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

Percentage Accurate: 95.5% → 97.7%

Time: 7.3s

Alternatives: 25

Speedup: 1.1×

• 36.1% 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: 95.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift--.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. lift--.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. lift-+.f64 N/A

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

   10. lift--.f64 N/A

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

   11. +-commutative N/A

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

   12. lower-fma.f64 N/A

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

   13. lift--.f64 N/A

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

   14. +-commutative N/A

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

   15. lower-+.f64 N/A

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

   16. associate--l- N/A

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

   17. *-commutative N/A

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

   18. *-commutative N/A

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

4. Applied rewrites 98.0%

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

Alternative 2: 49.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot y\\ t_2 := \left(b - a\right) \cdot t\\ t_3 := a + y \cdot b\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{+112}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-26}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-141}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-247}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-31}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+122}:\\ \;\;\;\;x + b \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* z y))) (t_2 (* (- b a) t)) (t_3 (+ a (* y b))))
   (if (<= t -3.1e+112)
     t_2
     (if (<= t -1.3e+45)
       t_1
       (if (<= t -1.15e-26)
         (* (- 1.0 y) z)
         (if (<= t -9.5e-141)
           t_3
           (if (<= t 4.3e-247)
             t_1
             (if (<= t 1.55e-31)
               t_3
               (if (<= t 7.5e+122) (+ x (* b y)) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (z * y);
	double t_2 = (b - a) * t;
	double t_3 = a + (y * b);
	double tmp;
	if (t <= -3.1e+112) {
		tmp = t_2;
	} else if (t <= -1.3e+45) {
		tmp = t_1;
	} else if (t <= -1.15e-26) {
		tmp = (1.0 - y) * z;
	} else if (t <= -9.5e-141) {
		tmp = t_3;
	} else if (t <= 4.3e-247) {
		tmp = t_1;
	} else if (t <= 1.55e-31) {
		tmp = t_3;
	} else if (t <= 7.5e+122) {
		tmp = x + (b * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x - (z * y)
    t_2 = (b - a) * t
    t_3 = a + (y * b)
    if (t <= (-3.1d+112)) then
        tmp = t_2
    else if (t <= (-1.3d+45)) then
        tmp = t_1
    else if (t <= (-1.15d-26)) then
        tmp = (1.0d0 - y) * z
    else if (t <= (-9.5d-141)) then
        tmp = t_3
    else if (t <= 4.3d-247) then
        tmp = t_1
    else if (t <= 1.55d-31) then
        tmp = t_3
    else if (t <= 7.5d+122) then
        tmp = x + (b * y)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (z * y);
	double t_2 = (b - a) * t;
	double t_3 = a + (y * b);
	double tmp;
	if (t <= -3.1e+112) {
		tmp = t_2;
	} else if (t <= -1.3e+45) {
		tmp = t_1;
	} else if (t <= -1.15e-26) {
		tmp = (1.0 - y) * z;
	} else if (t <= -9.5e-141) {
		tmp = t_3;
	} else if (t <= 4.3e-247) {
		tmp = t_1;
	} else if (t <= 1.55e-31) {
		tmp = t_3;
	} else if (t <= 7.5e+122) {
		tmp = x + (b * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (z * y)
	t_2 = (b - a) * t
	t_3 = a + (y * b)
	tmp = 0
	if t <= -3.1e+112:
		tmp = t_2
	elif t <= -1.3e+45:
		tmp = t_1
	elif t <= -1.15e-26:
		tmp = (1.0 - y) * z
	elif t <= -9.5e-141:
		tmp = t_3
	elif t <= 4.3e-247:
		tmp = t_1
	elif t <= 1.55e-31:
		tmp = t_3
	elif t <= 7.5e+122:
		tmp = x + (b * y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(z * y))
	t_2 = Float64(Float64(b - a) * t)
	t_3 = Float64(a + Float64(y * b))
	tmp = 0.0
	if (t <= -3.1e+112)
		tmp = t_2;
	elseif (t <= -1.3e+45)
		tmp = t_1;
	elseif (t <= -1.15e-26)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (t <= -9.5e-141)
		tmp = t_3;
	elseif (t <= 4.3e-247)
		tmp = t_1;
	elseif (t <= 1.55e-31)
		tmp = t_3;
	elseif (t <= 7.5e+122)
		tmp = Float64(x + Float64(b * y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (z * y);
	t_2 = (b - a) * t;
	t_3 = a + (y * b);
	tmp = 0.0;
	if (t <= -3.1e+112)
		tmp = t_2;
	elseif (t <= -1.3e+45)
		tmp = t_1;
	elseif (t <= -1.15e-26)
		tmp = (1.0 - y) * z;
	elseif (t <= -9.5e-141)
		tmp = t_3;
	elseif (t <= 4.3e-247)
		tmp = t_1;
	elseif (t <= 1.55e-31)
		tmp = t_3;
	elseif (t <= 7.5e+122)
		tmp = x + (b * y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$3 = N[(a + N[(y * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.1e+112], t$95$2, If[LessEqual[t, -1.3e+45], t$95$1, If[LessEqual[t, -1.15e-26], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t, -9.5e-141], t$95$3, If[LessEqual[t, 4.3e-247], t$95$1, If[LessEqual[t, 1.55e-31], t$95$3, If[LessEqual[t, 7.5e+122], N[(x + N[(b * y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.09999999999999983e112 or 7.5000000000000002e122 < t

   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 t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 77.0

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

   5. Applied rewrites 77.0%

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

   if -3.09999999999999983e112 < t < -1.30000000000000004e45 or -9.49999999999999996e-141 < t < 4.30000000000000005e-247

   1. Initial program 98.1%

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

   3. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 82.1

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

   5. Applied rewrites 82.1%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

         \[\leadsto x - z \cdot y \]

      2. lower-*.f64 60.6

         \[\leadsto x - z \cdot y \]

   8. Applied rewrites 60.6%

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

   if -1.30000000000000004e45 < t < -1.15000000000000004e-26

   1. Initial program 99.9%

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

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 59.3

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

   5. Applied rewrites 59.3%

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

   if -1.15000000000000004e-26 < t < -9.49999999999999996e-141 or 4.30000000000000005e-247 < t < 1.55e-31

   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 a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 66.1

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

   5. Applied rewrites 66.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 66.1%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 58.3%

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

   if 1.55e-31 < t < 7.5000000000000002e122

   1. Initial program 96.7%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 66.0%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 38.0

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

   8. Applied rewrites 38.0%

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

   9. Taylor expanded in y around inf

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

       1. lower-*.f64 56.1

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

   11. Applied rewrites 56.1%

       \[\leadsto x + \color{blue}{b \cdot y} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 3: 87.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - 1\right) \cdot z\\ \mathbf{if}\;b \leq -9.5 \cdot 10^{-47} \lor \neg \left(b \leq 2.2 \cdot 10^{-42}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- y 1.0) z)))
   (if (or (<= b -9.5e-47) (not (<= b 2.2e-42)))
     (fma (- (+ t y) 2.0) b (- x t_1))
     (- x (fma (- t 1.0) a t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y - 1.0) * z;
	double tmp;
	if ((b <= -9.5e-47) || !(b <= 2.2e-42)) {
		tmp = fma(((t + y) - 2.0), b, (x - t_1));
	} else {
		tmp = x - fma((t - 1.0), a, t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y - 1.0) * z)
	tmp = 0.0
	if ((b <= -9.5e-47) || !(b <= 2.2e-42))
		tmp = fma(Float64(Float64(t + y) - 2.0), b, Float64(x - t_1));
	else
		tmp = Float64(x - fma(Float64(t - 1.0), a, t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]}, If[Or[LessEqual[b, -9.5e-47], N[Not[LessEqual[b, 2.2e-42]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[(x - t$95$1), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -9.4999999999999991e-47 or 2.20000000000000005e-42 < b

   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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. associate--l- N/A

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

      17. *-commutative N/A

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

      18. *-commutative N/A

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

   4. Applied rewrites 96.5%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 87.6

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

   7. Applied rewrites 87.6%

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

   if -9.4999999999999991e-47 < b < 2.20000000000000005e-42

   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 b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 95.8

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

   5. Applied rewrites 95.8%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{-47} \lor \neg \left(b \leq 2.2 \cdot 10^{-42}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(y - 1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - 1\right) \cdot z\\ \mathbf{if}\;b \leq -9.5 \cdot 10^{-47} \lor \neg \left(b \leq 2.2 \cdot 10^{-42}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- y 1.0) z)))
   (if (or (<= b -9.5e-47) (not (<= b 2.2e-42)))
     (- (fma (- (+ t y) 2.0) b x) t_1)
     (- x (fma (- t 1.0) a t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y - 1.0) * z;
	double tmp;
	if ((b <= -9.5e-47) || !(b <= 2.2e-42)) {
		tmp = fma(((t + y) - 2.0), b, x) - t_1;
	} else {
		tmp = x - fma((t - 1.0), a, t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y - 1.0) * z)
	tmp = 0.0
	if ((b <= -9.5e-47) || !(b <= 2.2e-42))
		tmp = Float64(fma(Float64(Float64(t + y) - 2.0), b, x) - t_1);
	else
		tmp = Float64(x - fma(Float64(t - 1.0), a, t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]}, If[Or[LessEqual[b, -9.5e-47], N[Not[LessEqual[b, 2.2e-42]], $MachinePrecision]], N[(N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - t$95$1), $MachinePrecision], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -9.4999999999999991e-47 or 2.20000000000000005e-42 < b

   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 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. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift--.f64 86.2

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

   5. Applied rewrites 86.2%

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

   if -9.4999999999999991e-47 < b < 2.20000000000000005e-42

   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 b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 95.8

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

   5. Applied rewrites 95.8%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{-47} \lor \neg \left(b \leq 2.2 \cdot 10^{-42}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(y - 1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+45}:\\ \;\;\;\;x - z \cdot y\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-27}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+122}:\\ \;\;\;\;x + b \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -3.1e+112)
     t_1
     (if (<= t -1.3e+45)
       (- x (* z y))
       (if (<= t -2.4e-27)
         (* (- 1.0 y) z)
         (if (<= t 7.5e+122) (+ x (* b y)) 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 <= -3.1e+112) {
		tmp = t_1;
	} else if (t <= -1.3e+45) {
		tmp = x - (z * y);
	} else if (t <= -2.4e-27) {
		tmp = (1.0 - y) * z;
	} else if (t <= 7.5e+122) {
		tmp = x + (b * y);
	} 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 <= (-3.1d+112)) then
        tmp = t_1
    else if (t <= (-1.3d+45)) then
        tmp = x - (z * y)
    else if (t <= (-2.4d-27)) then
        tmp = (1.0d0 - y) * z
    else if (t <= 7.5d+122) then
        tmp = x + (b * y)
    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 <= -3.1e+112) {
		tmp = t_1;
	} else if (t <= -1.3e+45) {
		tmp = x - (z * y);
	} else if (t <= -2.4e-27) {
		tmp = (1.0 - y) * z;
	} else if (t <= 7.5e+122) {
		tmp = x + (b * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -3.1e+112:
		tmp = t_1
	elif t <= -1.3e+45:
		tmp = x - (z * y)
	elif t <= -2.4e-27:
		tmp = (1.0 - y) * z
	elif t <= 7.5e+122:
		tmp = x + (b * y)
	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 <= -3.1e+112)
		tmp = t_1;
	elseif (t <= -1.3e+45)
		tmp = Float64(x - Float64(z * y));
	elseif (t <= -2.4e-27)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (t <= 7.5e+122)
		tmp = Float64(x + Float64(b * y));
	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 <= -3.1e+112)
		tmp = t_1;
	elseif (t <= -1.3e+45)
		tmp = x - (z * y);
	elseif (t <= -2.4e-27)
		tmp = (1.0 - y) * z;
	elseif (t <= 7.5e+122)
		tmp = x + (b * y);
	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, -3.1e+112], t$95$1, If[LessEqual[t, -1.3e+45], N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.4e-27], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t, 7.5e+122], N[(x + N[(b * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.09999999999999983e112 or 7.5000000000000002e122 < t

   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 t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 77.0

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

   5. Applied rewrites 77.0%

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

   if -3.09999999999999983e112 < t < -1.30000000000000004e45

   1. Initial program 95.5%

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

   3. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 86.6

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

   5. Applied rewrites 86.6%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

         \[\leadsto x - z \cdot y \]

      2. lower-*.f64 60.4

         \[\leadsto x - z \cdot y \]

   8. Applied rewrites 60.4%

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

   if -1.30000000000000004e45 < t < -2.40000000000000002e-27

   1. Initial program 99.9%

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

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 59.3

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

   5. Applied rewrites 59.3%

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

   if -2.40000000000000002e-27 < t < 7.5000000000000002e122

   1. Initial program 97.9%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 58.4%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 32.8

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

   8. Applied rewrites 32.8%

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

   9. Taylor expanded in y around inf

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

       1. lower-*.f64 49.7

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

   11. Applied rewrites 49.7%

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

Alternative 6: 84.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+20} \lor \neg \left(b \leq 2.5 \cdot 10^{-42}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.55e+20) (not (<= b 2.5e-42)))
   (fma (- (+ t y) 2.0) b (- x (- z)))
   (- x (fma (- t 1.0) a (* (- y 1.0) z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.55e+20) || !(b <= 2.5e-42)) {
		tmp = fma(((t + y) - 2.0), b, (x - -z));
	} else {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.55e+20) || !(b <= 2.5e-42))
		tmp = fma(Float64(Float64(t + y) - 2.0), b, Float64(x - Float64(-z)));
	else
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.55e+20], N[Not[LessEqual[b, 2.5e-42]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[(x - (-z)), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.55e20 or 2.50000000000000001e-42 < b

   1. Initial program 92.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. associate--l- N/A

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

      17. *-commutative N/A

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

      18. *-commutative N/A

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

   4. Applied rewrites 96.1%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 89.8

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

   7. Applied rewrites 89.8%

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

   8. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 83.1

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

   10. Applied rewrites 83.1%

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

   if -1.55e20 < b < 2.50000000000000001e-42

   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 b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 92.0

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

   5. Applied rewrites 92.0%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+20} \lor \neg \left(b \leq 2.5 \cdot 10^{-42}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, a\right)\\ \mathbf{if}\;b \leq -1.35 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-182}:\\ \;\;\;\;x - a \cdot \left(t - 1\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-29}:\\ \;\;\;\;x - z \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ t y) 2.0) b a)))
   (if (<= b -1.35e+20)
     t_1
     (if (<= b 2.8e-182)
       (- x (* a (- t 1.0)))
       (if (<= b 2e-29) (- x (* z (- y 1.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((t + y) - 2.0), b, a);
	double tmp;
	if (b <= -1.35e+20) {
		tmp = t_1;
	} else if (b <= 2.8e-182) {
		tmp = x - (a * (t - 1.0));
	} else if (b <= 2e-29) {
		tmp = x - (z * (y - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(t + y) - 2.0), b, a)
	tmp = 0.0
	if (b <= -1.35e+20)
		tmp = t_1;
	elseif (b <= 2.8e-182)
		tmp = Float64(x - Float64(a * Float64(t - 1.0)));
	elseif (b <= 2e-29)
		tmp = Float64(x - Float64(z * Float64(y - 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + a), $MachinePrecision]}, If[LessEqual[b, -1.35e+20], t$95$1, If[LessEqual[b, 2.8e-182], N[(x - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e-29], N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.35e20 or 1.99999999999999989e-29 < b

   1. Initial program 91.8%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 74.4

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

   5. Applied rewrites 74.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 73.6%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 73.6

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

      10. associate--l- 73.6

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

      11. +-commutative 73.6

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

   10. Applied rewrites 73.6%

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

   if -1.35e20 < b < 2.79999999999999993e-182

   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 b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 92.2

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

   5. Applied rewrites 92.2%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 64.0

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

   8. Applied rewrites 64.0%

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

   if 2.79999999999999993e-182 < b < 1.99999999999999989e-29

   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 b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 90.0

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

   5. Applied rewrites 90.0%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 70.0

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

   8. Applied rewrites 70.0%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, a\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-182}:\\ \;\;\;\;x - a \cdot \left(t - 1\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-29}:\\ \;\;\;\;x - z \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 27.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot t\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+132}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq -1000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a) t)))
   (if (<= t -1.15e+248)
     t_1
     (if (<= t -3.5e+132)
       (* b t)
       (if (<= t -1000000.0) t_1 (if (<= t 3.2e+42) x (* b t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a * t;
	double tmp;
	if (t <= -1.15e+248) {
		tmp = t_1;
	} else if (t <= -3.5e+132) {
		tmp = b * t;
	} else if (t <= -1000000.0) {
		tmp = t_1;
	} else if (t <= 3.2e+42) {
		tmp = x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -a * t
    if (t <= (-1.15d+248)) then
        tmp = t_1
    else if (t <= (-3.5d+132)) then
        tmp = b * t
    else if (t <= (-1000000.0d0)) then
        tmp = t_1
    else if (t <= 3.2d+42) then
        tmp = x
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a * t;
	double tmp;
	if (t <= -1.15e+248) {
		tmp = t_1;
	} else if (t <= -3.5e+132) {
		tmp = b * t;
	} else if (t <= -1000000.0) {
		tmp = t_1;
	} else if (t <= 3.2e+42) {
		tmp = x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -a * t
	tmp = 0
	if t <= -1.15e+248:
		tmp = t_1
	elif t <= -3.5e+132:
		tmp = b * t
	elif t <= -1000000.0:
		tmp = t_1
	elif t <= 3.2e+42:
		tmp = x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-a) * t)
	tmp = 0.0
	if (t <= -1.15e+248)
		tmp = t_1;
	elseif (t <= -3.5e+132)
		tmp = Float64(b * t);
	elseif (t <= -1000000.0)
		tmp = t_1;
	elseif (t <= 3.2e+42)
		tmp = x;
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -a * t;
	tmp = 0.0;
	if (t <= -1.15e+248)
		tmp = t_1;
	elseif (t <= -3.5e+132)
		tmp = b * t;
	elseif (t <= -1000000.0)
		tmp = t_1;
	elseif (t <= 3.2e+42)
		tmp = x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) * t), $MachinePrecision]}, If[LessEqual[t, -1.15e+248], t$95$1, If[LessEqual[t, -3.5e+132], N[(b * t), $MachinePrecision], If[LessEqual[t, -1000000.0], t$95$1, If[LessEqual[t, 3.2e+42], x, N[(b * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1500000000000001e248 or -3.5000000000000002e132 < t < -1e6

   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 t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 54.2

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

   5. Applied rewrites 54.2%

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

   6. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 44.7

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

   8. Applied rewrites 44.7%

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

   if -1.1500000000000001e248 < t < -3.5000000000000002e132 or 3.20000000000000002e42 < t

   1. Initial program 95.6%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 62.1

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

   5. Applied rewrites 62.1%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 45.4%

      \[\leadsto b \cdot t \]

   if -1e6 < t < 3.20000000000000002e42

   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 x around inf

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

   5. Applied rewrites 24.8%

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

Alternative 9: 73.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{-60} \lor \neg \left(b \leq 1.55 \cdot 10^{-42}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y - 1, -a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -9.8e-60) (not (<= b 1.55e-42)))
   (fma (- (+ t y) 2.0) b (- x (- z)))
   (- x (fma z (- y 1.0) (- a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -9.8e-60) || !(b <= 1.55e-42)) {
		tmp = fma(((t + y) - 2.0), b, (x - -z));
	} else {
		tmp = x - fma(z, (y - 1.0), -a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -9.8e-60) || !(b <= 1.55e-42))
		tmp = fma(Float64(Float64(t + y) - 2.0), b, Float64(x - Float64(-z)));
	else
		tmp = Float64(x - fma(z, Float64(y - 1.0), Float64(-a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -9.8e-60], N[Not[LessEqual[b, 1.55e-42]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[(x - (-z)), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(y - 1.0), $MachinePrecision] + (-a)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.79999999999999977e-60 or 1.5500000000000001e-42 < b

   1. Initial program 93.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 N/A

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

      16. associate--l- N/A

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

      17. *-commutative N/A

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

      18. *-commutative N/A

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

   4. Applied rewrites 96.6%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 87.2

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

   7. Applied rewrites 87.2%

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

   8. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 79.9

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

   10. Applied rewrites 79.9%

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

   if -9.79999999999999977e-60 < b < 1.5500000000000001e-42

   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 b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 96.6

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

   5. Applied rewrites 96.6%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 77.9

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

   8. Applied rewrites 77.9%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{-60} \lor \neg \left(b \leq 1.55 \cdot 10^{-42}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y - 1, -a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.05 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-182}:\\ \;\;\;\;x - a \cdot \left(t - 1\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-29}:\\ \;\;\;\;x - z \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -2.05e+21)
     t_1
     (if (<= b 2.8e-182)
       (- x (* a (- t 1.0)))
       (if (<= b 2.7e-29) (- x (* z (- y 1.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -2.05e+21) {
		tmp = t_1;
	} else if (b <= 2.8e-182) {
		tmp = x - (a * (t - 1.0));
	} else if (b <= 2.7e-29) {
		tmp = x - (z * (y - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t + y) - 2.0d0) * b
    if (b <= (-2.05d+21)) then
        tmp = t_1
    else if (b <= 2.8d-182) then
        tmp = x - (a * (t - 1.0d0))
    else if (b <= 2.7d-29) then
        tmp = x - (z * (y - 1.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -2.05e+21) {
		tmp = t_1;
	} else if (b <= 2.8e-182) {
		tmp = x - (a * (t - 1.0));
	} else if (b <= 2.7e-29) {
		tmp = x - (z * (y - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t + y) - 2.0) * b
	tmp = 0
	if b <= -2.05e+21:
		tmp = t_1
	elif b <= 2.8e-182:
		tmp = x - (a * (t - 1.0))
	elif b <= 2.7e-29:
		tmp = x - (z * (y - 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -2.05e+21)
		tmp = t_1;
	elseif (b <= 2.8e-182)
		tmp = Float64(x - Float64(a * Float64(t - 1.0)));
	elseif (b <= 2.7e-29)
		tmp = Float64(x - Float64(z * Float64(y - 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t + y) - 2.0) * b;
	tmp = 0.0;
	if (b <= -2.05e+21)
		tmp = t_1;
	elseif (b <= 2.8e-182)
		tmp = x - (a * (t - 1.0));
	elseif (b <= 2.7e-29)
		tmp = x - (z * (y - 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.05e+21], t$95$1, If[LessEqual[b, 2.8e-182], N[(x - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.7e-29], N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.05e21 or 2.70000000000000023e-29 < b

   1. Initial program 91.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 69.6

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 69.6

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

   5. Applied rewrites 69.6%

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

   if -2.05e21 < b < 2.79999999999999993e-182

   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 b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 92.2

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

   5. Applied rewrites 92.2%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 64.0

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

   8. Applied rewrites 64.0%

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

   if 2.79999999999999993e-182 < b < 2.70000000000000023e-29

   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 b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 90.0

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

   5. Applied rewrites 90.0%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 70.0

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

   8. Applied rewrites 70.0%

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

Alternative 11: 55.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-182}:\\ \;\;\;\;x - a \cdot t\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-30}:\\ \;\;\;\;x - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -1.3e+20)
     t_1
     (if (<= b 2.8e-182) (- x (* a t)) (if (<= b 3e-30) (- x (* z y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -1.3e+20) {
		tmp = t_1;
	} else if (b <= 2.8e-182) {
		tmp = x - (a * t);
	} else if (b <= 3e-30) {
		tmp = x - (z * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t + y) - 2.0d0) * b
    if (b <= (-1.3d+20)) then
        tmp = t_1
    else if (b <= 2.8d-182) then
        tmp = x - (a * t)
    else if (b <= 3d-30) then
        tmp = x - (z * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -1.3e+20) {
		tmp = t_1;
	} else if (b <= 2.8e-182) {
		tmp = x - (a * t);
	} else if (b <= 3e-30) {
		tmp = x - (z * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t + y) - 2.0) * b
	tmp = 0
	if b <= -1.3e+20:
		tmp = t_1
	elif b <= 2.8e-182:
		tmp = x - (a * t)
	elif b <= 3e-30:
		tmp = x - (z * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -1.3e+20)
		tmp = t_1;
	elseif (b <= 2.8e-182)
		tmp = Float64(x - Float64(a * t));
	elseif (b <= 3e-30)
		tmp = Float64(x - Float64(z * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t + y) - 2.0) * b;
	tmp = 0.0;
	if (b <= -1.3e+20)
		tmp = t_1;
	elseif (b <= 2.8e-182)
		tmp = x - (a * t);
	elseif (b <= 3e-30)
		tmp = x - (z * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.3e+20], t$95$1, If[LessEqual[b, 2.8e-182], N[(x - N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e-30], N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.3e20 or 2.9999999999999999e-30 < b

   1. Initial program 91.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 69.6

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 69.6

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

   5. Applied rewrites 69.6%

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

   if -1.3e20 < b < 2.79999999999999993e-182

   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 b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 92.2

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

   5. Applied rewrites 92.2%

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

   6. Taylor expanded in t around inf

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

      1. lower-*.f64 45.4

         \[\leadsto x - a \cdot t \]

   8. Applied rewrites 45.4%

      \[\leadsto x - a \cdot \color{blue}{t} \]

   if 2.79999999999999993e-182 < b < 2.9999999999999999e-30

   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 b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 90.0

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

   5. Applied rewrites 90.0%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

         \[\leadsto x - z \cdot y \]

      2. lower-*.f64 51.8

         \[\leadsto x - z \cdot y \]

   8. Applied rewrites 51.8%

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

Alternative 12: 69.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{-60} \lor \neg \left(b \leq 4600\right):\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y - 1, -a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -9.8e-60) (not (<= b 4600.0)))
   (+ x (* (- (+ y t) 2.0) b))
   (- x (fma z (- y 1.0) (- a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -9.8e-60) || !(b <= 4600.0)) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = x - fma(z, (y - 1.0), -a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -9.8e-60) || !(b <= 4600.0))
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	else
		tmp = Float64(x - fma(z, Float64(y - 1.0), Float64(-a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -9.8e-60], N[Not[LessEqual[b, 4600.0]], $MachinePrecision]], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(y - 1.0), $MachinePrecision] + (-a)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.79999999999999977e-60 or 4600 < b

   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 x around inf

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

   5. Applied rewrites 77.0%

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

   if -9.79999999999999977e-60 < b < 4600

   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 b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 93.8

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

   5. Applied rewrites 93.8%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 76.7

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

   8. Applied rewrites 76.7%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{-60} \lor \neg \left(b \leq 4600\right):\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y - 1, -a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 69.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+42} \lor \neg \left(b \leq 2.7 \cdot 10^{-29}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y - 1, -a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -7.2e+42) (not (<= b 2.7e-29)))
   (fma (- (+ t y) 2.0) b a)
   (- x (fma z (- y 1.0) (- a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.2e+42) || !(b <= 2.7e-29)) {
		tmp = fma(((t + y) - 2.0), b, a);
	} else {
		tmp = x - fma(z, (y - 1.0), -a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -7.2e+42) || !(b <= 2.7e-29))
		tmp = fma(Float64(Float64(t + y) - 2.0), b, a);
	else
		tmp = Float64(x - fma(z, Float64(y - 1.0), Float64(-a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -7.2e+42], N[Not[LessEqual[b, 2.7e-29]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + a), $MachinePrecision], N[(x - N[(z * N[(y - 1.0), $MachinePrecision] + (-a)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.2000000000000002e42 or 2.70000000000000023e-29 < b

   1. Initial program 91.4%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 75.8

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

   5. Applied rewrites 75.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 75.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 75.0

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

      10. associate--l- 75.0

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

      11. +-commutative 75.0

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

   10. Applied rewrites 75.0%

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

   if -7.2000000000000002e42 < b < 2.70000000000000023e-29

   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 b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 90.5

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

   5. Applied rewrites 90.5%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 72.8

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

   8. Applied rewrites 72.8%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+42} \lor \neg \left(b \leq 2.7 \cdot 10^{-29}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y - 1, -a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-243}:\\ \;\;\;\;x - a \cdot t\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+25}:\\ \;\;\;\;x + b \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -5.2e+67)
     t_1
     (if (<= y 7.2e-243)
       (- x (* a t))
       (if (<= y 3.4e+25) (+ x (* b t)) 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 <= -5.2e+67) {
		tmp = t_1;
	} else if (y <= 7.2e-243) {
		tmp = x - (a * t);
	} else if (y <= 3.4e+25) {
		tmp = x + (b * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - z) * y
    if (y <= (-5.2d+67)) then
        tmp = t_1
    else if (y <= 7.2d-243) then
        tmp = x - (a * t)
    else if (y <= 3.4d+25) then
        tmp = x + (b * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -5.2e+67) {
		tmp = t_1;
	} else if (y <= 7.2e-243) {
		tmp = x - (a * t);
	} else if (y <= 3.4e+25) {
		tmp = x + (b * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - z) * y
	tmp = 0
	if y <= -5.2e+67:
		tmp = t_1
	elif y <= 7.2e-243:
		tmp = x - (a * t)
	elif y <= 3.4e+25:
		tmp = x + (b * t)
	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 <= -5.2e+67)
		tmp = t_1;
	elseif (y <= 7.2e-243)
		tmp = Float64(x - Float64(a * t));
	elseif (y <= 3.4e+25)
		tmp = Float64(x + Float64(b * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - z) * y;
	tmp = 0.0;
	if (y <= -5.2e+67)
		tmp = t_1;
	elseif (y <= 7.2e-243)
		tmp = x - (a * t);
	elseif (y <= 3.4e+25)
		tmp = x + (b * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -5.2e+67], t$95$1, If[LessEqual[y, 7.2e-243], N[(x - N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e+25], N[(x + N[(b * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.2000000000000001e67 or 3.39999999999999984e25 < y

   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 y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 66.8

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

   5. Applied rewrites 66.8%

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

   if -5.2000000000000001e67 < y < 7.2000000000000003e-243

   1. Initial program 96.3%

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

   3. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 77.3

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

   5. Applied rewrites 77.3%

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

   6. Taylor expanded in t around inf

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

      1. lower-*.f64 46.3

         \[\leadsto x - a \cdot t \]

   8. Applied rewrites 46.3%

      \[\leadsto x - a \cdot \color{blue}{t} \]

   if 7.2000000000000003e-243 < y < 3.39999999999999984e25

   1. Initial program 98.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 61.0%

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

   6. Taylor expanded in t around inf

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

      1. lower-*.f64 47.6

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

   8. Applied rewrites 47.6%

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

Alternative 15: 50.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.55 \cdot 10^{-301}:\\ \;\;\;\;x - a \cdot t\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+61}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -5.2e+67)
     t_1
     (if (<= y 3.55e-301)
       (- x (* a t))
       (if (<= y 3.6e+61) (* (- b a) t) 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 <= -5.2e+67) {
		tmp = t_1;
	} else if (y <= 3.55e-301) {
		tmp = x - (a * t);
	} else if (y <= 3.6e+61) {
		tmp = (b - a) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - z) * y
    if (y <= (-5.2d+67)) then
        tmp = t_1
    else if (y <= 3.55d-301) then
        tmp = x - (a * t)
    else if (y <= 3.6d+61) then
        tmp = (b - a) * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -5.2e+67) {
		tmp = t_1;
	} else if (y <= 3.55e-301) {
		tmp = x - (a * t);
	} else if (y <= 3.6e+61) {
		tmp = (b - a) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - z) * y
	tmp = 0
	if y <= -5.2e+67:
		tmp = t_1
	elif y <= 3.55e-301:
		tmp = x - (a * t)
	elif y <= 3.6e+61:
		tmp = (b - a) * t
	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 <= -5.2e+67)
		tmp = t_1;
	elseif (y <= 3.55e-301)
		tmp = Float64(x - Float64(a * t));
	elseif (y <= 3.6e+61)
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - z) * y;
	tmp = 0.0;
	if (y <= -5.2e+67)
		tmp = t_1;
	elseif (y <= 3.55e-301)
		tmp = x - (a * t);
	elseif (y <= 3.6e+61)
		tmp = (b - a) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -5.2e+67], t$95$1, If[LessEqual[y, 3.55e-301], N[(x - N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+61], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.2000000000000001e67 or 3.6000000000000001e61 < y

   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 y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 69.1

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

   5. Applied rewrites 69.1%

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

   if -5.2000000000000001e67 < y < 3.55e-301

   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 b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 77.8

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

   5. Applied rewrites 77.8%

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

   6. Taylor expanded in t around inf

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

      1. lower-*.f64 48.9

         \[\leadsto x - a \cdot t \]

   8. Applied rewrites 48.9%

      \[\leadsto x - a \cdot \color{blue}{t} \]

   if 3.55e-301 < y < 3.6000000000000001e61

   1. Initial program 98.6%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 39.2

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

   5. Applied rewrites 39.2%

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

Alternative 16: 61.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{+21} \lor \neg \left(b \leq 3.1 \cdot 10^{-30}\right):\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(t - 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.05e+21) (not (<= b 3.1e-30)))
   (* (- (+ t y) 2.0) b)
   (- x (* a (- t 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.05e+21) || !(b <= 3.1e-30)) {
		tmp = ((t + y) - 2.0) * b;
	} else {
		tmp = x - (a * (t - 1.0));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.05d+21)) .or. (.not. (b <= 3.1d-30))) then
        tmp = ((t + y) - 2.0d0) * b
    else
        tmp = x - (a * (t - 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.05e+21) || !(b <= 3.1e-30)) {
		tmp = ((t + y) - 2.0) * b;
	} else {
		tmp = x - (a * (t - 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.05e+21) or not (b <= 3.1e-30):
		tmp = ((t + y) - 2.0) * b
	else:
		tmp = x - (a * (t - 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.05e+21) || !(b <= 3.1e-30))
		tmp = Float64(Float64(Float64(t + y) - 2.0) * b);
	else
		tmp = Float64(x - Float64(a * Float64(t - 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.05e+21) || ~((b <= 3.1e-30)))
		tmp = ((t + y) - 2.0) * b;
	else
		tmp = x - (a * (t - 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.05e+21], N[Not[LessEqual[b, 3.1e-30]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], N[(x - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.05e21 or 3.09999999999999991e-30 < b

   1. Initial program 91.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 69.6

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 69.6

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

   5. Applied rewrites 69.6%

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

   if -2.05e21 < b < 3.09999999999999991e-30

   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 b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 91.6

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

   5. Applied rewrites 91.6%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 59.7

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

   8. Applied rewrites 59.7%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{+21} \lor \neg \left(b \leq 3.1 \cdot 10^{-30}\right):\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(t - 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 26.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+132}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{+68}:\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.95e+132)
   (* b t)
   (if (<= t -2.9e+68) (* (- y) z) (if (<= t 3.2e+42) x (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.95e+132) {
		tmp = b * t;
	} else if (t <= -2.9e+68) {
		tmp = -y * z;
	} else if (t <= 3.2e+42) {
		tmp = x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.95d+132)) then
        tmp = b * t
    else if (t <= (-2.9d+68)) then
        tmp = -y * z
    else if (t <= 3.2d+42) then
        tmp = x
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.95e+132) {
		tmp = b * t;
	} else if (t <= -2.9e+68) {
		tmp = -y * z;
	} else if (t <= 3.2e+42) {
		tmp = x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.95e+132:
		tmp = b * t
	elif t <= -2.9e+68:
		tmp = -y * z
	elif t <= 3.2e+42:
		tmp = x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.95e+132)
		tmp = Float64(b * t);
	elseif (t <= -2.9e+68)
		tmp = Float64(Float64(-y) * z);
	elseif (t <= 3.2e+42)
		tmp = x;
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.95e+132)
		tmp = b * t;
	elseif (t <= -2.9e+68)
		tmp = -y * z;
	elseif (t <= 3.2e+42)
		tmp = x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.95e+132], N[(b * t), $MachinePrecision], If[LessEqual[t, -2.9e+68], N[((-y) * z), $MachinePrecision], If[LessEqual[t, 3.2e+42], x, N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.95000000000000001e132 or 3.20000000000000002e42 < t

   1. Initial program 91.4%

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

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 68.1

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

   5. Applied rewrites 68.1%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 44.4%

      \[\leadsto b \cdot t \]

   if -1.95000000000000001e132 < t < -2.90000000000000011e68

   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

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 48.6

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

   5. Applied rewrites 48.6%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(y\right)\right) \cdot z \]

      2. lower-neg.f64 42.3

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

   8. Applied rewrites 42.3%

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

   if -2.90000000000000011e68 < t < 3.20000000000000002e42

   1. Initial program 98.7%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 24.4%

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

Alternative 18: 50.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+22} \lor \neg \left(y \leq 3.6 \cdot 10^{+61}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.5e+22) (not (<= y 3.6e+61))) (* (- 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 <= -5.5e+22) || !(y <= 3.6e+61)) {
		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 <= (-5.5d+22)) .or. (.not. (y <= 3.6d+61))) 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 <= -5.5e+22) || !(y <= 3.6e+61)) {
		tmp = (b - z) * y;
	} else {
		tmp = (b - a) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.5e+22) or not (y <= 3.6e+61):
		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 <= -5.5e+22) || !(y <= 3.6e+61))
		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 <= -5.5e+22) || ~((y <= 3.6e+61)))
		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, -5.5e+22], N[Not[LessEqual[y, 3.6e+61]], $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 < -5.50000000000000021e22 or 3.6000000000000001e61 < y

   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 y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 67.6

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

   5. Applied rewrites 67.6%

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

   if -5.50000000000000021e22 < y < 3.6000000000000001e61

   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 t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 36.9

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

   5. Applied rewrites 36.9%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+22} \lor \neg \left(y \leq 3.6 \cdot 10^{+61}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 46.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+111} \lor \neg \left(t \leq 2 \cdot 10^{+128}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.8e+111) (not (<= t 2e+128))) (* (- b a) t) (* (- 1.0 y) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.8e+111) || !(t <= 2e+128)) {
		tmp = (b - a) * t;
	} else {
		tmp = (1.0 - y) * z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.8d+111)) .or. (.not. (t <= 2d+128))) then
        tmp = (b - a) * t
    else
        tmp = (1.0d0 - y) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.8e+111) || !(t <= 2e+128)) {
		tmp = (b - a) * t;
	} else {
		tmp = (1.0 - y) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.8e+111) or not (t <= 2e+128):
		tmp = (b - a) * t
	else:
		tmp = (1.0 - y) * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.8e+111) || !(t <= 2e+128))
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = Float64(Float64(1.0 - y) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.8e+111) || ~((t <= 2e+128)))
		tmp = (b - a) * t;
	else
		tmp = (1.0 - y) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.8e+111], N[Not[LessEqual[t, 2e+128]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.8000000000000001e111 or 2.0000000000000002e128 < t

   1. Initial program 90.6%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 81.5

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

   5. Applied rewrites 81.5%

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

   if -1.8000000000000001e111 < t < 2.0000000000000002e128

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 32.3

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

   5. Applied rewrites 32.3%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+111} \lor \neg \left(t \leq 2 \cdot 10^{+128}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 42.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-13} \lor \neg \left(z \leq 5.5 \cdot 10^{+78}\right):\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.2e-13) (not (<= z 5.5e+78)))
   (* (- 1.0 y) z)
   (* (- 1.0 t) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.2e-13) || !(z <= 5.5e+78)) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = (1.0 - t) * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4.2d-13)) .or. (.not. (z <= 5.5d+78))) then
        tmp = (1.0d0 - y) * z
    else
        tmp = (1.0d0 - t) * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.2e-13) || !(z <= 5.5e+78)) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = (1.0 - t) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.2e-13) or not (z <= 5.5e+78):
		tmp = (1.0 - y) * z
	else:
		tmp = (1.0 - t) * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.2e-13) || !(z <= 5.5e+78))
		tmp = Float64(Float64(1.0 - y) * z);
	else
		tmp = Float64(Float64(1.0 - t) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.2e-13) || ~((z <= 5.5e+78)))
		tmp = (1.0 - y) * z;
	else
		tmp = (1.0 - t) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.2e-13], N[Not[LessEqual[z, 5.5e+78]], $MachinePrecision]], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.19999999999999977e-13 or 5.4999999999999997e78 < z

   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 z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 51.4

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

   5. Applied rewrites 51.4%

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

   if -4.19999999999999977e-13 < z < 5.4999999999999997e78

   1. Initial program 96.6%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 35.3

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

   5. Applied rewrites 35.3%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-13} \lor \neg \left(z \leq 5.5 \cdot 10^{+78}\right):\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 33.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.3 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+124}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -5.3e+75) x (if (<= x 3.6e+124) (* (- 1.0 t) a) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5.3e+75) {
		tmp = x;
	} else if (x <= 3.6e+124) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = 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 (x <= (-5.3d+75)) then
        tmp = x
    else if (x <= 3.6d+124) then
        tmp = (1.0d0 - t) * a
    else
        tmp = 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 (x <= -5.3e+75) {
		tmp = x;
	} else if (x <= 3.6e+124) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -5.3e+75:
		tmp = x
	elif x <= 3.6e+124:
		tmp = (1.0 - t) * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -5.3e+75)
		tmp = x;
	elseif (x <= 3.6e+124)
		tmp = Float64(Float64(1.0 - t) * a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -5.3e+75)
		tmp = x;
	elseif (x <= 3.6e+124)
		tmp = (1.0 - t) * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -5.3e+75], x, If[LessEqual[x, 3.6e+124], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.2999999999999998e75 or 3.59999999999999986e124 < x

   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 x around inf

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

   5. Applied rewrites 43.6%

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

   if -5.2999999999999998e75 < x < 3.59999999999999986e124

   1. Initial program 97.1%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 34.0

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

   5. Applied rewrites 34.0%

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

Alternative 22: 21.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+36}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-275}:\\ \;\;\;\;1 \cdot a\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+99}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.2e+36) x (if (<= x 1.5e-275) (* 1.0 a) (if (<= x 4e+99) z x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.2e+36) {
		tmp = x;
	} else if (x <= 1.5e-275) {
		tmp = 1.0 * a;
	} else if (x <= 4e+99) {
		tmp = z;
	} else {
		tmp = 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 (x <= (-6.2d+36)) then
        tmp = x
    else if (x <= 1.5d-275) then
        tmp = 1.0d0 * a
    else if (x <= 4d+99) then
        tmp = z
    else
        tmp = 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 (x <= -6.2e+36) {
		tmp = x;
	} else if (x <= 1.5e-275) {
		tmp = 1.0 * a;
	} else if (x <= 4e+99) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6.2e+36:
		tmp = x
	elif x <= 1.5e-275:
		tmp = 1.0 * a
	elif x <= 4e+99:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.2e+36)
		tmp = x;
	elseif (x <= 1.5e-275)
		tmp = Float64(1.0 * a);
	elseif (x <= 4e+99)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6.2e+36)
		tmp = x;
	elseif (x <= 1.5e-275)
		tmp = 1.0 * a;
	elseif (x <= 4e+99)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.2e+36], x, If[LessEqual[x, 1.5e-275], N[(1.0 * a), $MachinePrecision], If[LessEqual[x, 4e+99], z, x]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.1999999999999999e36 or 3.9999999999999999e99 < x

   1. Initial program 94.2%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 39.6%

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

   if -6.1999999999999999e36 < x < 1.5e-275

   1. Initial program 98.6%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 40.0

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

   5. Applied rewrites 40.0%

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

   6. Taylor expanded in t around 0

      \[\leadsto 1 \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 26.2%

      \[\leadsto 1 \cdot a \]

   if 1.5e-275 < x < 3.9999999999999999e99

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 29.7

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

   5. Applied rewrites 29.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 18.5%

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

Alternative 23: 26.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+98} \lor \neg \left(t \leq 3.2 \cdot 10^{+42}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.26e+98) (not (<= t 3.2e+42))) (* b t) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.26e+98) || !(t <= 3.2e+42)) {
		tmp = b * t;
	} else {
		tmp = 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 ((t <= (-1.26d+98)) .or. (.not. (t <= 3.2d+42))) then
        tmp = b * t
    else
        tmp = 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 ((t <= -1.26e+98) || !(t <= 3.2e+42)) {
		tmp = b * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.26e+98) or not (t <= 3.2e+42):
		tmp = b * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.26e+98) || !(t <= 3.2e+42))
		tmp = Float64(b * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.26e+98) || ~((t <= 3.2e+42)))
		tmp = b * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.26e+98], N[Not[LessEqual[t, 3.2e+42]], $MachinePrecision]], N[(b * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -1.25999999999999999e98 or 3.20000000000000002e42 < t

   1. Initial program 92.0%

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

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 68.0

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

   5. Applied rewrites 68.0%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 41.5%

      \[\leadsto b \cdot t \]

   if -1.25999999999999999e98 < t < 3.20000000000000002e42

   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 x around inf

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

   5. Applied rewrites 24.1%

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

4. Final simplification 30.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+98} \lor \neg \left(t \leq 3.2 \cdot 10^{+42}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 21.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+99}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.4e-10) x (if (<= x 4e+99) z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.4e-10) {
		tmp = x;
	} else if (x <= 4e+99) {
		tmp = z;
	} else {
		tmp = 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 (x <= (-1.4d-10)) then
        tmp = x
    else if (x <= 4d+99) then
        tmp = z
    else
        tmp = 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 (x <= -1.4e-10) {
		tmp = x;
	} else if (x <= 4e+99) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.4e-10:
		tmp = x
	elif x <= 4e+99:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.4e-10)
		tmp = x;
	elseif (x <= 4e+99)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.4e-10)
		tmp = x;
	elseif (x <= 4e+99)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.4e-10], x, If[LessEqual[x, 4e+99], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.40000000000000008e-10 or 3.9999999999999999e99 < x

   1. Initial program 94.5%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 38.0%

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

   if -1.40000000000000008e-10 < x < 3.9999999999999999e99

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 31.1

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

   5. Applied rewrites 31.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 16.1%

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

Alternative 25: 16.1% accurate, 37.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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 x around inf

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

5. Applied rewrites 18.2%

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

Reproduce

herbie shell --seed 2025038 
(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)))