Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2

Percentage Accurate: 95.2% → 97.3%

Time: 8.8s

Alternatives: 26

Speedup: 0.5×

• 35.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - 1\right) \cdot z\\ t_2 := \left(\left(x - t\_1\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;t\_2 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- y 1.0) z))
        (t_2 (+ (- (- x t_1) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b))))
   (if (<= t_2 INFINITY) t_2 (- x (fma (- t 1.0) a t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y - 1.0) * z;
	double t_2 = ((x - t_1) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = x - fma((t - 1.0), a, t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y - 1.0) * z)
	t_2 = Float64(Float64(Float64(x - t_1) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(x - fma(Float64(t - 1.0), a, t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x - t$95$1), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

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

   1. Initial program 0.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 75.0%

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

Alternative 2: 96.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 99.2%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

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

   1. Initial program 0.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 75.0%

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

Alternative 3: 72.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(-2, b, x\right)\right) + a\\ t_2 := z + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.1 \cdot 10^{+180}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -300000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-8}:\\ \;\;\;\;\left(x + a\right) - \left(y - 1\right) \cdot z\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (fma (- b a) t (fma -2.0 b x)) a))
        (t_2 (+ z (* (- (+ y t) 2.0) b))))
   (if (<= b -1.1e+180)
     t_2
     (if (<= b -300000000.0)
       t_1
       (if (<= b 3.6e-8)
         (- (+ x a) (* (- y 1.0) z))
         (if (<= b 7e+62) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((b - a), t, fma(-2.0, b, x)) + a;
	double t_2 = z + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.1e+180) {
		tmp = t_2;
	} else if (b <= -300000000.0) {
		tmp = t_1;
	} else if (b <= 3.6e-8) {
		tmp = (x + a) - ((y - 1.0) * z);
	} else if (b <= 7e+62) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(Float64(b - a), t, fma(-2.0, b, x)) + a)
	t_2 = Float64(z + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -1.1e+180)
		tmp = t_2;
	elseif (b <= -300000000.0)
		tmp = t_1;
	elseif (b <= 3.6e-8)
		tmp = Float64(Float64(x + a) - Float64(Float64(y - 1.0) * z));
	elseif (b <= 7e+62)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(b - a), $MachinePrecision] * t + N[(-2.0 * b + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]}, Block[{t$95$2 = N[(z + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.1e+180], t$95$2, If[LessEqual[b, -300000000.0], t$95$1, If[LessEqual[b, 3.6e-8], N[(N[(x + a), $MachinePrecision] - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e+62], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.1e180 or 6.99999999999999967e62 < b

   1. Initial program 93.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 89.3%

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

   6. Taylor expanded in y around 0

      \[\leadsto z + \left(\left(y + t\right) - 2\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 90.6%

      \[\leadsto z + \left(\left(y + t\right) - 2\right) \cdot b \]

   if -1.1e180 < b < -3e8 or 3.59999999999999981e-8 < b < 6.99999999999999967e62

   1. Initial program 89.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 94.9%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in z around 0

      \[\leadsto a + \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 88.2%

      \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + \color{blue}{a} \]

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(b - a, t, x + -2 \cdot b\right) + a \]
   10. Step-by-step derivation

   11. Applied rewrites 80.1%

       \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(-2, b, x\right)\right) + a \]

   if -3e8 < b < 3.59999999999999981e-8

   1. Initial program 99.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 99.2%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 77.8%

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

Alternative 4: 32.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.68 \cdot 10^{+156}:\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-118}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-175}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-132}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-35}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;b \cdot y + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.68e+156)
   (* (- y) z)
   (if (<= y -3.5e-118)
     (* (- 1.0 t) a)
     (if (<= y 1.15e-175)
       (+ x a)
       (if (<= y 9e-132) (* b t) (if (<= y 1.85e-35) z (+ (* b y) a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.68e+156) {
		tmp = -y * z;
	} else if (y <= -3.5e-118) {
		tmp = (1.0 - t) * a;
	} else if (y <= 1.15e-175) {
		tmp = x + a;
	} else if (y <= 9e-132) {
		tmp = b * t;
	} else if (y <= 1.85e-35) {
		tmp = z;
	} else {
		tmp = (b * y) + a;
	}
	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, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.68d+156)) then
        tmp = -y * z
    else if (y <= (-3.5d-118)) then
        tmp = (1.0d0 - t) * a
    else if (y <= 1.15d-175) then
        tmp = x + a
    else if (y <= 9d-132) then
        tmp = b * t
    else if (y <= 1.85d-35) then
        tmp = z
    else
        tmp = (b * y) + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.68e+156) {
		tmp = -y * z;
	} else if (y <= -3.5e-118) {
		tmp = (1.0 - t) * a;
	} else if (y <= 1.15e-175) {
		tmp = x + a;
	} else if (y <= 9e-132) {
		tmp = b * t;
	} else if (y <= 1.85e-35) {
		tmp = z;
	} else {
		tmp = (b * y) + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.68e+156:
		tmp = -y * z
	elif y <= -3.5e-118:
		tmp = (1.0 - t) * a
	elif y <= 1.15e-175:
		tmp = x + a
	elif y <= 9e-132:
		tmp = b * t
	elif y <= 1.85e-35:
		tmp = z
	else:
		tmp = (b * y) + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.68e+156)
		tmp = Float64(Float64(-y) * z);
	elseif (y <= -3.5e-118)
		tmp = Float64(Float64(1.0 - t) * a);
	elseif (y <= 1.15e-175)
		tmp = Float64(x + a);
	elseif (y <= 9e-132)
		tmp = Float64(b * t);
	elseif (y <= 1.85e-35)
		tmp = z;
	else
		tmp = Float64(Float64(b * y) + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.68e+156)
		tmp = -y * z;
	elseif (y <= -3.5e-118)
		tmp = (1.0 - t) * a;
	elseif (y <= 1.15e-175)
		tmp = x + a;
	elseif (y <= 9e-132)
		tmp = b * t;
	elseif (y <= 1.85e-35)
		tmp = z;
	else
		tmp = (b * y) + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.68e+156], N[((-y) * z), $MachinePrecision], If[LessEqual[y, -3.5e-118], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[y, 1.15e-175], N[(x + a), $MachinePrecision], If[LessEqual[y, 9e-132], N[(b * t), $MachinePrecision], If[LessEqual[y, 1.85e-35], z, N[(N[(b * y), $MachinePrecision] + a), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.68e156

   1. Initial program 96.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 59.1%

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

   6. Taylor expanded in y around inf

      \[\leadsto \left(-1 \cdot y\right) \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 59.1%

      \[\leadsto \left(-y\right) \cdot z \]

   if -1.68e156 < y < -3.5e-118

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 47.2%

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

   if -3.5e-118 < y < 1.15e-175

   1. Initial program 97.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in z around 0

      \[\leadsto a + \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 77.5%

      \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + \color{blue}{a} \]

   9. Taylor expanded in x around inf

      \[\leadsto x + a \]
   10. Step-by-step derivation

   11. Applied rewrites 40.3%

       \[\leadsto x + a \]

   if 1.15e-175 < y < 8.9999999999999999e-132

   1. Initial program 87.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 62.7%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   6. Taylor expanded in a around 0

      \[\leadsto b \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 62.8%

      \[\leadsto b \cdot t \]

   if 8.9999999999999999e-132 < y < 1.8499999999999999e-35

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 46.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto z \]
   7. Step-by-step derivation

   8. Applied rewrites 46.0%

      \[\leadsto z \]

   if 1.8499999999999999e-35 < y

   1. Initial program 90.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 90.3%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in z around 0

      \[\leadsto a + \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 75.7%

      \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + \color{blue}{a} \]

   9. Taylor expanded in y around inf

      \[\leadsto b \cdot y + a \]
   10. Step-by-step derivation

   11. Applied rewrites 36.6%

       \[\leadsto b \cdot y + a \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 5: 82.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.1 \cdot 10^{+180}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -350000000:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(-2, b, x\right)\right) + a\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+62}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (* (- (+ y t) 2.0) b))))
   (if (<= b -1.1e+180)
     t_1
     (if (<= b -350000000.0)
       (+ (fma (- b a) t (fma -2.0 b x)) a)
       (if (<= b 3.6e+62) (- x (fma (- t 1.0) a (* (- y 1.0) z))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.1e+180) {
		tmp = t_1;
	} else if (b <= -350000000.0) {
		tmp = fma((b - a), t, fma(-2.0, b, x)) + a;
	} else if (b <= 3.6e+62) {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -1.1e+180)
		tmp = t_1;
	elseif (b <= -350000000.0)
		tmp = Float64(fma(Float64(b - a), t, fma(-2.0, b, x)) + a);
	elseif (b <= 3.6e+62)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.1e+180], t$95$1, If[LessEqual[b, -350000000.0], N[(N[(N[(b - a), $MachinePrecision] * t + N[(-2.0 * b + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[b, 3.6e+62], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.1e180 or 3.6e62 < b

   1. Initial program 93.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 89.3%

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

   6. Taylor expanded in y around 0

      \[\leadsto z + \left(\left(y + t\right) - 2\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 90.6%

      \[\leadsto z + \left(\left(y + t\right) - 2\right) \cdot b \]

   if -1.1e180 < b < -3.5e8

   1. Initial program 86.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 93.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in z around 0

      \[\leadsto a + \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 86.5%

      \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + \color{blue}{a} \]

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(b - a, t, x + -2 \cdot b\right) + a \]
   10. Step-by-step derivation

   11. Applied rewrites 77.6%

       \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(-2, b, x\right)\right) + a \]

   if -3.5e8 < b < 3.6e62

   1. Initial program 99.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 92.1%

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

Alternative 6: 88.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -350000000:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\\ \mathbf{elif}\;b \leq 46:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, t - 1, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -350000000.0)
   (+ (fma (- b a) t (fma (- y 2.0) b x)) a)
   (if (<= b 46.0)
     (- x (fma (- t 1.0) a (* (- y 1.0) z)))
     (fma (- a) (- t 1.0) (fma (- (+ t y) 2.0) b x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -350000000.0) {
		tmp = fma((b - a), t, fma((y - 2.0), b, x)) + a;
	} else if (b <= 46.0) {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	} else {
		tmp = fma(-a, (t - 1.0), fma(((t + y) - 2.0), b, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -350000000.0)
		tmp = Float64(fma(Float64(b - a), t, fma(Float64(y - 2.0), b, x)) + a);
	elseif (b <= 46.0)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	else
		tmp = fma(Float64(-a), Float64(t - 1.0), fma(Float64(Float64(t + y) - 2.0), b, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -350000000.0], N[(N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[b, 46.0], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-a) * N[(t - 1.0), $MachinePrecision] + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.5e8

   1. Initial program 91.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 94.4%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in z around 0

      \[\leadsto a + \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 87.2%

      \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + \color{blue}{a} \]

   if -3.5e8 < b < 46

   1. Initial program 99.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 94.5%

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

   if 46 < b

   1. Initial program 91.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 91.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, t - 1, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 55.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -2.75 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-68}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-254}:\\ \;\;\;\;\left(x + a\right) - \left(-z\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+83}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -2.75e+41)
     t_1
     (if (<= y -6.5e-68)
       (* (- b a) t)
       (if (<= y 2.4e-254)
         (- (+ x a) (- z))
         (if (<= y 2.05e+83) (fma (- t 2.0) b x) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -2.75e+41) {
		tmp = t_1;
	} else if (y <= -6.5e-68) {
		tmp = (b - a) * t;
	} else if (y <= 2.4e-254) {
		tmp = (x + a) - -z;
	} else if (y <= 2.05e+83) {
		tmp = fma((t - 2.0), b, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -2.75e+41)
		tmp = t_1;
	elseif (y <= -6.5e-68)
		tmp = Float64(Float64(b - a) * t);
	elseif (y <= 2.4e-254)
		tmp = Float64(Float64(x + a) - Float64(-z));
	elseif (y <= 2.05e+83)
		tmp = fma(Float64(t - 2.0), b, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -2.75e+41], t$95$1, If[LessEqual[y, -6.5e-68], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 2.4e-254], N[(N[(x + a), $MachinePrecision] - (-z)), $MachinePrecision], If[LessEqual[y, 2.05e+83], N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.7500000000000002e41 or 2.05e83 < y

   1. Initial program 93.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 71.9%

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

   if -2.7500000000000002e41 < y < -6.4999999999999997e-68

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 62.8%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   if -6.4999999999999997e-68 < y < 2.40000000000000002e-254

   1. Initial program 97.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 60.2%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 60.2%

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

   if 2.40000000000000002e-254 < y < 2.05e83

   1. Initial program 95.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 63.2%

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

   6. Taylor expanded in y around 0

      \[\leadsto x + \left(\color{blue}{t} - 2\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 58.1%

      \[\leadsto x + \left(\color{blue}{t} - 2\right) \cdot b \]
   9. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 58.1

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - 2, b, x\right)} \]

   10. Applied rewrites 58.1%

       \[\leadsto \color{blue}{\mathsf{fma}\left(t - 2, b, x\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 8: 87.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -350000000 \lor \neg \left(b \leq 46\right):\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -350000000.0) (not (<= b 46.0)))
   (+ (fma (- b a) t (fma (- y 2.0) b x)) a)
   (- x (fma (- t 1.0) a (* (- y 1.0) z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -350000000.0) || !(b <= 46.0)) {
		tmp = fma((b - a), t, fma((y - 2.0), b, x)) + a;
	} else {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -350000000.0) || !(b <= 46.0))
		tmp = Float64(fma(Float64(b - a), t, fma(Float64(y - 2.0), b, x)) + a);
	else
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -350000000.0], N[Not[LessEqual[b, 46.0]], $MachinePrecision]], N[(N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.5e8 or 46 < b

   1. Initial program 91.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 94.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in z around 0

      \[\leadsto a + \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 88.3%

      \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + \color{blue}{a} \]

   if -3.5e8 < b < 46

   1. Initial program 99.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 94.5%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -350000000 \lor \neg \left(b \leq 46\right):\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -2.75 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-68}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-22}:\\ \;\;\;\;\left(x + a\right) - \left(-z\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+83}:\\ \;\;\;\;x + t \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -2.75e+41)
     t_1
     (if (<= y -6.5e-68)
       (* (- b a) t)
       (if (<= y 6.6e-22)
         (- (+ x a) (- z))
         (if (<= y 2.05e+83) (+ x (* t b)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -2.75e+41) {
		tmp = t_1;
	} else if (y <= -6.5e-68) {
		tmp = (b - a) * t;
	} else if (y <= 6.6e-22) {
		tmp = (x + a) - -z;
	} else if (y <= 2.05e+83) {
		tmp = x + (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - z) * y
    if (y <= (-2.75d+41)) then
        tmp = t_1
    else if (y <= (-6.5d-68)) then
        tmp = (b - a) * t
    else if (y <= 6.6d-22) then
        tmp = (x + a) - -z
    else if (y <= 2.05d+83) then
        tmp = x + (t * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -2.75e+41) {
		tmp = t_1;
	} else if (y <= -6.5e-68) {
		tmp = (b - a) * t;
	} else if (y <= 6.6e-22) {
		tmp = (x + a) - -z;
	} else if (y <= 2.05e+83) {
		tmp = x + (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - z) * y
	tmp = 0
	if y <= -2.75e+41:
		tmp = t_1
	elif y <= -6.5e-68:
		tmp = (b - a) * t
	elif y <= 6.6e-22:
		tmp = (x + a) - -z
	elif y <= 2.05e+83:
		tmp = x + (t * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -2.75e+41)
		tmp = t_1;
	elseif (y <= -6.5e-68)
		tmp = Float64(Float64(b - a) * t);
	elseif (y <= 6.6e-22)
		tmp = Float64(Float64(x + a) - Float64(-z));
	elseif (y <= 2.05e+83)
		tmp = Float64(x + Float64(t * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - z) * y;
	tmp = 0.0;
	if (y <= -2.75e+41)
		tmp = t_1;
	elseif (y <= -6.5e-68)
		tmp = (b - a) * t;
	elseif (y <= 6.6e-22)
		tmp = (x + a) - -z;
	elseif (y <= 2.05e+83)
		tmp = x + (t * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -2.75e+41], t$95$1, If[LessEqual[y, -6.5e-68], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 6.6e-22], N[(N[(x + a), $MachinePrecision] - (-z)), $MachinePrecision], If[LessEqual[y, 2.05e+83], N[(x + N[(t * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.7500000000000002e41 or 2.05e83 < y

   1. Initial program 93.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 71.9%

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

   if -2.7500000000000002e41 < y < -6.4999999999999997e-68

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 62.8%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   if -6.4999999999999997e-68 < y < 6.6000000000000002e-22

   1. Initial program 96.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 55.5%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 55.5%

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

   if 6.6000000000000002e-22 < y < 2.05e83

   1. Initial program 94.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 81.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 64.4%

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

Alternative 10: 50.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-99}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-237}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+16}:\\ \;\;\;\;b \cdot y + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -4.4e+31)
     t_1
     (if (<= t -1.8e-99)
       (* (- 1.0 y) z)
       (if (<= t 7e-237) (+ x a) (if (<= t 2.6e+16) (+ (* b y) a) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -4.4e+31) {
		tmp = t_1;
	} else if (t <= -1.8e-99) {
		tmp = (1.0 - y) * z;
	} else if (t <= 7e-237) {
		tmp = x + a;
	} else if (t <= 2.6e+16) {
		tmp = (b * y) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - a) * t
    if (t <= (-4.4d+31)) then
        tmp = t_1
    else if (t <= (-1.8d-99)) then
        tmp = (1.0d0 - y) * z
    else if (t <= 7d-237) then
        tmp = x + a
    else if (t <= 2.6d+16) then
        tmp = (b * y) + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -4.4e+31) {
		tmp = t_1;
	} else if (t <= -1.8e-99) {
		tmp = (1.0 - y) * z;
	} else if (t <= 7e-237) {
		tmp = x + a;
	} else if (t <= 2.6e+16) {
		tmp = (b * y) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -4.4e+31:
		tmp = t_1
	elif t <= -1.8e-99:
		tmp = (1.0 - y) * z
	elif t <= 7e-237:
		tmp = x + a
	elif t <= 2.6e+16:
		tmp = (b * y) + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -4.4e+31)
		tmp = t_1;
	elseif (t <= -1.8e-99)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (t <= 7e-237)
		tmp = Float64(x + a);
	elseif (t <= 2.6e+16)
		tmp = Float64(Float64(b * y) + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	tmp = 0.0;
	if (t <= -4.4e+31)
		tmp = t_1;
	elseif (t <= -1.8e-99)
		tmp = (1.0 - y) * z;
	elseif (t <= 7e-237)
		tmp = x + a;
	elseif (t <= 2.6e+16)
		tmp = (b * y) + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -4.4e+31], t$95$1, If[LessEqual[t, -1.8e-99], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t, 7e-237], N[(x + a), $MachinePrecision], If[LessEqual[t, 2.6e+16], N[(N[(b * y), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.4000000000000002e31 or 2.6e16 < t

   1. Initial program 91.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 63.4%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   if -4.4000000000000002e31 < t < -1.8e-99

   1. Initial program 96.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 54.8%

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

   if -1.8e-99 < t < 6.99999999999999966e-237

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in z around 0

      \[\leadsto a + \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 65.3%

      \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + \color{blue}{a} \]

   9. Taylor expanded in x around inf

      \[\leadsto x + a \]
   10. Step-by-step derivation

   11. Applied rewrites 42.9%

       \[\leadsto x + a \]

   if 6.99999999999999966e-237 < t < 2.6e16

   1. Initial program 98.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 98.4%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in z around 0

      \[\leadsto a + \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 74.9%

      \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + \color{blue}{a} \]

   9. Taylor expanded in y around inf

      \[\leadsto b \cdot y + a \]
   10. Step-by-step derivation

   11. Applied rewrites 48.7%

       \[\leadsto b \cdot y + a \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 11: 31.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+41}:\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-175}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-132}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-35}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.75e+41)
   (* (- y) z)
   (if (<= y 1.15e-175)
     (+ x a)
     (if (<= y 9e-132) (* b t) (if (<= y 1.9e-35) z (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.75e+41) {
		tmp = -y * z;
	} else if (y <= 1.15e-175) {
		tmp = x + a;
	} else if (y <= 9e-132) {
		tmp = b * t;
	} else if (y <= 1.9e-35) {
		tmp = z;
	} else {
		tmp = y * b;
	}
	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, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.75d+41)) then
        tmp = -y * z
    else if (y <= 1.15d-175) then
        tmp = x + a
    else if (y <= 9d-132) then
        tmp = b * t
    else if (y <= 1.9d-35) then
        tmp = z
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.75e+41) {
		tmp = -y * z;
	} else if (y <= 1.15e-175) {
		tmp = x + a;
	} else if (y <= 9e-132) {
		tmp = b * t;
	} else if (y <= 1.9e-35) {
		tmp = z;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.75e+41:
		tmp = -y * z
	elif y <= 1.15e-175:
		tmp = x + a
	elif y <= 9e-132:
		tmp = b * t
	elif y <= 1.9e-35:
		tmp = z
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.75e+41)
		tmp = Float64(Float64(-y) * z);
	elseif (y <= 1.15e-175)
		tmp = Float64(x + a);
	elseif (y <= 9e-132)
		tmp = Float64(b * t);
	elseif (y <= 1.9e-35)
		tmp = z;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.75e+41)
		tmp = -y * z;
	elseif (y <= 1.15e-175)
		tmp = x + a;
	elseif (y <= 9e-132)
		tmp = b * t;
	elseif (y <= 1.9e-35)
		tmp = z;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.75e+41], N[((-y) * z), $MachinePrecision], If[LessEqual[y, 1.15e-175], N[(x + a), $MachinePrecision], If[LessEqual[y, 9e-132], N[(b * t), $MachinePrecision], If[LessEqual[y, 1.9e-35], z, N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.7500000000000002e41

   1. Initial program 98.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 45.7%

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

   6. Taylor expanded in y around inf

      \[\leadsto \left(-1 \cdot y\right) \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 45.7%

      \[\leadsto \left(-y\right) \cdot z \]

   if -2.7500000000000002e41 < y < 1.15e-175

   1. Initial program 98.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 99.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in z around 0

      \[\leadsto a + \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 81.7%

      \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + \color{blue}{a} \]

   9. Taylor expanded in x around inf

      \[\leadsto x + a \]
   10. Step-by-step derivation

   11. Applied rewrites 38.5%

       \[\leadsto x + a \]

   if 1.15e-175 < y < 8.9999999999999999e-132

   1. Initial program 87.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 62.7%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   6. Taylor expanded in a around 0

      \[\leadsto b \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 62.8%

      \[\leadsto b \cdot t \]

   if 8.9999999999999999e-132 < y < 1.9000000000000001e-35

   1. Initial program 95.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 46.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto z \]
   7. Step-by-step derivation

   8. Applied rewrites 46.0%

      \[\leadsto z \]

   if 1.9000000000000001e-35 < y

   1. Initial program 90.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 90.3%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 49.0%

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

   9. Taylor expanded in y around inf

      \[\leadsto y \cdot b \]
   10. Step-by-step derivation

   11. Applied rewrites 35.7%

       \[\leadsto y \cdot b \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 12: 61.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.8 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -26500000:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x\right) + a\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+27}:\\ \;\;\;\;x - \left(y - 1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -1.8e+174)
     t_1
     (if (<= b -26500000.0)
       (+ (fma (- y 2.0) b x) a)
       (if (<= b 6.6e+27) (- x (* (- y 1.0) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -1.8e+174) {
		tmp = t_1;
	} else if (b <= -26500000.0) {
		tmp = fma((y - 2.0), b, x) + a;
	} else if (b <= 6.6e+27) {
		tmp = x - ((y - 1.0) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -1.8e+174)
		tmp = t_1;
	elseif (b <= -26500000.0)
		tmp = Float64(fma(Float64(y - 2.0), b, x) + a);
	elseif (b <= 6.6e+27)
		tmp = Float64(x - Float64(Float64(y - 1.0) * z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.8e+174], t$95$1, If[LessEqual[b, -26500000.0], N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[b, 6.6e+27], N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.8000000000000001e174 or 6.5999999999999996e27 < b

   1. Initial program 94.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 82.2%

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

   if -1.8000000000000001e174 < b < -2.65e7

   1. Initial program 85.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 92.8%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in z around 0

      \[\leadsto a + \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 86.2%

      \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + \color{blue}{a} \]

   9. Taylor expanded in t around 0

      \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) + a \]
   10. Step-by-step derivation

   11. Applied rewrites 51.3%

       \[\leadsto \mathsf{fma}\left(y - 2, b, x\right) + a \]

   if -2.65e7 < b < 6.5999999999999996e27

   1. Initial program 99.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 99.2%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 66.8%

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

Alternative 13: 61.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -4 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-13}:\\ \;\;\;\;\left(x + a\right) - z \cdot y\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+27}:\\ \;\;\;\;x - \left(y - 1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -4e+107)
     t_1
     (if (<= b -3e-13)
       (- (+ x a) (* z y))
       (if (<= b 6.6e+27) (- x (* (- y 1.0) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -4e+107) {
		tmp = t_1;
	} else if (b <= -3e-13) {
		tmp = (x + a) - (z * y);
	} else if (b <= 6.6e+27) {
		tmp = x - ((y - 1.0) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t + y) - 2.0d0) * b
    if (b <= (-4d+107)) then
        tmp = t_1
    else if (b <= (-3d-13)) then
        tmp = (x + a) - (z * y)
    else if (b <= 6.6d+27) then
        tmp = x - ((y - 1.0d0) * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -4e+107) {
		tmp = t_1;
	} else if (b <= -3e-13) {
		tmp = (x + a) - (z * y);
	} else if (b <= 6.6e+27) {
		tmp = x - ((y - 1.0) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t + y) - 2.0) * b
	tmp = 0
	if b <= -4e+107:
		tmp = t_1
	elif b <= -3e-13:
		tmp = (x + a) - (z * y)
	elif b <= 6.6e+27:
		tmp = x - ((y - 1.0) * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -4e+107)
		tmp = t_1;
	elseif (b <= -3e-13)
		tmp = Float64(Float64(x + a) - Float64(z * y));
	elseif (b <= 6.6e+27)
		tmp = Float64(x - Float64(Float64(y - 1.0) * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t + y) - 2.0) * b;
	tmp = 0.0;
	if (b <= -4e+107)
		tmp = t_1;
	elseif (b <= -3e-13)
		tmp = (x + a) - (z * y);
	elseif (b <= 6.6e+27)
		tmp = x - ((y - 1.0) * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -4e+107], t$95$1, If[LessEqual[b, -3e-13], N[(N[(x + a), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.6e+27], N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.9999999999999999e107 or 6.5999999999999996e27 < b

   1. Initial program 91.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 77.0%

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

   if -3.9999999999999999e107 < b < -2.99999999999999984e-13

   1. Initial program 89.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 93.1%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 56.9%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 52.7%

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

   if -2.99999999999999984e-13 < b < 6.5999999999999996e27

   1. Initial program 99.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 99.2%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 66.1%

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

Alternative 14: 61.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -8.7 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{+39}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+27}:\\ \;\;\;\;x - \left(y - 1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -8.7e+83)
     t_1
     (if (<= b -4.5e+39)
       (* (- 1.0 t) a)
       (if (<= b 6.6e+27) (- x (* (- y 1.0) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -8.7e+83) {
		tmp = t_1;
	} else if (b <= -4.5e+39) {
		tmp = (1.0 - t) * a;
	} else if (b <= 6.6e+27) {
		tmp = x - ((y - 1.0) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t + y) - 2.0d0) * b
    if (b <= (-8.7d+83)) then
        tmp = t_1
    else if (b <= (-4.5d+39)) then
        tmp = (1.0d0 - t) * a
    else if (b <= 6.6d+27) then
        tmp = x - ((y - 1.0d0) * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -8.7e+83) {
		tmp = t_1;
	} else if (b <= -4.5e+39) {
		tmp = (1.0 - t) * a;
	} else if (b <= 6.6e+27) {
		tmp = x - ((y - 1.0) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t + y) - 2.0) * b
	tmp = 0
	if b <= -8.7e+83:
		tmp = t_1
	elif b <= -4.5e+39:
		tmp = (1.0 - t) * a
	elif b <= 6.6e+27:
		tmp = x - ((y - 1.0) * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -8.7e+83)
		tmp = t_1;
	elseif (b <= -4.5e+39)
		tmp = Float64(Float64(1.0 - t) * a);
	elseif (b <= 6.6e+27)
		tmp = Float64(x - Float64(Float64(y - 1.0) * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t + y) - 2.0) * b;
	tmp = 0.0;
	if (b <= -8.7e+83)
		tmp = t_1;
	elseif (b <= -4.5e+39)
		tmp = (1.0 - t) * a;
	elseif (b <= 6.6e+27)
		tmp = x - ((y - 1.0) * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -8.7e+83], t$95$1, If[LessEqual[b, -4.5e+39], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[b, 6.6e+27], N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.7000000000000005e83 or 6.5999999999999996e27 < b

   1. Initial program 90.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 73.3%

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

   if -8.7000000000000005e83 < b < -4.49999999999999996e39

   1. Initial program 90.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 68.1%

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

   if -4.49999999999999996e39 < b < 6.5999999999999996e27

   1. Initial program 99.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 99.3%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 65.2%

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

Alternative 15: 36.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+206}:\\ \;\;\;\;\left(-a\right) \cdot t\\ \mathbf{elif}\;t \leq -160000000 \lor \neg \left(t \leq 2.4 \cdot 10^{+102}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;b \cdot y + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1e+206)
   (* (- a) t)
   (if (or (<= t -160000000.0) (not (<= t 2.4e+102))) (* b t) (+ (* b y) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1e+206) {
		tmp = -a * t;
	} else if ((t <= -160000000.0) || !(t <= 2.4e+102)) {
		tmp = b * t;
	} else {
		tmp = (b * y) + a;
	}
	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, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1d+206)) then
        tmp = -a * t
    else if ((t <= (-160000000.0d0)) .or. (.not. (t <= 2.4d+102))) then
        tmp = b * t
    else
        tmp = (b * y) + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1e+206) {
		tmp = -a * t;
	} else if ((t <= -160000000.0) || !(t <= 2.4e+102)) {
		tmp = b * t;
	} else {
		tmp = (b * y) + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1e+206:
		tmp = -a * t
	elif (t <= -160000000.0) or not (t <= 2.4e+102):
		tmp = b * t
	else:
		tmp = (b * y) + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1e+206)
		tmp = Float64(Float64(-a) * t);
	elseif ((t <= -160000000.0) || !(t <= 2.4e+102))
		tmp = Float64(b * t);
	else
		tmp = Float64(Float64(b * y) + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1e+206)
		tmp = -a * t;
	elseif ((t <= -160000000.0) || ~((t <= 2.4e+102)))
		tmp = b * t;
	else
		tmp = (b * y) + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1e+206], N[((-a) * t), $MachinePrecision], If[Or[LessEqual[t, -160000000.0], N[Not[LessEqual[t, 2.4e+102]], $MachinePrecision]], N[(b * t), $MachinePrecision], N[(N[(b * y), $MachinePrecision] + a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1e206

   1. Initial program 84.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 88.2%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   6. Taylor expanded in a around inf

      \[\leadsto \left(-1 \cdot a\right) \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 53.1%

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

   if -1e206 < t < -1.6e8 or 2.39999999999999994e102 < t

   1. Initial program 94.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 56.6%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   6. Taylor expanded in a around 0

      \[\leadsto b \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 39.6%

      \[\leadsto b \cdot t \]

   if -1.6e8 < t < 2.39999999999999994e102

   1. Initial program 97.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 98.6%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in z around 0

      \[\leadsto a + \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 70.8%

      \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + \color{blue}{a} \]

   9. Taylor expanded in y around inf

      \[\leadsto b \cdot y + a \]
   10. Step-by-step derivation

   11. Applied rewrites 38.8%

       \[\leadsto b \cdot y + a \]
3. Recombined 3 regimes into one program.

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+206}:\\ \;\;\;\;\left(-a\right) \cdot t\\ \mathbf{elif}\;t \leq -160000000 \lor \neg \left(t \leq 2.4 \cdot 10^{+102}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;b \cdot y + a\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 71.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+107} \lor \neg \left(b \leq 3.3 \cdot 10^{+22}\right):\\ \;\;\;\;z + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) - \left(y - 1\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4e+107) (not (<= b 3.3e+22)))
   (+ z (* (- (+ y t) 2.0) b))
   (- (+ x a) (* (- y 1.0) z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4e+107) || !(b <= 3.3e+22)) {
		tmp = z + (((y + t) - 2.0) * b);
	} else {
		tmp = (x + a) - ((y - 1.0) * z);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-4d+107)) .or. (.not. (b <= 3.3d+22))) then
        tmp = z + (((y + t) - 2.0d0) * b)
    else
        tmp = (x + a) - ((y - 1.0d0) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4e+107) || !(b <= 3.3e+22)) {
		tmp = z + (((y + t) - 2.0) * b);
	} else {
		tmp = (x + a) - ((y - 1.0) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4e+107) or not (b <= 3.3e+22):
		tmp = z + (((y + t) - 2.0) * b)
	else:
		tmp = (x + a) - ((y - 1.0) * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4e+107) || !(b <= 3.3e+22))
		tmp = Float64(z + Float64(Float64(Float64(y + t) - 2.0) * b));
	else
		tmp = Float64(Float64(x + a) - Float64(Float64(y - 1.0) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4e+107) || ~((b <= 3.3e+22)))
		tmp = z + (((y + t) - 2.0) * b);
	else
		tmp = (x + a) - ((y - 1.0) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4e+107], N[Not[LessEqual[b, 3.3e+22]], $MachinePrecision]], N[(z + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(N[(x + a), $MachinePrecision] - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.9999999999999999e107 or 3.2999999999999998e22 < b

   1. Initial program 92.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 81.2%

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

   6. Taylor expanded in y around 0

      \[\leadsto z + \left(\left(y + t\right) - 2\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 82.2%

      \[\leadsto z + \left(\left(y + t\right) - 2\right) \cdot b \]

   if -3.9999999999999999e107 < b < 3.2999999999999998e22

   1. Initial program 97.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 98.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 71.6%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+107} \lor \neg \left(b \leq 3.3 \cdot 10^{+22}\right):\\ \;\;\;\;z + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) - \left(y - 1\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 71.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+107} \lor \neg \left(b \leq 66000\right):\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) - \left(y - 1\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4e+107) (not (<= b 66000.0)))
   (+ x (* (- (+ y t) 2.0) b))
   (- (+ x a) (* (- y 1.0) z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4e+107) || !(b <= 66000.0)) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = (x + a) - ((y - 1.0) * z);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-4d+107)) .or. (.not. (b <= 66000.0d0))) then
        tmp = x + (((y + t) - 2.0d0) * b)
    else
        tmp = (x + a) - ((y - 1.0d0) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4e+107) || !(b <= 66000.0)) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = (x + a) - ((y - 1.0) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4e+107) or not (b <= 66000.0):
		tmp = x + (((y + t) - 2.0) * b)
	else:
		tmp = (x + a) - ((y - 1.0) * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4e+107) || !(b <= 66000.0))
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	else
		tmp = Float64(Float64(x + a) - Float64(Float64(y - 1.0) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4e+107) || ~((b <= 66000.0)))
		tmp = x + (((y + t) - 2.0) * b);
	else
		tmp = (x + a) - ((y - 1.0) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4e+107], N[Not[LessEqual[b, 66000.0]], $MachinePrecision]], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(N[(x + a), $MachinePrecision] - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.9999999999999999e107 or 66000 < b

   1. Initial program 92.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 78.8%

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

   if -3.9999999999999999e107 < b < 66000

   1. Initial program 97.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 98.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 71.8%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+107} \lor \neg \left(b \leq 66000\right):\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) - \left(y - 1\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 68.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+134} \lor \neg \left(b \leq 3.3 \cdot 10^{+22}\right):\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) - \left(y - 1\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.5e+134) (not (<= b 3.3e+22)))
   (* (- (+ t y) 2.0) b)
   (- (+ x a) (* (- y 1.0) z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.5e+134) || !(b <= 3.3e+22)) {
		tmp = ((t + y) - 2.0) * b;
	} else {
		tmp = (x + a) - ((y - 1.0) * z);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-6.5d+134)) .or. (.not. (b <= 3.3d+22))) then
        tmp = ((t + y) - 2.0d0) * b
    else
        tmp = (x + a) - ((y - 1.0d0) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.5e+134) || !(b <= 3.3e+22)) {
		tmp = ((t + y) - 2.0) * b;
	} else {
		tmp = (x + a) - ((y - 1.0) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6.5e+134) or not (b <= 3.3e+22):
		tmp = ((t + y) - 2.0) * b
	else:
		tmp = (x + a) - ((y - 1.0) * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6.5e+134) || !(b <= 3.3e+22))
		tmp = Float64(Float64(Float64(t + y) - 2.0) * b);
	else
		tmp = Float64(Float64(x + a) - Float64(Float64(y - 1.0) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -6.5e+134) || ~((b <= 3.3e+22)))
		tmp = ((t + y) - 2.0) * b;
	else
		tmp = (x + a) - ((y - 1.0) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6.5e+134], N[Not[LessEqual[b, 3.3e+22]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], N[(N[(x + a), $MachinePrecision] - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.5e134 or 3.2999999999999998e22 < b

   1. Initial program 92.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 77.3%

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

   if -6.5e134 < b < 3.2999999999999998e22

   1. Initial program 96.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 70.9%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+134} \lor \neg \left(b \leq 3.3 \cdot 10^{+22}\right):\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) - \left(y - 1\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 55.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -2.75 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-68}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+67}:\\ \;\;\;\;\left(x + a\right) - \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -2.75e+41)
     t_1
     (if (<= y -6.5e-68)
       (* (- b a) t)
       (if (<= y 6.2e+67) (- (+ x a) (- z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -2.75e+41) {
		tmp = t_1;
	} else if (y <= -6.5e-68) {
		tmp = (b - a) * t;
	} else if (y <= 6.2e+67) {
		tmp = (x + a) - -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - z) * y
    if (y <= (-2.75d+41)) then
        tmp = t_1
    else if (y <= (-6.5d-68)) then
        tmp = (b - a) * t
    else if (y <= 6.2d+67) then
        tmp = (x + a) - -z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -2.75e+41) {
		tmp = t_1;
	} else if (y <= -6.5e-68) {
		tmp = (b - a) * t;
	} else if (y <= 6.2e+67) {
		tmp = (x + a) - -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - z) * y
	tmp = 0
	if y <= -2.75e+41:
		tmp = t_1
	elif y <= -6.5e-68:
		tmp = (b - a) * t
	elif y <= 6.2e+67:
		tmp = (x + a) - -z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -2.75e+41)
		tmp = t_1;
	elseif (y <= -6.5e-68)
		tmp = Float64(Float64(b - a) * t);
	elseif (y <= 6.2e+67)
		tmp = Float64(Float64(x + a) - Float64(-z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - z) * y;
	tmp = 0.0;
	if (y <= -2.75e+41)
		tmp = t_1;
	elseif (y <= -6.5e-68)
		tmp = (b - a) * t;
	elseif (y <= 6.2e+67)
		tmp = (x + a) - -z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -2.75e+41], t$95$1, If[LessEqual[y, -6.5e-68], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 6.2e+67], N[(N[(x + a), $MachinePrecision] - (-z)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7500000000000002e41 or 6.19999999999999992e67 < y

   1. Initial program 93.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 71.9%

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

   if -2.7500000000000002e41 < y < -6.4999999999999997e-68

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 62.8%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   if -6.4999999999999997e-68 < y < 6.19999999999999992e67

   1. Initial program 96.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 54.7%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 53.2%

       \[\leadsto \left(x + a\right) - \left(-z\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 20: 50.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -160000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-174}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+16}:\\ \;\;\;\;b \cdot y + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -160000000.0)
     t_1
     (if (<= t 3e-174) (* (- b z) y) (if (<= t 2.6e+16) (+ (* b y) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -160000000.0) {
		tmp = t_1;
	} else if (t <= 3e-174) {
		tmp = (b - z) * y;
	} else if (t <= 2.6e+16) {
		tmp = (b * y) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - a) * t
    if (t <= (-160000000.0d0)) then
        tmp = t_1
    else if (t <= 3d-174) then
        tmp = (b - z) * y
    else if (t <= 2.6d+16) then
        tmp = (b * y) + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -160000000.0) {
		tmp = t_1;
	} else if (t <= 3e-174) {
		tmp = (b - z) * y;
	} else if (t <= 2.6e+16) {
		tmp = (b * y) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -160000000.0:
		tmp = t_1
	elif t <= 3e-174:
		tmp = (b - z) * y
	elif t <= 2.6e+16:
		tmp = (b * y) + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -160000000.0)
		tmp = t_1;
	elseif (t <= 3e-174)
		tmp = Float64(Float64(b - z) * y);
	elseif (t <= 2.6e+16)
		tmp = Float64(Float64(b * y) + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	tmp = 0.0;
	if (t <= -160000000.0)
		tmp = t_1;
	elseif (t <= 3e-174)
		tmp = (b - z) * y;
	elseif (t <= 2.6e+16)
		tmp = (b * y) + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -160000000.0], t$95$1, If[LessEqual[t, 3e-174], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 2.6e+16], N[(N[(b * y), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6e8 or 2.6e16 < t

   1. Initial program 92.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 62.0%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   if -1.6e8 < t < 3.00000000000000021e-174

   1. Initial program 97.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 45.3%

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

   if 3.00000000000000021e-174 < t < 2.6e16

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in z around 0

      \[\leadsto a + \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 78.7%

      \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + \color{blue}{a} \]

   9. Taylor expanded in y around inf

      \[\leadsto b \cdot y + a \]
   10. Step-by-step derivation

   11. Applied rewrites 48.1%

       \[\leadsto b \cdot y + a \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 41.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-227}:\\ \;\;\;\;b \cdot y + a\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+119}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 y) z)))
   (if (<= z -9.5e+79)
     t_1
     (if (<= z 6.6e-227) (+ (* b y) a) (if (<= z 2.7e+119) (+ x a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double tmp;
	if (z <= -9.5e+79) {
		tmp = t_1;
	} else if (z <= 6.6e-227) {
		tmp = (b * y) + a;
	} else if (z <= 2.7e+119) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (1.0d0 - y) * z
    if (z <= (-9.5d+79)) then
        tmp = t_1
    else if (z <= 6.6d-227) then
        tmp = (b * y) + a
    else if (z <= 2.7d+119) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double tmp;
	if (z <= -9.5e+79) {
		tmp = t_1;
	} else if (z <= 6.6e-227) {
		tmp = (b * y) + a;
	} else if (z <= 2.7e+119) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 - y) * z
	tmp = 0
	if z <= -9.5e+79:
		tmp = t_1
	elif z <= 6.6e-227:
		tmp = (b * y) + a
	elif z <= 2.7e+119:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (z <= -9.5e+79)
		tmp = t_1;
	elseif (z <= 6.6e-227)
		tmp = Float64(Float64(b * y) + a);
	elseif (z <= 2.7e+119)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 - y) * z;
	tmp = 0.0;
	if (z <= -9.5e+79)
		tmp = t_1;
	elseif (z <= 6.6e-227)
		tmp = (b * y) + a;
	elseif (z <= 2.7e+119)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -9.5e+79], t$95$1, If[LessEqual[z, 6.6e-227], N[(N[(b * y), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[z, 2.7e+119], N[(x + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.49999999999999994e79 or 2.6999999999999998e119 < z

   1. Initial program 90.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 61.5%

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

   if -9.49999999999999994e79 < z < 6.5999999999999999e-227

   1. Initial program 97.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in z around 0

      \[\leadsto a + \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 92.7%

      \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + \color{blue}{a} \]

   9. Taylor expanded in y around inf

      \[\leadsto b \cdot y + a \]
   10. Step-by-step derivation

   11. Applied rewrites 42.5%

       \[\leadsto b \cdot y + a \]

   if 6.5999999999999999e-227 < z < 2.6999999999999998e119

   1. Initial program 97.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 97.4%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in z around 0

      \[\leadsto a + \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 84.0%

      \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + \color{blue}{a} \]

   9. Taylor expanded in x around inf

      \[\leadsto x + a \]
   10. Step-by-step derivation

   11. Applied rewrites 39.9%

       \[\leadsto x + a \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 22: 36.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.95 \cdot 10^{+58}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+42}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+102}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.95e+58)
   (* b t)
   (if (<= t 2.5e+42) (+ x a) (if (<= t 2.4e+102) (* y b) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.95e+58) {
		tmp = b * t;
	} else if (t <= 2.5e+42) {
		tmp = x + a;
	} else if (t <= 2.4e+102) {
		tmp = y * b;
	} else {
		tmp = b * 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, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.95d+58)) then
        tmp = b * t
    else if (t <= 2.5d+42) then
        tmp = x + a
    else if (t <= 2.4d+102) then
        tmp = y * b
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.95e+58) {
		tmp = b * t;
	} else if (t <= 2.5e+42) {
		tmp = x + a;
	} else if (t <= 2.4e+102) {
		tmp = y * b;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.95e+58:
		tmp = b * t
	elif t <= 2.5e+42:
		tmp = x + a
	elif t <= 2.4e+102:
		tmp = y * b
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.95e+58)
		tmp = Float64(b * t);
	elseif (t <= 2.5e+42)
		tmp = Float64(x + a);
	elseif (t <= 2.4e+102)
		tmp = Float64(y * b);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.95e+58)
		tmp = b * t;
	elseif (t <= 2.5e+42)
		tmp = x + a;
	elseif (t <= 2.4e+102)
		tmp = y * b;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.95e+58], N[(b * t), $MachinePrecision], If[LessEqual[t, 2.5e+42], N[(x + a), $MachinePrecision], If[LessEqual[t, 2.4e+102], N[(y * b), $MachinePrecision], N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.95000000000000002e58 or 2.39999999999999994e102 < t

   1. Initial program 90.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 66.6%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   6. Taylor expanded in a around 0

      \[\leadsto b \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 41.3%

      \[\leadsto b \cdot t \]

   if -4.95000000000000002e58 < t < 2.50000000000000003e42

   1. Initial program 98.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 98.6%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in z around 0

      \[\leadsto a + \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 69.4%

      \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + \color{blue}{a} \]

   9. Taylor expanded in x around inf

      \[\leadsto x + a \]
   10. Step-by-step derivation

   11. Applied rewrites 36.5%

       \[\leadsto x + a \]

   if 2.50000000000000003e42 < t < 2.39999999999999994e102

   1. Initial program 92.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 45.0%

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

   9. Taylor expanded in y around inf

      \[\leadsto y \cdot b \]
   10. Step-by-step derivation

   11. Applied rewrites 38.0%

       \[\leadsto y \cdot b \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 23: 36.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.95 \cdot 10^{+58} \lor \neg \left(t \leq 1.6 \cdot 10^{+42}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.95e+58) (not (<= t 1.6e+42))) (* b t) (+ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.95e+58) || !(t <= 1.6e+42)) {
		tmp = b * t;
	} else {
		tmp = x + a;
	}
	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, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-4.95d+58)) .or. (.not. (t <= 1.6d+42))) then
        tmp = b * t
    else
        tmp = x + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.95e+58) || !(t <= 1.6e+42)) {
		tmp = b * t;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.95e+58) or not (t <= 1.6e+42):
		tmp = b * t
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.95e+58) || !(t <= 1.6e+42))
		tmp = Float64(b * t);
	else
		tmp = Float64(x + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4.95e+58) || ~((t <= 1.6e+42)))
		tmp = b * t;
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.95e+58], N[Not[LessEqual[t, 1.6e+42]], $MachinePrecision]], N[(b * t), $MachinePrecision], N[(x + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.95000000000000002e58 or 1.60000000000000001e42 < t

   1. Initial program 91.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 64.7%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   6. Taylor expanded in a around 0

      \[\leadsto b \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 37.2%

      \[\leadsto b \cdot t \]

   if -4.95000000000000002e58 < t < 1.60000000000000001e42

   1. Initial program 98.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 98.6%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in z around 0

      \[\leadsto a + \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 69.4%

      \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + \color{blue}{a} \]

   9. Taylor expanded in x around inf

      \[\leadsto x + a \]
   10. Step-by-step derivation

   11. Applied rewrites 36.5%

       \[\leadsto x + a \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.95 \cdot 10^{+58} \lor \neg \left(t \leq 1.6 \cdot 10^{+42}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 30.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+159} \lor \neg \left(z \leq 1.55 \cdot 10^{+121}\right):\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7.8e+159) (not (<= z 1.55e+121))) z (+ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.8e+159) || !(z <= 1.55e+121)) {
		tmp = z;
	} else {
		tmp = x + a;
	}
	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, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-7.8d+159)) .or. (.not. (z <= 1.55d+121))) then
        tmp = z
    else
        tmp = x + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.8e+159) || !(z <= 1.55e+121)) {
		tmp = z;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7.8e+159) or not (z <= 1.55e+121):
		tmp = z
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7.8e+159) || !(z <= 1.55e+121))
		tmp = z;
	else
		tmp = Float64(x + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7.8e+159) || ~((z <= 1.55e+121)))
		tmp = z;
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7.8e+159], N[Not[LessEqual[z, 1.55e+121]], $MachinePrecision]], z, N[(x + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.8000000000000001e159 or 1.55000000000000004e121 < z

   1. Initial program 90.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 66.5%

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

   6. Taylor expanded in y around 0

      \[\leadsto z \]
   7. Step-by-step derivation

   8. Applied rewrites 31.0%

      \[\leadsto z \]

   if -7.8000000000000001e159 < z < 1.55000000000000004e121

   1. Initial program 97.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 97.8%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\right) - \left(y - 1\right) \cdot z} \]

   6. Taylor expanded in z around 0

      \[\leadsto a + \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 86.7%

      \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + \color{blue}{a} \]

   9. Taylor expanded in x around inf

      \[\leadsto x + a \]
   10. Step-by-step derivation

   11. Applied rewrites 31.9%

       \[\leadsto x + a \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+159} \lor \neg \left(z \leq 1.55 \cdot 10^{+121}\right):\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 20.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-21}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+121}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.5e-21) z (if (<= z 1.3e+121) x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.5e-21) {
		tmp = z;
	} else if (z <= 1.3e+121) {
		tmp = x;
	} else {
		tmp = 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, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-4.5d-21)) then
        tmp = z
    else if (z <= 1.3d+121) then
        tmp = x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.5e-21) {
		tmp = z;
	} else if (z <= 1.3e+121) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.5e-21:
		tmp = z
	elif z <= 1.3e+121:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.5e-21)
		tmp = z;
	elseif (z <= 1.3e+121)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4.5e-21)
		tmp = z;
	elseif (z <= 1.3e+121)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.5e-21], z, If[LessEqual[z, 1.3e+121], x, z]]

Derivation

1. Split input into 2 regimes

2. if z < -4.49999999999999968e-21 or 1.2999999999999999e121 < z

   1. Initial program 92.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 53.4%

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

   6. Taylor expanded in y around 0

      \[\leadsto z \]
   7. Step-by-step derivation

   8. Applied rewrites 22.6%

      \[\leadsto z \]

   if -4.49999999999999968e-21 < z < 1.2999999999999999e121

   1. Initial program 97.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 24.5%

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

Alternative 26: 16.0% accurate, 37.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

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, a, b)
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), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 95.3%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in x around inf

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

5. Applied rewrites 16.2%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2025019 
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))