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

Percentage Accurate: 95.6% → 97.5%

Time: 9.8s

Alternatives: 20

Speedup: 1.1×

• 35.0% 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: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.5% accurate, 1.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 93.3%

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

3. Taylor expanded in 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. +-commutative N/A

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

   2. associate--l+ N/A

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

   3. +-commutative N/A

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

   4. associate-+l+ N/A

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

   5. *-commutative N/A

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

   6. associate--l+ N/A

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

   7. +-commutative N/A

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

   8. lower-fma.f64 N/A

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

   9. lower--.f64 N/A

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

   10. +-commutative N/A

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

   11. associate--l+ N/A

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

   12. *-commutative N/A

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

   13. lower-fma.f64 N/A

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

   14. lower--.f64 N/A

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

5. Applied rewrites 98.0%

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

Alternative 2: 42.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+296}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+300}:\\ \;\;\;\;\left(a + x\right) + z\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b))))
   (if (<= t_1 -5e+296) (* b t) (if (<= t_1 2e+300) (+ (+ a x) z) (* b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	double tmp;
	if (t_1 <= -5e+296) {
		tmp = b * t;
	} else if (t_1 <= 2e+300) {
		tmp = (a + x) + z;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
    if (t_1 <= (-5d+296)) then
        tmp = b * t
    else if (t_1 <= 2d+300) then
        tmp = (a + x) + z
    else
        tmp = b * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	double tmp;
	if (t_1 <= -5e+296) {
		tmp = b * t;
	} else if (t_1 <= 2e+300) {
		tmp = (a + x) + z;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)
	tmp = 0
	if t_1 <= -5e+296:
		tmp = b * t
	elif t_1 <= 2e+300:
		tmp = (a + x) + z
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (t_1 <= -5e+296)
		tmp = Float64(b * t);
	elseif (t_1 <= 2e+300)
		tmp = Float64(Float64(a + x) + z);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (t_1 <= -5e+296)
		tmp = b * t;
	elseif (t_1 <= 2e+300)
		tmp = (a + x) + z;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+296], N[(b * t), $MachinePrecision], If[LessEqual[t$95$1, 2e+300], N[(N[(a + x), $MachinePrecision] + z), $MachinePrecision], N[(b * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < -5.0000000000000001e296

   1. Initial program 100.0%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 96.9%

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

   6. Taylor expanded in b around -inf

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

   8. Applied rewrites 60.5%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 45.1%

       \[\leadsto b \cdot t \]

   if -5.0000000000000001e296 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < 2.0000000000000001e300

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 79.1

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

   5. Applied rewrites 79.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 56.9%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 50.9%

       \[\leadsto \left(a + x\right) + z \]

   if 2.0000000000000001e300 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 70.7%

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

   3. Taylor expanded in t around 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 93.1%

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

   6. Taylor expanded in b around -inf

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

   8. Applied rewrites 52.6%

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

   9. Taylor expanded in y around inf

      \[\leadsto b \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 37.1%

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

Alternative 3: 32.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+296} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+292}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b))))
   (if (or (<= t_1 -5e+296) (not (<= t_1 2e+292))) (* b t) (+ z x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	double tmp;
	if ((t_1 <= -5e+296) || !(t_1 <= 2e+292)) {
		tmp = b * t;
	} else {
		tmp = z + 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) :: t_1
    real(8) :: tmp
    t_1 = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
    if ((t_1 <= (-5d+296)) .or. (.not. (t_1 <= 2d+292))) then
        tmp = b * t
    else
        tmp = z + 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 t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	double tmp;
	if ((t_1 <= -5e+296) || !(t_1 <= 2e+292)) {
		tmp = b * t;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)
	tmp = 0
	if (t_1 <= -5e+296) or not (t_1 <= 2e+292):
		tmp = b * t
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if ((t_1 <= -5e+296) || !(t_1 <= 2e+292))
		tmp = Float64(b * t);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if ((t_1 <= -5e+296) || ~((t_1 <= 2e+292)))
		tmp = b * t;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+296], N[Not[LessEqual[t$95$1, 2e+292]], $MachinePrecision]], N[(b * t), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < -5.0000000000000001e296 or 2e292 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 82.3%

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

   3. Taylor expanded in t around 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 94.8%

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

   6. Taylor expanded in b around -inf

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

   8. Applied rewrites 56.1%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 35.9%

       \[\leadsto b \cdot t \]

   if -5.0000000000000001e296 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < 2e292

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 78.9

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

   5. Applied rewrites 78.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 57.8%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 51.5%

       \[\leadsto \left(a + x\right) + z \]

   12. Taylor expanded in a around 0

       \[\leadsto x + z \]
   13. Step-by-step derivation

   14. Applied rewrites 41.6%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \leq -5 \cdot 10^{+296} \lor \neg \left(\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \leq 2 \cdot 10^{+292}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right) + a\right)\\ t_2 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -9.4 \cdot 10^{+213}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.065:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, x - \mathsf{fma}\left(t - 1, a, -z\right)\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+183}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- b a) t (+ (fma (- y 2.0) b x) a))) (t_2 (* (- b z) y)))
   (if (<= y -9.4e+213)
     t_2
     (if (<= y -4.7e-13)
       t_1
       (if (<= y 0.065)
         (fma (- t 2.0) b (- x (fma (- t 1.0) a (- z))))
         (if (<= y 6.8e+183) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((b - a), t, (fma((y - 2.0), b, x) + a));
	double t_2 = (b - z) * y;
	double tmp;
	if (y <= -9.4e+213) {
		tmp = t_2;
	} else if (y <= -4.7e-13) {
		tmp = t_1;
	} else if (y <= 0.065) {
		tmp = fma((t - 2.0), b, (x - fma((t - 1.0), a, -z)));
	} else if (y <= 6.8e+183) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(b - a), t, Float64(fma(Float64(y - 2.0), b, x) + a))
	t_2 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -9.4e+213)
		tmp = t_2;
	elseif (y <= -4.7e-13)
		tmp = t_1;
	elseif (y <= 0.065)
		tmp = fma(Float64(t - 2.0), b, Float64(x - fma(Float64(t - 1.0), a, Float64(-z))));
	elseif (y <= 6.8e+183)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t + N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -9.4e+213], t$95$2, If[LessEqual[y, -4.7e-13], t$95$1, If[LessEqual[y, 0.065], N[(N[(t - 2.0), $MachinePrecision] * b + N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e+183], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.3999999999999995e213 or 6.8e183 < y

   1. Initial program 80.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 90.0

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

   5. Applied rewrites 90.0%

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

   if -9.3999999999999995e213 < y < -4.7000000000000002e-13 or 0.065000000000000002 < y < 6.8e183

   1. Initial program 93.4%

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

   3. Taylor expanded in t around 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 96.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 83.7%

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

   if -4.7000000000000002e-13 < y < 0.065000000000000002

   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 y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 98.6

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

   5. Applied rewrites 98.6%

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

Alternative 5: 66.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-59}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, a + x\right)\\ \mathbf{elif}\;y \leq 1.86 \cdot 10^{-116}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z + x\right)\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+94}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -4.6e+209)
     t_1
     (if (<= y -8e-59)
       (fma (- b a) t (+ a x))
       (if (<= y 1.86e-116)
         (fma (- t 2.0) b (+ z x))
         (if (<= y 4.7e+94) (fma (- b a) t (fma (- y 2.0) b a)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -4.6e+209) {
		tmp = t_1;
	} else if (y <= -8e-59) {
		tmp = fma((b - a), t, (a + x));
	} else if (y <= 1.86e-116) {
		tmp = fma((t - 2.0), b, (z + x));
	} else if (y <= 4.7e+94) {
		tmp = fma((b - a), t, fma((y - 2.0), b, a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -4.6e+209)
		tmp = t_1;
	elseif (y <= -8e-59)
		tmp = fma(Float64(b - a), t, Float64(a + x));
	elseif (y <= 1.86e-116)
		tmp = fma(Float64(t - 2.0), b, Float64(z + x));
	elseif (y <= 4.7e+94)
		tmp = fma(Float64(b - a), t, fma(Float64(y - 2.0), b, a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -4.6e+209], t$95$1, If[LessEqual[y, -8e-59], N[(N[(b - a), $MachinePrecision] * t + N[(a + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.86e-116], N[(N[(t - 2.0), $MachinePrecision] * b + N[(z + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.7e+94], N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.60000000000000019e209 or 4.70000000000000017e94 < y

   1. Initial program 84.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 83.5

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

   5. Applied rewrites 83.5%

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

   if -4.60000000000000019e209 < y < -8.0000000000000002e-59

   1. Initial program 95.7%

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

   3. Taylor expanded in t around 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 95.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 85.0%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 69.2%

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

   if -8.0000000000000002e-59 < y < 1.86e-116

   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 y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 99.0

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

   5. Applied rewrites 99.0%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 79.0%

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

   if 1.86e-116 < y < 4.70000000000000017e94

   1. Initial program 94.4%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 83.0%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 74.9%

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

Alternative 6: 88.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, -a\right)\right)\\ \mathbf{if}\;y \leq -1.96 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-13}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right) + a\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, x - \mathsf{fma}\left(t - 1, a, -z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- y 2.0) b (- x (fma (- y 1.0) z (- a))))))
   (if (<= y -1.96e+93)
     t_1
     (if (<= y -4.7e-13)
       (fma (- b a) t (+ (fma (- y 2.0) b x) a))
       (if (<= y 2.25e+80)
         (fma (- t 2.0) b (- 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 = fma((y - 2.0), b, (x - fma((y - 1.0), z, -a)));
	double tmp;
	if (y <= -1.96e+93) {
		tmp = t_1;
	} else if (y <= -4.7e-13) {
		tmp = fma((b - a), t, (fma((y - 2.0), b, x) + a));
	} else if (y <= 2.25e+80) {
		tmp = fma((t - 2.0), b, (x - fma((t - 1.0), a, -z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(y - 2.0), b, Float64(x - fma(Float64(y - 1.0), z, Float64(-a))))
	tmp = 0.0
	if (y <= -1.96e+93)
		tmp = t_1;
	elseif (y <= -4.7e-13)
		tmp = fma(Float64(b - a), t, Float64(fma(Float64(y - 2.0), b, x) + a));
	elseif (y <= 2.25e+80)
		tmp = fma(Float64(t - 2.0), b, 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[(y - 2.0), $MachinePrecision] * b + N[(x - N[(N[(y - 1.0), $MachinePrecision] * z + (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.96e+93], t$95$1, If[LessEqual[y, -4.7e-13], N[(N[(b - a), $MachinePrecision] * t + N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.25e+80], N[(N[(t - 2.0), $MachinePrecision] * b + N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9600000000000001e93 or 2.25000000000000003e80 < y

   1. Initial program 84.9%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 87.4

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

   5. Applied rewrites 87.4%

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

   if -1.9600000000000001e93 < y < -4.7000000000000002e-13

   1. Initial program 96.3%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 96.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 89.5%

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

   if -4.7000000000000002e-13 < y < 2.25000000000000003e80

   1. Initial program 98.5%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 97.1

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

   5. Applied rewrites 97.1%

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

Alternative 7: 67.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b - a, t, a + x\right)\\ t_2 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+209}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-116}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z + x\right)\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- b a) t (+ a x))) (t_2 (* (- b z) y)))
   (if (<= y -4.6e+209)
     t_2
     (if (<= y -8e-59)
       t_1
       (if (<= y 1.9e-116)
         (fma (- t 2.0) b (+ z x))
         (if (<= y 4.7e+94) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((b - a), t, (a + x));
	double t_2 = (b - z) * y;
	double tmp;
	if (y <= -4.6e+209) {
		tmp = t_2;
	} else if (y <= -8e-59) {
		tmp = t_1;
	} else if (y <= 1.9e-116) {
		tmp = fma((t - 2.0), b, (z + x));
	} else if (y <= 4.7e+94) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(b - a), t, Float64(a + x))
	t_2 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -4.6e+209)
		tmp = t_2;
	elseif (y <= -8e-59)
		tmp = t_1;
	elseif (y <= 1.9e-116)
		tmp = fma(Float64(t - 2.0), b, Float64(z + x));
	elseif (y <= 4.7e+94)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t + N[(a + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -4.6e+209], t$95$2, If[LessEqual[y, -8e-59], t$95$1, If[LessEqual[y, 1.9e-116], N[(N[(t - 2.0), $MachinePrecision] * b + N[(z + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.7e+94], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.60000000000000019e209 or 4.70000000000000017e94 < y

   1. Initial program 84.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 83.5

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

   5. Applied rewrites 83.5%

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

   if -4.60000000000000019e209 < y < -8.0000000000000002e-59 or 1.9000000000000001e-116 < y < 4.70000000000000017e94

   1. Initial program 95.2%

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

   3. Taylor expanded in t around 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 97.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 84.1%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 70.6%

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

   if -8.0000000000000002e-59 < y < 1.9000000000000001e-116

   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 y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 99.0

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

   5. Applied rewrites 99.0%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 79.0%

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

Alternative 8: 89.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -225:\\ \;\;\;\;\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + b \cdot y\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, x - \mathsf{fma}\left(t - 1, a, -z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, -a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -225.0)
   (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* b y))
   (if (<= y 2.25e+80)
     (fma (- t 2.0) b (- x (fma (- t 1.0) a (- z))))
     (fma (- 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) {
	double tmp;
	if (y <= -225.0) {
		tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (b * y);
	} else if (y <= 2.25e+80) {
		tmp = fma((t - 2.0), b, (x - fma((t - 1.0), a, -z)));
	} else {
		tmp = fma((y - 2.0), b, (x - fma((y - 1.0), z, -a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -225.0)
		tmp = Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(b * y));
	elseif (y <= 2.25e+80)
		tmp = fma(Float64(t - 2.0), b, Float64(x - fma(Float64(t - 1.0), a, Float64(-z))));
	else
		tmp = fma(Float64(y - 2.0), b, Float64(x - fma(Float64(y - 1.0), z, Float64(-a))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -225.0], N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(b * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.25e+80], N[(N[(t - 2.0), $MachinePrecision] * b + N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - 2.0), $MachinePrecision] * b + N[(x - N[(N[(y - 1.0), $MachinePrecision] * z + (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -225

   1. Initial program 88.9%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 83.2

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

   5. Applied rewrites 83.2%

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

   if -225 < y < 2.25000000000000003e80

   1. Initial program 98.5%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 97.1

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

   5. Applied rewrites 97.1%

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

   if 2.25000000000000003e80 < y

   1. Initial program 84.6%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 88.8

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

   5. Applied rewrites 88.8%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -225:\\ \;\;\;\;\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + b \cdot y\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, x - \mathsf{fma}\left(t - 1, a, -z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, -a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+157} \lor \neg \left(z \leq 1.9 \cdot 10^{+66}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y - 1, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right) + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8e+157) (not (<= z 1.9e+66)))
   (fma (- 1.0 t) a (fma (- z) (- y 1.0) x))
   (fma (- b a) t (+ (fma (- y 2.0) b x) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8e+157) || !(z <= 1.9e+66)) {
		tmp = fma((1.0 - t), a, fma(-z, (y - 1.0), x));
	} else {
		tmp = fma((b - a), t, (fma((y - 2.0), b, x) + a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8e+157) || !(z <= 1.9e+66))
		tmp = fma(Float64(1.0 - t), a, fma(Float64(-z), Float64(y - 1.0), x));
	else
		tmp = fma(Float64(b - a), t, Float64(fma(Float64(y - 2.0), b, x) + a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8e+157], N[Not[LessEqual[z, 1.9e+66]], $MachinePrecision]], N[(N[(1.0 - t), $MachinePrecision] * a + N[((-z) * N[(y - 1.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(N[(b - a), $MachinePrecision] * t + N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.99999999999999987e157 or 1.9000000000000001e66 < z

   1. Initial program 84.9%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 98.6%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 86.1%

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

   if -7.99999999999999987e157 < z < 1.9000000000000001e66

   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 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 97.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 89.5%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+157} \lor \neg \left(z \leq 1.9 \cdot 10^{+66}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y - 1, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right) + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.4 \cdot 10^{+14} \lor \neg \left(b \leq 1.46 \cdot 10^{-5}\right):\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y - 1, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -9.4e+14) (not (<= b 1.46e-5)))
   (fma (- b a) t (fma (- y 2.0) b x))
   (fma (- 1.0 t) a (fma (- z) (- y 1.0) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -9.4e+14) || !(b <= 1.46e-5)) {
		tmp = fma((b - a), t, fma((y - 2.0), b, x));
	} else {
		tmp = fma((1.0 - t), a, fma(-z, (y - 1.0), x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -9.4e+14) || !(b <= 1.46e-5))
		tmp = fma(Float64(b - a), t, fma(Float64(y - 2.0), b, x));
	else
		tmp = fma(Float64(1.0 - t), a, fma(Float64(-z), Float64(y - 1.0), x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -9.4e+14], N[Not[LessEqual[b, 1.46e-5]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a + N[((-z) * N[(y - 1.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.4e14 or 1.46000000000000008e-5 < b

   1. Initial program 88.9%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 96.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 85.5%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 74.0%

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

   12. Taylor expanded in a around 0

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

   14. Applied rewrites 83.3%

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

   if -9.4e14 < b < 1.46000000000000008e-5

   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 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 99.2%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 89.3%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.4 \cdot 10^{+14} \lor \neg \left(b \leq 1.46 \cdot 10^{-5}\right):\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y - 1, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+228}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y - 1, -a\right)\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+66}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-\mathsf{fma}\left(a, t - 1, z \cdot \left(y - 1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8e+228)
   (- x (fma z (- y 1.0) (- a)))
   (if (<= z 3.25e+66)
     (fma (- b a) t (fma (- y 2.0) b x))
     (- (fma a (- t 1.0) (* z (- y 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8e+228) {
		tmp = x - fma(z, (y - 1.0), -a);
	} else if (z <= 3.25e+66) {
		tmp = fma((b - a), t, fma((y - 2.0), b, x));
	} else {
		tmp = -fma(a, (t - 1.0), (z * (y - 1.0)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8e+228)
		tmp = Float64(x - fma(z, Float64(y - 1.0), Float64(-a)));
	elseif (z <= 3.25e+66)
		tmp = fma(Float64(b - a), t, fma(Float64(y - 2.0), b, x));
	else
		tmp = Float64(-fma(a, Float64(t - 1.0), Float64(z * Float64(y - 1.0))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -8e+228], N[(x - N[(z * N[(y - 1.0), $MachinePrecision] + (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.25e+66], N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], (-N[(a * N[(t - 1.0), $MachinePrecision] + N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if z < -7.9999999999999994e228

   1. Initial program 71.4%

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

   3. Taylor expanded in t around 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 32.2%

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

   9. Taylor expanded in b around 0

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

       1. lower--.f64 N/A

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

       2. lower-fma.f64 N/A

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

       3. lower--.f64 N/A

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

       4. lower-*.f64 N/A

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

       5. lower--.f64 76.9

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

   11. Applied rewrites 76.9%

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

   12. Taylor expanded in t around 0

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

   14. Applied rewrites 77.4%

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

   if -7.9999999999999994e228 < z < 3.2500000000000001e66

   1. Initial program 95.9%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 97.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 88.2%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 70.4%

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

   12. Taylor expanded in a around 0

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

   14. Applied rewrites 80.2%

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

   if 3.2500000000000001e66 < z

   1. Initial program 89.3%

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

   3. Taylor expanded in t around 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 35.9%

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

   9. Taylor expanded in b around 0

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

       1. lower--.f64 N/A

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

       2. lower-fma.f64 N/A

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

       3. lower--.f64 N/A

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

       4. lower-*.f64 N/A

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

       5. lower--.f64 91.6

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

   11. Applied rewrites 91.6%

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

   12. Taylor expanded in x around 0

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

   14. Applied rewrites 83.2%

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

Alternative 12: 73.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+228} \lor \neg \left(z \leq 1.9 \cdot 10^{+100}\right):\\ \;\;\;\;x - \mathsf{fma}\left(z, y - 1, -a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8e+228) (not (<= z 1.9e+100)))
   (- x (fma z (- y 1.0) (- a)))
   (fma (- b a) t (fma (- y 2.0) b x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8e+228) || !(z <= 1.9e+100)) {
		tmp = x - fma(z, (y - 1.0), -a);
	} else {
		tmp = fma((b - a), t, fma((y - 2.0), b, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8e+228) || !(z <= 1.9e+100))
		tmp = Float64(x - fma(z, Float64(y - 1.0), Float64(-a)));
	else
		tmp = fma(Float64(b - a), t, fma(Float64(y - 2.0), b, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8e+228], N[Not[LessEqual[z, 1.9e+100]], $MachinePrecision]], N[(x - N[(z * N[(y - 1.0), $MachinePrecision] + (-a)), $MachinePrecision]), $MachinePrecision], N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.9999999999999994e228 or 1.89999999999999982e100 < z

   1. Initial program 82.7%

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

   3. Taylor expanded in t around 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 29.5%

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

   9. Taylor expanded in b around 0

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

       1. lower--.f64 N/A

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

       2. lower-fma.f64 N/A

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

       3. lower--.f64 N/A

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

       4. lower-*.f64 N/A

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

       5. lower--.f64 89.9

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

   11. Applied rewrites 89.9%

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

   12. Taylor expanded in t around 0

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

   14. Applied rewrites 84.6%

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

   if -7.9999999999999994e228 < z < 1.89999999999999982e100

   1. Initial program 96.0%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 97.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 87.2%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 70.2%

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

   12. Taylor expanded in a around 0

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

   14. Applied rewrites 79.2%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+228} \lor \neg \left(z \leq 1.9 \cdot 10^{+100}\right):\\ \;\;\;\;x - \mathsf{fma}\left(z, y - 1, -a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{-240}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, z + x\right) + a\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+94}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -4.6e+61)
     t_1
     (if (<= y 1.62e-240)
       (+ (fma -2.0 b (+ z x)) a)
       (if (<= y 4.6e+94) (* (- 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 <= -4.6e+61) {
		tmp = t_1;
	} else if (y <= 1.62e-240) {
		tmp = fma(-2.0, b, (z + x)) + a;
	} else if (y <= 4.6e+94) {
		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 <= -4.6e+61)
		tmp = t_1;
	elseif (y <= 1.62e-240)
		tmp = Float64(fma(-2.0, b, Float64(z + x)) + a);
	elseif (y <= 4.6e+94)
		tmp = Float64(Float64(b - a) * t);
	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, -4.6e+61], t$95$1, If[LessEqual[y, 1.62e-240], N[(N[(-2.0 * b + N[(z + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[y, 4.6e+94], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5999999999999999e61 or 4.5999999999999999e94 < y

   1. Initial program 86.6%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 75.3

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

   5. Applied rewrites 75.3%

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

   if -4.5999999999999999e61 < y < 1.61999999999999995e-240

   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 y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 95.1

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

   5. Applied rewrites 95.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 60.6%

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

   if 1.61999999999999995e-240 < y < 4.5999999999999999e94

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 55.8

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

   5. Applied rewrites 55.8%

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

Alternative 14: 53.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-241}:\\ \;\;\;\;\left(a + x\right) + z\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+94}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -4.6e+61)
     t_1
     (if (<= y 6.8e-241)
       (+ (+ a x) z)
       (if (<= y 4.6e+94) (* (- 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 <= -4.6e+61) {
		tmp = t_1;
	} else if (y <= 6.8e-241) {
		tmp = (a + x) + z;
	} else if (y <= 4.6e+94) {
		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 <= (-4.6d+61)) then
        tmp = t_1
    else if (y <= 6.8d-241) then
        tmp = (a + x) + z
    else if (y <= 4.6d+94) 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 <= -4.6e+61) {
		tmp = t_1;
	} else if (y <= 6.8e-241) {
		tmp = (a + x) + z;
	} else if (y <= 4.6e+94) {
		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 <= -4.6e+61:
		tmp = t_1
	elif y <= 6.8e-241:
		tmp = (a + x) + z
	elif y <= 4.6e+94:
		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 <= -4.6e+61)
		tmp = t_1;
	elseif (y <= 6.8e-241)
		tmp = Float64(Float64(a + x) + z);
	elseif (y <= 4.6e+94)
		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 <= -4.6e+61)
		tmp = t_1;
	elseif (y <= 6.8e-241)
		tmp = (a + x) + z;
	elseif (y <= 4.6e+94)
		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, -4.6e+61], t$95$1, If[LessEqual[y, 6.8e-241], N[(N[(a + x), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[y, 4.6e+94], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5999999999999999e61 or 4.5999999999999999e94 < y

   1. Initial program 86.6%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 75.3

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

   5. Applied rewrites 75.3%

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

   if -4.5999999999999999e61 < y < 6.7999999999999998e-241

   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 y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 95.1

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

   5. Applied rewrites 95.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 60.6%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 52.3%

       \[\leadsto \left(a + x\right) + z \]

   if 6.7999999999999998e-241 < y < 4.5999999999999999e94

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 55.8

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

   5. Applied rewrites 55.8%

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

Alternative 15: 66.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+209} \lor \neg \left(y \leq 4.7 \cdot 10^{+94}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, a + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.6e+209) (not (<= y 4.7e+94)))
   (* (- b z) y)
   (fma (- b a) t (+ a x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.6e+209) || !(y <= 4.7e+94)) {
		tmp = (b - z) * y;
	} else {
		tmp = fma((b - a), t, (a + x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.6e+209) || !(y <= 4.7e+94))
		tmp = Float64(Float64(b - z) * y);
	else
		tmp = fma(Float64(b - a), t, Float64(a + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.6e+209], N[Not[LessEqual[y, 4.7e+94]], $MachinePrecision]], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], N[(N[(b - a), $MachinePrecision] * t + N[(a + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.60000000000000019e209 or 4.70000000000000017e94 < y

   1. Initial program 84.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 83.5

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

   5. Applied rewrites 83.5%

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

   if -4.60000000000000019e209 < y < 4.70000000000000017e94

   1. Initial program 97.2%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 98.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 80.0%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 68.6%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+209} \lor \neg \left(y \leq 4.7 \cdot 10^{+94}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, a + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 56.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+14} \lor \neg \left(t \leq 3.2 \cdot 10^{+53}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(a + x\right) + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -7e+14) (not (<= t 3.2e+53))) (* (- b a) t) (+ (+ a x) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7e+14) || !(t <= 3.2e+53)) {
		tmp = (b - a) * t;
	} else {
		tmp = (a + x) + z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-7d+14)) .or. (.not. (t <= 3.2d+53))) then
        tmp = (b - a) * t
    else
        tmp = (a + x) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7e+14) || !(t <= 3.2e+53)) {
		tmp = (b - a) * t;
	} else {
		tmp = (a + x) + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -7e+14) or not (t <= 3.2e+53):
		tmp = (b - a) * t
	else:
		tmp = (a + x) + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -7e+14) || !(t <= 3.2e+53))
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = Float64(Float64(a + x) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -7e+14) || ~((t <= 3.2e+53)))
		tmp = (b - a) * t;
	else
		tmp = (a + x) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -7e+14], N[Not[LessEqual[t, 3.2e+53]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], N[(N[(a + x), $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7e14 or 3.2e53 < t

   1. Initial program 90.4%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 67.9

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

   5. Applied rewrites 67.9%

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

   if -7e14 < t < 3.2e53

   1. Initial program 96.1%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 63.1

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

   5. Applied rewrites 63.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 58.8%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 50.9%

       \[\leadsto \left(a + x\right) + z \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+14} \lor \neg \left(t \leq 3.2 \cdot 10^{+53}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(a + x\right) + z\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 45.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+127} \lor \neg \left(b \leq 1.1 \cdot 10^{+141}\right):\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(a + x\right) + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -9e+127) (not (<= b 1.1e+141))) (* (- t 2.0) b) (+ (+ a x) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -9e+127) || !(b <= 1.1e+141)) {
		tmp = (t - 2.0) * b;
	} else {
		tmp = (a + x) + z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-9d+127)) .or. (.not. (b <= 1.1d+141))) then
        tmp = (t - 2.0d0) * b
    else
        tmp = (a + x) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -9e+127) || !(b <= 1.1e+141)) {
		tmp = (t - 2.0) * b;
	} else {
		tmp = (a + x) + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -9e+127) or not (b <= 1.1e+141):
		tmp = (t - 2.0) * b
	else:
		tmp = (a + x) + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -9e+127) || !(b <= 1.1e+141))
		tmp = Float64(Float64(t - 2.0) * b);
	else
		tmp = Float64(Float64(a + x) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -9e+127) || ~((b <= 1.1e+141)))
		tmp = (t - 2.0) * b;
	else
		tmp = (a + x) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -9e+127], N[Not[LessEqual[b, 1.1e+141]], $MachinePrecision]], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision], N[(N[(a + x), $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.00000000000000068e127 or 1.1e141 < b

   1. Initial program 87.1%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 62.8

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

   5. Applied rewrites 62.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 22.6%

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

   9. Taylor expanded in b around inf

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

   11. Applied rewrites 57.9%

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

   if -9.00000000000000068e127 < b < 1.1e141

   1. Initial program 96.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 73.8

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

   5. Applied rewrites 73.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 45.4%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 44.2%

       \[\leadsto \left(a + x\right) + z \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+127} \lor \neg \left(b \leq 1.1 \cdot 10^{+141}\right):\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(a + x\right) + z\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 35.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+55} \lor \neg \left(y \leq 3.7\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.7e+55) (not (<= y 3.7))) (* b y) (+ z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.7e+55) || !(y <= 3.7)) {
		tmp = b * y;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.7d+55)) .or. (.not. (y <= 3.7d0))) then
        tmp = b * y
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.7e+55) || !(y <= 3.7)) {
		tmp = b * y;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.7e+55) or not (y <= 3.7):
		tmp = b * y
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.7e+55) || !(y <= 3.7))
		tmp = Float64(b * y);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.7e+55) || ~((y <= 3.7)))
		tmp = b * y;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.7e+55], N[Not[LessEqual[y, 3.7]], $MachinePrecision]], N[(b * y), $MachinePrecision], N[(z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6999999999999999e55 or 3.7000000000000002 < y

   1. Initial program 86.6%

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

   3. Taylor expanded in t around 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 96.4%

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

   6. Taylor expanded in b around -inf

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

   8. Applied rewrites 46.2%

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

   9. Taylor expanded in y around inf

      \[\leadsto b \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 40.1%

       \[\leadsto b \cdot y \]

   if -1.6999999999999999e55 < y < 3.7000000000000002

   1. Initial program 98.6%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 95.5

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

   5. Applied rewrites 95.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 56.4%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 49.5%

       \[\leadsto \left(a + x\right) + z \]

   12. Taylor expanded in a around 0

       \[\leadsto x + z \]
   13. Step-by-step derivation

   14. Applied rewrites 41.6%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+55} \lor \neg \left(y \leq 3.7\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.25 \cdot 10^{+46} \lor \neg \left(x \leq 2.5 \cdot 10^{+14}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -3.25e+46) (not (<= x 2.5e+14))) (+ z x) (+ a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -3.25e+46) || !(x <= 2.5e+14)) {
		tmp = z + x;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-3.25d+46)) .or. (.not. (x <= 2.5d+14))) then
        tmp = z + x
    else
        tmp = a + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -3.25e+46) || !(x <= 2.5e+14)) {
		tmp = z + x;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -3.25e+46) or not (x <= 2.5e+14):
		tmp = z + x
	else:
		tmp = a + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -3.25e+46) || !(x <= 2.5e+14))
		tmp = Float64(z + x);
	else
		tmp = Float64(a + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -3.25e+46) || ~((x <= 2.5e+14)))
		tmp = z + x;
	else
		tmp = a + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -3.25e+46], N[Not[LessEqual[x, 2.5e+14]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(a + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.25000000000000004e46 or 2.5e14 < x

   1. Initial program 93.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 78.3

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

   5. Applied rewrites 78.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 46.9%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 46.2%

       \[\leadsto \left(a + x\right) + z \]

   12. Taylor expanded in a around 0

       \[\leadsto x + z \]
   13. Step-by-step derivation

   14. Applied rewrites 43.1%

       \[\leadsto z + x \]

   if -3.25000000000000004e46 < x < 2.5e14

   1. Initial program 92.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 64.0

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

   5. Applied rewrites 64.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 31.5%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 24.1%

       \[\leadsto \left(a + x\right) + z \]

   12. Taylor expanded in x around 0

       \[\leadsto a + z \]
   13. Step-by-step derivation

   14. Applied rewrites 24.1%

       \[\leadsto a + z \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.25 \cdot 10^{+46} \lor \neg \left(x \leq 2.5 \cdot 10^{+14}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 20.8% accurate, 9.3× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

function code(x, y, z, t, a, b)
	return Float64(a + z)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(a + z), $MachinePrecision]

Derivation

1. Initial program 93.3%

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

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. associate--l+ N/A

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

   3. *-commutative N/A

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

   4. lower-fma.f64 N/A

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

   5. lower--.f64 N/A

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

   6. lower--.f64 N/A

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

   7. +-commutative N/A

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

   8. *-commutative N/A

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

   9. lower-fma.f64 N/A

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

   10. lower--.f64 N/A

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

   11. mul-1-neg N/A

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

   12. lower-neg.f64 70.4

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

5. Applied rewrites 70.4%

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

6. Taylor expanded in t around 0

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

8. Applied rewrites 38.4%

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

9. Taylor expanded in b around 0

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

11. Applied rewrites 34.0%

    \[\leadsto \left(a + x\right) + z \]

12. Taylor expanded in x around 0

    \[\leadsto a + z \]
13. Step-by-step derivation

14. Applied rewrites 19.0%

    \[\leadsto a + z \]
15. Add Preprocessing

Reproduce

herbie shell --seed 2024359 
(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)))