

   11. metadata-eval N/A

       \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

   12. metadata-eval N/A

       \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

   13. metadata-eval N/A

       \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

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

       \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

   15. metadata-eval N/A

       \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

   16. lower--.f64 N/A

       \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

5. Applied rewrites 67.6%

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

6. Taylor expanded in z around inf

   \[\leadsto 2 \cdot \frac{1}{t} - \color{blue}{2} \]
7. Step-by-step derivation

8. Applied rewrites 35.4%

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

9. Taylor expanded in t around inf

   \[\leadsto -2 \]
10. Step-by-step derivation

11. Applied rewrites 16.9%

    \[\leadsto -2 \]
12. Add Preprocessing

Developer Target 1: 99.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right) \end{array} \]

FPCore

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

C

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

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 = (((2.0d0 / z) + 2.0d0) / t) - (2.0d0 - (x / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2025016 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ (+ (/ 2 z) 2) t) (- 2 (/ x y))))

  (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))