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

Percentage Accurate: 95.1% → 96.2%

Time: 8.9s

Alternatives: 23

Speedup: 1.1×

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

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.1% 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: 96.2% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.1%

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

3. Taylor expanded in t around 0

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

   1. lower--.f64 N/A

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

   2. +-commutative N/A

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

   3. lower-+.f64 N/A

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

   4. +-commutative N/A

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

   5. *-commutative N/A

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

   6. lower-fma.f64 N/A

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

   7. lower--.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. lower--.f64 N/A

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

   11. +-commutative N/A

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

   12. *-commutative N/A

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

   13. lower-fma.f64 N/A

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

   14. lift--.f64 N/A

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

   15. mul-1-neg N/A

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

   16. lower-neg.f64 96.2

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

5. Applied rewrites 96.2%

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

Alternative 2: 41.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-265}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-269}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-250}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+124}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 y) z)))
   (if (<= z -6.5e-7)
     t_1
     (if (<= z -8.4e-265)
       (* (- b a) t)
       (if (<= z 2.3e-269)
         x
         (if (<= z 2.3e-250)
           (* b y)
           (if (<= z 2.8e+124) (* (- 1.0 t) a) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double tmp;
	if (z <= -6.5e-7) {
		tmp = t_1;
	} else if (z <= -8.4e-265) {
		tmp = (b - a) * t;
	} else if (z <= 2.3e-269) {
		tmp = x;
	} else if (z <= 2.3e-250) {
		tmp = b * y;
	} else if (z <= 2.8e+124) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (1.0d0 - y) * z
    if (z <= (-6.5d-7)) then
        tmp = t_1
    else if (z <= (-8.4d-265)) then
        tmp = (b - a) * t
    else if (z <= 2.3d-269) then
        tmp = x
    else if (z <= 2.3d-250) then
        tmp = b * y
    else if (z <= 2.8d+124) then
        tmp = (1.0d0 - t) * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double tmp;
	if (z <= -6.5e-7) {
		tmp = t_1;
	} else if (z <= -8.4e-265) {
		tmp = (b - a) * t;
	} else if (z <= 2.3e-269) {
		tmp = x;
	} else if (z <= 2.3e-250) {
		tmp = b * y;
	} else if (z <= 2.8e+124) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 - y) * z
	tmp = 0
	if z <= -6.5e-7:
		tmp = t_1
	elif z <= -8.4e-265:
		tmp = (b - a) * t
	elif z <= 2.3e-269:
		tmp = x
	elif z <= 2.3e-250:
		tmp = b * y
	elif z <= 2.8e+124:
		tmp = (1.0 - t) * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (z <= -6.5e-7)
		tmp = t_1;
	elseif (z <= -8.4e-265)
		tmp = Float64(Float64(b - a) * t);
	elseif (z <= 2.3e-269)
		tmp = x;
	elseif (z <= 2.3e-250)
		tmp = Float64(b * y);
	elseif (z <= 2.8e+124)
		tmp = Float64(Float64(1.0 - t) * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 - y) * z;
	tmp = 0.0;
	if (z <= -6.5e-7)
		tmp = t_1;
	elseif (z <= -8.4e-265)
		tmp = (b - a) * t;
	elseif (z <= 2.3e-269)
		tmp = x;
	elseif (z <= 2.3e-250)
		tmp = b * y;
	elseif (z <= 2.8e+124)
		tmp = (1.0 - t) * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -6.5e-7], t$95$1, If[LessEqual[z, -8.4e-265], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 2.3e-269], x, If[LessEqual[z, 2.3e-250], N[(b * y), $MachinePrecision], If[LessEqual[z, 2.8e+124], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.50000000000000024e-7 or 2.8e124 < z

   1. Initial program 92.2%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 55.2

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

   5. Applied rewrites 55.2%

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

   if -6.50000000000000024e-7 < z < -8.40000000000000015e-265

   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 t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 38.0

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

   5. Applied rewrites 38.0%

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

   if -8.40000000000000015e-265 < z < 2.3e-269

   1. Initial program 96.7%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 22.1%

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

   if 2.3e-269 < z < 2.2999999999999999e-250

   1. Initial program 99.2%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 44.5

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 44.5

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

   5. Applied rewrites 44.5%

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

   6. Taylor expanded in y around inf

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

      1. +-commutative N/A

         \[\leadsto b \cdot y \]

      2. lower-*.f64 19.0

         \[\leadsto b \cdot y \]

   8. Applied rewrites 19.0%

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

   if 2.2999999999999999e-250 < z < 2.8e124

   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 a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 32.3

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

   5. Applied rewrites 32.3%

      \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 3: 57.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot y\\ t_2 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.26 \cdot 10^{+42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-287}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-236}:\\ \;\;\;\;x - a \cdot \left(t - 1\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* z y))) (t_2 (* (- (+ t y) 2.0) b)))
   (if (<= b -1.26e+42)
     t_2
     (if (<= b -1.15e-287)
       t_1
       (if (<= b 4e-236) (- x (* a (- t 1.0))) (if (<= b 1.5e+45) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (z * y);
	double t_2 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -1.26e+42) {
		tmp = t_2;
	} else if (b <= -1.15e-287) {
		tmp = t_1;
	} else if (b <= 4e-236) {
		tmp = x - (a * (t - 1.0));
	} else if (b <= 1.5e+45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (z * y)
    t_2 = ((t + y) - 2.0d0) * b
    if (b <= (-1.26d+42)) then
        tmp = t_2
    else if (b <= (-1.15d-287)) then
        tmp = t_1
    else if (b <= 4d-236) then
        tmp = x - (a * (t - 1.0d0))
    else if (b <= 1.5d+45) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (z * y);
	double t_2 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -1.26e+42) {
		tmp = t_2;
	} else if (b <= -1.15e-287) {
		tmp = t_1;
	} else if (b <= 4e-236) {
		tmp = x - (a * (t - 1.0));
	} else if (b <= 1.5e+45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (z * y)
	t_2 = ((t + y) - 2.0) * b
	tmp = 0
	if b <= -1.26e+42:
		tmp = t_2
	elif b <= -1.15e-287:
		tmp = t_1
	elif b <= 4e-236:
		tmp = x - (a * (t - 1.0))
	elif b <= 1.5e+45:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(z * y))
	t_2 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -1.26e+42)
		tmp = t_2;
	elseif (b <= -1.15e-287)
		tmp = t_1;
	elseif (b <= 4e-236)
		tmp = Float64(x - Float64(a * Float64(t - 1.0)));
	elseif (b <= 1.5e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (z * y);
	t_2 = ((t + y) - 2.0) * b;
	tmp = 0.0;
	if (b <= -1.26e+42)
		tmp = t_2;
	elseif (b <= -1.15e-287)
		tmp = t_1;
	elseif (b <= 4e-236)
		tmp = x - (a * (t - 1.0));
	elseif (b <= 1.5e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.26e+42], t$95$2, If[LessEqual[b, -1.15e-287], t$95$1, If[LessEqual[b, 4e-236], N[(x - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.5e+45], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.26e42 or 1.50000000000000005e45 < b

   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 b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 70.8

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 70.8

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

   5. Applied rewrites 70.8%

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

   if -1.26e42 < b < -1.14999999999999993e-287 or 4.0000000000000002e-236 < b < 1.50000000000000005e45

   1. Initial program 98.9%

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

   3. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 88.2

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

   5. Applied rewrites 88.2%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 43.9

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

   8. Applied rewrites 43.9%

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

   if -1.14999999999999993e-287 < b < 4.0000000000000002e-236

   1. Initial program 99.5%

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

   3. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 99.8

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 62.8

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

   8. Applied rewrites 62.8%

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

Alternative 4: 83.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -6.4 \cdot 10^{+44}:\\ \;\;\;\;\left(1 - t\right) \cdot a + t\_1\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+121}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - y\right) \cdot z + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -6.4e+44)
     (+ (* (- 1.0 t) a) t_1)
     (if (<= b 4.4e+121)
       (- x (fma (- t 1.0) a (* (- y 1.0) z)))
       (+ (* (- 1.0 y) z) 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 <= -6.4e+44) {
		tmp = ((1.0 - t) * a) + t_1;
	} else if (b <= 4.4e+121) {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	} else {
		tmp = ((1.0 - y) * z) + 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 <= -6.4e+44)
		tmp = Float64(Float64(Float64(1.0 - t) * a) + t_1);
	elseif (b <= 4.4e+121)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	else
		tmp = Float64(Float64(Float64(1.0 - y) * z) + 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, -6.4e+44], N[(N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, 4.4e+121], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.40000000000000009e44

   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 a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 77.6

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

   5. Applied rewrites 77.6%

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

   if -6.40000000000000009e44 < b < 4.40000000000000003e121

   1. Initial program 98.3%

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

   3. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 86.2

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

   5. Applied rewrites 86.2%

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

   if 4.40000000000000003e121 < b

   1. Initial program 89.4%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 82.4

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

   5. Applied rewrites 82.4%

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

Alternative 5: 84.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - t\right) \cdot a + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -6.4 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+45}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* (- 1.0 t) a) (* (- (+ y t) 2.0) b))))
   (if (<= b -6.4e+44)
     t_1
     (if (<= b 2.8e+45) (- x (fma (- t 1.0) a (* (- y 1.0) z))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((1.0 - t) * a) + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -6.4e+44) {
		tmp = t_1;
	} else if (b <= 2.8e+45) {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(1.0 - t) * a) + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -6.4e+44)
		tmp = t_1;
	elseif (b <= 2.8e+45)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.4e+44], t$95$1, If[LessEqual[b, 2.8e+45], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.40000000000000009e44 or 2.7999999999999999e45 < b

   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 a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 77.1

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

   5. Applied rewrites 77.1%

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

   if -6.40000000000000009e44 < b < 2.7999999999999999e45

   1. Initial program 98.9%

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

   3. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 89.6

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

   5. Applied rewrites 89.6%

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

Alternative 6: 83.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -8.5 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{+124}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (* (- (+ y t) 2.0) b))))
   (if (<= b -8.5e+45)
     t_1
     (if (<= b 1.42e+124) (- x (fma (- t 1.0) a (* (- y 1.0) z))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -8.5e+45) {
		tmp = t_1;
	} else if (b <= 1.42e+124) {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -8.5e+45)
		tmp = t_1;
	elseif (b <= 1.42e+124)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.5e+45], t$95$1, If[LessEqual[b, 1.42e+124], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -8.4999999999999996e45 or 1.42e124 < b

   1. Initial program 89.6%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 79.2

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

   5. Applied rewrites 79.2%

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

   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 78.8%

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

   if -8.4999999999999996e45 < b < 1.42e124

   1. Initial program 98.3%

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

   3. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 86.1

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

   5. Applied rewrites 86.1%

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

Alternative 7: 27.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-y\right) \cdot z\\ \mathbf{if}\;b \leq -3.5 \cdot 10^{+44}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-236}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- y) z)))
   (if (<= b -3.5e+44)
     (* b y)
     (if (<= b -4e-274)
       t_1
       (if (<= b 3.5e-236) x (if (<= b 1.6e+95) t_1 (* b t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -y * z;
	double tmp;
	if (b <= -3.5e+44) {
		tmp = b * y;
	} else if (b <= -4e-274) {
		tmp = t_1;
	} else if (b <= 3.5e-236) {
		tmp = x;
	} else if (b <= 1.6e+95) {
		tmp = t_1;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -y * z
    if (b <= (-3.5d+44)) then
        tmp = b * y
    else if (b <= (-4d-274)) then
        tmp = t_1
    else if (b <= 3.5d-236) then
        tmp = x
    else if (b <= 1.6d+95) then
        tmp = t_1
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -y * z;
	double tmp;
	if (b <= -3.5e+44) {
		tmp = b * y;
	} else if (b <= -4e-274) {
		tmp = t_1;
	} else if (b <= 3.5e-236) {
		tmp = x;
	} else if (b <= 1.6e+95) {
		tmp = t_1;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -y * z
	tmp = 0
	if b <= -3.5e+44:
		tmp = b * y
	elif b <= -4e-274:
		tmp = t_1
	elif b <= 3.5e-236:
		tmp = x
	elif b <= 1.6e+95:
		tmp = t_1
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-y) * z)
	tmp = 0.0
	if (b <= -3.5e+44)
		tmp = Float64(b * y);
	elseif (b <= -4e-274)
		tmp = t_1;
	elseif (b <= 3.5e-236)
		tmp = x;
	elseif (b <= 1.6e+95)
		tmp = t_1;
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -y * z;
	tmp = 0.0;
	if (b <= -3.5e+44)
		tmp = b * y;
	elseif (b <= -4e-274)
		tmp = t_1;
	elseif (b <= 3.5e-236)
		tmp = x;
	elseif (b <= 1.6e+95)
		tmp = t_1;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-y) * z), $MachinePrecision]}, If[LessEqual[b, -3.5e+44], N[(b * y), $MachinePrecision], If[LessEqual[b, -4e-274], t$95$1, If[LessEqual[b, 3.5e-236], x, If[LessEqual[b, 1.6e+95], t$95$1, N[(b * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.4999999999999999e44

   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 b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 71.2

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 71.2

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

   5. Applied rewrites 71.2%

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

   6. Taylor expanded in y around inf

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

      1. +-commutative N/A

         \[\leadsto b \cdot y \]

      2. lower-*.f64 33.4

         \[\leadsto b \cdot y \]

   8. Applied rewrites 33.4%

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

   if -3.4999999999999999e44 < b < -3.99999999999999986e-274 or 3.49999999999999994e-236 < b < 1.6e95

   1. Initial program 98.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 35.1

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

   5. Applied rewrites 35.1%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 24.0

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

   8. Applied rewrites 24.0%

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

   if -3.99999999999999986e-274 < b < 3.49999999999999994e-236

   1. Initial program 99.5%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 23.3%

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

   if 1.6e95 < b

   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 t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 38.6

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

   5. Applied rewrites 38.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 34.5%

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

Alternative 8: 48.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-263}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{+17}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -3.8e-5)
     t_1
     (if (<= y -3.8e-263)
       (* (- 1.0 t) a)
       (if (<= y 1.18e+17) (* (- 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 - z) * y;
	double tmp;
	if (y <= -3.8e-5) {
		tmp = t_1;
	} else if (y <= -3.8e-263) {
		tmp = (1.0 - t) * a;
	} else if (y <= 1.18e+17) {
		tmp = (t - 2.0) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - z) * y
    if (y <= (-3.8d-5)) then
        tmp = t_1
    else if (y <= (-3.8d-263)) then
        tmp = (1.0d0 - t) * a
    else if (y <= 1.18d+17) then
        tmp = (t - 2.0d0) * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -3.8e-5) {
		tmp = t_1;
	} else if (y <= -3.8e-263) {
		tmp = (1.0 - t) * a;
	} else if (y <= 1.18e+17) {
		tmp = (t - 2.0) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - z) * y
	tmp = 0
	if y <= -3.8e-5:
		tmp = t_1
	elif y <= -3.8e-263:
		tmp = (1.0 - t) * a
	elif y <= 1.18e+17:
		tmp = (t - 2.0) * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -3.8e-5)
		tmp = t_1;
	elseif (y <= -3.8e-263)
		tmp = Float64(Float64(1.0 - t) * a);
	elseif (y <= 1.18e+17)
		tmp = Float64(Float64(t - 2.0) * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - z) * y;
	tmp = 0.0;
	if (y <= -3.8e-5)
		tmp = t_1;
	elseif (y <= -3.8e-263)
		tmp = (1.0 - t) * a;
	elseif (y <= 1.18e+17)
		tmp = (t - 2.0) * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -3.8e-5], t$95$1, If[LessEqual[y, -3.8e-263], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[y, 1.18e+17], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8000000000000002e-5 or 1.18e17 < y

   1. Initial program 92.5%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 64.2

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

   5. Applied rewrites 64.2%

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

   if -3.8000000000000002e-5 < y < -3.80000000000000005e-263

   1. Initial program 97.7%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 34.0

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

   5. Applied rewrites 34.0%

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

   if -3.80000000000000005e-263 < y < 1.18e17

   1. Initial program 97.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 33.9

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 33.9

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

   5. Applied rewrites 33.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 33.3%

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

Alternative 9: 50.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{-269}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+17}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -3.8e-5)
     t_1
     (if (<= y -2.45e-269)
       (* (- 1.0 t) a)
       (if (<= y 8.8e+17) (* (- b a) t) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -3.8e-5) {
		tmp = t_1;
	} else if (y <= -2.45e-269) {
		tmp = (1.0 - t) * a;
	} else if (y <= 8.8e+17) {
		tmp = (b - a) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - z) * y
    if (y <= (-3.8d-5)) then
        tmp = t_1
    else if (y <= (-2.45d-269)) then
        tmp = (1.0d0 - t) * a
    else if (y <= 8.8d+17) then
        tmp = (b - a) * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -3.8e-5) {
		tmp = t_1;
	} else if (y <= -2.45e-269) {
		tmp = (1.0 - t) * a;
	} else if (y <= 8.8e+17) {
		tmp = (b - a) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - z) * y
	tmp = 0
	if y <= -3.8e-5:
		tmp = t_1
	elif y <= -2.45e-269:
		tmp = (1.0 - t) * a
	elif y <= 8.8e+17:
		tmp = (b - a) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -3.8e-5)
		tmp = t_1;
	elseif (y <= -2.45e-269)
		tmp = Float64(Float64(1.0 - t) * a);
	elseif (y <= 8.8e+17)
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - z) * y;
	tmp = 0.0;
	if (y <= -3.8e-5)
		tmp = t_1;
	elseif (y <= -2.45e-269)
		tmp = (1.0 - t) * a;
	elseif (y <= 8.8e+17)
		tmp = (b - a) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -3.8e-5], t$95$1, If[LessEqual[y, -2.45e-269], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[y, 8.8e+17], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8000000000000002e-5 or 8.8e17 < y

   1. Initial program 92.4%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 64.3

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

   5. Applied rewrites 64.3%

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

   if -3.8000000000000002e-5 < y < -2.45e-269

   1. Initial program 97.8%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 34.1

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

   5. Applied rewrites 34.1%

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

   if -2.45e-269 < y < 8.8e17

   1. Initial program 97.7%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 39.7

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

   5. Applied rewrites 39.7%

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

Alternative 10: 71.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -3.3 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+45}:\\ \;\;\;\;x - \mathsf{fma}\left(y - 1, z, -a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (* (- (+ y t) 2.0) b))))
   (if (<= b -3.3e+44)
     t_1
     (if (<= b 2.1e+45) (- x (fma (- y 1.0) z (- a))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -3.3e+44) {
		tmp = t_1;
	} else if (b <= 2.1e+45) {
		tmp = x - fma((y - 1.0), z, -a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -3.3e+44)
		tmp = t_1;
	elseif (b <= 2.1e+45)
		tmp = Float64(x - fma(Float64(y - 1.0), z, Float64(-a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.3e+44], t$95$1, If[LessEqual[b, 2.1e+45], N[(x - N[(N[(y - 1.0), $MachinePrecision] * z + (-a)), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.30000000000000013e44 or 2.09999999999999995e45 < b

   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 a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 77.1

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

   5. Applied rewrites 77.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 75.4%

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

   if -3.30000000000000013e44 < b < 2.09999999999999995e45

   1. Initial program 99.0%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 99.1

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

   5. Applied rewrites 99.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 68.3%

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

Alternative 11: 70.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.04 \cdot 10^{+49}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+67}:\\ \;\;\;\;x - \mathsf{fma}\left(y - 1, z, -a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.04e+49)
   (+ x (* (- (+ y t) 2.0) b))
   (if (<= b 9.5e+67) (- x (fma (- y 1.0) z (- a))) (* (- (+ t y) 2.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.04e+49) {
		tmp = x + (((y + t) - 2.0) * b);
	} else if (b <= 9.5e+67) {
		tmp = x - fma((y - 1.0), z, -a);
	} else {
		tmp = ((t + y) - 2.0) * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.04e+49)
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	elseif (b <= 9.5e+67)
		tmp = Float64(x - fma(Float64(y - 1.0), z, Float64(-a)));
	else
		tmp = Float64(Float64(Float64(t + y) - 2.0) * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.04e+49], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e+67], N[(x - N[(N[(y - 1.0), $MachinePrecision] * z + (-a)), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.03999999999999998e49

   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 x around inf

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

   5. Applied rewrites 78.0%

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

   if -1.03999999999999998e49 < b < 9.5000000000000002e67

   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 t around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 98.8

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

   5. Applied rewrites 98.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 67.4%

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

   if 9.5000000000000002e67 < b

   1. Initial program 90.5%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 73.2

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 73.2

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

   5. Applied rewrites 73.2%

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

Alternative 12: 69.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.96 \cdot 10^{+49}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, b \cdot y\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+67}:\\ \;\;\;\;x - \mathsf{fma}\left(y - 1, z, -a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.96e+49)
   (fma (- t 2.0) b (* b y))
   (if (<= b 9.5e+67) (- x (fma (- y 1.0) z (- a))) (* (- (+ t y) 2.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.96e+49) {
		tmp = fma((t - 2.0), b, (b * y));
	} else if (b <= 9.5e+67) {
		tmp = x - fma((y - 1.0), z, -a);
	} else {
		tmp = ((t + y) - 2.0) * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.96e+49)
		tmp = fma(Float64(t - 2.0), b, Float64(b * y));
	elseif (b <= 9.5e+67)
		tmp = Float64(x - fma(Float64(y - 1.0), z, Float64(-a)));
	else
		tmp = Float64(Float64(Float64(t + y) - 2.0) * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.96e+49], N[(N[(t - 2.0), $MachinePrecision] * b + N[(b * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e+67], N[(x - N[(N[(y - 1.0), $MachinePrecision] * z + (-a)), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.96000000000000012e49

   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 b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 72.0

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 72.0

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

   5. Applied rewrites 72.0%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. distribute-lft-out N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower-*.f64 70.3

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

   7. Applied rewrites 70.3%

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

   if -1.96000000000000012e49 < b < 9.5000000000000002e67

   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 t around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 98.8

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

   5. Applied rewrites 98.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 67.4%

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

   if 9.5000000000000002e67 < b

   1. Initial program 90.5%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 73.2

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 73.2

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

   5. Applied rewrites 73.2%

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

Alternative 13: 69.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.96 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+67}:\\ \;\;\;\;x - \mathsf{fma}\left(y - 1, z, -a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -1.96e+49)
     t_1
     (if (<= b 9.5e+67) (- x (fma (- y 1.0) z (- a))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -1.96e+49) {
		tmp = t_1;
	} else if (b <= 9.5e+67) {
		tmp = x - fma((y - 1.0), z, -a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -1.96e+49)
		tmp = t_1;
	elseif (b <= 9.5e+67)
		tmp = Float64(x - fma(Float64(y - 1.0), z, Float64(-a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.96e+49], t$95$1, If[LessEqual[b, 9.5e+67], N[(x - N[(N[(y - 1.0), $MachinePrecision] * z + (-a)), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.96000000000000012e49 or 9.5000000000000002e67 < b

   1. Initial program 90.1%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 72.6

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 72.6

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

   5. Applied rewrites 72.6%

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

   if -1.96000000000000012e49 < b < 9.5000000000000002e67

   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 t around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 98.8

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

   5. Applied rewrites 98.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 67.4%

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

Alternative 14: 67.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -8.4 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 14500000:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, -z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -8.4e+34)
     t_1
     (if (<= y 14500000.0) (- x (fma (- t 1.0) a (- z))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -8.4e+34) {
		tmp = t_1;
	} else if (y <= 14500000.0) {
		tmp = x - fma((t - 1.0), a, -z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -8.4e+34)
		tmp = t_1;
	elseif (y <= 14500000.0)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(-z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -8.4e+34], t$95$1, If[LessEqual[y, 14500000.0], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + (-z)), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.4000000000000007e34 or 1.45e7 < y

   1. Initial program 92.2%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 66.3

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

   5. Applied rewrites 66.3%

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

   if -8.4000000000000007e34 < y < 1.45e7

   1. Initial program 97.8%

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

   3. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 69.8

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

   5. Applied rewrites 69.8%

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

   6. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 68.6

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

   8. Applied rewrites 68.6%

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

Alternative 15: 35.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-y\right) \cdot z\\ \mathbf{if}\;y \leq -8.8 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5600000:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+274}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- y) z)))
   (if (<= y -8.8e+29)
     t_1
     (if (<= y 5600000.0) (* (- 1.0 t) a) (if (<= y 9.8e+274) t_1 (* b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -y * z;
	double tmp;
	if (y <= -8.8e+29) {
		tmp = t_1;
	} else if (y <= 5600000.0) {
		tmp = (1.0 - t) * a;
	} else if (y <= 9.8e+274) {
		tmp = t_1;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -y * z
    if (y <= (-8.8d+29)) then
        tmp = t_1
    else if (y <= 5600000.0d0) then
        tmp = (1.0d0 - t) * a
    else if (y <= 9.8d+274) then
        tmp = t_1
    else
        tmp = b * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -y * z;
	double tmp;
	if (y <= -8.8e+29) {
		tmp = t_1;
	} else if (y <= 5600000.0) {
		tmp = (1.0 - t) * a;
	} else if (y <= 9.8e+274) {
		tmp = t_1;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -y * z
	tmp = 0
	if y <= -8.8e+29:
		tmp = t_1
	elif y <= 5600000.0:
		tmp = (1.0 - t) * a
	elif y <= 9.8e+274:
		tmp = t_1
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-y) * z)
	tmp = 0.0
	if (y <= -8.8e+29)
		tmp = t_1;
	elseif (y <= 5600000.0)
		tmp = Float64(Float64(1.0 - t) * a);
	elseif (y <= 9.8e+274)
		tmp = t_1;
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -y * z;
	tmp = 0.0;
	if (y <= -8.8e+29)
		tmp = t_1;
	elseif (y <= 5600000.0)
		tmp = (1.0 - t) * a;
	elseif (y <= 9.8e+274)
		tmp = t_1;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-y) * z), $MachinePrecision]}, If[LessEqual[y, -8.8e+29], t$95$1, If[LessEqual[y, 5600000.0], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[y, 9.8e+274], t$95$1, N[(b * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.8000000000000005e29 or 5.6e6 < y < 9.8000000000000005e274

   1. Initial program 92.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 37.8

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

   5. Applied rewrites 37.8%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 37.7

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

   8. Applied rewrites 37.7%

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

   if -8.8000000000000005e29 < y < 5.6e6

   1. Initial program 97.8%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.3

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

   5. Applied rewrites 33.3%

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

   if 9.8000000000000005e274 < y

   1. Initial program 80.9%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 46.0

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 46.0

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

   5. Applied rewrites 46.0%

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

   6. Taylor expanded in y around inf

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

      1. +-commutative N/A

         \[\leadsto b \cdot y \]

      2. lower-*.f64 44.6

         \[\leadsto b \cdot y \]

   8. Applied rewrites 44.6%

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

Alternative 16: 25.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+44}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-133}:\\ \;\;\;\;z\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.15e+44)
   (* b y)
   (if (<= b -7.5e-133) z (if (<= b 2.4e+63) x (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e+44) {
		tmp = b * y;
	} else if (b <= -7.5e-133) {
		tmp = z;
	} else if (b <= 2.4e+63) {
		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 (b <= (-1.15d+44)) then
        tmp = b * y
    else if (b <= (-7.5d-133)) then
        tmp = z
    else if (b <= 2.4d+63) 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 (b <= -1.15e+44) {
		tmp = b * y;
	} else if (b <= -7.5e-133) {
		tmp = z;
	} else if (b <= 2.4e+63) {
		tmp = x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.15e+44:
		tmp = b * y
	elif b <= -7.5e-133:
		tmp = z
	elif b <= 2.4e+63:
		tmp = x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.15e+44)
		tmp = Float64(b * y);
	elseif (b <= -7.5e-133)
		tmp = z;
	elseif (b <= 2.4e+63)
		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 (b <= -1.15e+44)
		tmp = b * y;
	elseif (b <= -7.5e-133)
		tmp = z;
	elseif (b <= 2.4e+63)
		tmp = x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.15e+44], N[(b * y), $MachinePrecision], If[LessEqual[b, -7.5e-133], z, If[LessEqual[b, 2.4e+63], x, N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.15000000000000002e44

   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 b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 71.2

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 71.2

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

   5. Applied rewrites 71.2%

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

   6. Taylor expanded in y around inf

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

      1. +-commutative N/A

         \[\leadsto b \cdot y \]

      2. lower-*.f64 33.4

         \[\leadsto b \cdot y \]

   8. Applied rewrites 33.4%

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

   if -1.15000000000000002e44 < b < -7.4999999999999999e-133

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 34.4

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

   5. Applied rewrites 34.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 12.6%

      \[\leadsto z \]

   if -7.4999999999999999e-133 < b < 2.4e63

   1. Initial program 98.7%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 22.0%

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

   if 2.4e63 < b

   1. Initial program 90.3%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 38.8

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

   5. Applied rewrites 38.8%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 33.3%

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

Alternative 17: 24.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+44}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-133}:\\ \;\;\;\;z\\ \mathbf{elif}\;b \leq 5.9 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.15e+44)
   (* b y)
   (if (<= b -7.5e-133) z (if (<= b 5.9e-89) x (* b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e+44) {
		tmp = b * y;
	} else if (b <= -7.5e-133) {
		tmp = z;
	} else if (b <= 5.9e-89) {
		tmp = x;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.15d+44)) then
        tmp = b * y
    else if (b <= (-7.5d-133)) then
        tmp = z
    else if (b <= 5.9d-89) then
        tmp = x
    else
        tmp = b * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e+44) {
		tmp = b * y;
	} else if (b <= -7.5e-133) {
		tmp = z;
	} else if (b <= 5.9e-89) {
		tmp = x;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.15e+44:
		tmp = b * y
	elif b <= -7.5e-133:
		tmp = z
	elif b <= 5.9e-89:
		tmp = x
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.15e+44)
		tmp = Float64(b * y);
	elseif (b <= -7.5e-133)
		tmp = z;
	elseif (b <= 5.9e-89)
		tmp = x;
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.15e+44)
		tmp = b * y;
	elseif (b <= -7.5e-133)
		tmp = z;
	elseif (b <= 5.9e-89)
		tmp = x;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.15e+44], N[(b * y), $MachinePrecision], If[LessEqual[b, -7.5e-133], z, If[LessEqual[b, 5.9e-89], x, N[(b * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.15000000000000002e44 or 5.90000000000000021e-89 < b

   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 b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 61.2

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 61.2

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

   5. Applied rewrites 61.2%

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

   6. Taylor expanded in y around inf

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

      1. +-commutative N/A

         \[\leadsto b \cdot y \]

      2. lower-*.f64 28.5

         \[\leadsto b \cdot y \]

   8. Applied rewrites 28.5%

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

   if -1.15000000000000002e44 < b < -7.4999999999999999e-133

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 34.4

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

   5. Applied rewrites 34.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 12.6%

      \[\leadsto z \]

   if -7.4999999999999999e-133 < b < 5.90000000000000021e-89

   1. Initial program 99.2%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 22.9%

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

Alternative 18: 62.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+45}:\\ \;\;\;\;x - z \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -1.45e+44) t_1 (if (<= b 2.1e+45) (- x (* z (- y 1.0))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -1.45e+44) {
		tmp = t_1;
	} else if (b <= 2.1e+45) {
		tmp = x - (z * (y - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t + y) - 2.0d0) * b
    if (b <= (-1.45d+44)) then
        tmp = t_1
    else if (b <= 2.1d+45) then
        tmp = x - (z * (y - 1.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -1.45e+44) {
		tmp = t_1;
	} else if (b <= 2.1e+45) {
		tmp = x - (z * (y - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t + y) - 2.0) * b
	tmp = 0
	if b <= -1.45e+44:
		tmp = t_1
	elif b <= 2.1e+45:
		tmp = x - (z * (y - 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -1.45e+44)
		tmp = t_1;
	elseif (b <= 2.1e+45)
		tmp = Float64(x - Float64(z * Float64(y - 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t + y) - 2.0) * b;
	tmp = 0.0;
	if (b <= -1.45e+44)
		tmp = t_1;
	elseif (b <= 2.1e+45)
		tmp = x - (z * (y - 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.45e+44], t$95$1, If[LessEqual[b, 2.1e+45], N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.4500000000000001e44 or 2.09999999999999995e45 < b

   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 b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 70.9

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 70.9

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

   5. Applied rewrites 70.9%

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

   if -1.4500000000000001e44 < b < 2.09999999999999995e45

   1. Initial program 99.0%

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

   3. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 89.6

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

   5. Applied rewrites 89.6%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 56.3

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

   8. Applied rewrites 56.3%

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

Alternative 19: 56.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.26 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+45}:\\ \;\;\;\;x - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -1.26e+42) t_1 (if (<= b 1.5e+45) (- x (* z y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -1.26e+42) {
		tmp = t_1;
	} else if (b <= 1.5e+45) {
		tmp = x - (z * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t + y) - 2.0d0) * b
    if (b <= (-1.26d+42)) then
        tmp = t_1
    else if (b <= 1.5d+45) then
        tmp = x - (z * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -1.26e+42) {
		tmp = t_1;
	} else if (b <= 1.5e+45) {
		tmp = x - (z * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t + y) - 2.0) * b
	tmp = 0
	if b <= -1.26e+42:
		tmp = t_1
	elif b <= 1.5e+45:
		tmp = x - (z * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -1.26e+42)
		tmp = t_1;
	elseif (b <= 1.5e+45)
		tmp = Float64(x - Float64(z * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t + y) - 2.0) * b;
	tmp = 0.0;
	if (b <= -1.26e+42)
		tmp = t_1;
	elseif (b <= 1.5e+45)
		tmp = x - (z * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.26e+42], t$95$1, If[LessEqual[b, 1.5e+45], N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.26e42 or 1.50000000000000005e45 < b

   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 b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 70.8

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 70.8

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

   5. Applied rewrites 70.8%

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

   if -1.26e42 < b < 1.50000000000000005e45

   1. Initial program 99.0%

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

   3. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 89.7

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

   5. Applied rewrites 89.7%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 44.8

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

   8. Applied rewrites 44.8%

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

Alternative 20: 42.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+124}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 y) z)))
   (if (<= z -8.6e-14) t_1 (if (<= z 2.8e+124) (* (- 1.0 t) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double tmp;
	if (z <= -8.6e-14) {
		tmp = t_1;
	} else if (z <= 2.8e+124) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (1.0d0 - y) * z
    if (z <= (-8.6d-14)) then
        tmp = t_1
    else if (z <= 2.8d+124) then
        tmp = (1.0d0 - t) * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double tmp;
	if (z <= -8.6e-14) {
		tmp = t_1;
	} else if (z <= 2.8e+124) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 - y) * z
	tmp = 0
	if z <= -8.6e-14:
		tmp = t_1
	elif z <= 2.8e+124:
		tmp = (1.0 - t) * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (z <= -8.6e-14)
		tmp = t_1;
	elseif (z <= 2.8e+124)
		tmp = Float64(Float64(1.0 - t) * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 - y) * z;
	tmp = 0.0;
	if (z <= -8.6e-14)
		tmp = t_1;
	elseif (z <= 2.8e+124)
		tmp = (1.0 - t) * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -8.6e-14], t$95$1, If[LessEqual[z, 2.8e+124], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.59999999999999996e-14 or 2.8e124 < z

   1. Initial program 92.2%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 54.7

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

   5. Applied rewrites 54.7%

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

   if -8.59999999999999996e-14 < z < 2.8e124

   1. Initial program 97.1%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.7

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

   5. Applied rewrites 33.7%

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

Alternative 21: 20.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -50000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-284}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+113}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -50000000000.0) x (if (<= x 4.8e-284) a (if (<= x 9.5e+113) z x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -50000000000.0) {
		tmp = x;
	} else if (x <= 4.8e-284) {
		tmp = a;
	} else if (x <= 9.5e+113) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-50000000000.0d0)) then
        tmp = x
    else if (x <= 4.8d-284) then
        tmp = a
    else if (x <= 9.5d+113) then
        tmp = z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -50000000000.0) {
		tmp = x;
	} else if (x <= 4.8e-284) {
		tmp = a;
	} else if (x <= 9.5e+113) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -50000000000.0:
		tmp = x
	elif x <= 4.8e-284:
		tmp = a
	elif x <= 9.5e+113:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -50000000000.0)
		tmp = x;
	elseif (x <= 4.8e-284)
		tmp = a;
	elseif (x <= 9.5e+113)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -50000000000.0)
		tmp = x;
	elseif (x <= 4.8e-284)
		tmp = a;
	elseif (x <= 9.5e+113)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -50000000000.0], x, If[LessEqual[x, 4.8e-284], a, If[LessEqual[x, 9.5e+113], z, x]]]

Derivation

1. Split input into 3 regimes

2. if x < -5e10 or 9.5000000000000001e113 < x

   1. Initial program 95.3%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 33.2%

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

   if -5e10 < x < 4.80000000000000006e-284

   1. Initial program 94.5%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 32.8

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

   5. Applied rewrites 32.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 12.8%

      \[\leadsto a \]

   if 4.80000000000000006e-284 < x < 9.5000000000000001e113

   1. Initial program 95.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 31.4

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

   5. Applied rewrites 31.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 12.0%

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

Alternative 22: 21.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -50000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+43}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -50000000000.0) x (if (<= x 1.2e+43) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -50000000000.0) {
		tmp = x;
	} else if (x <= 1.2e+43) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-50000000000.0d0)) then
        tmp = x
    else if (x <= 1.2d+43) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -50000000000.0) {
		tmp = x;
	} else if (x <= 1.2e+43) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -50000000000.0:
		tmp = x
	elif x <= 1.2e+43:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -50000000000.0)
		tmp = x;
	elseif (x <= 1.2e+43)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -50000000000.0)
		tmp = x;
	elseif (x <= 1.2e+43)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -50000000000.0], x, If[LessEqual[x, 1.2e+43], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -5e10 or 1.20000000000000012e43 < x

   1. Initial program 95.3%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 30.5%

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

   if -5e10 < x < 1.20000000000000012e43

   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 a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 32.4

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

   5. Applied rewrites 32.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 13.3%

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

Alternative 23: 15.8% accurate, 37.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.1%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 15.8%

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

Reproduce

herbie shell --seed 2025088 
(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)))