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

Percentage Accurate: 95.3% → 97.7%

Time: 12.0s

Alternatives: 21

Speedup: 1.1×

• 35.7% 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: 95.3% 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: 97.7% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.3%

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

3. Applied rewrites 97.7%

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

Alternative 2: 87.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.000108:\\ \;\;\;\;a + \left(x + \mathsf{fma}\left(b, y - 2, z \cdot \left(1 - y\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+67}:\\ \;\;\;\;x + \left(z + \mathsf{fma}\left(a, 1 - t, b \cdot \left(t - 2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - \left(2 - t\right), b, \mathsf{fma}\left(1 - y, z, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -0.000108)
   (+ a (+ x (fma b (- y 2.0) (* z (- 1.0 y)))))
   (if (<= y 1.3e+67)
     (+ x (+ z (fma a (- 1.0 t) (* b (- t 2.0)))))
     (fma (- y (- 2.0 t)) b (fma (- 1.0 y) z x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -0.000108) {
		tmp = a + (x + fma(b, (y - 2.0), (z * (1.0 - y))));
	} else if (y <= 1.3e+67) {
		tmp = x + (z + fma(a, (1.0 - t), (b * (t - 2.0))));
	} else {
		tmp = fma((y - (2.0 - t)), b, fma((1.0 - y), z, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -0.000108)
		tmp = Float64(a + Float64(x + fma(b, Float64(y - 2.0), Float64(z * Float64(1.0 - y)))));
	elseif (y <= 1.3e+67)
		tmp = Float64(x + Float64(z + fma(a, Float64(1.0 - t), Float64(b * Float64(t - 2.0)))));
	else
		tmp = fma(Float64(y - Float64(2.0 - t)), b, fma(Float64(1.0 - y), z, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -0.000108], N[(a + N[(x + N[(b * N[(y - 2.0), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+67], N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision] + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - N[(2.0 - t), $MachinePrecision]), $MachinePrecision] * b + N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.08e-4

   1. Initial program 95.3%

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

   3. Applied rewrites 97.7%

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

   4. Taylor expanded in t around 0

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

   6. Applied rewrites 70.9%

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

   if -1.08e-4 < y < 1.3e67

   1. Initial program 95.3%

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

   3. Applied rewrites 97.7%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 70.4%

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

   if 1.3e67 < y

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 73.9%

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

Alternative 3: 87.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+20}:\\ \;\;\;\;z + \mathsf{fma}\left(a, 1 - t, b \cdot \left(t - 2\right)\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+56}:\\ \;\;\;\;a + \left(x + \mathsf{fma}\left(b, y - 2, z \cdot \left(1 - y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.4e+20)
   (+ z (fma a (- 1.0 t) (* b (- t 2.0))))
   (if (<= t 6.5e+56)
     (+ a (+ x (fma b (- y 2.0) (* z (- 1.0 y)))))
     (* t (- b a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.4e+20) {
		tmp = z + fma(a, (1.0 - t), (b * (t - 2.0)));
	} else if (t <= 6.5e+56) {
		tmp = a + (x + fma(b, (y - 2.0), (z * (1.0 - y))));
	} else {
		tmp = t * (b - a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.4e+20)
		tmp = Float64(z + fma(a, Float64(1.0 - t), Float64(b * Float64(t - 2.0))));
	elseif (t <= 6.5e+56)
		tmp = Float64(a + Float64(x + fma(b, Float64(y - 2.0), Float64(z * Float64(1.0 - y)))));
	else
		tmp = Float64(t * Float64(b - a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.4e+20], N[(z + N[(a * N[(1.0 - t), $MachinePrecision] + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e+56], N[(a + N[(x + N[(b * N[(y - 2.0), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.4e20

   1. Initial program 95.3%

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

   3. Applied rewrites 97.7%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 70.4%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 56.3%

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

   if -3.4e20 < t < 6.5000000000000001e56

   1. Initial program 95.3%

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

   3. Applied rewrites 97.7%

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

   4. Taylor expanded in t around 0

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

   6. Applied rewrites 70.9%

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

   if 6.5000000000000001e56 < t

   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. Taylor expanded in t around inf

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

   4. Applied rewrites 32.3%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 86.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \mathsf{fma}\left(a, t - 1, z \cdot \left(y - 1\right)\right)\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+107}:\\ \;\;\;\;\mathsf{fma}\left(y - \left(2 - t\right), b, x\right) - \left(z \cdot y - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (fma a (- t 1.0) (* z (- y 1.0))))))
   (if (<= a -1.8e+77)
     t_1
     (if (<= a 2.2e+107) (- (fma (- y (- 2.0 t)) b x) (- (* z y) z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - fma(a, (t - 1.0), (z * (y - 1.0)));
	double tmp;
	if (a <= -1.8e+77) {
		tmp = t_1;
	} else if (a <= 2.2e+107) {
		tmp = fma((y - (2.0 - t)), b, x) - ((z * y) - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - fma(a, Float64(t - 1.0), Float64(z * Float64(y - 1.0))))
	tmp = 0.0
	if (a <= -1.8e+77)
		tmp = t_1;
	elseif (a <= 2.2e+107)
		tmp = Float64(fma(Float64(y - Float64(2.0 - t)), b, x) - Float64(Float64(z * y) - z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(a * N[(t - 1.0), $MachinePrecision] + N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e+77], t$95$1, If[LessEqual[a, 2.2e+107], N[(N[(N[(y - N[(2.0 - t), $MachinePrecision]), $MachinePrecision] * b + x), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.7999999999999999e77 or 2.2e107 < a

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 73.9%

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

   7. Taylor expanded in b around 0

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

   9. Applied rewrites 68.2%

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

   if -1.7999999999999999e77 < a < 2.2e107

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 72.9%

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

Alternative 5: 84.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \mathsf{fma}\left(a, t - 1, z \cdot \left(y - 1\right)\right)\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+107}:\\ \;\;\;\;\mathsf{fma}\left(y - \left(2 - t\right), b, \mathsf{fma}\left(1 - y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (fma a (- t 1.0) (* z (- y 1.0))))))
   (if (<= a -4.8e+100)
     t_1
     (if (<= a 2.25e+107) (fma (- y (- 2.0 t)) b (fma (- 1.0 y) z x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - fma(a, (t - 1.0), (z * (y - 1.0)));
	double tmp;
	if (a <= -4.8e+100) {
		tmp = t_1;
	} else if (a <= 2.25e+107) {
		tmp = fma((y - (2.0 - t)), b, fma((1.0 - y), z, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - fma(a, Float64(t - 1.0), Float64(z * Float64(y - 1.0))))
	tmp = 0.0
	if (a <= -4.8e+100)
		tmp = t_1;
	elseif (a <= 2.25e+107)
		tmp = fma(Float64(y - Float64(2.0 - t)), b, fma(Float64(1.0 - y), z, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(a * N[(t - 1.0), $MachinePrecision] + N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.8e+100], t$95$1, If[LessEqual[a, 2.25e+107], N[(N[(y - N[(2.0 - t), $MachinePrecision]), $MachinePrecision] * b + N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -4.80000000000000023e100 or 2.25e107 < a

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 73.9%

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

   7. Taylor expanded in b around 0

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

   9. Applied rewrites 68.2%

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

   if -4.80000000000000023e100 < a < 2.25e107

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 73.9%

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

Alternative 6: 84.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(y - \left(2 - t\right), b, x + z\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+115}:\\ \;\;\;\;x - \mathsf{fma}\left(a, t - 1, z \cdot \left(y - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(a \cdot t\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.1e-12)
   (fma (- y (- 2.0 t)) b (+ x z))
   (if (<= b 1.55e+115)
     (- x (fma a (- t 1.0) (* z (- y 1.0))))
     (+ (* -1.0 (* a t)) (* (- (+ y t) 2.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.1e-12) {
		tmp = fma((y - (2.0 - t)), b, (x + z));
	} else if (b <= 1.55e+115) {
		tmp = x - fma(a, (t - 1.0), (z * (y - 1.0)));
	} else {
		tmp = (-1.0 * (a * t)) + (((y + t) - 2.0) * b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.1e-12)
		tmp = fma(Float64(y - Float64(2.0 - t)), b, Float64(x + z));
	elseif (b <= 1.55e+115)
		tmp = Float64(x - fma(a, Float64(t - 1.0), Float64(z * Float64(y - 1.0))));
	else
		tmp = Float64(Float64(-1.0 * Float64(a * t)) + Float64(Float64(Float64(y + t) - 2.0) * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.1e-12], N[(N[(y - N[(2.0 - t), $MachinePrecision]), $MachinePrecision] * b + N[(x + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.55e+115], N[(x - N[(a * N[(t - 1.0), $MachinePrecision] + N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-1.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.1000000000000001e-12

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 73.9%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 60.1%

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

   if -3.1000000000000001e-12 < b < 1.55000000000000002e115

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 73.9%

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

   7. Taylor expanded in b around 0

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

   9. Applied rewrites 68.2%

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

   if 1.55000000000000002e115 < b

   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. Taylor expanded in t around inf

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

   4. Applied rewrites 50.1%

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

Alternative 7: 83.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(y - \left(2 - t\right), b, x + z\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+114}:\\ \;\;\;\;x - \mathsf{fma}\left(a, t - 1, z \cdot \left(y - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.1e-12)
   (fma (- y (- 2.0 t)) b (+ x z))
   (if (<= b 4.2e+114)
     (- x (fma a (- t 1.0) (* z (- y 1.0))))
     (+ x (* b (- (+ t y) 2.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.1e-12) {
		tmp = fma((y - (2.0 - t)), b, (x + z));
	} else if (b <= 4.2e+114) {
		tmp = x - fma(a, (t - 1.0), (z * (y - 1.0)));
	} else {
		tmp = x + (b * ((t + y) - 2.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.1e-12)
		tmp = fma(Float64(y - Float64(2.0 - t)), b, Float64(x + z));
	elseif (b <= 4.2e+114)
		tmp = Float64(x - fma(a, Float64(t - 1.0), Float64(z * Float64(y - 1.0))));
	else
		tmp = Float64(x + Float64(b * Float64(Float64(t + y) - 2.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.1e-12], N[(N[(y - N[(2.0 - t), $MachinePrecision]), $MachinePrecision] * b + N[(x + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e+114], N[(x - N[(a * N[(t - 1.0), $MachinePrecision] + N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.1000000000000001e-12

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 73.9%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 60.1%

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

   if -3.1000000000000001e-12 < b < 4.2000000000000001e114

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 73.9%

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

   7. Taylor expanded in b around 0

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

   9. Applied rewrites 68.2%

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

   if 4.2000000000000001e114 < b

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 73.9%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 46.1%

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

   10. Taylor expanded in z around 0

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

   12. Applied rewrites 50.7%

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

Alternative 8: 73.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - \left(2 - t\right), b, x + z\right)\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{-65}:\\ \;\;\;\;x - z \cdot \left(y - 1\right)\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-16}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- y (- 2.0 t)) b (+ x z))))
   (if (<= b -1.45e-14)
     t_1
     (if (<= b -8.8e-65)
       (- x (* z (- y 1.0)))
       (if (<= b 4.1e-16) (+ x (+ z (* a (- 1.0 t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((y - (2.0 - t)), b, (x + z));
	double tmp;
	if (b <= -1.45e-14) {
		tmp = t_1;
	} else if (b <= -8.8e-65) {
		tmp = x - (z * (y - 1.0));
	} else if (b <= 4.1e-16) {
		tmp = x + (z + (a * (1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(y - Float64(2.0 - t)), b, Float64(x + z))
	tmp = 0.0
	if (b <= -1.45e-14)
		tmp = t_1;
	elseif (b <= -8.8e-65)
		tmp = Float64(x - Float64(z * Float64(y - 1.0)));
	elseif (b <= 4.1e-16)
		tmp = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y - N[(2.0 - t), $MachinePrecision]), $MachinePrecision] * b + N[(x + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.45e-14], t$95$1, If[LessEqual[b, -8.8e-65], N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.1e-16], N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.4500000000000001e-14 or 4.10000000000000006e-16 < b

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 73.9%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 60.1%

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

   if -1.4500000000000001e-14 < b < -8.80000000000000084e-65

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 60.3%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 42.0%

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

   if -8.80000000000000084e-65 < b < 4.10000000000000006e-16

   1. Initial program 95.3%

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

   3. Applied rewrites 97.7%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 70.4%

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

   7. Taylor expanded in b around 0

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

   9. Applied rewrites 52.3%

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

Alternative 9: 71.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -5.1 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{-65}:\\ \;\;\;\;x - z \cdot \left(y - 1\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+55}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ t y) 2.0)))))
   (if (<= b -5.1e-14)
     t_1
     (if (<= b -8.8e-65)
       (- x (* z (- y 1.0)))
       (if (<= b 2.7e+55) (+ x (+ z (* a (- 1.0 t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((t + y) - 2.0));
	double tmp;
	if (b <= -5.1e-14) {
		tmp = t_1;
	} else if (b <= -8.8e-65) {
		tmp = x - (z * (y - 1.0));
	} else if (b <= 2.7e+55) {
		tmp = x + (z + (a * (1.0 - t)));
	} 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 = x + (b * ((t + y) - 2.0d0))
    if (b <= (-5.1d-14)) then
        tmp = t_1
    else if (b <= (-8.8d-65)) then
        tmp = x - (z * (y - 1.0d0))
    else if (b <= 2.7d+55) then
        tmp = x + (z + (a * (1.0d0 - t)))
    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 = x + (b * ((t + y) - 2.0));
	double tmp;
	if (b <= -5.1e-14) {
		tmp = t_1;
	} else if (b <= -8.8e-65) {
		tmp = x - (z * (y - 1.0));
	} else if (b <= 2.7e+55) {
		tmp = x + (z + (a * (1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((t + y) - 2.0))
	tmp = 0
	if b <= -5.1e-14:
		tmp = t_1
	elif b <= -8.8e-65:
		tmp = x - (z * (y - 1.0))
	elif b <= 2.7e+55:
		tmp = x + (z + (a * (1.0 - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(Float64(t + y) - 2.0)))
	tmp = 0.0
	if (b <= -5.1e-14)
		tmp = t_1;
	elseif (b <= -8.8e-65)
		tmp = Float64(x - Float64(z * Float64(y - 1.0)));
	elseif (b <= 2.7e+55)
		tmp = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * ((t + y) - 2.0));
	tmp = 0.0;
	if (b <= -5.1e-14)
		tmp = t_1;
	elseif (b <= -8.8e-65)
		tmp = x - (z * (y - 1.0));
	elseif (b <= 2.7e+55)
		tmp = x + (z + (a * (1.0 - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.1e-14], t$95$1, If[LessEqual[b, -8.8e-65], N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.7e+55], N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.0999999999999997e-14 or 2.69999999999999977e55 < b

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 73.9%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 46.1%

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

   10. Taylor expanded in z around 0

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

   12. Applied rewrites 50.7%

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

   if -5.0999999999999997e-14 < b < -8.80000000000000084e-65

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 60.3%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 42.0%

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

   if -8.80000000000000084e-65 < b < 2.69999999999999977e55

   1. Initial program 95.3%

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

   3. Applied rewrites 97.7%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 70.4%

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

   7. Taylor expanded in b around 0

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

   9. Applied rewrites 52.3%

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

Alternative 10: 69.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+55}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ t y) 2.0))))
   (if (<= b -2.3e+100)
     t_1
     (if (<= b 3.6e+55) (+ x (+ z (* a (- 1.0 t)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -2.3e+100) {
		tmp = t_1;
	} else if (b <= 3.6e+55) {
		tmp = x + (z + (a * (1.0 - t)));
	} 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 * ((t + y) - 2.0d0)
    if (b <= (-2.3d+100)) then
        tmp = t_1
    else if (b <= 3.6d+55) then
        tmp = x + (z + (a * (1.0d0 - t)))
    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 * ((t + y) - 2.0);
	double tmp;
	if (b <= -2.3e+100) {
		tmp = t_1;
	} else if (b <= 3.6e+55) {
		tmp = x + (z + (a * (1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((t + y) - 2.0)
	tmp = 0
	if b <= -2.3e+100:
		tmp = t_1
	elif b <= 3.6e+55:
		tmp = x + (z + (a * (1.0 - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(t + y) - 2.0))
	tmp = 0.0
	if (b <= -2.3e+100)
		tmp = t_1;
	elseif (b <= 3.6e+55)
		tmp = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((t + y) - 2.0);
	tmp = 0.0;
	if (b <= -2.3e+100)
		tmp = t_1;
	elseif (b <= 3.6e+55)
		tmp = x + (z + (a * (1.0 - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.3e+100], t$95$1, If[LessEqual[b, 3.6e+55], N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.2999999999999999e100 or 3.59999999999999987e55 < b

   1. Initial program 95.3%

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

   3. Applied rewrites 97.7%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 70.4%

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

   7. Taylor expanded in b around inf

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

   9. Applied rewrites 36.9%

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

   if -2.2999999999999999e100 < b < 3.59999999999999987e55

   1. Initial program 95.3%

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

   3. Applied rewrites 97.7%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 70.4%

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

   7. Taylor expanded in b around 0

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

   9. Applied rewrites 52.3%

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

Alternative 11: 61.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-10}:\\ \;\;\;\;x - z \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ t y) 2.0))))
   (if (<= b -2.3e+62) t_1 (if (<= b 8e-10) (- x (* z (- y 1.0))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -2.3e+62) {
		tmp = t_1;
	} else if (b <= 8e-10) {
		tmp = x - (z * (y - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, 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 * ((t + y) - 2.0d0)
    if (b <= (-2.3d+62)) then
        tmp = t_1
    else if (b <= 8d-10) then
        tmp = x - (z * (y - 1.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -2.3e+62) {
		tmp = t_1;
	} else if (b <= 8e-10) {
		tmp = x - (z * (y - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((t + y) - 2.0)
	tmp = 0
	if b <= -2.3e+62:
		tmp = t_1
	elif b <= 8e-10:
		tmp = x - (z * (y - 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(t + y) - 2.0))
	tmp = 0.0
	if (b <= -2.3e+62)
		tmp = t_1;
	elseif (b <= 8e-10)
		tmp = Float64(x - Float64(z * Float64(y - 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((t + y) - 2.0);
	tmp = 0.0;
	if (b <= -2.3e+62)
		tmp = t_1;
	elseif (b <= 8e-10)
		tmp = x - (z * (y - 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.3e+62], t$95$1, If[LessEqual[b, 8e-10], N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.29999999999999984e62 or 8.00000000000000029e-10 < b

   1. Initial program 95.3%

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

   3. Applied rewrites 97.7%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 70.4%

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

   7. Taylor expanded in b around inf

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

   9. Applied rewrites 36.9%

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

   if -2.29999999999999984e62 < b < 8.00000000000000029e-10

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 60.3%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 42.0%

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

Alternative 12: 57.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -760000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+50}:\\ \;\;\;\;x - z \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -760000000000.0)
     t_1
     (if (<= t 3.2e+50) (- x (* z (- y 1.0))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -760000000000.0) {
		tmp = t_1;
	} else if (t <= 3.2e+50) {
		tmp = x - (z * (y - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, 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 * (b - a)
    if (t <= (-760000000000.0d0)) then
        tmp = t_1
    else if (t <= 3.2d+50) then
        tmp = x - (z * (y - 1.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -760000000000.0) {
		tmp = t_1;
	} else if (t <= 3.2e+50) {
		tmp = x - (z * (y - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -760000000000.0:
		tmp = t_1
	elif t <= 3.2e+50:
		tmp = x - (z * (y - 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -760000000000.0)
		tmp = t_1;
	elseif (t <= 3.2e+50)
		tmp = Float64(x - Float64(z * Float64(y - 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -760000000000.0)
		tmp = t_1;
	elseif (t <= 3.2e+50)
		tmp = x - (z * (y - 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -760000000000.0], t$95$1, If[LessEqual[t, 3.2e+50], N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.6e11 or 3.19999999999999983e50 < t

   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. Taylor expanded in t around inf

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

   4. Applied rewrites 32.3%

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

   if -7.6e11 < t < 3.19999999999999983e50

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 60.3%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 42.0%

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

Alternative 13: 50.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{-284}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (* y (- b z))))
   (if (<= y -1.3e+15)
     t_2
     (if (<= y -1.1e-47)
       t_1
       (if (<= y -2.45e-284) (+ x z) (if (<= y 3.3e+46) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -1.3e+15) {
		tmp = t_2;
	} else if (y <= -1.1e-47) {
		tmp = t_1;
	} else if (y <= -2.45e-284) {
		tmp = x + z;
	} else if (y <= 3.3e+46) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = t * (b - a)
    t_2 = y * (b - z)
    if (y <= (-1.3d+15)) then
        tmp = t_2
    else if (y <= (-1.1d-47)) then
        tmp = t_1
    else if (y <= (-2.45d-284)) then
        tmp = x + z
    else if (y <= 3.3d+46) then
        tmp = t_1
    else
        tmp = t_2
    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 * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -1.3e+15) {
		tmp = t_2;
	} else if (y <= -1.1e-47) {
		tmp = t_1;
	} else if (y <= -2.45e-284) {
		tmp = x + z;
	} else if (y <= 3.3e+46) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = y * (b - z)
	tmp = 0
	if y <= -1.3e+15:
		tmp = t_2
	elif y <= -1.1e-47:
		tmp = t_1
	elif y <= -2.45e-284:
		tmp = x + z
	elif y <= 3.3e+46:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.3e+15)
		tmp = t_2;
	elseif (y <= -1.1e-47)
		tmp = t_1;
	elseif (y <= -2.45e-284)
		tmp = Float64(x + z);
	elseif (y <= 3.3e+46)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.3e+15)
		tmp = t_2;
	elseif (y <= -1.1e-47)
		tmp = t_1;
	elseif (y <= -2.45e-284)
		tmp = x + z;
	elseif (y <= 3.3e+46)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e+15], t$95$2, If[LessEqual[y, -1.1e-47], t$95$1, If[LessEqual[y, -2.45e-284], N[(x + z), $MachinePrecision], If[LessEqual[y, 3.3e+46], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3e15 or 3.2999999999999998e46 < y

   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. Taylor expanded in y around inf

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

   4. Applied rewrites 32.6%

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

   if -1.3e15 < y < -1.10000000000000009e-47 or -2.44999999999999995e-284 < y < 3.2999999999999998e46

   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. Taylor expanded in t around inf

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

   4. Applied rewrites 32.3%

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

   if -1.10000000000000009e-47 < y < -2.44999999999999995e-284

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 73.9%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 46.1%

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

   10. Taylor expanded in b around 0

       \[\leadsto x + z \]

   12. Applied rewrites 25.0%

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

Alternative 14: 44.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-39}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-294}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+49}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.25e+14)
     t_1
     (if (<= t -1.8e-39)
       (+ x z)
       (if (<= t -1.9e-294) (* z (- y)) (if (<= t 7.8e+49) (+ x z) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.25e+14) {
		tmp = t_1;
	} else if (t <= -1.8e-39) {
		tmp = x + z;
	} else if (t <= -1.9e-294) {
		tmp = z * -y;
	} else if (t <= 7.8e+49) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, 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 * (b - a)
    if (t <= (-1.25d+14)) then
        tmp = t_1
    else if (t <= (-1.8d-39)) then
        tmp = x + z
    else if (t <= (-1.9d-294)) then
        tmp = z * -y
    else if (t <= 7.8d+49) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.25e+14) {
		tmp = t_1;
	} else if (t <= -1.8e-39) {
		tmp = x + z;
	} else if (t <= -1.9e-294) {
		tmp = z * -y;
	} else if (t <= 7.8e+49) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -1.25e+14:
		tmp = t_1
	elif t <= -1.8e-39:
		tmp = x + z
	elif t <= -1.9e-294:
		tmp = z * -y
	elif t <= 7.8e+49:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.25e+14)
		tmp = t_1;
	elseif (t <= -1.8e-39)
		tmp = Float64(x + z);
	elseif (t <= -1.9e-294)
		tmp = Float64(z * Float64(-y));
	elseif (t <= 7.8e+49)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.25e+14)
		tmp = t_1;
	elseif (t <= -1.8e-39)
		tmp = x + z;
	elseif (t <= -1.9e-294)
		tmp = z * -y;
	elseif (t <= 7.8e+49)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e+14], t$95$1, If[LessEqual[t, -1.8e-39], N[(x + z), $MachinePrecision], If[LessEqual[t, -1.9e-294], N[(z * (-y)), $MachinePrecision], If[LessEqual[t, 7.8e+49], N[(x + z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.25e14 or 7.8000000000000002e49 < t

   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. Taylor expanded in t around inf

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

   4. Applied rewrites 32.3%

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

   if -1.25e14 < t < -1.8e-39 or -1.9e-294 < t < 7.8000000000000002e49

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 73.9%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 46.1%

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

   10. Taylor expanded in b around 0

       \[\leadsto x + z \]

   12. Applied rewrites 25.0%

       \[\leadsto x + z \]

   if -1.8e-39 < t < -1.9e-294

   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. Taylor expanded in z around inf

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

   4. Applied rewrites 28.2%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 19.0%

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

   9. Applied rewrites 19.0%

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

Alternative 15: 40.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-202}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{+32}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -3.5e+69)
     t_1
     (if (<= a -2.55e-202) (* b t) (if (<= a 1.18e+32) (+ x z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -3.5e+69) {
		tmp = t_1;
	} else if (a <= -2.55e-202) {
		tmp = b * t;
	} else if (a <= 1.18e+32) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, 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 = a * (1.0d0 - t)
    if (a <= (-3.5d+69)) then
        tmp = t_1
    else if (a <= (-2.55d-202)) then
        tmp = b * t
    else if (a <= 1.18d+32) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -3.5e+69) {
		tmp = t_1;
	} else if (a <= -2.55e-202) {
		tmp = b * t;
	} else if (a <= 1.18e+32) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -3.5e+69:
		tmp = t_1
	elif a <= -2.55e-202:
		tmp = b * t
	elif a <= 1.18e+32:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -3.5e+69)
		tmp = t_1;
	elseif (a <= -2.55e-202)
		tmp = Float64(b * t);
	elseif (a <= 1.18e+32)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -3.5e+69)
		tmp = t_1;
	elseif (a <= -2.55e-202)
		tmp = b * t;
	elseif (a <= 1.18e+32)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e+69], t$95$1, If[LessEqual[a, -2.55e-202], N[(b * t), $MachinePrecision], If[LessEqual[a, 1.18e+32], N[(x + z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.49999999999999987e69 or 1.1800000000000001e32 < a

   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. Taylor expanded in a around inf

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

   4. Applied rewrites 29.1%

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

   if -3.49999999999999987e69 < a < -2.54999999999999998e-202

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 73.9%

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

   7. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{t} \]

   9. Applied rewrites 16.7%

      \[\leadsto b \cdot \color{blue}{t} \]

   if -2.54999999999999998e-202 < a < 1.1800000000000001e32

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 73.9%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 46.1%

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

   10. Taylor expanded in b around 0

       \[\leadsto x + z \]

   12. Applied rewrites 25.0%

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

Alternative 16: 36.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+24}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+46}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.4e+24) (* y b) (if (<= y 7.2e+46) (+ x z) (* z (- y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.4e+24) {
		tmp = y * b;
	} else if (y <= 7.2e+46) {
		tmp = x + z;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, 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 <= (-4.4d+24)) then
        tmp = y * b
    else if (y <= 7.2d+46) then
        tmp = x + z
    else
        tmp = z * -y
    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 <= -4.4e+24) {
		tmp = y * b;
	} else if (y <= 7.2e+46) {
		tmp = x + z;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.4e+24:
		tmp = y * b
	elif y <= 7.2e+46:
		tmp = x + z
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.4e+24)
		tmp = Float64(y * b);
	elseif (y <= 7.2e+46)
		tmp = Float64(x + z);
	else
		tmp = Float64(z * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.4e+24)
		tmp = y * b;
	elseif (y <= 7.2e+46)
		tmp = x + z;
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.4e+24], N[(y * b), $MachinePrecision], If[LessEqual[y, 7.2e+46], N[(x + z), $MachinePrecision], N[(z * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.40000000000000003e24

   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. Taylor expanded in y around inf

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

   4. Applied rewrites 32.6%

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

   5. Taylor expanded in z around 0

      \[\leadsto y \cdot b \]

   7. Applied rewrites 17.9%

      \[\leadsto y \cdot b \]

   if -4.40000000000000003e24 < y < 7.1999999999999997e46

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 73.9%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 46.1%

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

   10. Taylor expanded in b around 0

       \[\leadsto x + z \]

   12. Applied rewrites 25.0%

       \[\leadsto x + z \]

   if 7.1999999999999997e46 < y

   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. Taylor expanded in z around inf

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

   4. Applied rewrites 28.2%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 19.0%

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

   9. Applied rewrites 19.0%

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

Alternative 17: 33.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+62}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+83}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.3e+62) (* b t) (if (<= b 2.8e+83) (+ x z) (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.3e+62) {
		tmp = b * t;
	} else if (b <= 2.8e+83) {
		tmp = x + 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 (b <= (-2.3d+62)) then
        tmp = b * t
    else if (b <= 2.8d+83) then
        tmp = x + 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 (b <= -2.3e+62) {
		tmp = b * t;
	} else if (b <= 2.8e+83) {
		tmp = x + z;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.3e+62:
		tmp = b * t
	elif b <= 2.8e+83:
		tmp = x + z
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.3e+62)
		tmp = Float64(b * t);
	elseif (b <= 2.8e+83)
		tmp = Float64(x + 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 (b <= -2.3e+62)
		tmp = b * t;
	elseif (b <= 2.8e+83)
		tmp = x + z;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.3e+62], N[(b * t), $MachinePrecision], If[LessEqual[b, 2.8e+83], N[(x + z), $MachinePrecision], N[(y * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.29999999999999984e62

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 73.9%

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

   7. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{t} \]

   9. Applied rewrites 16.7%

      \[\leadsto b \cdot \color{blue}{t} \]

   if -2.29999999999999984e62 < b < 2.8e83

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 73.9%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 46.1%

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

   10. Taylor expanded in b around 0

       \[\leadsto x + z \]

   12. Applied rewrites 25.0%

       \[\leadsto x + z \]

   if 2.8e83 < b

   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. Taylor expanded in y around inf

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

   4. Applied rewrites 32.6%

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

   5. Taylor expanded in z around 0

      \[\leadsto y \cdot b \]

   7. Applied rewrites 17.9%

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

Alternative 18: 32.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+62}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{+49}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.3e+62) (* b t) (if (<= b 1.06e+49) (+ x z) (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.3e+62) {
		tmp = b * t;
	} else if (b <= 1.06e+49) {
		tmp = x + z;
	} 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 (b <= (-2.3d+62)) then
        tmp = b * t
    else if (b <= 1.06d+49) then
        tmp = x + z
    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 (b <= -2.3e+62) {
		tmp = b * t;
	} else if (b <= 1.06e+49) {
		tmp = x + z;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.3e+62:
		tmp = b * t
	elif b <= 1.06e+49:
		tmp = x + z
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.3e+62)
		tmp = Float64(b * t);
	elseif (b <= 1.06e+49)
		tmp = Float64(x + z);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.3e+62)
		tmp = b * t;
	elseif (b <= 1.06e+49)
		tmp = x + z;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.3e+62], N[(b * t), $MachinePrecision], If[LessEqual[b, 1.06e+49], N[(x + z), $MachinePrecision], N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.29999999999999984e62 or 1.06e49 < b

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 73.9%

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

   7. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{t} \]

   9. Applied rewrites 16.7%

      \[\leadsto b \cdot \color{blue}{t} \]

   if -2.29999999999999984e62 < b < 1.06e49

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 73.9%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 46.1%

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

   10. Taylor expanded in b around 0

       \[\leadsto x + z \]

   12. Applied rewrites 25.0%

       \[\leadsto x + z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 28.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{+263}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+161}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -4.7e+263) a (if (<= a 1.1e+161) (+ x z) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.7e+263) {
		tmp = a;
	} else if (a <= 1.1e+161) {
		tmp = x + z;
	} else {
		tmp = 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 (a <= (-4.7d+263)) then
        tmp = a
    else if (a <= 1.1d+161) then
        tmp = x + z
    else
        tmp = 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 (a <= -4.7e+263) {
		tmp = a;
	} else if (a <= 1.1e+161) {
		tmp = x + z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4.7e+263:
		tmp = a
	elif a <= 1.1e+161:
		tmp = x + z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4.7e+263)
		tmp = a;
	elseif (a <= 1.1e+161)
		tmp = Float64(x + z);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -4.7e+263)
		tmp = a;
	elseif (a <= 1.1e+161)
		tmp = x + z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4.7e+263], a, If[LessEqual[a, 1.1e+161], N[(x + z), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if a < -4.69999999999999973e263 or 1.1e161 < a

   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. Taylor expanded in a around inf

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

   4. Applied rewrites 29.1%

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

   5. Taylor expanded in t around 0

      \[\leadsto a \]

   7. Applied rewrites 11.5%

      \[\leadsto a \]

   if -4.69999999999999973e263 < a < 1.1e161

   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. Taylor expanded in a around 0

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 73.9%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 46.1%

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

   10. Taylor expanded in b around 0

       \[\leadsto x + z \]

   12. Applied rewrites 25.0%

       \[\leadsto x + z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 17.6% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+56}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 35000000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3.1e+56) a (if (<= a 35000000.0) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.1e+56) {
		tmp = a;
	} else if (a <= 35000000.0) {
		tmp = z;
	} else {
		tmp = 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 (a <= (-3.1d+56)) then
        tmp = a
    else if (a <= 35000000.0d0) then
        tmp = z
    else
        tmp = 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 (a <= -3.1e+56) {
		tmp = a;
	} else if (a <= 35000000.0) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3.1e+56:
		tmp = a
	elif a <= 35000000.0:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3.1e+56)
		tmp = a;
	elseif (a <= 35000000.0)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -3.1e+56)
		tmp = a;
	elseif (a <= 35000000.0)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3.1e+56], a, If[LessEqual[a, 35000000.0], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -3.10000000000000005e56 or 3.5e7 < a

   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. Taylor expanded in a around inf

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

   4. Applied rewrites 29.1%

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

   5. Taylor expanded in t around 0

      \[\leadsto a \]

   7. Applied rewrites 11.5%

      \[\leadsto a \]

   if -3.10000000000000005e56 < a < 3.5e7

   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. Taylor expanded in z around inf

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

   4. Applied rewrites 28.2%

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

   5. Taylor expanded in y around 0

      \[\leadsto z \]

   7. Applied rewrites 11.3%

      \[\leadsto z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 11.5% accurate, 28.4× speedup

Math

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

FPCore

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

C

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

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 = a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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. Taylor expanded in a around inf

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

4. Applied rewrites 29.1%

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

5. Taylor expanded in t around 0

   \[\leadsto a \]

7. Applied rewrites 11.5%

   \[\leadsto a \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025153 
(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)))