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

Percentage Accurate: 95.0% → 96.3%

Time: 9.1s

Alternatives: 22

Speedup: 1.1×

• 35.3% 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: 95.0% 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: 96.3% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.9%

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

3. Taylor expanded in y around 0

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

5. Applied rewrites 96.9%

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

Alternative 2: 64.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+108}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-7}:\\ \;\;\;\;\left(b - z\right) \cdot y - \left(t - 1\right) \cdot a\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-19}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, z + x\right) + a\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+116}:\\ \;\;\;\;x + \mathsf{fma}\left(y, b, \left(t - 2\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, x - a \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.3e+108)
   (* (- b a) t)
   (if (<= t -1.6e-7)
     (- (* (- b z) y) (* (- t 1.0) a))
     (if (<= t 4.9e-19)
       (+ (fma -2.0 b (+ z x)) a)
       (if (<= t 7e+116)
         (+ x (fma y b (* (- t 2.0) b)))
         (fma (- t 2.0) b (- x (* a t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.3e+108) {
		tmp = (b - a) * t;
	} else if (t <= -1.6e-7) {
		tmp = ((b - z) * y) - ((t - 1.0) * a);
	} else if (t <= 4.9e-19) {
		tmp = fma(-2.0, b, (z + x)) + a;
	} else if (t <= 7e+116) {
		tmp = x + fma(y, b, ((t - 2.0) * b));
	} else {
		tmp = fma((t - 2.0), b, (x - (a * t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.3e+108)
		tmp = Float64(Float64(b - a) * t);
	elseif (t <= -1.6e-7)
		tmp = Float64(Float64(Float64(b - z) * y) - Float64(Float64(t - 1.0) * a));
	elseif (t <= 4.9e-19)
		tmp = Float64(fma(-2.0, b, Float64(z + x)) + a);
	elseif (t <= 7e+116)
		tmp = Float64(x + fma(y, b, Float64(Float64(t - 2.0) * b)));
	else
		tmp = fma(Float64(t - 2.0), b, Float64(x - Float64(a * t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.3e+108], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, -1.6e-7], N[(N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.9e-19], N[(N[(-2.0 * b + N[(z + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t, 7e+116], N[(x + N[(y * b + N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - 2.0), $MachinePrecision] * b + N[(x - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.2999999999999999e108

   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 t around inf

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

   5. Applied rewrites 84.8%

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

   if -2.2999999999999999e108 < t < -1.6e-7

   1. Initial program 96.9%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 96.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 72.8%

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

   if -1.6e-7 < t < 4.89999999999999993e-19

   1. Initial program 97.4%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 72.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 72.4%

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

   if 4.89999999999999993e-19 < t < 6.99999999999999993e116

   1. Initial program 88.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 81.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. distribute-rgt-in N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 81.2

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

   7. Applied rewrites 81.2%

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

   if 6.99999999999999993e116 < t

   1. Initial program 90.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 92.6%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 90.2%

      \[\leadsto \mathsf{fma}\left(t - 2, b, x - a \cdot t\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 3: 49.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - y\right) \cdot z\\ t_2 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-165}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-157}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 y) z)) (t_2 (* (- b a) t)))
   (if (<= t -2.5e+33)
     t_2
     (if (<= t -3.6e-165)
       t_1
       (if (<= t 3e-157)
         (fma y b x)
         (if (<= t 2e-29) t_1 (if (<= t 3.1e+112) (fma y b x) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -2.5e+33) {
		tmp = t_2;
	} else if (t <= -3.6e-165) {
		tmp = t_1;
	} else if (t <= 3e-157) {
		tmp = fma(y, b, x);
	} else if (t <= 2e-29) {
		tmp = t_1;
	} else if (t <= 3.1e+112) {
		tmp = fma(y, b, x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - y) * z)
	t_2 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -2.5e+33)
		tmp = t_2;
	elseif (t <= -3.6e-165)
		tmp = t_1;
	elseif (t <= 3e-157)
		tmp = fma(y, b, x);
	elseif (t <= 2e-29)
		tmp = t_1;
	elseif (t <= 3.1e+112)
		tmp = fma(y, b, x);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -2.5e+33], t$95$2, If[LessEqual[t, -3.6e-165], t$95$1, If[LessEqual[t, 3e-157], N[(y * b + x), $MachinePrecision], If[LessEqual[t, 2e-29], t$95$1, If[LessEqual[t, 3.1e+112], N[(y * b + x), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.49999999999999986e33 or 3.09999999999999983e112 < t

   1. Initial program 93.4%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 81.4%

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

   if -2.49999999999999986e33 < t < -3.59999999999999984e-165 or 3e-157 < t < 1.99999999999999989e-29

   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 z around inf

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

   5. Applied rewrites 47.2%

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

   if -3.59999999999999984e-165 < t < 3e-157 or 1.99999999999999989e-29 < t < 3.09999999999999983e112

   1. Initial program 95.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 63.1%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 58.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 58.2

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

   10. Applied rewrites 58.2%

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

   11. Taylor expanded in y around inf

       \[\leadsto \mathsf{fma}\left(\color{blue}{y}, b, x\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 50.0%

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

Alternative 4: 68.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot a\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{+124}:\\ \;\;\;\;\left(x + z\right) - t\_1\\ \mathbf{elif}\;a \leq -0.014 \lor \neg \left(a \leq 9.2 \cdot 10^{-79}\right):\\ \;\;\;\;\left(b - z\right) \cdot y - t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y - 1, x\right) + t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 1.0) a)))
   (if (<= a -2.5e+124)
     (- (+ x z) t_1)
     (if (or (<= a -0.014) (not (<= a 9.2e-79)))
       (- (* (- b z) y) t_1)
       (+ (fma (- z) (- y 1.0) x) (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 1.0) * a;
	double tmp;
	if (a <= -2.5e+124) {
		tmp = (x + z) - t_1;
	} else if ((a <= -0.014) || !(a <= 9.2e-79)) {
		tmp = ((b - z) * y) - t_1;
	} else {
		tmp = fma(-z, (y - 1.0), x) + (t * b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - 1.0) * a)
	tmp = 0.0
	if (a <= -2.5e+124)
		tmp = Float64(Float64(x + z) - t_1);
	elseif ((a <= -0.014) || !(a <= 9.2e-79))
		tmp = Float64(Float64(Float64(b - z) * y) - t_1);
	else
		tmp = Float64(fma(Float64(-z), Float64(y - 1.0), x) + Float64(t * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -2.5e+124], N[(N[(x + z), $MachinePrecision] - t$95$1), $MachinePrecision], If[Or[LessEqual[a, -0.014], N[Not[LessEqual[a, 9.2e-79]], $MachinePrecision]], N[(N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[((-z) * N[(y - 1.0), $MachinePrecision] + x), $MachinePrecision] + N[(t * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.4999999999999998e124

   1. Initial program 89.7%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 89.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 89.3%

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

   if -2.4999999999999998e124 < a < -0.0140000000000000003 or 9.20000000000000047e-79 < a

   1. Initial program 94.3%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 96.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 77.0%

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

   if -0.0140000000000000003 < a < 9.20000000000000047e-79

   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 x around inf

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

   5. Applied rewrites 70.1%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 51.2%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 78.1%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+124}:\\ \;\;\;\;\left(x + z\right) - \left(t - 1\right) \cdot a\\ \mathbf{elif}\;a \leq -0.014 \lor \neg \left(a \leq 9.2 \cdot 10^{-79}\right):\\ \;\;\;\;\left(b - z\right) \cdot y - \left(t - 1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y - 1, x\right) + t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2 \cdot 10^{+124}:\\ \;\;\;\;x + t\_1\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{-35}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(-z, y - 1, x\right) + t \cdot b\\ \mathbf{else}:\\ \;\;\;\;a + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -2e+124)
     (+ x t_1)
     (if (<= b 2.25e-35)
       (- x (fma (- t 1.0) a (* (- y 1.0) z)))
       (if (<= b 5.2e+53) (+ (fma (- z) (- y 1.0) x) (* t b)) (+ a t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -2e+124) {
		tmp = x + t_1;
	} else if (b <= 2.25e-35) {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	} else if (b <= 5.2e+53) {
		tmp = fma(-z, (y - 1.0), x) + (t * b);
	} else {
		tmp = a + t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -2e+124)
		tmp = Float64(x + t_1);
	elseif (b <= 2.25e-35)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	elseif (b <= 5.2e+53)
		tmp = Float64(fma(Float64(-z), Float64(y - 1.0), x) + Float64(t * b));
	else
		tmp = Float64(a + t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2e+124], N[(x + t$95$1), $MachinePrecision], If[LessEqual[b, 2.25e-35], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.2e+53], N[(N[((-z) * N[(y - 1.0), $MachinePrecision] + x), $MachinePrecision] + N[(t * b), $MachinePrecision]), $MachinePrecision], N[(a + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.9999999999999999e124

   1. Initial program 89.1%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 89.1%

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

   if -1.9999999999999999e124 < b < 2.25000000000000005e-35

   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 b around 0

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

   5. Applied rewrites 86.4%

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

   if 2.25000000000000005e-35 < b < 5.19999999999999996e53

   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 x around inf

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

   5. Applied rewrites 54.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 50.2%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 90.4%

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

   if 5.19999999999999996e53 < b

   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 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

   5. Applied rewrites 76.7%

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

   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 74.7%

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

Alternative 6: 86.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -800 \lor \neg \left(y \leq 1.65 \cdot 10^{+109}\right):\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right) + z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, x - \mathsf{fma}\left(t - 1, a, -z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -800.0) (not (<= y 1.65e+109)))
   (+ (fma (- b z) y (fma (- t 2.0) b x)) z)
   (fma (- t 2.0) b (- x (fma (- t 1.0) a (- z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -800.0) || !(y <= 1.65e+109)) {
		tmp = fma((b - z), y, fma((t - 2.0), b, x)) + z;
	} else {
		tmp = fma((t - 2.0), b, (x - fma((t - 1.0), a, -z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -800.0) || !(y <= 1.65e+109))
		tmp = Float64(fma(Float64(b - z), y, fma(Float64(t - 2.0), b, x)) + z);
	else
		tmp = fma(Float64(t - 2.0), b, Float64(x - fma(Float64(t - 1.0), a, Float64(-z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -800.0], N[Not[LessEqual[y, 1.65e+109]], $MachinePrecision]], N[(N[(N[(b - z), $MachinePrecision] * y + N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], N[(N[(t - 2.0), $MachinePrecision] * b + N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -800 or 1.6499999999999999e109 < y

   1. Initial program 89.7%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 94.8%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 80.1%

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

   if -800 < y < 1.6499999999999999e109

   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 y around 0

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

   5. Applied rewrites 96.2%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -800 \lor \neg \left(y \leq 1.65 \cdot 10^{+109}\right):\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right) + z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, x - \mathsf{fma}\left(t - 1, a, -z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - 2, b, x - a \cdot t\right)\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-19}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, z + x\right) + a\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+116}:\\ \;\;\;\;x + \mathsf{fma}\left(y, b, \left(t - 2\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- t 2.0) b (- x (* a t)))))
   (if (<= t -2.2e+33)
     t_1
     (if (<= t 4.9e-19)
       (+ (fma -2.0 b (+ z x)) a)
       (if (<= t 7e+116) (+ x (fma y b (* (- t 2.0) b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((t - 2.0), b, (x - (a * t)));
	double tmp;
	if (t <= -2.2e+33) {
		tmp = t_1;
	} else if (t <= 4.9e-19) {
		tmp = fma(-2.0, b, (z + x)) + a;
	} else if (t <= 7e+116) {
		tmp = x + fma(y, b, ((t - 2.0) * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(t - 2.0), b, Float64(x - Float64(a * t)))
	tmp = 0.0
	if (t <= -2.2e+33)
		tmp = t_1;
	elseif (t <= 4.9e-19)
		tmp = Float64(fma(-2.0, b, Float64(z + x)) + a);
	elseif (t <= 7e+116)
		tmp = Float64(x + fma(y, b, Float64(Float64(t - 2.0) * b)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - 2.0), $MachinePrecision] * b + N[(x - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e+33], t$95$1, If[LessEqual[t, 4.9e-19], N[(N[(-2.0 * b + N[(z + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t, 7e+116], N[(x + N[(y * b + N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.19999999999999994e33 or 6.99999999999999993e116 < t

   1. Initial program 94.3%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 84.4%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 82.6%

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

   if -2.19999999999999994e33 < t < 4.89999999999999993e-19

   1. Initial program 96.8%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 71.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 69.4%

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

   if 4.89999999999999993e-19 < t < 6.99999999999999993e116

   1. Initial program 88.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 81.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. associate--l+ N/A

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

      6. lift--.f64 N/A

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

      7. distribute-rgt-in N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 81.2

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

   7. Applied rewrites 81.2%

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

Alternative 8: 65.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - 2, b, x - a \cdot t\right)\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-19}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, z + x\right) + a\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+116}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- t 2.0) b (- x (* a t)))))
   (if (<= t -2.2e+33)
     t_1
     (if (<= t 4.9e-19)
       (+ (fma -2.0 b (+ z x)) a)
       (if (<= t 7e+116) (+ x (* (- (+ y t) 2.0) b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((t - 2.0), b, (x - (a * t)));
	double tmp;
	if (t <= -2.2e+33) {
		tmp = t_1;
	} else if (t <= 4.9e-19) {
		tmp = fma(-2.0, b, (z + x)) + a;
	} else if (t <= 7e+116) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(t - 2.0), b, Float64(x - Float64(a * t)))
	tmp = 0.0
	if (t <= -2.2e+33)
		tmp = t_1;
	elseif (t <= 4.9e-19)
		tmp = Float64(fma(-2.0, b, Float64(z + x)) + a);
	elseif (t <= 7e+116)
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - 2.0), $MachinePrecision] * b + N[(x - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e+33], t$95$1, If[LessEqual[t, 4.9e-19], N[(N[(-2.0 * b + N[(z + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t, 7e+116], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.19999999999999994e33 or 6.99999999999999993e116 < t

   1. Initial program 94.3%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 84.4%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 82.6%

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

   if -2.19999999999999994e33 < t < 4.89999999999999993e-19

   1. Initial program 96.8%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 71.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 69.4%

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

   if 4.89999999999999993e-19 < t < 6.99999999999999993e116

   1. Initial program 88.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 81.2%

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

Alternative 9: 87.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+33} \lor \neg \left(a \leq 5.2 \cdot 10^{+96}\right):\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right) + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -3.5e+33) (not (<= a 5.2e+96)))
   (- x (fma (- t 1.0) a (* (- y 1.0) z)))
   (+ (fma (- b z) y (fma (- t 2.0) b x)) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.5e+33) || !(a <= 5.2e+96)) {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	} else {
		tmp = fma((b - z), y, fma((t - 2.0), b, x)) + z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -3.5e+33) || !(a <= 5.2e+96))
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	else
		tmp = Float64(fma(Float64(b - z), y, fma(Float64(t - 2.0), b, x)) + z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -3.5e+33], N[Not[LessEqual[a, 5.2e+96]], $MachinePrecision]], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b - z), $MachinePrecision] * y + N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.5000000000000001e33 or 5.2e96 < a

   1. Initial program 93.3%

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

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 85.9%

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

   if -3.5000000000000001e33 < a < 5.2e96

   1. Initial program 96.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 89.6%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+33} \lor \neg \left(a \leq 5.2 \cdot 10^{+96}\right):\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right) + z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.05 \cdot 10^{-144}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-29}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -1.85e+25)
     t_1
     (if (<= t 5.05e-144)
       (fma (- y 2.0) b x)
       (if (<= t 2e-29)
         (* (- 1.0 y) z)
         (if (<= t 3.1e+112) (fma y b x) 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 <= -1.85e+25) {
		tmp = t_1;
	} else if (t <= 5.05e-144) {
		tmp = fma((y - 2.0), b, x);
	} else if (t <= 2e-29) {
		tmp = (1.0 - y) * z;
	} else if (t <= 3.1e+112) {
		tmp = fma(y, b, x);
	} 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 <= -1.85e+25)
		tmp = t_1;
	elseif (t <= 5.05e-144)
		tmp = fma(Float64(y - 2.0), b, x);
	elseif (t <= 2e-29)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (t <= 3.1e+112)
		tmp = fma(y, b, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.85e+25], t$95$1, If[LessEqual[t, 5.05e-144], N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision], If[LessEqual[t, 2e-29], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t, 3.1e+112], N[(y * b + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.8499999999999999e25 or 3.09999999999999983e112 < t

   1. Initial program 93.4%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 80.7%

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

   if -1.8499999999999999e25 < t < 5.0499999999999999e-144

   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

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

   5. Applied rewrites 48.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 48.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 48.2

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

   10. Applied rewrites 48.2%

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

   if 5.0499999999999999e-144 < t < 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 z around inf

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

   5. Applied rewrites 62.8%

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

   if 1.99999999999999989e-29 < t < 3.09999999999999983e112

   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 x around inf

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

   5. Applied rewrites 80.4%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 64.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 64.7

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

   10. Applied rewrites 64.7%

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

   11. Taylor expanded in y around inf

       \[\leadsto \mathsf{fma}\left(\color{blue}{y}, b, x\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 64.9%

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

Alternative 11: 46.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - t\right) \cdot a\\ \mathbf{if}\;a \leq -4.1 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-18}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-80}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+65}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 t) a)))
   (if (<= a -4.1e+68)
     t_1
     (if (<= a -1.4e-18)
       (fma y b x)
       (if (<= a 2.6e-80)
         (fma t b x)
         (if (<= a 1.5e+65) (* (- 1.0 y) z) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - t) * a;
	double tmp;
	if (a <= -4.1e+68) {
		tmp = t_1;
	} else if (a <= -1.4e-18) {
		tmp = fma(y, b, x);
	} else if (a <= 2.6e-80) {
		tmp = fma(t, b, x);
	} else if (a <= 1.5e+65) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - t) * a)
	tmp = 0.0
	if (a <= -4.1e+68)
		tmp = t_1;
	elseif (a <= -1.4e-18)
		tmp = fma(y, b, x);
	elseif (a <= 2.6e-80)
		tmp = fma(t, b, x);
	elseif (a <= 1.5e+65)
		tmp = Float64(Float64(1.0 - y) * z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -4.1e+68], t$95$1, If[LessEqual[a, -1.4e-18], N[(y * b + x), $MachinePrecision], If[LessEqual[a, 2.6e-80], N[(t * b + x), $MachinePrecision], If[LessEqual[a, 1.5e+65], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.0999999999999999e68 or 1.5000000000000001e65 < a

   1. Initial program 91.7%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 69.5%

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

   if -4.0999999999999999e68 < a < -1.40000000000000006e-18

   1. Initial program 95.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 61.4%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 57.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 57.0

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

   10. Applied rewrites 57.0%

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

   11. Taylor expanded in y around inf

       \[\leadsto \mathsf{fma}\left(\color{blue}{y}, b, x\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 52.1%

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

   if -1.40000000000000006e-18 < a < 2.6000000000000001e-80

   1. Initial program 97.2%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 70.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 52.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 52.3

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

   10. Applied rewrites 52.3%

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

   if 2.6000000000000001e-80 < a < 1.5000000000000001e65

   1. Initial program 97.0%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 41.6%

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

Alternative 12: 63.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-19}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, z + x\right) + a\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+112}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -2.5e+33)
     t_1
     (if (<= t 4.9e-19)
       (+ (fma -2.0 b (+ z x)) a)
       (if (<= t 5.8e+112) (+ x (* (- (+ y t) 2.0) b)) 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 <= -2.5e+33) {
		tmp = t_1;
	} else if (t <= 4.9e-19) {
		tmp = fma(-2.0, b, (z + x)) + a;
	} else if (t <= 5.8e+112) {
		tmp = x + (((y + t) - 2.0) * b);
	} 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 <= -2.5e+33)
		tmp = t_1;
	elseif (t <= 4.9e-19)
		tmp = Float64(fma(-2.0, b, Float64(z + x)) + a);
	elseif (t <= 5.8e+112)
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -2.5e+33], t$95$1, If[LessEqual[t, 4.9e-19], N[(N[(-2.0 * b + N[(z + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t, 5.8e+112], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.49999999999999986e33 or 5.8000000000000004e112 < t

   1. Initial program 93.4%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 81.4%

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

   if -2.49999999999999986e33 < t < 4.89999999999999993e-19

   1. Initial program 96.8%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 71.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 69.4%

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

   if 4.89999999999999993e-19 < t < 5.8000000000000004e112

   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 x around inf

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

   5. Applied rewrites 80.4%

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

Alternative 13: 61.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-19}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, z + x\right) + a\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -2.5e+33)
     t_1
     (if (<= t 4.9e-19)
       (+ (fma -2.0 b (+ z x)) a)
       (if (<= t 3.1e+112) (fma y b x) 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 <= -2.5e+33) {
		tmp = t_1;
	} else if (t <= 4.9e-19) {
		tmp = fma(-2.0, b, (z + x)) + a;
	} else if (t <= 3.1e+112) {
		tmp = fma(y, b, x);
	} 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 <= -2.5e+33)
		tmp = t_1;
	elseif (t <= 4.9e-19)
		tmp = Float64(fma(-2.0, b, Float64(z + x)) + a);
	elseif (t <= 3.1e+112)
		tmp = fma(y, b, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -2.5e+33], t$95$1, If[LessEqual[t, 4.9e-19], N[(N[(-2.0 * b + N[(z + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t, 3.1e+112], N[(y * b + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.49999999999999986e33 or 3.09999999999999983e112 < t

   1. Initial program 93.4%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 81.4%

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

   if -2.49999999999999986e33 < t < 4.89999999999999993e-19

   1. Initial program 96.8%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 71.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 69.4%

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

   if 4.89999999999999993e-19 < t < 3.09999999999999983e112

   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 x around inf

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

   5. Applied rewrites 80.4%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 64.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 64.7

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

   10. Applied rewrites 64.7%

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

   11. Taylor expanded in y around inf

       \[\leadsto \mathsf{fma}\left(\color{blue}{y}, b, x\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 64.9%

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

Alternative 14: 46.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - t\right) \cdot a\\ \mathbf{if}\;a \leq -4.1 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-18}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+54}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 t) a)))
   (if (<= a -4.1e+68)
     t_1
     (if (<= a -1.4e-18) (fma y b x) (if (<= a 1.4e+54) (fma t b x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - t) * a;
	double tmp;
	if (a <= -4.1e+68) {
		tmp = t_1;
	} else if (a <= -1.4e-18) {
		tmp = fma(y, b, x);
	} else if (a <= 1.4e+54) {
		tmp = fma(t, b, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - t) * a)
	tmp = 0.0
	if (a <= -4.1e+68)
		tmp = t_1;
	elseif (a <= -1.4e-18)
		tmp = fma(y, b, x);
	elseif (a <= 1.4e+54)
		tmp = fma(t, b, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -4.1e+68], t$95$1, If[LessEqual[a, -1.4e-18], N[(y * b + x), $MachinePrecision], If[LessEqual[a, 1.4e+54], N[(t * b + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.0999999999999999e68 or 1.40000000000000008e54 < a

   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

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

   5. Applied rewrites 68.8%

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

   if -4.0999999999999999e68 < a < -1.40000000000000006e-18

   1. Initial program 95.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 61.4%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 57.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 57.0

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

   10. Applied rewrites 57.0%

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

   11. Taylor expanded in y around inf

       \[\leadsto \mathsf{fma}\left(\color{blue}{y}, b, x\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 52.1%

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

   if -1.40000000000000006e-18 < a < 1.40000000000000008e54

   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 x around inf

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

   5. Applied rewrites 64.7%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 46.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 46.2

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

   10. Applied rewrites 46.2%

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

Alternative 15: 70.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -7.8 \cdot 10^{+48}:\\ \;\;\;\;x + t\_1\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{+52}:\\ \;\;\;\;\left(x + z\right) - \left(t - 1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;a + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -7.8e+48)
     (+ x t_1)
     (if (<= b 1.65e+52) (- (+ x z) (* (- t 1.0) a)) (+ a t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -7.8e+48) {
		tmp = x + t_1;
	} else if (b <= 1.65e+52) {
		tmp = (x + z) - ((t - 1.0) * a);
	} else {
		tmp = a + 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 = ((y + t) - 2.0d0) * b
    if (b <= (-7.8d+48)) then
        tmp = x + t_1
    else if (b <= 1.65d+52) then
        tmp = (x + z) - ((t - 1.0d0) * a)
    else
        tmp = a + 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 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -7.8e+48) {
		tmp = x + t_1;
	} else if (b <= 1.65e+52) {
		tmp = (x + z) - ((t - 1.0) * a);
	} else {
		tmp = a + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -7.8e+48:
		tmp = x + t_1
	elif b <= 1.65e+52:
		tmp = (x + z) - ((t - 1.0) * a)
	else:
		tmp = a + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -7.8e+48)
		tmp = Float64(x + t_1);
	elseif (b <= 1.65e+52)
		tmp = Float64(Float64(x + z) - Float64(Float64(t - 1.0) * a));
	else
		tmp = Float64(a + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -7.8e+48)
		tmp = x + t_1;
	elseif (b <= 1.65e+52)
		tmp = (x + z) - ((t - 1.0) * a);
	else
		tmp = a + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -7.8e+48], N[(x + t$95$1), $MachinePrecision], If[LessEqual[b, 1.65e+52], N[(N[(x + z), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(a + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.8000000000000002e48

   1. Initial program 88.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 79.0%

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

   if -7.8000000000000002e48 < b < 1.65e52

   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 y around 0

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

   5. Applied rewrites 98.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 71.7%

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

   if 1.65e52 < b

   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 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

   5. Applied rewrites 76.7%

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

   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 74.7%

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

Alternative 16: 38.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot t\\ \mathbf{if}\;a \leq -1.16 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-18}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+54}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a) t)))
   (if (<= a -1.16e+73)
     t_1
     (if (<= a -1.4e-18) (fma y b x) (if (<= a 1.6e+54) (fma t b x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a * t;
	double tmp;
	if (a <= -1.16e+73) {
		tmp = t_1;
	} else if (a <= -1.4e-18) {
		tmp = fma(y, b, x);
	} else if (a <= 1.6e+54) {
		tmp = fma(t, b, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-a) * t)
	tmp = 0.0
	if (a <= -1.16e+73)
		tmp = t_1;
	elseif (a <= -1.4e-18)
		tmp = fma(y, b, x);
	elseif (a <= 1.6e+54)
		tmp = fma(t, b, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) * t), $MachinePrecision]}, If[LessEqual[a, -1.16e+73], t$95$1, If[LessEqual[a, -1.4e-18], N[(y * b + x), $MachinePrecision], If[LessEqual[a, 1.6e+54], N[(t * b + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.16000000000000007e73 or 1.6e54 < a

   1. Initial program 91.8%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 47.6%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 42.4%

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

   if -1.16000000000000007e73 < a < -1.40000000000000006e-18

   1. Initial program 95.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 61.4%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 57.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 57.0

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

   10. Applied rewrites 57.0%

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

   11. Taylor expanded in y around inf

       \[\leadsto \mathsf{fma}\left(\color{blue}{y}, b, x\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 52.1%

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

   if -1.40000000000000006e-18 < a < 1.6e54

   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 x around inf

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

   5. Applied rewrites 64.7%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 46.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 46.2

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

   10. Applied rewrites 46.2%

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

Alternative 17: 60.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+54} \lor \neg \left(b \leq 3.2 \cdot 10^{-21}\right):\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x - \left(t - 1\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.2e+54) (not (<= b 3.2e-21)))
   (* (- (+ t y) 2.0) b)
   (- x (* (- t 1.0) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.2e+54) || !(b <= 3.2e-21)) {
		tmp = ((t + y) - 2.0) * b;
	} else {
		tmp = x - ((t - 1.0) * 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 ((b <= (-5.2d+54)) .or. (.not. (b <= 3.2d-21))) then
        tmp = ((t + y) - 2.0d0) * b
    else
        tmp = x - ((t - 1.0d0) * 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 ((b <= -5.2e+54) || !(b <= 3.2e-21)) {
		tmp = ((t + y) - 2.0) * b;
	} else {
		tmp = x - ((t - 1.0) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5.2e+54) or not (b <= 3.2e-21):
		tmp = ((t + y) - 2.0) * b
	else:
		tmp = x - ((t - 1.0) * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.2e+54) || !(b <= 3.2e-21))
		tmp = Float64(Float64(Float64(t + y) - 2.0) * b);
	else
		tmp = Float64(x - Float64(Float64(t - 1.0) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -5.2e+54) || ~((b <= 3.2e-21)))
		tmp = ((t + y) - 2.0) * b;
	else
		tmp = x - ((t - 1.0) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.2e+54], N[Not[LessEqual[b, 3.2e-21]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.20000000000000013e54 or 3.2000000000000002e-21 < b

   1. Initial program 91.1%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 63.9%

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

   if -5.20000000000000013e54 < b < 3.2000000000000002e-21

   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 y around 0

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

   5. Applied rewrites 98.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 67.4%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+54} \lor \neg \left(b \leq 3.2 \cdot 10^{-21}\right):\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x - \left(t - 1\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 25.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+40}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-52}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.8e+40)
   (* b t)
   (if (<= t 3.1e-52) a (if (<= t 3.1e+112) x (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.8e+40) {
		tmp = b * t;
	} else if (t <= 3.1e-52) {
		tmp = a;
	} else if (t <= 3.1e+112) {
		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 <= (-1.8d+40)) then
        tmp = b * t
    else if (t <= 3.1d-52) then
        tmp = a
    else if (t <= 3.1d+112) 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 <= -1.8e+40) {
		tmp = b * t;
	} else if (t <= 3.1e-52) {
		tmp = a;
	} else if (t <= 3.1e+112) {
		tmp = x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.8e+40:
		tmp = b * t
	elif t <= 3.1e-52:
		tmp = a
	elif t <= 3.1e+112:
		tmp = x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.8e+40)
		tmp = Float64(b * t);
	elseif (t <= 3.1e-52)
		tmp = a;
	elseif (t <= 3.1e+112)
		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 <= -1.8e+40)
		tmp = b * t;
	elseif (t <= 3.1e-52)
		tmp = a;
	elseif (t <= 3.1e+112)
		tmp = x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.8e+40], N[(b * t), $MachinePrecision], If[LessEqual[t, 3.1e-52], a, If[LessEqual[t, 3.1e+112], x, N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.79999999999999998e40 or 3.09999999999999983e112 < t

   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. Taylor expanded in t around inf

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

   5. Applied rewrites 81.9%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 43.5%

      \[\leadsto b \cdot t \]

   if -1.79999999999999998e40 < t < 3.0999999999999999e-52

   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 a around inf

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

   5. Applied rewrites 29.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 26.2%

      \[\leadsto a \]

   if 3.0999999999999999e-52 < t < 3.09999999999999983e112

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 33.0%

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

Alternative 19: 40.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+72} \lor \neg \left(y \leq 1.05 \cdot 10^{+158}\right):\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.45e+72) (not (<= y 1.05e+158))) (fma y b x) (fma t b x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.45e+72) || !(y <= 1.05e+158)) {
		tmp = fma(y, b, x);
	} else {
		tmp = fma(t, b, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.45e+72) || !(y <= 1.05e+158))
		tmp = fma(y, b, x);
	else
		tmp = fma(t, b, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.45e+72], N[Not[LessEqual[y, 1.05e+158]], $MachinePrecision]], N[(y * b + x), $MachinePrecision], N[(t * b + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.45000000000000009e72 or 1.0499999999999999e158 < y

   1. Initial program 88.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 51.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 49.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 49.4

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

   10. Applied rewrites 49.4%

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

   11. Taylor expanded in y around inf

       \[\leadsto \mathsf{fma}\left(\color{blue}{y}, b, x\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 49.4%

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

   if -1.45000000000000009e72 < y < 1.0499999999999999e158

   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 x around inf

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

   5. Applied rewrites 48.4%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 40.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 40.1

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

   10. Applied rewrites 40.1%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+72} \lor \neg \left(y \leq 1.05 \cdot 10^{+158}\right):\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 33.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+115}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -5.5e+115) a (if (<= a 3.5e+86) (fma t b x) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5.5e+115) {
		tmp = a;
	} else if (a <= 3.5e+86) {
		tmp = fma(t, b, x);
	} else {
		tmp = a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -5.5e+115)
		tmp = a;
	elseif (a <= 3.5e+86)
		tmp = fma(t, b, x);
	else
		tmp = a;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -5.5e+115], a, If[LessEqual[a, 3.5e+86], N[(t * b + x), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if a < -5.5e115 or 3.50000000000000019e86 < a

   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 a around inf

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

   5. Applied rewrites 73.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 31.6%

      \[\leadsto a \]

   if -5.5e115 < a < 3.50000000000000019e86

   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 x around inf

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

   5. Applied rewrites 63.1%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 42.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 42.7

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

   10. Applied rewrites 42.7%

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

Alternative 21: 19.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+72}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.7e+72) a (if (<= a 1.35e-73) x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.7e+72) {
		tmp = a;
	} else if (a <= 1.35e-73) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-2.7d+72)) then
        tmp = a
    else if (a <= 1.35d-73) then
        tmp = x
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.7e+72) {
		tmp = a;
	} else if (a <= 1.35e-73) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.7e+72:
		tmp = a
	elif a <= 1.35e-73:
		tmp = x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.7e+72)
		tmp = a;
	elseif (a <= 1.35e-73)
		tmp = x;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.7e+72)
		tmp = a;
	elseif (a <= 1.35e-73)
		tmp = x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.7e+72], a, If[LessEqual[a, 1.35e-73], x, a]]

Derivation

1. Split input into 2 regimes

2. if a < -2.7000000000000001e72 or 1.34999999999999997e-73 < a

   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 inf

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

   5. Applied rewrites 59.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 25.0%

      \[\leadsto a \]

   if -2.7000000000000001e72 < a < 1.34999999999999997e-73

   1. Initial program 96.9%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 23.0%

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

Alternative 22: 16.2% 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 94.9%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 14.9%

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

Reproduce

herbie shell --seed 2025026 
(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)))