AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1

Percentage Accurate: 59.6% → 93.5%

Time: 6.4s

Alternatives: 16

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

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) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 59.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := z \cdot \frac{x + y}{t\_1}\\ t_3 := \left(y + x\right) + t\\ t_4 := \frac{t + y}{t\_3}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+70}:\\ \;\;\;\;\mathsf{fma}\left(t\_4, a, \mathsf{fma}\left(-1, b, t\_2\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+163}:\\ \;\;\;\;\mathsf{fma}\left(t\_4, a, \mathsf{fma}\left(-1, \frac{b \cdot y}{t\_1}, t\_2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b \cdot \frac{y}{t\_3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y)))
        (t_2 (* z (/ (+ x y) t_1)))
        (t_3 (+ (+ y x) t))
        (t_4 (/ (+ t y) t_3)))
   (if (<= y -9e+70)
     (fma t_4 a (fma -1.0 b t_2))
     (if (<= y 4.2e+163)
       (fma t_4 a (fma -1.0 (/ (* b y) t_1) t_2))
       (- (+ a z) (* b (/ y t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = z * ((x + y) / t_1);
	double t_3 = (y + x) + t;
	double t_4 = (t + y) / t_3;
	double tmp;
	if (y <= -9e+70) {
		tmp = fma(t_4, a, fma(-1.0, b, t_2));
	} else if (y <= 4.2e+163) {
		tmp = fma(t_4, a, fma(-1.0, ((b * y) / t_1), t_2));
	} else {
		tmp = (a + z) - (b * (y / t_3));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(z * Float64(Float64(x + y) / t_1))
	t_3 = Float64(Float64(y + x) + t)
	t_4 = Float64(Float64(t + y) / t_3)
	tmp = 0.0
	if (y <= -9e+70)
		tmp = fma(t_4, a, fma(-1.0, b, t_2));
	elseif (y <= 4.2e+163)
		tmp = fma(t_4, a, fma(-1.0, Float64(Float64(b * y) / t_1), t_2));
	else
		tmp = Float64(Float64(a + z) - Float64(b * Float64(y / t_3)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t + y), $MachinePrecision] / t$95$3), $MachinePrecision]}, If[LessEqual[y, -9e+70], N[(t$95$4 * a + N[(-1.0 * b + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+163], N[(t$95$4 * a + N[(-1.0 * N[(N[(b * y), $MachinePrecision] / t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - N[(b * N[(y / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.9999999999999999e70

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   3. Applied rewrites 71.1%

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

   4. Taylor expanded in z around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. div-add-rev N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-+.f64 86.5

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

   6. Applied rewrites 86.5%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 72.4%

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

   if -8.9999999999999999e70 < y < 4.2000000000000001e163

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   3. Applied rewrites 71.1%

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

   4. Taylor expanded in z around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. div-add-rev N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-+.f64 86.5

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

   6. Applied rewrites 86.5%

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

   if 4.2000000000000001e163 < y

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   3. Applied rewrites 64.5%

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

   4. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 35.0

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

   6. Applied rewrites 35.0%

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

   7. Taylor expanded in y around inf

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

      1. lift-+.f64 71.2

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

   9. Applied rewrites 71.2%

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

Alternative 2: 92.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := \left(y + x\right) + t\\ t_3 := \frac{t + y}{t\_2}\\ t_4 := \mathsf{fma}\left(t\_3, a, \mathsf{fma}\left(-1, b, z \cdot \frac{x + y}{t + \left(x + y\right)}\right)\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+266}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+140}:\\ \;\;\;\;\mathsf{fma}\left(t\_3, a, \frac{\left(y + x\right) \cdot z - b \cdot y}{t\_2}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_2 (+ (+ y x) t))
        (t_3 (/ (+ t y) t_2))
        (t_4 (fma t_3 a (fma -1.0 b (* z (/ (+ x y) (+ t (+ x y))))))))
   (if (<= t_1 -5e+266)
     t_4
     (if (<= t_1 5e+140) (fma t_3 a (/ (- (* (+ y x) z) (* b y)) t_2)) t_4))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double t_2 = (y + x) + t;
	double t_3 = (t + y) / t_2;
	double t_4 = fma(t_3, a, fma(-1.0, b, (z * ((x + y) / (t + (x + y))))));
	double tmp;
	if (t_1 <= -5e+266) {
		tmp = t_4;
	} else if (t_1 <= 5e+140) {
		tmp = fma(t_3, a, ((((y + x) * z) - (b * y)) / t_2));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	t_2 = Float64(Float64(y + x) + t)
	t_3 = Float64(Float64(t + y) / t_2)
	t_4 = fma(t_3, a, fma(-1.0, b, Float64(z * Float64(Float64(x + y) / Float64(t + Float64(x + y))))))
	tmp = 0.0
	if (t_1 <= -5e+266)
		tmp = t_4;
	elseif (t_1 <= 5e+140)
		tmp = fma(t_3, a, Float64(Float64(Float64(Float64(y + x) * z) - Float64(b * y)) / t_2));
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t + y), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 * a + N[(-1.0 * b + N[(z * N[(N[(x + y), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+266], t$95$4, If[LessEqual[t$95$1, 5e+140], N[(t$95$3 * a + N[(N[(N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -4.9999999999999999e266 or 5.00000000000000008e140 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   3. Applied rewrites 71.1%

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

   4. Taylor expanded in z around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. div-add-rev N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-+.f64 86.5

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

   6. Applied rewrites 86.5%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 72.4%

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

   if -4.9999999999999999e266 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000008e140

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   3. Applied rewrites 71.1%

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

Alternative 3: 92.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := \mathsf{fma}\left(\frac{t + y}{\left(y + x\right) + t}, a, \mathsf{fma}\left(-1, b, z \cdot \frac{x + y}{t + \left(x + y\right)}\right)\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+266}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_2
         (fma
          (/ (+ t y) (+ (+ y x) t))
          a
          (fma -1.0 b (* z (/ (+ x y) (+ t (+ x y))))))))
   (if (<= t_1 -5e+266) t_2 (if (<= t_1 5e+140) t_1 t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double t_2 = fma(((t + y) / ((y + x) + t)), a, fma(-1.0, b, (z * ((x + y) / (t + (x + y))))));
	double tmp;
	if (t_1 <= -5e+266) {
		tmp = t_2;
	} else if (t_1 <= 5e+140) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	t_2 = fma(Float64(Float64(t + y) / Float64(Float64(y + x) + t)), a, fma(-1.0, b, Float64(z * Float64(Float64(x + y) / Float64(t + Float64(x + y))))))
	tmp = 0.0
	if (t_1 <= -5e+266)
		tmp = t_2;
	elseif (t_1 <= 5e+140)
		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[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t + y), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] * a + N[(-1.0 * b + N[(z * N[(N[(x + y), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+266], t$95$2, If[LessEqual[t$95$1, 5e+140], t$95$1, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -4.9999999999999999e266 or 5.00000000000000008e140 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   3. Applied rewrites 71.1%

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

   4. Taylor expanded in z around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. div-add-rev N/A

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

      8. lower-/.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-+.f64 86.5

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

   6. Applied rewrites 86.5%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 72.4%

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

   if -4.9999999999999999e266 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000008e140

   1. Initial program 59.6%

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

Alternative 4: 92.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := \left(a + z\right) - b \cdot \frac{y}{\left(y + x\right) + t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+246}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_2 (- (+ a z) (* b (/ y (+ (+ y x) t))))))
   (if (<= t_1 (- INFINITY)) t_2 (if (<= t_1 2e+246) t_1 t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double t_2 = (a + z) - (b * (y / ((y + x) + t)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 2e+246) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double t_2 = (a + z) - (b * (y / ((y + x) + t)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= 2e+246) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
	t_2 = (a + z) - (b * (y / ((y + x) + t)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= 2e+246:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	t_2 = Float64(Float64(a + z) - Float64(b * Float64(y / Float64(Float64(y + x) + t))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 2e+246)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	t_2 = (a + z) - (b * (y / ((y + x) + t)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= 2e+246)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a + z), $MachinePrecision] - N[(b * N[(y / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 2e+246], t$95$1, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 2.00000000000000014e246 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   3. Applied rewrites 64.5%

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

   4. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 35.0

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

   6. Applied rewrites 35.0%

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

   7. Taylor expanded in y around inf

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

      1. lift-+.f64 71.2

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

   9. Applied rewrites 71.2%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000014e246

   1. Initial program 59.6%

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

Alternative 5: 92.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := \left(a + z\right) - b \cdot \frac{y}{\left(y + x\right) + t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+246}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, \mathsf{fma}\left(\left(a + z\right) - b, y, z \cdot x\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) t_1))
        (t_3 (- (+ a z) (* b (/ y (+ (+ y x) t))))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 2e+246)
       (/ (fma a t (fma (- (+ a z) b) y (* z x))) t_1)
       t_3))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / t_1;
	double t_3 = (a + z) - (b * (y / ((y + x) + t)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= 2e+246) {
		tmp = fma(a, t, fma(((a + z) - b), y, (z * x))) / t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(a + z) - Float64(b * Float64(y / Float64(Float64(y + x) + t))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= 2e+246)
		tmp = Float64(fma(a, t, fma(Float64(Float64(a + z) - b), y, Float64(z * x))) / t_1);
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a + z), $MachinePrecision] - N[(b * N[(y / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, 2e+246], N[(N[(a * t + N[(N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision] * y + N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 2.00000000000000014e246 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   3. Applied rewrites 64.5%

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

   4. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 35.0

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

   6. Applied rewrites 35.0%

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

   7. Taylor expanded in y around inf

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

      1. lift-+.f64 71.2

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

   9. Applied rewrites 71.2%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000014e246

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   2. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 59.9

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

   4. Applied rewrites 59.9%

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

Alternative 6: 73.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) \cdot a\\ t_2 := \left(x + t\right) + y\\ t_3 := \frac{\left(\left(x + y\right) \cdot z + t\_1\right) - y \cdot b}{t\_2}\\ t_4 := \left(y + x\right) + t\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{+144}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t + y}{t\_4}, a, z - b\right)\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{-35}:\\ \;\;\;\;\frac{t\_1 - y \cdot b}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b \cdot \frac{y}{t\_4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ t y) a))
        (t_2 (+ (+ x t) y))
        (t_3 (/ (- (+ (* (+ x y) z) t_1) (* y b)) t_2))
        (t_4 (+ (+ y x) t)))
   (if (<= t_3 -5e+144)
     (fma (/ (+ t y) t_4) a (- z b))
     (if (<= t_3 4e-35) (/ (- t_1 (* y b)) t_2) (- (+ a z) (* b (/ y t_4)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) * a;
	double t_2 = (x + t) + y;
	double t_3 = ((((x + y) * z) + t_1) - (y * b)) / t_2;
	double t_4 = (y + x) + t;
	double tmp;
	if (t_3 <= -5e+144) {
		tmp = fma(((t + y) / t_4), a, (z - b));
	} else if (t_3 <= 4e-35) {
		tmp = (t_1 - (y * b)) / t_2;
	} else {
		tmp = (a + z) - (b * (y / t_4));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) * a)
	t_2 = Float64(Float64(x + t) + y)
	t_3 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + t_1) - Float64(y * b)) / t_2)
	t_4 = Float64(Float64(y + x) + t)
	tmp = 0.0
	if (t_3 <= -5e+144)
		tmp = fma(Float64(Float64(t + y) / t_4), a, Float64(z - b));
	elseif (t_3 <= 4e-35)
		tmp = Float64(Float64(t_1 - Float64(y * b)) / t_2);
	else
		tmp = Float64(Float64(a + z) - Float64(b * Float64(y / t_4)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+144], N[(N[(N[(t + y), $MachinePrecision] / t$95$4), $MachinePrecision] * a + N[(z - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 4e-35], N[(N[(t$95$1 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - N[(b * N[(y / t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -4.9999999999999999e144

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   3. Applied rewrites 71.1%

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

   4. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\frac{t + y}{\left(y + x\right) + t}, a, \color{blue}{z - b}\right) \]
   5. Step-by-step derivation

      1. lower--.f64 64.2

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

   6. Applied rewrites 64.2%

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

   if -4.9999999999999999e144 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.00000000000000003e-35

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   2. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lift-+.f64 N/A

         \[\leadsto \frac{\left(t + y\right) \cdot a - y \cdot b}{\left(x + t\right) + y} \]

      3. lift-*.f64 37.8

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

   4. Applied rewrites 37.8%

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

   if 4.00000000000000003e-35 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   3. Applied rewrites 64.5%

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

   4. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 35.0

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

   6. Applied rewrites 35.0%

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

   7. Taylor expanded in y around inf

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

      1. lift-+.f64 71.2

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

   9. Applied rewrites 71.2%

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

Alternative 7: 73.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) + t\\ t_2 := \mathsf{fma}\left(\frac{t + y}{t\_1}, a, z - b\right)\\ \mathbf{if}\;a \leq -4 \cdot 10^{+112}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-23}:\\ \;\;\;\;\left(a + z\right) - b \cdot \frac{y}{t\_1}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+61}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y x) t)) (t_2 (fma (/ (+ t y) t_1) a (- z b))))
   (if (<= a -4e+112)
     t_2
     (if (<= a 1.45e-23)
       (- (+ a z) (* b (/ y t_1)))
       (if (<= a 2.3e+61) (/ (fma a t (* z x)) (+ t x)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + x) + t;
	double t_2 = fma(((t + y) / t_1), a, (z - b));
	double tmp;
	if (a <= -4e+112) {
		tmp = t_2;
	} else if (a <= 1.45e-23) {
		tmp = (a + z) - (b * (y / t_1));
	} else if (a <= 2.3e+61) {
		tmp = fma(a, t, (z * x)) / (t + x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + x) + t)
	t_2 = fma(Float64(Float64(t + y) / t_1), a, Float64(z - b))
	tmp = 0.0
	if (a <= -4e+112)
		tmp = t_2;
	elseif (a <= 1.45e-23)
		tmp = Float64(Float64(a + z) - Float64(b * Float64(y / t_1)));
	elseif (a <= 2.3e+61)
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision] * a + N[(z - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4e+112], t$95$2, If[LessEqual[a, 1.45e-23], N[(N[(a + z), $MachinePrecision] - N[(b * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e+61], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.9999999999999997e112 or 2.3e61 < a

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   3. Applied rewrites 71.1%

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

   4. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\frac{t + y}{\left(y + x\right) + t}, a, \color{blue}{z - b}\right) \]
   5. Step-by-step derivation

      1. lower--.f64 64.2

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

   6. Applied rewrites 64.2%

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

   if -3.9999999999999997e112 < a < 1.4500000000000001e-23

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   3. Applied rewrites 64.5%

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

   4. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 35.0

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

   6. Applied rewrites 35.0%

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

   7. Taylor expanded in y around inf

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

      1. lift-+.f64 71.2

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

   9. Applied rewrites 71.2%

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

   if 1.4500000000000001e-23 < a < 2.3e61

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{a \cdot t + x \cdot z}{t + x}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{a \cdot t + x \cdot z}{\color{blue}{t + x}} \]

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x} \]

      5. lower-+.f64 40.3

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

   4. Applied rewrites 40.3%

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

Alternative 8: 72.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x + y}{t + \left(x + y\right)}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+187}:\\ \;\;\;\;\left(a + z\right) - b \cdot \frac{y}{\left(y + x\right) + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (/ (+ x y) (+ t (+ x y))))))
   (if (<= z -4.8e+143)
     t_1
     (if (<= z 3.2e+187) (- (+ a z) (* b (/ y (+ (+ y x) t)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * ((x + y) / (t + (x + y)));
	double tmp;
	if (z <= -4.8e+143) {
		tmp = t_1;
	} else if (z <= 3.2e+187) {
		tmp = (a + z) - (b * (y / ((y + x) + 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 = z * ((x + y) / (t + (x + y)))
    if (z <= (-4.8d+143)) then
        tmp = t_1
    else if (z <= 3.2d+187) then
        tmp = (a + z) - (b * (y / ((y + x) + 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 = z * ((x + y) / (t + (x + y)));
	double tmp;
	if (z <= -4.8e+143) {
		tmp = t_1;
	} else if (z <= 3.2e+187) {
		tmp = (a + z) - (b * (y / ((y + x) + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * ((x + y) / (t + (x + y)))
	tmp = 0
	if z <= -4.8e+143:
		tmp = t_1
	elif z <= 3.2e+187:
		tmp = (a + z) - (b * (y / ((y + x) + t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(Float64(x + y) / Float64(t + Float64(x + y))))
	tmp = 0.0
	if (z <= -4.8e+143)
		tmp = t_1;
	elseif (z <= 3.2e+187)
		tmp = Float64(Float64(a + z) - Float64(b * Float64(y / Float64(Float64(y + x) + t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * ((x + y) / (t + (x + y)));
	tmp = 0.0;
	if (z <= -4.8e+143)
		tmp = t_1;
	elseif (z <= 3.2e+187)
		tmp = (a + z) - (b * (y / ((y + x) + t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(N[(x + y), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e+143], t$95$1, If[LessEqual[z, 3.2e+187], N[(N[(a + z), $MachinePrecision] - N[(b * N[(y / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.79999999999999959e143 or 3.19999999999999993e187 < z

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   3. Applied rewrites 71.1%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. div-add-rev N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-+.f64 39.3

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

   6. Applied rewrites 39.3%

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

   if -4.79999999999999959e143 < z < 3.19999999999999993e187

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   3. Applied rewrites 64.5%

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

   4. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 35.0

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

   6. Applied rewrites 35.0%

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

   7. Taylor expanded in y around inf

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

      1. lift-+.f64 71.2

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

   9. Applied rewrites 71.2%

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

Alternative 9: 67.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+237}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{x + y}, a, z - b\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+48}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b \cdot \frac{y}{y + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (<= t_1 -1e+237)
     (fma (/ y (+ x y)) a (- z b))
     (if (<= t_1 2e+48)
       (/ (fma a t (* z x)) (+ t x))
       (- (+ a z) (* b (/ y (+ y t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if (t_1 <= -1e+237) {
		tmp = fma((y / (x + y)), a, (z - b));
	} else if (t_1 <= 2e+48) {
		tmp = fma(a, t, (z * x)) / (t + x);
	} else {
		tmp = (a + z) - (b * (y / (y + t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if (t_1 <= -1e+237)
		tmp = fma(Float64(y / Float64(x + y)), a, Float64(z - b));
	elseif (t_1 <= 2e+48)
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	else
		tmp = Float64(Float64(a + z) - Float64(b * Float64(y / Float64(y + t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+237], N[(N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision] * a + N[(z - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+48], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - N[(b * N[(y / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -9.9999999999999994e236

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   3. Applied rewrites 71.1%

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

   4. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\frac{t + y}{\left(y + x\right) + t}, a, \color{blue}{z - b}\right) \]
   5. Step-by-step derivation

      1. lower--.f64 64.2

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

   6. Applied rewrites 64.2%

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

   7. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-+.f64 56.5

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

   9. Applied rewrites 56.5%

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

   if -9.9999999999999994e236 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000009e48

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{a \cdot t + x \cdot z}{t + x}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{a \cdot t + x \cdot z}{\color{blue}{t + x}} \]

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x} \]

      5. lower-+.f64 40.3

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

   4. Applied rewrites 40.3%

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

   if 2.00000000000000009e48 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   3. Applied rewrites 64.5%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 49.7%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 48.6%

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

   10. Taylor expanded in x around 0

       \[\leadsto \frac{\mathsf{fma}\left(t + y, a, y \cdot z\right)}{y + t} - b \cdot \frac{y}{\color{blue}{y} + t} \]
   11. Step-by-step derivation

   12. Applied rewrites 43.5%

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

   13. Taylor expanded in y around inf

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

       1. lower-+.f64 64.9

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

   15. Applied rewrites 64.9%

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

Alternative 10: 65.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+237}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{x + y}, a, z - b\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+178}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (<= t_1 -1e+237)
     (fma (/ y (+ x y)) a (- z b))
     (if (<= t_1 2e+178) (/ (fma a t (* z x)) (+ t x)) (- (+ a z) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if (t_1 <= -1e+237) {
		tmp = fma((y / (x + y)), a, (z - b));
	} else if (t_1 <= 2e+178) {
		tmp = fma(a, t, (z * x)) / (t + x);
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if (t_1 <= -1e+237)
		tmp = fma(Float64(y / Float64(x + y)), a, Float64(z - b));
	elseif (t_1 <= 2e+178)
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+237], N[(N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision] * a + N[(z - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+178], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -9.9999999999999994e236

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   3. Applied rewrites 71.1%

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

   4. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\frac{t + y}{\left(y + x\right) + t}, a, \color{blue}{z - b}\right) \]
   5. Step-by-step derivation

      1. lower--.f64 64.2

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

   6. Applied rewrites 64.2%

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

   7. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-+.f64 56.5

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

   9. Applied rewrites 56.5%

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

   if -9.9999999999999994e236 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e178

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{a \cdot t + x \cdot z}{t + x}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{a \cdot t + x \cdot z}{\color{blue}{t + x}} \]

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x} \]

      5. lower-+.f64 40.3

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

   4. Applied rewrites 40.3%

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

   if 2.0000000000000001e178 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   2. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \left(a + z\right) - \color{blue}{b} \]

      2. lower-+.f64 56.2

         \[\leadsto \left(a + z\right) - b \]

   4. Applied rewrites 56.2%

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

Alternative 11: 62.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{+210}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{t + x}, a, z - b\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+220}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{x + y}, a, z - b\right)\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.9e+210)
   a
   (if (<= t -5e-5)
     (fma (/ t (+ t x)) a (- z b))
     (if (<= t 1.45e+220) (fma (/ y (+ x y)) a (- z b)) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.9e+210) {
		tmp = a;
	} else if (t <= -5e-5) {
		tmp = fma((t / (t + x)), a, (z - b));
	} else if (t <= 1.45e+220) {
		tmp = fma((y / (x + y)), a, (z - b));
	} else {
		tmp = a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.9e+210)
		tmp = a;
	elseif (t <= -5e-5)
		tmp = fma(Float64(t / Float64(t + x)), a, Float64(z - b));
	elseif (t <= 1.45e+220)
		tmp = fma(Float64(y / Float64(x + y)), a, Float64(z - b));
	else
		tmp = a;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.9e+210], a, If[LessEqual[t, -5e-5], N[(N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision] * a + N[(z - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e+220], N[(N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision] * a + N[(z - b), $MachinePrecision]), $MachinePrecision], a]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.90000000000000007e210 or 1.44999999999999996e220 < t

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{a} \]
   3. Step-by-step derivation

   4. Applied rewrites 32.8%

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

   if -4.90000000000000007e210 < t < -5.00000000000000024e-5

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   3. Applied rewrites 71.1%

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

   4. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\frac{t + y}{\left(y + x\right) + t}, a, \color{blue}{z - b}\right) \]
   5. Step-by-step derivation

      1. lower--.f64 64.2

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

   6. Applied rewrites 64.2%

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

   7. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 56.0

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

   9. Applied rewrites 56.0%

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

   if -5.00000000000000024e-5 < t < 1.44999999999999996e220

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   3. Applied rewrites 71.1%

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

   4. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\frac{t + y}{\left(y + x\right) + t}, a, \color{blue}{z - b}\right) \]
   5. Step-by-step derivation

      1. lower--.f64 64.2

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

   6. Applied rewrites 64.2%

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

   7. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-+.f64 56.5

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

   9. Applied rewrites 56.5%

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

Alternative 12: 59.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-89}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-23}:\\ \;\;\;\;\frac{a \cdot t}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{t + x}, a, z - b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (<= t_1 -2e-89)
     (- (+ a z) b)
     (if (<= t_1 5e-23) (/ (* a t) (+ t x)) (fma (/ t (+ t x)) a (- z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if (t_1 <= -2e-89) {
		tmp = (a + z) - b;
	} else if (t_1 <= 5e-23) {
		tmp = (a * t) / (t + x);
	} else {
		tmp = fma((t / (t + x)), a, (z - b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if (t_1 <= -2e-89)
		tmp = Float64(Float64(a + z) - b);
	elseif (t_1 <= 5e-23)
		tmp = Float64(Float64(a * t) / Float64(t + x));
	else
		tmp = fma(Float64(t / Float64(t + x)), a, Float64(z - b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-89], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t$95$1, 5e-23], N[(N[(a * t), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], N[(N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision] * a + N[(z - b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -2.00000000000000008e-89

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   2. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \left(a + z\right) - \color{blue}{b} \]

      2. lower-+.f64 56.2

         \[\leadsto \left(a + z\right) - b \]

   4. Applied rewrites 56.2%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   if -2.00000000000000008e-89 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000002e-23

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   2. Taylor expanded in a around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-+.f64 N/A

         \[\leadsto \frac{\left(t + y\right) \cdot a}{t + \left(x + y\right)} \]

      4. lift-*.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. +-commutative N/A

         \[\leadsto \frac{\left(t + y\right) \cdot a}{\left(y + x\right) + t} \]

      8. lower-+.f64 25.0

         \[\leadsto \frac{\left(t + y\right) \cdot a}{\left(y + x\right) + t} \]

   4. Applied rewrites 25.0%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

         \[\leadsto \frac{a \cdot t}{t + x} \]

      3. lower-+.f64 21.8

         \[\leadsto \frac{a \cdot t}{t + x} \]

   7. Applied rewrites 21.8%

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

   if 5.0000000000000002e-23 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   3. Applied rewrites 71.1%

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

   4. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\frac{t + y}{\left(y + x\right) + t}, a, \color{blue}{z - b}\right) \]
   5. Step-by-step derivation

      1. lower--.f64 64.2

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

   6. Applied rewrites 64.2%

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

   7. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 56.0

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

   9. Applied rewrites 56.0%

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

Alternative 13: 56.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+210}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+220}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.7e+210) a (if (<= t 1.55e+220) (- (+ a z) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.7e+210) {
		tmp = a;
	} else if (t <= 1.55e+220) {
		tmp = (a + z) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.7d+210)) then
        tmp = a
    else if (t <= 1.55d+220) then
        tmp = (a + z) - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.7e+210) {
		tmp = a;
	} else if (t <= 1.55e+220) {
		tmp = (a + z) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.7e+210:
		tmp = a
	elif t <= 1.55e+220:
		tmp = (a + z) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.7e+210)
		tmp = a;
	elseif (t <= 1.55e+220)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.7e+210)
		tmp = a;
	elseif (t <= 1.55e+220)
		tmp = (a + z) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.7e+210], a, If[LessEqual[t, 1.55e+220], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -4.7000000000000001e210 or 1.55e220 < t

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{a} \]
   3. Step-by-step derivation

   4. Applied rewrites 32.8%

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

   if -4.7000000000000001e210 < t < 1.55e220

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   2. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \left(a + z\right) - \color{blue}{b} \]

      2. lower-+.f64 56.2

         \[\leadsto \left(a + z\right) - b \]

   4. Applied rewrites 56.2%

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

Alternative 14: 47.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -110000:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-27}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -110000.0) z (if (<= x 1.1e-27) (- a b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -110000.0) {
		tmp = z;
	} else if (x <= 1.1e-27) {
		tmp = a - b;
	} else {
		tmp = 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 <= (-110000.0d0)) then
        tmp = z
    else if (x <= 1.1d-27) then
        tmp = a - b
    else
        tmp = 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 <= -110000.0) {
		tmp = z;
	} else if (x <= 1.1e-27) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -110000.0:
		tmp = z
	elif x <= 1.1e-27:
		tmp = a - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -110000.0)
		tmp = z;
	elseif (x <= 1.1e-27)
		tmp = Float64(a - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -110000.0)
		tmp = z;
	elseif (x <= 1.1e-27)
		tmp = a - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -110000.0], z, If[LessEqual[x, 1.1e-27], N[(a - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1e5 or 1.09999999999999993e-27 < x

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 32.1%

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

   if -1.1e5 < x < 1.09999999999999993e-27

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   2. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

         \[\leadsto \left(a + z\right) - \color{blue}{b} \]

      2. lower-+.f64 56.2

         \[\leadsto \left(a + z\right) - b \]

   4. Applied rewrites 56.2%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   5. Taylor expanded in z around 0

      \[\leadsto a - b \]
   6. Step-by-step derivation

   7. Applied rewrites 38.2%

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

Alternative 15: 44.1% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+20}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-27}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.5e+20) z (if (<= x 1.15e-27) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.5e+20) {
		tmp = z;
	} else if (x <= 1.15e-27) {
		tmp = a;
	} else {
		tmp = 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 <= (-6.5d+20)) then
        tmp = z
    else if (x <= 1.15d-27) then
        tmp = a
    else
        tmp = 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 <= -6.5e+20) {
		tmp = z;
	} else if (x <= 1.15e-27) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6.5e+20:
		tmp = z
	elif x <= 1.15e-27:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.5e+20)
		tmp = z;
	elseif (x <= 1.15e-27)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6.5e+20)
		tmp = z;
	elseif (x <= 1.15e-27)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.5e+20], z, If[LessEqual[x, 1.15e-27], a, z]]

Derivation

1. Split input into 2 regimes

2. if x < -6.5e20 or 1.15e-27 < x

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 32.1%

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

   if -6.5e20 < x < 1.15e-27

   1. Initial program 59.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{a} \]
   3. Step-by-step derivation

   4. Applied rewrites 32.8%

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

Alternative 16: 32.8% accurate, 29.5× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 59.6%

   \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

2. Taylor expanded in t around inf

   \[\leadsto \color{blue}{a} \]
3. Step-by-step derivation

4. Applied rewrites 32.8%

   \[\leadsto \color{blue}{a} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025130 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64
  (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))