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

Percentage Accurate: 59.7% → 93.9%

Time: 7.8s

Alternatives: 21

Speedup: 1.2×

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: 59.7% 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: 93.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\left(y + x\right) \cdot \left(y + x\right)}\\ t_2 := \left(t + y\right) \cdot \left(t + y\right)\\ t_3 := \frac{z}{t + y}\\ t_4 := t + \left(x + y\right)\\ t_5 := \frac{y}{y + x}\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+145}:\\ \;\;\;\;z + \left(\mathsf{fma}\left(\mathsf{fma}\left(b, t\_1, \frac{a}{y + x}\right) - \mathsf{fma}\left(a, t\_1, \frac{z}{y + x}\right), t, a \cdot t\_5\right) - b \cdot t\_5\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+199}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y + x}{\left(y + x\right) + t}, z, \mathsf{fma}\left(-1, \frac{b \cdot y}{t\_4}, a \cdot \frac{t + y}{t\_4}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + \mathsf{fma}\left(\mathsf{fma}\left(b, \frac{y}{t\_2}, t\_3\right) - \mathsf{fma}\left(y, \frac{z}{t\_2}, \frac{a}{t + y}\right), x, y \cdot t\_3\right)\right) - b \cdot \frac{y}{t + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ y (* (+ y x) (+ y x))))
        (t_2 (* (+ t y) (+ t y)))
        (t_3 (/ z (+ t y)))
        (t_4 (+ t (+ x y)))
        (t_5 (/ y (+ y x))))
   (if (<= y -1.02e+145)
     (+
      z
      (-
       (fma
        (- (fma b t_1 (/ a (+ y x))) (fma a t_1 (/ z (+ y x))))
        t
        (* a t_5))
       (* b t_5)))
     (if (<= y 1.8e+199)
       (fma
        (/ (+ y x) (+ (+ y x) t))
        z
        (fma -1.0 (/ (* b y) t_4) (* a (/ (+ t y) t_4))))
       (-
        (+
         a
         (fma
          (- (fma b (/ y t_2) t_3) (fma y (/ z t_2) (/ a (+ t y))))
          x
          (* y t_3)))
        (* b (/ y (+ t y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y / ((y + x) * (y + x));
	double t_2 = (t + y) * (t + y);
	double t_3 = z / (t + y);
	double t_4 = t + (x + y);
	double t_5 = y / (y + x);
	double tmp;
	if (y <= -1.02e+145) {
		tmp = z + (fma((fma(b, t_1, (a / (y + x))) - fma(a, t_1, (z / (y + x)))), t, (a * t_5)) - (b * t_5));
	} else if (y <= 1.8e+199) {
		tmp = fma(((y + x) / ((y + x) + t)), z, fma(-1.0, ((b * y) / t_4), (a * ((t + y) / t_4))));
	} else {
		tmp = (a + fma((fma(b, (y / t_2), t_3) - fma(y, (z / t_2), (a / (t + y)))), x, (y * t_3))) - (b * (y / (t + y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y / Float64(Float64(y + x) * Float64(y + x)))
	t_2 = Float64(Float64(t + y) * Float64(t + y))
	t_3 = Float64(z / Float64(t + y))
	t_4 = Float64(t + Float64(x + y))
	t_5 = Float64(y / Float64(y + x))
	tmp = 0.0
	if (y <= -1.02e+145)
		tmp = Float64(z + Float64(fma(Float64(fma(b, t_1, Float64(a / Float64(y + x))) - fma(a, t_1, Float64(z / Float64(y + x)))), t, Float64(a * t_5)) - Float64(b * t_5)));
	elseif (y <= 1.8e+199)
		tmp = fma(Float64(Float64(y + x) / Float64(Float64(y + x) + t)), z, fma(-1.0, Float64(Float64(b * y) / t_4), Float64(a * Float64(Float64(t + y) / t_4))));
	else
		tmp = Float64(Float64(a + fma(Float64(fma(b, Float64(y / t_2), t_3) - fma(y, Float64(z / t_2), Float64(a / Float64(t + y)))), x, Float64(y * t_3))) - Float64(b * Float64(y / Float64(t + y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y / N[(N[(y + x), $MachinePrecision] * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t + y), $MachinePrecision] * N[(t + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z / N[(t + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y / N[(y + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.02e+145], N[(z + N[(N[(N[(N[(b * t$95$1 + N[(a / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * t$95$1 + N[(z / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t + N[(a * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(b * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+199], N[(N[(N[(y + x), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] * z + N[(-1.0 * N[(N[(b * y), $MachinePrecision] / t$95$4), $MachinePrecision] + N[(a * N[(N[(t + y), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + N[(N[(N[(b * N[(y / t$95$2), $MachinePrecision] + t$95$3), $MachinePrecision] - N[(y * N[(z / t$95$2), $MachinePrecision] + N[(a / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x + N[(y * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.02e145

   1. Initial program 59.7%

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

   2. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 65.8%

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

   if -1.02e145 < y < 1.80000000000000001e199

   1. Initial program 59.7%

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

   3. Applied rewrites 71.7%

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

   4. Taylor expanded in a around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. div-add-rev N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-+.f64 87.3

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

   6. Applied rewrites 87.3%

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

   if 1.80000000000000001e199 < y

   1. Initial program 59.7%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 64.9%

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

Alternative 2: 93.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\left(y + x\right) \cdot \left(y + x\right)}\\ t_2 := t + \left(x + y\right)\\ t_3 := \frac{y}{y + x}\\ t_4 := z + \left(\mathsf{fma}\left(\mathsf{fma}\left(b, t\_1, \frac{a}{y + x}\right) - \mathsf{fma}\left(a, t\_1, \frac{z}{y + x}\right), t, a \cdot t\_3\right) - b \cdot t\_3\right)\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+145}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+159}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y + x}{\left(y + x\right) + t}, z, \mathsf{fma}\left(-1, \frac{b \cdot y}{t\_2}, a \cdot \frac{t + y}{t\_2}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ y (* (+ y x) (+ y x))))
        (t_2 (+ t (+ x y)))
        (t_3 (/ y (+ y x)))
        (t_4
         (+
          z
          (-
           (fma
            (- (fma b t_1 (/ a (+ y x))) (fma a t_1 (/ z (+ y x))))
            t
            (* a t_3))
           (* b t_3)))))
   (if (<= y -1.02e+145)
     t_4
     (if (<= y 7.5e+159)
       (fma
        (/ (+ y x) (+ (+ y x) t))
        z
        (fma -1.0 (/ (* b y) t_2) (* a (/ (+ t y) t_2))))
       t_4))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y / ((y + x) * (y + x));
	double t_2 = t + (x + y);
	double t_3 = y / (y + x);
	double t_4 = z + (fma((fma(b, t_1, (a / (y + x))) - fma(a, t_1, (z / (y + x)))), t, (a * t_3)) - (b * t_3));
	double tmp;
	if (y <= -1.02e+145) {
		tmp = t_4;
	} else if (y <= 7.5e+159) {
		tmp = fma(((y + x) / ((y + x) + t)), z, fma(-1.0, ((b * y) / t_2), (a * ((t + y) / t_2))));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y / Float64(Float64(y + x) * Float64(y + x)))
	t_2 = Float64(t + Float64(x + y))
	t_3 = Float64(y / Float64(y + x))
	t_4 = Float64(z + Float64(fma(Float64(fma(b, t_1, Float64(a / Float64(y + x))) - fma(a, t_1, Float64(z / Float64(y + x)))), t, Float64(a * t_3)) - Float64(b * t_3)))
	tmp = 0.0
	if (y <= -1.02e+145)
		tmp = t_4;
	elseif (y <= 7.5e+159)
		tmp = fma(Float64(Float64(y + x) / Float64(Float64(y + x) + t)), z, fma(-1.0, Float64(Float64(b * y) / t_2), Float64(a * Float64(Float64(t + y) / t_2))));
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y / N[(N[(y + x), $MachinePrecision] * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y / N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z + N[(N[(N[(N[(b * t$95$1 + N[(a / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * t$95$1 + N[(z / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t + N[(a * t$95$3), $MachinePrecision]), $MachinePrecision] - N[(b * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.02e+145], t$95$4, If[LessEqual[y, 7.5e+159], N[(N[(N[(y + x), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] * z + N[(-1.0 * N[(N[(b * y), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(a * N[(N[(t + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.02e145 or 7.4999999999999997e159 < y

   1. Initial program 59.7%

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

   2. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 65.8%

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

   if -1.02e145 < y < 7.4999999999999997e159

   1. Initial program 59.7%

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

   3. Applied rewrites 71.7%

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

   4. Taylor expanded in a around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. div-add-rev N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-+.f64 87.3

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

   6. Applied rewrites 87.3%

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

Alternative 3: 91.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) \cdot a\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + t\_1\right) - y \cdot b}{\left(x + t\right) + y}\\ t_3 := \left(y + x\right) + t\\ t_4 := \frac{y + x}{t\_3}\\ t_5 := \mathsf{fma}\left(t\_4, z, a \cdot \frac{t + y}{t + \left(x + y\right)}\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_2 \leq 10^{+300}:\\ \;\;\;\;\mathsf{fma}\left(t\_4, z, \frac{t\_1 - b \cdot y}{t\_3}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ t y) a))
        (t_2 (/ (- (+ (* (+ x y) z) t_1) (* y b)) (+ (+ x t) y)))
        (t_3 (+ (+ y x) t))
        (t_4 (/ (+ y x) t_3))
        (t_5 (fma t_4 z (* a (/ (+ t y) (+ t (+ x y)))))))
   (if (<= t_2 (- INFINITY))
     t_5
     (if (<= t_2 1e+300) (fma t_4 z (/ (- t_1 (* b y)) t_3)) t_5))))

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 + y) * z) + t_1) - (y * b)) / ((x + t) + y);
	double t_3 = (y + x) + t;
	double t_4 = (y + x) / t_3;
	double t_5 = fma(t_4, z, (a * ((t + y) / (t + (x + y)))));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_2 <= 1e+300) {
		tmp = fma(t_4, z, ((t_1 - (b * y)) / t_3));
	} else {
		tmp = t_5;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) * a)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + t_1) - Float64(y * b)) / Float64(Float64(x + t) + y))
	t_3 = Float64(Float64(y + x) + t)
	t_4 = Float64(Float64(y + x) / t_3)
	t_5 = fma(t_4, z, Float64(a * Float64(Float64(t + y) / Float64(t + Float64(x + y)))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_2 <= 1e+300)
		tmp = fma(t_4, z, Float64(Float64(t_1 - Float64(b * y)) / t_3));
	else
		tmp = t_5;
	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[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y + x), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 * z + N[(a * N[(N[(t + y), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$5, If[LessEqual[t$95$2, 1e+300], N[(t$95$4 * z + N[(N[(t$95$1 - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]

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 1.0000000000000001e300 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 59.7%

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

   3. Applied rewrites 71.7%

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

   4. Taylor expanded in a around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. div-add-rev N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-+.f64 87.3

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

   6. Applied rewrites 87.3%

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

   7. Taylor expanded in a around inf

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

      1. div-add-rev N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 78.1

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

   9. Applied rewrites 78.1%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.0000000000000001e300

   1. Initial program 59.7%

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

   3. Applied rewrites 71.7%

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

Alternative 4: 91.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) \cdot a\\ t_2 := \left(x + t\right) + y\\ t_3 := \frac{\left(\left(x + y\right) \cdot z + t\_1\right) - y \cdot b}{t\_2}\\ t_4 := \mathsf{fma}\left(\frac{y + x}{\left(y + x\right) + t}, z, a \cdot \frac{t + y}{t + \left(x + y\right)}\right)\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq 10^{+300}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, t\_1 - b \cdot y\right)}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

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
         (fma (/ (+ y x) (+ (+ y x) t)) z (* a (/ (+ t y) (+ t (+ x y)))))))
   (if (<= t_3 (- INFINITY))
     t_4
     (if (<= t_3 1e+300) (/ (fma (+ y x) z (- t_1 (* b y))) t_2) 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 = fma(((y + x) / ((y + x) + t)), z, (a * ((t + y) / (t + (x + y)))));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_3 <= 1e+300) {
		tmp = fma((y + x), z, (t_1 - (b * y))) / t_2;
	} else {
		tmp = 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 = fma(Float64(Float64(y + x) / Float64(Float64(y + x) + t)), z, Float64(a * Float64(Float64(t + y) / Float64(t + Float64(x + y)))))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_3 <= 1e+300)
		tmp = Float64(fma(Float64(y + x), z, Float64(t_1 - 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[(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[(N[(y + x), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] * z + N[(a * N[(N[(t + y), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$4, If[LessEqual[t$95$3, 1e+300], N[(N[(N[(y + x), $MachinePrecision] * z + N[(t$95$1 - N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $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)) < -inf.0 or 1.0000000000000001e300 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 59.7%

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

   3. Applied rewrites 71.7%

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

   4. Taylor expanded in a around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. div-add-rev N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-+.f64 87.3

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

   6. Applied rewrites 87.3%

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

   7. Taylor expanded in a around inf

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

      1. div-add-rev N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 78.1

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

   9. Applied rewrites 78.1%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.0000000000000001e300

   1. Initial program 59.7%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. associate--l+ N/A

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

      9. *-commutative N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 N/A

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

      14. lower--.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-+.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. lower-*.f64 59.8

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

   3. Applied rewrites 59.8%

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

Alternative 5: 89.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ \mathbf{if}\;y \leq -4.9 \cdot 10^{+219}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y + x}{\left(y + x\right) + t}, z, \mathsf{fma}\left(-1, \frac{b \cdot y}{t\_1}, a \cdot \frac{t + y}{t\_1}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y))))
   (if (<= y -4.9e+219)
     (- (+ a z) b)
     (fma
      (/ (+ y x) (+ (+ y x) t))
      z
      (fma -1.0 (/ (* b y) t_1) (* a (/ (+ t y) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double tmp;
	if (y <= -4.9e+219) {
		tmp = (a + z) - b;
	} else {
		tmp = fma(((y + x) / ((y + x) + t)), z, fma(-1.0, ((b * y) / t_1), (a * ((t + y) / t_1))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	tmp = 0.0
	if (y <= -4.9e+219)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = fma(Float64(Float64(y + x) / Float64(Float64(y + x) + t)), z, fma(-1.0, Float64(Float64(b * y) / t_1), Float64(a * Float64(Float64(t + y) / t_1))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.9e+219], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(y + x), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] * z + N[(-1.0 * N[(N[(b * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(a * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.90000000000000003e219

   1. Initial program 59.7%

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

   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 -4.90000000000000003e219 < y

   1. Initial program 59.7%

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

   3. Applied rewrites 71.7%

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

   4. Taylor expanded in a around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. div-add-rev N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-+.f64 87.3

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

   6. Applied rewrites 87.3%

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

Alternative 6: 87.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) \cdot a\\ t_2 := \left(x + t\right) + y\\ t_3 := \frac{\left(\left(x + y\right) \cdot z + t\_1\right) - y \cdot b}{t\_2}\\ t_4 := \mathsf{fma}\left(1, z, a \cdot \frac{t + y}{t + \left(x + y\right)}\right)\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq 10^{+300}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, t\_1 - b \cdot y\right)}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

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 (fma 1.0 z (* a (/ (+ t y) (+ t (+ x y)))))))
   (if (<= t_3 (- INFINITY))
     t_4
     (if (<= t_3 1e+300) (/ (fma (+ y x) z (- t_1 (* b y))) t_2) 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 = fma(1.0, z, (a * ((t + y) / (t + (x + y)))));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_3 <= 1e+300) {
		tmp = fma((y + x), z, (t_1 - (b * y))) / t_2;
	} else {
		tmp = 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 = fma(1.0, z, Float64(a * Float64(Float64(t + y) / Float64(t + Float64(x + y)))))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_3 <= 1e+300)
		tmp = Float64(fma(Float64(y + x), z, Float64(t_1 - 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[(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[(1.0 * z + N[(a * N[(N[(t + y), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$4, If[LessEqual[t$95$3, 1e+300], N[(N[(N[(y + x), $MachinePrecision] * z + N[(t$95$1 - N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $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)) < -inf.0 or 1.0000000000000001e300 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 59.7%

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

   3. Applied rewrites 71.7%

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

   4. Taylor expanded in a around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. div-add-rev N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-+.f64 87.3

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

   6. Applied rewrites 87.3%

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

   7. Taylor expanded in a around inf

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

      1. div-add-rev N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 78.1

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

   9. Applied rewrites 78.1%

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

   10. Taylor expanded in x around inf

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

   12. Applied rewrites 64.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.0000000000000001e300

   1. Initial program 59.7%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. associate--l+ N/A

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

      9. *-commutative N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 N/A

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

      14. lower--.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-+.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. lower-*.f64 59.8

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

   3. Applied rewrites 59.8%

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

Alternative 7: 87.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := \mathsf{fma}\left(1, z, a \cdot \frac{t + y}{t + \left(x + y\right)}\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+296}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{+300}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, \mathsf{fma}\left(\left(a + z\right) - b, y, z \cdot x\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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 (fma 1.0 z (* a (/ (+ t y) (+ t (+ x y)))))))
   (if (<= t_2 -1e+296)
     t_3
     (if (<= t_2 1e+300)
       (/ (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 = fma(1.0, z, (a * ((t + y) / (t + (x + y)))));
	double tmp;
	if (t_2 <= -1e+296) {
		tmp = t_3;
	} else if (t_2 <= 1e+300) {
		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 = fma(1.0, z, Float64(a * Float64(Float64(t + y) / Float64(t + Float64(x + y)))))
	tmp = 0.0
	if (t_2 <= -1e+296)
		tmp = t_3;
	elseif (t_2 <= 1e+300)
		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[(1.0 * z + N[(a * N[(N[(t + y), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+296], t$95$3, If[LessEqual[t$95$2, 1e+300], 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)) < -9.99999999999999981e295 or 1.0000000000000001e300 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 59.7%

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

   3. Applied rewrites 71.7%

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

   4. Taylor expanded in a around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. div-add-rev N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-+.f64 87.3

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

   6. Applied rewrites 87.3%

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

   7. Taylor expanded in a around inf

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

      1. div-add-rev N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 78.1

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

   9. Applied rewrites 78.1%

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

   10. Taylor expanded in x around inf

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

   12. Applied rewrites 64.9%

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

   if -9.99999999999999981e295 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.0000000000000001e300

   1. Initial program 59.7%

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

   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 8: 75.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+229}:\\ \;\;\;\;\mathsf{fma}\left(1, z, a \cdot \frac{t + y}{t + \left(x + y\right)}\right)\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{+52}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t + y, a, z \cdot y\right) - b \cdot y}{t + y}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+194}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t + y, a, \left(y + x\right) \cdot z\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) t_1)))
   (if (<= t_2 -1e+229)
     (fma 1.0 z (* a (/ (+ t y) (+ t (+ x y)))))
     (if (<= t_2 -1e+52)
       (/ (- (fma (+ t y) a (* z y)) (* b y)) (+ t y))
       (if (<= t_2 2e+194)
         (/ (fma (+ t y) a (* (+ y x) z)) t_1)
         (- (+ a z) b))))))

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 tmp;
	if (t_2 <= -1e+229) {
		tmp = fma(1.0, z, (a * ((t + y) / (t + (x + y)))));
	} else if (t_2 <= -1e+52) {
		tmp = (fma((t + y), a, (z * y)) - (b * y)) / (t + y);
	} else if (t_2 <= 2e+194) {
		tmp = fma((t + y), a, ((y + x) * z)) / t_1;
	} else {
		tmp = (a + z) - b;
	}
	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)
	tmp = 0.0
	if (t_2 <= -1e+229)
		tmp = fma(1.0, z, Float64(a * Float64(Float64(t + y) / Float64(t + Float64(x + y)))));
	elseif (t_2 <= -1e+52)
		tmp = Float64(Float64(fma(Float64(t + y), a, Float64(z * y)) - Float64(b * y)) / Float64(t + y));
	elseif (t_2 <= 2e+194)
		tmp = Float64(fma(Float64(t + y), a, Float64(Float64(y + x) * z)) / t_1);
	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[(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]}, If[LessEqual[t$95$2, -1e+229], N[(1.0 * z + N[(a * N[(N[(t + y), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e+52], N[(N[(N[(N[(t + y), $MachinePrecision] * a + N[(z * y), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+194], N[(N[(N[(t + y), $MachinePrecision] * a + N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -9.9999999999999999e228

   1. Initial program 59.7%

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

   3. Applied rewrites 71.7%

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

   4. Taylor expanded in a around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. div-add-rev N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-+.f64 87.3

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

   6. Applied rewrites 87.3%

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

   7. Taylor expanded in a around inf

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

      1. div-add-rev N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 78.1

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

   9. Applied rewrites 78.1%

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

   10. Taylor expanded in x around inf

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

   12. Applied rewrites 64.9%

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

   if -9.9999999999999999e228 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -9.9999999999999999e51

   1. Initial program 59.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-+.f64 39.7

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

   4. Applied rewrites 39.7%

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

   if -9.9999999999999999e51 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999989e194

   1. Initial program 59.7%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 46.9

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

   4. Applied rewrites 46.9%

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

   if 1.99999999999999989e194 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 59.7%

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

   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 4 regimes into one program.
4. Add Preprocessing

Alternative 9: 73.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(1, z, a \cdot \frac{t + y}{t + \left(x + y\right)}\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+194}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t + y, a, \left(y + x\right) \cdot z\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) t_1)))
   (if (<= t_2 (- INFINITY))
     (fma 1.0 z (* a (/ (+ t y) (+ t (+ x y)))))
     (if (<= t_2 2e+194)
       (/ (fma (+ t y) a (* (+ y x) z)) t_1)
       (- (+ a z) b)))))

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 tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = fma(1.0, z, (a * ((t + y) / (t + (x + y)))));
	} else if (t_2 <= 2e+194) {
		tmp = fma((t + y), a, ((y + x) * z)) / t_1;
	} else {
		tmp = (a + z) - b;
	}
	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)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = fma(1.0, z, Float64(a * Float64(Float64(t + y) / Float64(t + Float64(x + y)))));
	elseif (t_2 <= 2e+194)
		tmp = Float64(fma(Float64(t + y), a, Float64(Float64(y + x) * z)) / t_1);
	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[(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]}, If[LessEqual[t$95$2, (-Infinity)], N[(1.0 * z + N[(a * N[(N[(t + y), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+194], N[(N[(N[(t + y), $MachinePrecision] * a + N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $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)) < -inf.0

   1. Initial program 59.7%

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

   3. Applied rewrites 71.7%

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

   4. Taylor expanded in a around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. div-add-rev N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-+.f64 87.3

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

   6. Applied rewrites 87.3%

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

   7. Taylor expanded in a around inf

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

      1. div-add-rev N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 78.1

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

   9. Applied rewrites 78.1%

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

   10. Taylor expanded in x around inf

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

   12. Applied rewrites 64.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999989e194

   1. Initial program 59.7%

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

   2. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 46.9

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

   4. Applied rewrites 46.9%

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

   if 1.99999999999999989e194 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 59.7%

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

   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 10: 71.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1, z, a \cdot \frac{t + y}{t + \left(x + y\right)}\right)\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+96}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y + x}{\left(y + x\right) + t}, z, a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma 1.0 z (* a (/ (+ t y) (+ t (+ x y)))))))
   (if (<= a -6.5e+39)
     t_1
     (if (<= a 6.2e+96) (fma (/ (+ y x) (+ (+ y x) t)) z a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(1.0, z, (a * ((t + y) / (t + (x + y)))));
	double tmp;
	if (a <= -6.5e+39) {
		tmp = t_1;
	} else if (a <= 6.2e+96) {
		tmp = fma(((y + x) / ((y + x) + t)), z, a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(1.0, z, Float64(a * Float64(Float64(t + y) / Float64(t + Float64(x + y)))))
	tmp = 0.0
	if (a <= -6.5e+39)
		tmp = t_1;
	elseif (a <= 6.2e+96)
		tmp = fma(Float64(Float64(y + x) / Float64(Float64(y + x) + t)), z, a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 * z + N[(a * N[(N[(t + y), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.5e+39], t$95$1, If[LessEqual[a, 6.2e+96], N[(N[(N[(y + x), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] * z + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -6.5000000000000001e39 or 6.1999999999999996e96 < a

   1. Initial program 59.7%

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

   3. Applied rewrites 71.7%

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

   4. Taylor expanded in a around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. div-add-rev N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-+.f64 87.3

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

   6. Applied rewrites 87.3%

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

   7. Taylor expanded in a around inf

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

      1. div-add-rev N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 78.1

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

   9. Applied rewrites 78.1%

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

   10. Taylor expanded in x around inf

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

   12. Applied rewrites 64.9%

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

   if -6.5000000000000001e39 < a < 6.1999999999999996e96

   1. Initial program 59.7%

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

   3. Applied rewrites 71.7%

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

   4. Taylor expanded in t around inf

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

   6. Applied rewrites 65.5%

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

Alternative 11: 70.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \mathsf{fma}\left(-1, \frac{y}{t + y}, \frac{a}{b}\right)\\ \mathbf{if}\;b \leq -1 \cdot 10^{+217}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y + x}{\left(y + x\right) + t}, z, a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (fma -1.0 (/ y (+ t y)) (/ a b)))))
   (if (<= b -1e+217)
     t_1
     (if (<= b 1.5e+80) (fma (/ (+ y x) (+ (+ y x) t)) z a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * fma(-1.0, (y / (t + y)), (a / b));
	double tmp;
	if (b <= -1e+217) {
		tmp = t_1;
	} else if (b <= 1.5e+80) {
		tmp = fma(((y + x) / ((y + x) + t)), z, a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * fma(-1.0, Float64(y / Float64(t + y)), Float64(a / b)))
	tmp = 0.0
	if (b <= -1e+217)
		tmp = t_1;
	elseif (b <= 1.5e+80)
		tmp = fma(Float64(Float64(y + x) / Float64(Float64(y + x) + t)), z, a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(-1.0 * N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision] + N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1e+217], t$95$1, If[LessEqual[b, 1.5e+80], N[(N[(N[(y + x), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] * z + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -9.9999999999999996e216 or 1.49999999999999993e80 < b

   1. Initial program 59.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-+.f64 39.7

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

   4. Applied rewrites 39.7%

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

   5. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift-+.f64 46.3

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

   7. Applied rewrites 46.3%

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

   8. Taylor expanded in y around 0

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

      1. lift-/.f64 40.5

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

   10. Applied rewrites 40.5%

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

   if -9.9999999999999996e216 < b < 1.49999999999999993e80

   1. Initial program 59.7%

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

   3. Applied rewrites 71.7%

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

   4. Taylor expanded in t around inf

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

   6. Applied rewrites 65.5%

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

Alternative 12: 68.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y + x}{\left(y + x\right) + t}, z, a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a z) b)))
   (if (<= y -6.2e+30)
     t_1
     (if (<= y 4.8e+20) (fma (/ (+ y x) (+ (+ y x) t)) z a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -6.2e+30) {
		tmp = t_1;
	} else if (y <= 4.8e+20) {
		tmp = fma(((y + x) / ((y + x) + t)), z, a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (y <= -6.2e+30)
		tmp = t_1;
	elseif (y <= 4.8e+20)
		tmp = fma(Float64(Float64(y + x) / Float64(Float64(y + x) + t)), z, a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -6.2e+30], t$95$1, If[LessEqual[y, 4.8e+20], N[(N[(N[(y + x), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] * z + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.1999999999999995e30 or 4.8e20 < y

   1. Initial program 59.7%

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

   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 -6.1999999999999995e30 < y < 4.8e20

   1. Initial program 59.7%

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

   3. Applied rewrites 71.7%

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

   4. Taylor expanded in t around inf

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

   6. Applied rewrites 65.5%

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

Alternative 13: 66.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := \left(a + z\right) - b\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+164}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_2 (- (+ a z) b)))
   (if (<= t_1 -1e+52)
     t_2
     (if (<= t_1 1e+164) (/ (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 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double t_2 = (a + z) - b;
	double tmp;
	if (t_1 <= -1e+52) {
		tmp = t_2;
	} else if (t_1 <= 1e+164) {
		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(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) - b)
	tmp = 0.0
	if (t_1 <= -1e+52)
		tmp = t_2;
	elseif (t_1 <= 1e+164)
		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[(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] - b), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+52], t$95$2, If[LessEqual[t$95$1, 1e+164], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], 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)) < -9.9999999999999999e51 or 1e164 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 59.7%

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

   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 -9.9999999999999999e51 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1e164

   1. Initial program 59.7%

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

   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 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 59.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+90}:\\ \;\;\;\;z \cdot \frac{x}{t + x}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+36}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + t \cdot \frac{a - z}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.6e+90)
   (* z (/ x (+ t x)))
   (if (<= x 4.2e+36) (- (+ a z) b) (+ z (* t (/ (- a z) x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.6e+90) {
		tmp = z * (x / (t + x));
	} else if (x <= 4.2e+36) {
		tmp = (a + z) - b;
	} else {
		tmp = z + (t * ((a - z) / x));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.6d+90)) then
        tmp = z * (x / (t + x))
    else if (x <= 4.2d+36) then
        tmp = (a + z) - b
    else
        tmp = z + (t * ((a - z) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.6e+90) {
		tmp = z * (x / (t + x));
	} else if (x <= 4.2e+36) {
		tmp = (a + z) - b;
	} else {
		tmp = z + (t * ((a - z) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.6e+90:
		tmp = z * (x / (t + x))
	elif x <= 4.2e+36:
		tmp = (a + z) - b
	else:
		tmp = z + (t * ((a - z) / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.6e+90)
		tmp = Float64(z * Float64(x / Float64(t + x)));
	elseif (x <= 4.2e+36)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(z + Float64(t * Float64(Float64(a - z) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.6e+90)
		tmp = z * (x / (t + x));
	elseif (x <= 4.2e+36)
		tmp = (a + z) - b;
	else
		tmp = z + (t * ((a - z) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.6e+90], N[(z * N[(x / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e+36], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(z + N[(t * N[(N[(a - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.59999999999999999e90

   1. Initial program 59.7%

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

   3. Applied rewrites 71.7%

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

   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 39.9

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

   6. Applied rewrites 39.9%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 25.4%

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

   10. Taylor expanded in x around inf

       \[\leadsto z \cdot \frac{x}{t + x} \]
   11. Step-by-step derivation

   12. Applied rewrites 31.2%

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

   if -1.59999999999999999e90 < x < 4.20000000000000009e36

   1. Initial program 59.7%

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

   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 4.20000000000000009e36 < x

   1. Initial program 59.7%

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

   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%

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

   5. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 29.2

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

   7. Applied rewrites 29.2%

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

Alternative 15: 59.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{t + x}\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+86}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (/ x (+ t x)))))
   (if (<= x -1.6e+90) t_1 (if (<= x 3.8e+86) (- (+ a z) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (x / (t + x));
	double tmp;
	if (x <= -1.6e+90) {
		tmp = t_1;
	} else if (x <= 3.8e+86) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x / (t + x))
    if (x <= (-1.6d+90)) then
        tmp = t_1
    else if (x <= 3.8d+86) then
        tmp = (a + z) - b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (x / (t + x));
	double tmp;
	if (x <= -1.6e+90) {
		tmp = t_1;
	} else if (x <= 3.8e+86) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (x / (t + x))
	tmp = 0
	if x <= -1.6e+90:
		tmp = t_1
	elif x <= 3.8e+86:
		tmp = (a + z) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(x / Float64(t + x)))
	tmp = 0.0
	if (x <= -1.6e+90)
		tmp = t_1;
	elseif (x <= 3.8e+86)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (x / (t + x));
	tmp = 0.0;
	if (x <= -1.6e+90)
		tmp = t_1;
	elseif (x <= 3.8e+86)
		tmp = (a + z) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(x / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.6e+90], t$95$1, If[LessEqual[x, 3.8e+86], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.59999999999999999e90 or 3.79999999999999978e86 < x

   1. Initial program 59.7%

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

   3. Applied rewrites 71.7%

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

   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 39.9

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

   6. Applied rewrites 39.9%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 25.4%

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

   10. Taylor expanded in x around inf

       \[\leadsto z \cdot \frac{x}{t + x} \]
   11. Step-by-step derivation

   12. Applied rewrites 31.2%

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

   if -1.59999999999999999e90 < x < 3.79999999999999978e86

   1. Initial program 59.7%

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

   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 16: 59.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+122}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+213}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.5e+122) z (if (<= x 9e+213) (- (+ a z) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.5e+122) {
		tmp = z;
	} else if (x <= 9e+213) {
		tmp = (a + z) - 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 <= (-4.5d+122)) then
        tmp = z
    else if (x <= 9d+213) then
        tmp = (a + z) - 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 <= -4.5e+122) {
		tmp = z;
	} else if (x <= 9e+213) {
		tmp = (a + z) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.5e+122:
		tmp = z
	elif x <= 9e+213:
		tmp = (a + z) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.5e+122)
		tmp = z;
	elseif (x <= 9e+213)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -4.5e+122)
		tmp = z;
	elseif (x <= 9e+213)
		tmp = (a + z) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.5e+122], z, If[LessEqual[x, 9e+213], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -4.49999999999999997e122 or 9.0000000000000003e213 < x

   1. Initial program 59.7%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 32.4%

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

   if -4.49999999999999997e122 < x < 9.0000000000000003e213

   1. Initial program 59.7%

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

   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 17: 51.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+125}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+19}:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3.1e+125) (+ a z) (if (<= a 1.45e+19) (- z b) (+ a z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.1e+125) {
		tmp = a + z;
	} else if (a <= 1.45e+19) {
		tmp = z - b;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-3.1d+125)) then
        tmp = a + z
    else if (a <= 1.45d+19) then
        tmp = z - b
    else
        tmp = a + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.1e+125) {
		tmp = a + z;
	} else if (a <= 1.45e+19) {
		tmp = z - b;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3.1e+125:
		tmp = a + z
	elif a <= 1.45e+19:
		tmp = z - b
	else:
		tmp = a + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3.1e+125)
		tmp = Float64(a + z);
	elseif (a <= 1.45e+19)
		tmp = Float64(z - b);
	else
		tmp = Float64(a + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -3.1e+125)
		tmp = a + z;
	elseif (a <= 1.45e+19)
		tmp = z - b;
	else
		tmp = a + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3.1e+125], N[(a + z), $MachinePrecision], If[LessEqual[a, 1.45e+19], N[(z - b), $MachinePrecision], N[(a + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.1e125 or 1.45e19 < a

   1. Initial program 59.7%

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

   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 b around 0

      \[\leadsto a + \color{blue}{z} \]
   6. Step-by-step derivation

      1. lift-+.f64 52.3

         \[\leadsto a + z \]

   7. Applied rewrites 52.3%

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

   if -3.1e125 < a < 1.45e19

   1. Initial program 59.7%

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

   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 inf

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

   7. Applied rewrites 37.8%

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

Alternative 18: 48.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.95 \cdot 10^{+169}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+20}:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.95e+169) (- a b) (if (<= a 1.7e+20) (- z b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.95e+169) {
		tmp = a - b;
	} else if (a <= 1.7e+20) {
		tmp = 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 (a <= (-2.95d+169)) then
        tmp = a - b
    else if (a <= 1.7d+20) then
        tmp = 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 (a <= -2.95e+169) {
		tmp = a - b;
	} else if (a <= 1.7e+20) {
		tmp = z - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.95e+169:
		tmp = a - b
	elif a <= 1.7e+20:
		tmp = z - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.95e+169)
		tmp = Float64(a - b);
	elseif (a <= 1.7e+20)
		tmp = Float64(z - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.95e+169)
		tmp = a - b;
	elseif (a <= 1.7e+20)
		tmp = z - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.95e+169], N[(a - b), $MachinePrecision], If[LessEqual[a, 1.7e+20], N[(z - b), $MachinePrecision], a]]

Derivation

1. Split input into 3 regimes

2. if a < -2.95e169

   1. Initial program 59.7%

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

   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 37.5%

      \[\leadsto a - b \]

   if -2.95e169 < a < 1.7e20

   1. Initial program 59.7%

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

   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 inf

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

   7. Applied rewrites 37.8%

      \[\leadsto z - b \]

   if 1.7e20 < a

   1. Initial program 59.7%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 33.1%

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

Alternative 19: 48.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+69}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 0.0052:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9.5e+69) z (if (<= x 0.0052) (- a b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.5e+69) {
		tmp = z;
	} else if (x <= 0.0052) {
		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 <= (-9.5d+69)) then
        tmp = z
    else if (x <= 0.0052d0) 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 <= -9.5e+69) {
		tmp = z;
	} else if (x <= 0.0052) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -9.5e+69:
		tmp = z
	elif x <= 0.0052:
		tmp = a - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9.5e+69)
		tmp = z;
	elseif (x <= 0.0052)
		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 <= -9.5e+69)
		tmp = z;
	elseif (x <= 0.0052)
		tmp = a - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9.5e+69], z, If[LessEqual[x, 0.0052], N[(a - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -9.4999999999999995e69 or 0.0051999999999999998 < x

   1. Initial program 59.7%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 32.4%

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

   if -9.4999999999999995e69 < x < 0.0051999999999999998

   1. Initial program 59.7%

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

   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 37.5%

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

Alternative 20: 43.9% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+167}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 8.7 \cdot 10^{+14}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.4e+167) a (if (<= a 8.7e+14) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.4e+167) {
		tmp = a;
	} else if (a <= 8.7e+14) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-2.4d+167)) then
        tmp = a
    else if (a <= 8.7d+14) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.4e+167) {
		tmp = a;
	} else if (a <= 8.7e+14) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.4e+167:
		tmp = a
	elif a <= 8.7e+14:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.4e+167)
		tmp = a;
	elseif (a <= 8.7e+14)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.4e+167)
		tmp = a;
	elseif (a <= 8.7e+14)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.4e+167], a, If[LessEqual[a, 8.7e+14], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -2.39999999999999999e167 or 8.7e14 < a

   1. Initial program 59.7%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 33.1%

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

   if -2.39999999999999999e167 < a < 8.7e14

   1. Initial program 59.7%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 32.4%

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

Alternative 21: 33.1% 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 59.7%

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

2. Taylor expanded in t around inf

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

4. Applied rewrites 33.1%

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

Reproduce

herbie shell --seed 2025124 
(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)))