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

Percentage Accurate: 95.2% → 97.8%

Time: 10.9s

Alternatives: 21

Speedup: 0.5×

• 37.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 60.0%

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

Alternative 2: 33.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+302}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b))))
   (if (<= t_1 -5e+302) (* b t) (if (<= t_1 5e+305) (+ a x) (* b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	double tmp;
	if (t_1 <= -5e+302) {
		tmp = b * t;
	} else if (t_1 <= 5e+305) {
		tmp = a + x;
	} else {
		tmp = b * 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) :: t_1
    real(8) :: tmp
    t_1 = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
    if (t_1 <= (-5d+302)) then
        tmp = b * t
    else if (t_1 <= 5d+305) then
        tmp = a + x
    else
        tmp = b * 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 t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	double tmp;
	if (t_1 <= -5e+302) {
		tmp = b * t;
	} else if (t_1 <= 5e+305) {
		tmp = a + x;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)
	tmp = 0
	if t_1 <= -5e+302:
		tmp = b * t
	elif t_1 <= 5e+305:
		tmp = a + x
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (t_1 <= -5e+302)
		tmp = Float64(b * t);
	elseif (t_1 <= 5e+305)
		tmp = Float64(a + x);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (t_1 <= -5e+302)
		tmp = b * t;
	elseif (t_1 <= 5e+305)
		tmp = a + x;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, -5e+302], N[(b * t), $MachinePrecision], If[LessEqual[t$95$1, 5e+305], N[(a + x), $MachinePrecision], N[(b * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < -5e302

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower--.f64 71.9

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

   5. Applied rewrites 71.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 71.9%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 37.7%

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

   if -5e302 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < 5.00000000000000009e305

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 72.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 48.5%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 37.7%

       \[\leadsto a + x \]

   if 5.00000000000000009e305 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 74.1%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 72.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 40.9%

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

Alternative 3: 31.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot t\\ \mathbf{if}\;t \leq -4 \cdot 10^{+226}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq -6.8:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-303}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-127}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+139}:\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a) t)))
   (if (<= t -4e+226)
     (* b t)
     (if (<= t -6.8)
       t_1
       (if (<= t -5.6e-303)
         (+ a x)
         (if (<= t 5e-127) (* b y) (if (<= t 8e+139) (* (- y) z) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a * t;
	double tmp;
	if (t <= -4e+226) {
		tmp = b * t;
	} else if (t <= -6.8) {
		tmp = t_1;
	} else if (t <= -5.6e-303) {
		tmp = a + x;
	} else if (t <= 5e-127) {
		tmp = b * y;
	} else if (t <= 8e+139) {
		tmp = -y * 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 * t
    if (t <= (-4d+226)) then
        tmp = b * t
    else if (t <= (-6.8d0)) then
        tmp = t_1
    else if (t <= (-5.6d-303)) then
        tmp = a + x
    else if (t <= 5d-127) then
        tmp = b * y
    else if (t <= 8d+139) then
        tmp = -y * 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 * t;
	double tmp;
	if (t <= -4e+226) {
		tmp = b * t;
	} else if (t <= -6.8) {
		tmp = t_1;
	} else if (t <= -5.6e-303) {
		tmp = a + x;
	} else if (t <= 5e-127) {
		tmp = b * y;
	} else if (t <= 8e+139) {
		tmp = -y * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -a * t
	tmp = 0
	if t <= -4e+226:
		tmp = b * t
	elif t <= -6.8:
		tmp = t_1
	elif t <= -5.6e-303:
		tmp = a + x
	elif t <= 5e-127:
		tmp = b * y
	elif t <= 8e+139:
		tmp = -y * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-a) * t)
	tmp = 0.0
	if (t <= -4e+226)
		tmp = Float64(b * t);
	elseif (t <= -6.8)
		tmp = t_1;
	elseif (t <= -5.6e-303)
		tmp = Float64(a + x);
	elseif (t <= 5e-127)
		tmp = Float64(b * y);
	elseif (t <= 8e+139)
		tmp = Float64(Float64(-y) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -a * t;
	tmp = 0.0;
	if (t <= -4e+226)
		tmp = b * t;
	elseif (t <= -6.8)
		tmp = t_1;
	elseif (t <= -5.6e-303)
		tmp = a + x;
	elseif (t <= 5e-127)
		tmp = b * y;
	elseif (t <= 8e+139)
		tmp = -y * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) * t), $MachinePrecision]}, If[LessEqual[t, -4e+226], N[(b * t), $MachinePrecision], If[LessEqual[t, -6.8], t$95$1, If[LessEqual[t, -5.6e-303], N[(a + x), $MachinePrecision], If[LessEqual[t, 5e-127], N[(b * y), $MachinePrecision], If[LessEqual[t, 8e+139], N[((-y) * z), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.99999999999999985e226

   1. Initial program 93.8%

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

   3. Taylor expanded in 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. Step-by-step derivation

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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower--.f64 81.8

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

   5. Applied rewrites 81.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 76.0%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 63.2%

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

   if -3.99999999999999985e226 < t < -6.79999999999999982 or 8.00000000000000026e139 < t

   1. Initial program 91.1%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 67.4

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

   5. Applied rewrites 67.4%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 46.2%

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

   if -6.79999999999999982 < t < -5.6e-303

   1. Initial program 98.5%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 69.1%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 43.4%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 43.4%

       \[\leadsto a + x \]

   if -5.6e-303 < t < 4.9999999999999997e-127

   1. Initial program 97.2%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 78.3%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 45.9%

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

   if 4.9999999999999997e-127 < t < 8.00000000000000026e139

   1. Initial program 92.1%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 43.4

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

   5. Applied rewrites 43.4%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 35.5%

      \[\leadsto \left(-y\right) \cdot z \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 4: 60.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-z, y - 1, x\right)\\ t_2 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-238}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-193}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- z) (- y 1.0) x)) (t_2 (* (- (+ t y) 2.0) b)))
   (if (<= b -7.2e+33)
     t_2
     (if (<= b -2.2e-238)
       t_1
       (if (<= b 8.5e-193)
         (fma (- 1.0 t) a x)
         (if (<= b 2.3e+111) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(-z, (y - 1.0), x);
	double t_2 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -7.2e+33) {
		tmp = t_2;
	} else if (b <= -2.2e-238) {
		tmp = t_1;
	} else if (b <= 8.5e-193) {
		tmp = fma((1.0 - t), a, x);
	} else if (b <= 2.3e+111) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(-z), Float64(y - 1.0), x)
	t_2 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -7.2e+33)
		tmp = t_2;
	elseif (b <= -2.2e-238)
		tmp = t_1;
	elseif (b <= 8.5e-193)
		tmp = fma(Float64(1.0 - t), a, x);
	elseif (b <= 2.3e+111)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-z) * N[(y - 1.0), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -7.2e+33], t$95$2, If[LessEqual[b, -2.2e-238], t$95$1, If[LessEqual[b, 8.5e-193], N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision], If[LessEqual[b, 2.3e+111], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.2000000000000005e33 or 2.30000000000000002e111 < b

   1. Initial program 90.4%

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

   3. Taylor expanded in 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. Step-by-step derivation

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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower--.f64 82.2

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

   5. Applied rewrites 82.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 80.6%

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

   9. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 N/A

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

       4. lower-+.f64 79.8

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

   11. Applied rewrites 79.8%

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

   if -7.2000000000000005e33 < b < -2.19999999999999991e-238 or 8.50000000000000004e-193 < b < 2.30000000000000002e111

   1. Initial program 94.8%

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

   3. Taylor expanded in 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. Step-by-step derivation

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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower--.f64 72.8

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

   5. Applied rewrites 72.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 59.4%

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

   if -2.19999999999999991e-238 < b < 8.50000000000000004e-193

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 74.4%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 72.2%

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

Alternative 5: 57.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-z, y - 1, x\right)\\ t_2 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -5.4 \cdot 10^{+100}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-283}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.92 \cdot 10^{-121}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, a\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- z) (- y 1.0) x)) (t_2 (* (- b a) t)))
   (if (<= t -5.4e+100)
     t_2
     (if (<= t -4.2e-283)
       t_1
       (if (<= t 1.92e-121) (fma (- y 2.0) b a) (if (<= t 3e+19) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(-z, (y - 1.0), x);
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -5.4e+100) {
		tmp = t_2;
	} else if (t <= -4.2e-283) {
		tmp = t_1;
	} else if (t <= 1.92e-121) {
		tmp = fma((y - 2.0), b, a);
	} else if (t <= 3e+19) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(-z), Float64(y - 1.0), x)
	t_2 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -5.4e+100)
		tmp = t_2;
	elseif (t <= -4.2e-283)
		tmp = t_1;
	elseif (t <= 1.92e-121)
		tmp = fma(Float64(y - 2.0), b, a);
	elseif (t <= 3e+19)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-z) * N[(y - 1.0), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -5.4e+100], t$95$2, If[LessEqual[t, -4.2e-283], t$95$1, If[LessEqual[t, 1.92e-121], N[(N[(y - 2.0), $MachinePrecision] * b + a), $MachinePrecision], If[LessEqual[t, 3e+19], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.39999999999999997e100 or 3e19 < t

   1. Initial program 91.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.2

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

   5. Applied rewrites 73.2%

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

   if -5.39999999999999997e100 < t < -4.19999999999999994e-283 or 1.9199999999999999e-121 < t < 3e19

   1. Initial program 96.0%

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

   3. Taylor expanded in a around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower--.f64 79.5

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

   5. Applied rewrites 79.5%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 61.0%

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

   if -4.19999999999999994e-283 < t < 1.9199999999999999e-121

   1. Initial program 97.7%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 80.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 80.0%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 72.2%

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

Alternative 6: 87.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) - 2\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+32} \lor \neg \left(z \leq 2.45 \cdot 10^{+95}\right):\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, x - \left(y - 1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(t\_1, b, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ t y) 2.0)))
   (if (or (<= z -4.8e+32) (not (<= z 2.45e+95)))
     (fma t_1 b (- x (* (- y 1.0) z)))
     (fma (- 1.0 t) a (fma t_1 b x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) - 2.0;
	double tmp;
	if ((z <= -4.8e+32) || !(z <= 2.45e+95)) {
		tmp = fma(t_1, b, (x - ((y - 1.0) * z)));
	} else {
		tmp = fma((1.0 - t), a, fma(t_1, b, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) - 2.0)
	tmp = 0.0
	if ((z <= -4.8e+32) || !(z <= 2.45e+95))
		tmp = fma(t_1, b, Float64(x - Float64(Float64(y - 1.0) * z)));
	else
		tmp = fma(Float64(1.0 - t), a, fma(t_1, b, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[Or[LessEqual[z, -4.8e+32], N[Not[LessEqual[z, 2.45e+95]], $MachinePrecision]], N[(t$95$1 * b + N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a + N[(t$95$1 * b + x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.79999999999999983e32 or 2.4499999999999999e95 < z

   1. Initial program 93.6%

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

   3. Taylor expanded in 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. Step-by-step derivation

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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower--.f64 85.4

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

   5. Applied rewrites 85.4%

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

   if -4.79999999999999983e32 < z < 2.4499999999999999e95

   1. Initial program 94.4%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 93.9%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+32} \lor \neg \left(z \leq 2.45 \cdot 10^{+95}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(y - 1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+250}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y - 1, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8.8e+250)
   (* (- 1.0 y) z)
   (if (<= z 2.1e+99)
     (fma (- 1.0 t) a (fma (- (+ t y) 2.0) b x))
     (fma (- z) (- y 1.0) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.8e+250) {
		tmp = (1.0 - y) * z;
	} else if (z <= 2.1e+99) {
		tmp = fma((1.0 - t), a, fma(((t + y) - 2.0), b, x));
	} else {
		tmp = fma(-z, (y - 1.0), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8.8e+250)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (z <= 2.1e+99)
		tmp = fma(Float64(1.0 - t), a, fma(Float64(Float64(t + y) - 2.0), b, x));
	else
		tmp = fma(Float64(-z), Float64(y - 1.0), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -8.8e+250], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 2.1e+99], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], N[((-z) * N[(y - 1.0), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.80000000000000058e250

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 90.0

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

   5. Applied rewrites 90.0%

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

   if -8.80000000000000058e250 < z < 2.1000000000000001e99

   1. Initial program 95.0%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 88.6%

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

   if 2.1000000000000001e99 < z

   1. Initial program 89.1%

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

   3. Taylor expanded in 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. Step-by-step derivation

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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower--.f64 95.8

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

   5. Applied rewrites 95.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 83.2%

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

Alternative 8: 84.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+175}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right) + \mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x - z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5e+175)
   (* (- b z) y)
   (if (<= y 6.6e-9)
     (+ (fma (- t 2.0) b z) (fma (- 1.0 t) a x))
     (fma (- (+ t y) 2.0) b (- x (* z y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5e+175) {
		tmp = (b - z) * y;
	} else if (y <= 6.6e-9) {
		tmp = fma((t - 2.0), b, z) + fma((1.0 - t), a, x);
	} else {
		tmp = fma(((t + y) - 2.0), b, (x - (z * y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5e+175)
		tmp = Float64(Float64(b - z) * y);
	elseif (y <= 6.6e-9)
		tmp = Float64(fma(Float64(t - 2.0), b, z) + fma(Float64(1.0 - t), a, x));
	else
		tmp = fma(Float64(Float64(t + y) - 2.0), b, Float64(x - Float64(z * y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5e+175], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, 6.6e-9], N[(N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision] + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5e175

   1. Initial program 89.5%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 92.2

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

   5. Applied rewrites 92.2%

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

   if -5e175 < y < 6.60000000000000037e-9

   1. Initial program 96.0%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

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

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 88.6%

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

   if 6.60000000000000037e-9 < y

   1. Initial program 92.5%

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

   3. Taylor expanded in 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. Step-by-step derivation

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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower--.f64 82.2

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

   5. Applied rewrites 82.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 81.0%

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

Alternative 9: 48.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -6.8:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-303}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-126}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+14}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -6.8)
     t_1
     (if (<= t -5.6e-303)
       (+ a x)
       (if (<= t 4.2e-126) (* b y) (if (<= t 8.2e+14) (* (- 1.0 y) z) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -6.8) {
		tmp = t_1;
	} else if (t <= -5.6e-303) {
		tmp = a + x;
	} else if (t <= 4.2e-126) {
		tmp = b * y;
	} else if (t <= 8.2e+14) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - a) * t
    if (t <= (-6.8d0)) then
        tmp = t_1
    else if (t <= (-5.6d-303)) then
        tmp = a + x
    else if (t <= 4.2d-126) then
        tmp = b * y
    else if (t <= 8.2d+14) then
        tmp = (1.0d0 - y) * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -6.8) {
		tmp = t_1;
	} else if (t <= -5.6e-303) {
		tmp = a + x;
	} else if (t <= 4.2e-126) {
		tmp = b * y;
	} else if (t <= 8.2e+14) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -6.8:
		tmp = t_1
	elif t <= -5.6e-303:
		tmp = a + x
	elif t <= 4.2e-126:
		tmp = b * y
	elif t <= 8.2e+14:
		tmp = (1.0 - y) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -6.8)
		tmp = t_1;
	elseif (t <= -5.6e-303)
		tmp = Float64(a + x);
	elseif (t <= 4.2e-126)
		tmp = Float64(b * y);
	elseif (t <= 8.2e+14)
		tmp = Float64(Float64(1.0 - y) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	tmp = 0.0;
	if (t <= -6.8)
		tmp = t_1;
	elseif (t <= -5.6e-303)
		tmp = a + x;
	elseif (t <= 4.2e-126)
		tmp = b * y;
	elseif (t <= 8.2e+14)
		tmp = (1.0 - y) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -6.8], t$95$1, If[LessEqual[t, -5.6e-303], N[(a + x), $MachinePrecision], If[LessEqual[t, 4.2e-126], N[(b * y), $MachinePrecision], If[LessEqual[t, 8.2e+14], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.79999999999999982 or 8.2e14 < t

   1. Initial program 91.2%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 66.4

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

   5. Applied rewrites 66.4%

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

   if -6.79999999999999982 < t < -5.6e-303

   1. Initial program 98.5%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 69.1%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 43.4%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 43.4%

       \[\leadsto a + x \]

   if -5.6e-303 < t < 4.1999999999999997e-126

   1. Initial program 97.3%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 78.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 44.6%

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

   if 4.1999999999999997e-126 < t < 8.2e14

   1. Initial program 94.1%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 54.1

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

   5. Applied rewrites 54.1%

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

Alternative 10: 73.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+112} \lor \neg \left(a \leq 5.6 \cdot 10^{+73}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x - z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.7e+112) (not (<= a 5.6e+73)))
   (fma (- 1.0 t) a x)
   (fma (- (+ t y) 2.0) b (- x (* z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.7e+112) || !(a <= 5.6e+73)) {
		tmp = fma((1.0 - t), a, x);
	} else {
		tmp = fma(((t + y) - 2.0), b, (x - (z * y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.7e+112) || !(a <= 5.6e+73))
		tmp = fma(Float64(1.0 - t), a, x);
	else
		tmp = fma(Float64(Float64(t + y) - 2.0), b, Float64(x - Float64(z * y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.7e+112], N[Not[LessEqual[a, 5.6e+73]], $MachinePrecision]], N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.7000000000000001e112 or 5.60000000000000016e73 < a

   1. Initial program 91.1%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 82.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 73.6%

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

   if -2.7000000000000001e112 < a < 5.60000000000000016e73

   1. Initial program 96.1%

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

   3. Taylor expanded in 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. Step-by-step derivation

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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower--.f64 92.6

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

   5. Applied rewrites 92.6%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 80.9%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+112} \lor \neg \left(a \leq 5.6 \cdot 10^{+73}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x - z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -4 \cdot 10^{+175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-128}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{elif}\;y \leq 1.1:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, x\right) + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -4e+175)
     t_1
     (if (<= y -2.2e-128)
       (fma (- 1.0 t) a x)
       (if (<= y 1.1) (+ (fma (- t 2.0) b x) z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -4e+175) {
		tmp = t_1;
	} else if (y <= -2.2e-128) {
		tmp = fma((1.0 - t), a, x);
	} else if (y <= 1.1) {
		tmp = fma((t - 2.0), b, x) + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -4e+175)
		tmp = t_1;
	elseif (y <= -2.2e-128)
		tmp = fma(Float64(1.0 - t), a, x);
	elseif (y <= 1.1)
		tmp = Float64(fma(Float64(t - 2.0), b, x) + z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -4e+175], t$95$1, If[LessEqual[y, -2.2e-128], N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision], If[LessEqual[y, 1.1], N[(N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9999999999999997e175 or 1.1000000000000001 < y

   1. Initial program 91.3%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 75.2

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

   5. Applied rewrites 75.2%

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

   if -3.9999999999999997e175 < y < -2.20000000000000009e-128

   1. Initial program 97.0%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 83.5%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 65.0%

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

   if -2.20000000000000009e-128 < y < 1.1000000000000001

   1. Initial program 95.3%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

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

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 95.2%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 73.5%

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

Alternative 12: 64.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -5.4 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(-z, y - 1, x\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-27}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -5.4e+100)
     t_1
     (if (<= t -1.4e+24)
       (fma (- z) (- y 1.0) x)
       (if (<= t 8.5e-27) (+ (fma (- y 2.0) b x) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -5.4e+100) {
		tmp = t_1;
	} else if (t <= -1.4e+24) {
		tmp = fma(-z, (y - 1.0), x);
	} else if (t <= 8.5e-27) {
		tmp = fma((y - 2.0), b, x) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -5.4e+100)
		tmp = t_1;
	elseif (t <= -1.4e+24)
		tmp = fma(Float64(-z), Float64(y - 1.0), x);
	elseif (t <= 8.5e-27)
		tmp = Float64(fma(Float64(y - 2.0), b, x) + a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -5.4e+100], t$95$1, If[LessEqual[t, -1.4e+24], N[((-z) * N[(y - 1.0), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 8.5e-27], N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.39999999999999997e100 or 8.50000000000000033e-27 < t

   1. Initial program 90.3%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 71.3

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

   5. Applied rewrites 71.3%

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

   if -5.39999999999999997e100 < t < -1.4000000000000001e24

   1. Initial program 94.4%

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

   3. Taylor expanded in 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. Step-by-step derivation

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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower--.f64 72.9

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

   5. Applied rewrites 72.9%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 62.2%

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

   if -1.4000000000000001e24 < t < 8.50000000000000033e-27

   1. Initial program 97.6%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 72.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 70.2%

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

Alternative 13: 56.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-26}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, x\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-27}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -3.6e+98)
     t_1
     (if (<= t -2.55e-26)
       (fma (- t) a x)
       (if (<= t 8.5e-27) (fma (- y 2.0) b a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -3.6e+98) {
		tmp = t_1;
	} else if (t <= -2.55e-26) {
		tmp = fma(-t, a, x);
	} else if (t <= 8.5e-27) {
		tmp = fma((y - 2.0), b, a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -3.6e+98)
		tmp = t_1;
	elseif (t <= -2.55e-26)
		tmp = fma(Float64(-t), a, x);
	elseif (t <= 8.5e-27)
		tmp = fma(Float64(y - 2.0), b, a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -3.6e+98], t$95$1, If[LessEqual[t, -2.55e-26], N[((-t) * a + x), $MachinePrecision], If[LessEqual[t, 8.5e-27], N[(N[(y - 2.0), $MachinePrecision] * b + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.59999999999999981e98 or 8.50000000000000033e-27 < t

   1. Initial program 90.4%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 70.7

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

   5. Applied rewrites 70.7%

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

   if -3.59999999999999981e98 < t < -2.54999999999999995e-26

   1. Initial program 93.5%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 74.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 52.8%

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

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(-1 \cdot t, a, x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 50.5%

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

   if -2.54999999999999995e-26 < t < 8.50000000000000033e-27

   1. Initial program 98.2%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 71.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 71.0%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 57.4%

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

Alternative 14: 37.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+169}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-134}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -9.2e+169)
   (* b y)
   (if (<= y -1.4e-134)
     (* (- 1.0 t) a)
     (if (<= y 8e+84) (fma (- t) a x) (* b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9.2e+169) {
		tmp = b * y;
	} else if (y <= -1.4e-134) {
		tmp = (1.0 - t) * a;
	} else if (y <= 8e+84) {
		tmp = fma(-t, a, x);
	} else {
		tmp = b * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -9.2e+169)
		tmp = Float64(b * y);
	elseif (y <= -1.4e-134)
		tmp = Float64(Float64(1.0 - t) * a);
	elseif (y <= 8e+84)
		tmp = fma(Float64(-t), a, x);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -9.2e+169], N[(b * y), $MachinePrecision], If[LessEqual[y, -1.4e-134], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[y, 8e+84], N[((-t) * a + x), $MachinePrecision], N[(b * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.1999999999999997e169 or 8.00000000000000046e84 < y

   1. Initial program 90.7%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 70.0%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 51.4%

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

   if -9.1999999999999997e169 < y < -1.3999999999999999e-134

   1. Initial program 97.0%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 55.5

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

   5. Applied rewrites 55.5%

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

   if -1.3999999999999999e-134 < y < 8.00000000000000046e84

   1. Initial program 95.1%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 75.7%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 50.5%

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

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(-1 \cdot t, a, x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 39.2%

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

Alternative 15: 33.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+209}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+67}:\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+74}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7.5e+209)
   (* b y)
   (if (<= y -2e+67) (* (- y) z) (if (<= y 9.5e+74) (+ a x) (* b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.5e+209) {
		tmp = b * y;
	} else if (y <= -2e+67) {
		tmp = -y * z;
	} else if (y <= 9.5e+74) {
		tmp = a + x;
	} else {
		tmp = b * 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 <= (-7.5d+209)) then
        tmp = b * y
    else if (y <= (-2d+67)) then
        tmp = -y * z
    else if (y <= 9.5d+74) then
        tmp = a + x
    else
        tmp = b * 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 <= -7.5e+209) {
		tmp = b * y;
	} else if (y <= -2e+67) {
		tmp = -y * z;
	} else if (y <= 9.5e+74) {
		tmp = a + x;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7.5e+209:
		tmp = b * y
	elif y <= -2e+67:
		tmp = -y * z
	elif y <= 9.5e+74:
		tmp = a + x
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7.5e+209)
		tmp = Float64(b * y);
	elseif (y <= -2e+67)
		tmp = Float64(Float64(-y) * z);
	elseif (y <= 9.5e+74)
		tmp = Float64(a + x);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -7.5e+209)
		tmp = b * y;
	elseif (y <= -2e+67)
		tmp = -y * z;
	elseif (y <= 9.5e+74)
		tmp = a + x;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7.5e+209], N[(b * y), $MachinePrecision], If[LessEqual[y, -2e+67], N[((-y) * z), $MachinePrecision], If[LessEqual[y, 9.5e+74], N[(a + x), $MachinePrecision], N[(b * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.50000000000000055e209 or 9.5000000000000006e74 < y

   1. Initial program 89.7%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 73.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 55.2%

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

   if -7.50000000000000055e209 < y < -1.99999999999999997e67

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 38.4

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

   5. Applied rewrites 38.4%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 38.4%

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

   if -1.99999999999999997e67 < y < 9.5000000000000006e74

   1. Initial program 95.9%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 78.2%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 54.6%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 32.4%

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

Alternative 16: 56.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+175} \lor \neg \left(y \leq 5.6 \cdot 10^{+67}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4e+175) (not (<= y 5.6e+67)))
   (* (- b z) y)
   (fma (- 1.0 t) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4e+175) || !(y <= 5.6e+67)) {
		tmp = (b - z) * y;
	} else {
		tmp = fma((1.0 - t), a, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4e+175) || !(y <= 5.6e+67))
		tmp = Float64(Float64(b - z) * y);
	else
		tmp = fma(Float64(1.0 - t), a, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4e+175], N[Not[LessEqual[y, 5.6e+67]], $MachinePrecision]], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.9999999999999997e175 or 5.5999999999999995e67 < y

   1. Initial program 90.9%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 82.4

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

   5. Applied rewrites 82.4%

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

   if -3.9999999999999997e175 < y < 5.5999999999999995e67

   1. Initial program 95.8%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 78.6%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 55.9%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+175} \lor \neg \left(y \leq 5.6 \cdot 10^{+67}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 49.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.76 \cdot 10^{+167} \lor \neg \left(y \leq 850000000000\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.76e+167) (not (<= y 850000000000.0)))
   (* (- b z) y)
   (* (- b a) t)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.76e+167) || !(y <= 850000000000.0)) {
		tmp = (b - z) * y;
	} else {
		tmp = (b - a) * 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 ((y <= (-1.76d+167)) .or. (.not. (y <= 850000000000.0d0))) then
        tmp = (b - z) * y
    else
        tmp = (b - a) * 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 ((y <= -1.76e+167) || !(y <= 850000000000.0)) {
		tmp = (b - z) * y;
	} else {
		tmp = (b - a) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.76e+167) or not (y <= 850000000000.0):
		tmp = (b - z) * y
	else:
		tmp = (b - a) * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.76e+167) || !(y <= 850000000000.0))
		tmp = Float64(Float64(b - z) * y);
	else
		tmp = Float64(Float64(b - a) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.76e+167) || ~((y <= 850000000000.0)))
		tmp = (b - z) * y;
	else
		tmp = (b - a) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.76e+167], N[Not[LessEqual[y, 850000000000.0]], $MachinePrecision]], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7599999999999999e167 or 8.5e11 < y

   1. Initial program 91.2%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 75.7

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

   5. Applied rewrites 75.7%

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

   if -1.7599999999999999e167 < y < 8.5e11

   1. Initial program 96.1%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 44.7

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

   5. Applied rewrites 44.7%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.76 \cdot 10^{+167} \lor \neg \left(y \leq 850000000000\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 46.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+34} \lor \neg \left(z \leq 2.85 \cdot 10^{+78}\right):\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.6e+34) (not (<= z 2.85e+78)))
   (* (- 1.0 y) z)
   (fma (- t) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.6e+34) || !(z <= 2.85e+78)) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = fma(-t, a, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.6e+34) || !(z <= 2.85e+78))
		tmp = Float64(Float64(1.0 - y) * z);
	else
		tmp = fma(Float64(-t), a, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.6e+34], N[Not[LessEqual[z, 2.85e+78]], $MachinePrecision]], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], N[((-t) * a + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5999999999999999e34 or 2.84999999999999993e78 < z

   1. Initial program 92.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 66.2

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

   5. Applied rewrites 66.2%

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

   if -1.5999999999999999e34 < z < 2.84999999999999993e78

   1. Initial program 94.9%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 94.9%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 54.9%

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

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(-1 \cdot t, a, x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 42.5%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+34} \lor \neg \left(z \leq 2.85 \cdot 10^{+78}\right):\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 38.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+189} \lor \neg \left(y \leq 8 \cdot 10^{+84}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.9e+189) (not (<= y 8e+84))) (* b y) (fma (- t) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.9e+189) || !(y <= 8e+84)) {
		tmp = b * y;
	} else {
		tmp = fma(-t, a, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.9e+189) || !(y <= 8e+84))
		tmp = Float64(b * y);
	else
		tmp = fma(Float64(-t), a, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.9e+189], N[Not[LessEqual[y, 8e+84]], $MachinePrecision]], N[(b * y), $MachinePrecision], N[((-t) * a + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.90000000000000019e189 or 8.00000000000000046e84 < y

   1. Initial program 90.1%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 72.3%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 54.4%

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

   if -2.90000000000000019e189 < y < 8.00000000000000046e84

   1. Initial program 96.0%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 76.7%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 54.9%

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

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(-1 \cdot t, a, x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 41.9%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+189} \lor \neg \left(y \leq 8 \cdot 10^{+84}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 32.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+189} \lor \neg \left(y \leq 9.5 \cdot 10^{+74}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;a + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.7e+189) (not (<= y 9.5e+74))) (* b y) (+ a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.7e+189) || !(y <= 9.5e+74)) {
		tmp = b * y;
	} else {
		tmp = a + x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.7d+189)) .or. (.not. (y <= 9.5d+74))) then
        tmp = b * y
    else
        tmp = a + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.7e+189) || !(y <= 9.5e+74)) {
		tmp = b * y;
	} else {
		tmp = a + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.7e+189) or not (y <= 9.5e+74):
		tmp = b * y
	else:
		tmp = a + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.7e+189) || !(y <= 9.5e+74))
		tmp = Float64(b * y);
	else
		tmp = Float64(a + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.7e+189) || ~((y <= 9.5e+74)))
		tmp = b * y;
	else
		tmp = a + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.7e+189], N[Not[LessEqual[y, 9.5e+74]], $MachinePrecision]], N[(b * y), $MachinePrecision], N[(a + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.69999999999999994e189 or 9.5000000000000006e74 < y

   1. Initial program 90.2%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 72.7%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 53.8%

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

   if -2.69999999999999994e189 < y < 9.5000000000000006e74

   1. Initial program 96.0%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

   5. Applied rewrites 76.6%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 54.7%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 29.5%

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

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+189} \lor \neg \left(y \leq 9.5 \cdot 10^{+74}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;a + x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 23.4% accurate, 9.3× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = a + x
end function

Java

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

Python

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

Julia

function code(x, y, z, t, a, b)
	return Float64(a + x)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(a + x), $MachinePrecision]

Derivation

1. Initial program 94.1%

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

3. Taylor expanded in z around 0

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

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

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

   2. +-commutative N/A

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

   3. associate-+r+ N/A

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

   4. +-commutative N/A

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

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

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

   6. associate-+l- N/A

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

5. Applied rewrites 75.3%

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

6. Taylor expanded in b around 0

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

8. Applied rewrites 44.1%

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

9. Taylor expanded in t around 0

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

11. Applied rewrites 22.9%

    \[\leadsto a + x \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024364 
(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)))