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

Percentage Accurate: 61.4% → 97.9%

Time: 9.3s

Alternatives: 17

Speedup: 1.4×

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: 61.4% 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: 97.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) + t\\ t_2 := t + \left(x + y\right)\\ t_3 := \frac{y}{t\_1}\\ t_4 := \left(\left(\frac{t + y}{t\_1} + \frac{z}{a} \cdot \frac{y + x}{t\_1}\right) - \frac{b}{a} \cdot t\_3\right) \cdot a\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{+56}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;a \leq 0.0004:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{x + y}{t\_2}, \frac{a \cdot \left(t + y\right)}{t\_2}\right) - b \cdot t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y x) t))
        (t_2 (+ t (+ x y)))
        (t_3 (/ y t_1))
        (t_4
         (*
          (- (+ (/ (+ t y) t_1) (* (/ z a) (/ (+ y x) t_1))) (* (/ b a) t_3))
          a)))
   (if (<= a -1.6e+56)
     t_4
     (if (<= a 0.0004)
       (- (fma z (/ (+ x y) t_2) (/ (* a (+ t y)) t_2)) (* b t_3))
       t_4))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + x) + t;
	double t_2 = t + (x + y);
	double t_3 = y / t_1;
	double t_4 = ((((t + y) / t_1) + ((z / a) * ((y + x) / t_1))) - ((b / a) * t_3)) * a;
	double tmp;
	if (a <= -1.6e+56) {
		tmp = t_4;
	} else if (a <= 0.0004) {
		tmp = fma(z, ((x + y) / t_2), ((a * (t + y)) / t_2)) - (b * t_3);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + x) + t)
	t_2 = Float64(t + Float64(x + y))
	t_3 = Float64(y / t_1)
	t_4 = Float64(Float64(Float64(Float64(Float64(t + y) / t_1) + Float64(Float64(z / a) * Float64(Float64(y + x) / t_1))) - Float64(Float64(b / a) * t_3)) * a)
	tmp = 0.0
	if (a <= -1.6e+56)
		tmp = t_4;
	elseif (a <= 0.0004)
		tmp = Float64(fma(z, Float64(Float64(x + y) / t_2), Float64(Float64(a * Float64(t + y)) / t_2)) - Float64(b * t_3));
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] * N[(N[(y + x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b / a), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -1.6e+56], t$95$4, If[LessEqual[a, 0.0004], N[(N[(z * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] - N[(b * t$95$3), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.60000000000000002e56 or 4.00000000000000019e-4 < a

   1. Initial program 47.8%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 98.8%

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

   if -1.60000000000000002e56 < a < 4.00000000000000019e-4

   1. Initial program 72.9%

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

   4. Applied rewrites 78.9%

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

   5. Taylor expanded in z around 0

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

      1. lower-fma.f64 N/A

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

      2. div-add-rev N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-+.f64 97.2

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

   7. Applied rewrites 97.2%

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

Alternative 2: 88.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) + t\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_3 := \left(a + z\right) - b\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+232}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t + y}{t\_1}, a, \frac{\mathsf{fma}\left(y + x, z, \left(-b\right) \cdot y\right)}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y x) t))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_3 (- (+ a z) b)))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 2e+232)
       (fma (/ (+ t y) t_1) a (/ (fma (+ y x) z (* (- b) y)) t_1))
       t_3))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + x) + t;
	double t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double t_3 = (a + z) - b;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= 2e+232) {
		tmp = fma(((t + y) / t_1), a, (fma((y + x), z, (-b * y)) / t_1));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + x) + t)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	t_3 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= 2e+232)
		tmp = fma(Float64(Float64(t + y) / t_1), a, Float64(fma(Float64(y + x), z, Float64(Float64(-b) * y)) / t_1));
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(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$3 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, 2e+232], N[(N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision] * a + N[(N[(N[(y + x), $MachinePrecision] * z + N[((-b) * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 2.00000000000000011e232 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 9.7%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 73.3

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

   5. Applied rewrites 73.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000011e232

   1. Initial program 99.4%

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

   4. Applied rewrites 99.0%

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

Alternative 3: 88.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := \left(a + z\right) - b\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+232}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_2 (- (+ a z) b)))
   (if (<= t_1 (- INFINITY)) t_2 (if (<= t_1 2e+232) t_1 t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double t_2 = (a + z) - b;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 2e+232) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double t_2 = (a + z) - b;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= 2e+232) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
	t_2 = (a + z) - b
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= 2e+232:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	t_2 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 2e+232)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	t_2 = (a + z) - b;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= 2e+232)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 2e+232], t$95$1, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 2.00000000000000011e232 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 9.7%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 73.3

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

   5. Applied rewrites 73.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000011e232

   1. Initial program 99.4%

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

Alternative 4: 75.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := \left(a + z\right) - b\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{+141}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t + y, a, \left(y + x\right) \cdot z\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) t_1))
        (t_3 (- (+ a z) b)))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 1e+141) (/ (fma (+ t y) a (* (+ y x) z)) t_1) t_3))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / t_1;
	double t_3 = (a + z) - b;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= 1e+141) {
		tmp = fma((t + y), a, ((y + x) * z)) / t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= 1e+141)
		tmp = Float64(fma(Float64(t + y), a, Float64(Float64(y + x) * z)) / t_1);
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, 1e+141], N[(N[(N[(t + y), $MachinePrecision] * a + N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 1.00000000000000002e141 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 17.9%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 71.4

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

   5. Applied rewrites 71.4%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000002e141

   1. Initial program 99.4%

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

   3. Taylor expanded in b around 0

      \[\leadsto \frac{\color{blue}{a \cdot \left(t + y\right) + z \cdot \left(x + y\right)}}{\left(x + t\right) + y} \]
   4. 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. lift-*.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 78.6

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

   5. Applied rewrites 78.6%

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

Alternative 5: 67.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := \left(a + z\right) - b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+178}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+141}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -5e+178)
     t_2
     (if (<= t_1 1e+141) (/ (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 <= -5e+178) {
		tmp = t_2;
	} else if (t_1 <= 1e+141) {
		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 <= -5e+178)
		tmp = t_2;
	elseif (t_1 <= 1e+141)
		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, -5e+178], t$95$2, If[LessEqual[t$95$1, 1e+141], 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)) < -4.9999999999999999e178 or 1.00000000000000002e141 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 25.2%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 71.3

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

   5. Applied rewrites 71.3%

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

   if -4.9999999999999999e178 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000002e141

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{a \cdot t + x \cdot z}{t + x}} \]
   4. 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 63.0

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

   5. Applied rewrites 63.0%

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

Alternative 6: 88.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := \left(y + x\right) + t\\ t_3 := b \cdot \frac{y}{t\_2}\\ \mathbf{if}\;a \leq -1.02 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \frac{t + y}{t\_1} - t\_3\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+39}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{x + y}{t\_1}, \frac{a \cdot \left(t + y\right)}{t\_1}\right) - t\_3\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t + y}{t\_2}, a, \frac{\mathsf{fma}\left(y + x, z, \left(-b\right) \cdot y\right)}{t\_2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y))) (t_2 (+ (+ y x) t)) (t_3 (* b (/ y t_2))))
   (if (<= a -1.02e+58)
     (- (* a (/ (+ t y) t_1)) t_3)
     (if (<= a 1.1e+39)
       (- (fma z (/ (+ x y) t_1) (/ (* a (+ t y)) t_1)) t_3)
       (fma (/ (+ t y) t_2) a (/ (fma (+ y x) z (* (- b) y)) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = (y + x) + t;
	double t_3 = b * (y / t_2);
	double tmp;
	if (a <= -1.02e+58) {
		tmp = (a * ((t + y) / t_1)) - t_3;
	} else if (a <= 1.1e+39) {
		tmp = fma(z, ((x + y) / t_1), ((a * (t + y)) / t_1)) - t_3;
	} else {
		tmp = fma(((t + y) / t_2), a, (fma((y + x), z, (-b * y)) / t_2));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(Float64(y + x) + t)
	t_3 = Float64(b * Float64(y / t_2))
	tmp = 0.0
	if (a <= -1.02e+58)
		tmp = Float64(Float64(a * Float64(Float64(t + y) / t_1)) - t_3);
	elseif (a <= 1.1e+39)
		tmp = Float64(fma(z, Float64(Float64(x + y) / t_1), Float64(Float64(a * Float64(t + y)) / t_1)) - t_3);
	else
		tmp = fma(Float64(Float64(t + y) / t_2), a, Float64(fma(Float64(y + x), z, Float64(Float64(-b) * y)) / t_2));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.02e+58], N[(N[(a * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], If[LessEqual[a, 1.1e+39], N[(N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], N[(N[(N[(t + y), $MachinePrecision] / t$95$2), $MachinePrecision] * a + N[(N[(N[(y + x), $MachinePrecision] * z + N[((-b) * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.02000000000000005e58

   1. Initial program 44.8%

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

   4. Applied rewrites 46.3%

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

   5. Taylor expanded in z around 0

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

      1. lower-fma.f64 N/A

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

      2. div-add-rev N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-+.f64 53.4

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

   7. Applied rewrites 53.4%

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

   8. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. div-add-rev N/A

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

      3. lower-/.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-+.f64 79.5

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

   10. Applied rewrites 79.5%

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

   if -1.02000000000000005e58 < a < 1.1000000000000001e39

   1. Initial program 72.6%

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

   4. Applied rewrites 78.8%

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

   5. Taylor expanded in z around 0

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

      1. lower-fma.f64 N/A

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

      2. div-add-rev N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-+.f64 97.0

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

   7. Applied rewrites 97.0%

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

   if 1.1000000000000001e39 < a

   1. Initial program 47.2%

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

   4. Applied rewrites 73.2%

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

Alternative 7: 62.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a - b \cdot \frac{y}{\left(y + x\right) + t}\\ \mathbf{if}\;t \leq -2.05 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-8}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+43}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- a (* b (/ y (+ (+ y x) t))))))
   (if (<= t -2.05e+118)
     t_1
     (if (<= t -2.15e-8)
       (/ (fma a t (* z x)) (+ t x))
       (if (<= t 5.6e+43) (- (+ a z) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a - (b * (y / ((y + x) + t)));
	double tmp;
	if (t <= -2.05e+118) {
		tmp = t_1;
	} else if (t <= -2.15e-8) {
		tmp = fma(a, t, (z * x)) / (t + x);
	} else if (t <= 5.6e+43) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a - Float64(b * Float64(y / Float64(Float64(y + x) + t))))
	tmp = 0.0
	if (t <= -2.05e+118)
		tmp = t_1;
	elseif (t <= -2.15e-8)
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	elseif (t <= 5.6e+43)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a - N[(b * N[(y / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.05e+118], t$95$1, If[LessEqual[t, -2.15e-8], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e+43], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.0499999999999999e118 or 5.60000000000000038e43 < t

   1. Initial program 52.5%

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 64.1%

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

   if -2.0499999999999999e118 < t < -2.1500000000000001e-8

   1. Initial program 63.6%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{a \cdot t + x \cdot z}{t + x}} \]
   4. 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 45.9

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

   5. Applied rewrites 45.9%

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

   if -2.1500000000000001e-8 < t < 5.60000000000000038e43

   1. Initial program 67.2%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 64.8

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

   5. Applied rewrites 64.8%

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

Alternative 8: 65.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + y}{t + \left(x + y\right)} \cdot a\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+37}:\\ \;\;\;\;z - b \cdot \frac{y}{\left(y + x\right) + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (+ t y) (+ t (+ x y))) a)))
   (if (<= a -5.2e+174)
     t_1
     (if (<= a 3.2e+37) (- z (* b (/ y (+ (+ y x) t)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) / (t + (x + y))) * a;
	double tmp;
	if (a <= -5.2e+174) {
		tmp = t_1;
	} else if (a <= 3.2e+37) {
		tmp = z - (b * (y / ((y + x) + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t + y) / (t + (x + y))) * a
    if (a <= (-5.2d+174)) then
        tmp = t_1
    else if (a <= 3.2d+37) then
        tmp = z - (b * (y / ((y + x) + t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) / (t + (x + y))) * a;
	double tmp;
	if (a <= -5.2e+174) {
		tmp = t_1;
	} else if (a <= 3.2e+37) {
		tmp = z - (b * (y / ((y + x) + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t + y) / (t + (x + y))) * a
	tmp = 0
	if a <= -5.2e+174:
		tmp = t_1
	elif a <= 3.2e+37:
		tmp = z - (b * (y / ((y + x) + t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) / Float64(t + Float64(x + y))) * a)
	tmp = 0.0
	if (a <= -5.2e+174)
		tmp = t_1;
	elseif (a <= 3.2e+37)
		tmp = Float64(z - Float64(b * Float64(y / Float64(Float64(y + x) + t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t + y) / (t + (x + y))) * a;
	tmp = 0.0;
	if (a <= -5.2e+174)
		tmp = t_1;
	elseif (a <= 3.2e+37)
		tmp = z - (b * (y / ((y + x) + t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -5.2e+174], t$95$1, If[LessEqual[a, 3.2e+37], N[(z - N[(b * N[(y / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.1999999999999997e174 or 3.20000000000000014e37 < a

   1. Initial program 43.5%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 98.6%

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

   6. Taylor expanded in a around inf

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

      1. div-add-rev N/A

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

      2. lower-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-+.f64 71.8

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

   8. Applied rewrites 71.8%

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

   if -5.1999999999999997e174 < a < 3.20000000000000014e37

   1. Initial program 70.2%

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

   4. Applied rewrites 75.8%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 61.9%

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

Alternative 9: 62.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a - b \cdot \frac{y}{y + t}\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+151}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- a (* b (/ y (+ y t))))))
   (if (<= t -3.5e+87) t_1 (if (<= t 2.35e+151) (- (+ a z) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a - (b * (y / (y + t)));
	double tmp;
	if (t <= -3.5e+87) {
		tmp = t_1;
	} else if (t <= 2.35e+151) {
		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 = a - (b * (y / (y + t)))
    if (t <= (-3.5d+87)) then
        tmp = t_1
    else if (t <= 2.35d+151) 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 = a - (b * (y / (y + t)));
	double tmp;
	if (t <= -3.5e+87) {
		tmp = t_1;
	} else if (t <= 2.35e+151) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a - (b * (y / (y + t)))
	tmp = 0
	if t <= -3.5e+87:
		tmp = t_1
	elif t <= 2.35e+151:
		tmp = (a + z) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a - Float64(b * Float64(y / Float64(y + t))))
	tmp = 0.0
	if (t <= -3.5e+87)
		tmp = t_1;
	elseif (t <= 2.35e+151)
		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 = a - (b * (y / (y + t)));
	tmp = 0.0;
	if (t <= -3.5e+87)
		tmp = t_1;
	elseif (t <= 2.35e+151)
		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[(a - N[(b * N[(y / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e+87], t$95$1, If[LessEqual[t, 2.35e+151], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.49999999999999986e87 or 2.34999999999999995e151 < t

   1. Initial program 50.0%

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

   4. Applied rewrites 53.7%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 65.6%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 64.0%

       \[\leadsto a - b \cdot \frac{y}{\color{blue}{y} + t} \]

   if -3.49999999999999986e87 < t < 2.34999999999999995e151

   1. Initial program 66.4%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 61.7

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

   5. Applied rewrites 61.7%

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

Alternative 10: 60.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a - \frac{b \cdot y}{t + x}\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+151}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- a (/ (* b y) (+ t x)))))
   (if (<= t -3.5e+87) t_1 (if (<= t 2.35e+151) (- (+ a z) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a - ((b * y) / (t + x));
	double tmp;
	if (t <= -3.5e+87) {
		tmp = t_1;
	} else if (t <= 2.35e+151) {
		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 = a - ((b * y) / (t + x))
    if (t <= (-3.5d+87)) then
        tmp = t_1
    else if (t <= 2.35d+151) 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 = a - ((b * y) / (t + x));
	double tmp;
	if (t <= -3.5e+87) {
		tmp = t_1;
	} else if (t <= 2.35e+151) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a - ((b * y) / (t + x))
	tmp = 0
	if t <= -3.5e+87:
		tmp = t_1
	elif t <= 2.35e+151:
		tmp = (a + z) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a - Float64(Float64(b * y) / Float64(t + x)))
	tmp = 0.0
	if (t <= -3.5e+87)
		tmp = t_1;
	elseif (t <= 2.35e+151)
		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 = a - ((b * y) / (t + x));
	tmp = 0.0;
	if (t <= -3.5e+87)
		tmp = t_1;
	elseif (t <= 2.35e+151)
		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[(a - N[(N[(b * y), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e+87], t$95$1, If[LessEqual[t, 2.35e+151], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.49999999999999986e87 or 2.34999999999999995e151 < t

   1. Initial program 50.0%

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

   4. Applied rewrites 53.7%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 65.6%

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

   8. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 56.5

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

   10. Applied rewrites 56.5%

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

   if -3.49999999999999986e87 < t < 2.34999999999999995e151

   1. Initial program 66.4%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 61.7

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

   5. Applied rewrites 61.7%

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

Alternative 11: 61.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a - b \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+151}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- a (* b (/ y t)))))
   (if (<= t -1.15e+129) t_1 (if (<= t 2.35e+151) (- (+ a z) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a - (b * (y / t));
	double tmp;
	if (t <= -1.15e+129) {
		tmp = t_1;
	} else if (t <= 2.35e+151) {
		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 = a - (b * (y / t))
    if (t <= (-1.15d+129)) then
        tmp = t_1
    else if (t <= 2.35d+151) 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 = a - (b * (y / t));
	double tmp;
	if (t <= -1.15e+129) {
		tmp = t_1;
	} else if (t <= 2.35e+151) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a - (b * (y / t))
	tmp = 0
	if t <= -1.15e+129:
		tmp = t_1
	elif t <= 2.35e+151:
		tmp = (a + z) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a - Float64(b * Float64(y / t)))
	tmp = 0.0
	if (t <= -1.15e+129)
		tmp = t_1;
	elseif (t <= 2.35e+151)
		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 = a - (b * (y / t));
	tmp = 0.0;
	if (t <= -1.15e+129)
		tmp = t_1;
	elseif (t <= 2.35e+151)
		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[(a - N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+129], t$95$1, If[LessEqual[t, 2.35e+151], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.14999999999999995e129 or 2.34999999999999995e151 < t

   1. Initial program 49.0%

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

   4. Applied rewrites 52.5%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 66.7%

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

   8. Taylor expanded in t around inf

      \[\leadsto a - b \cdot \frac{y}{\color{blue}{t}} \]
   9. Step-by-step derivation

   10. Applied rewrites 61.8%

       \[\leadsto a - b \cdot \frac{y}{\color{blue}{t}} \]

   if -1.14999999999999995e129 < t < 2.34999999999999995e151

   1. Initial program 66.0%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 61.4

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

   5. Applied rewrites 61.4%

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

Alternative 12: 60.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a - \frac{b \cdot y}{t}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+151}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- a (/ (* b y) t))))
   (if (<= t -1.15e+129) t_1 (if (<= t 2.35e+151) (- (+ a z) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a - ((b * y) / t);
	double tmp;
	if (t <= -1.15e+129) {
		tmp = t_1;
	} else if (t <= 2.35e+151) {
		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 = a - ((b * y) / t)
    if (t <= (-1.15d+129)) then
        tmp = t_1
    else if (t <= 2.35d+151) 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 = a - ((b * y) / t);
	double tmp;
	if (t <= -1.15e+129) {
		tmp = t_1;
	} else if (t <= 2.35e+151) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a - ((b * y) / t)
	tmp = 0
	if t <= -1.15e+129:
		tmp = t_1
	elif t <= 2.35e+151:
		tmp = (a + z) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a - Float64(Float64(b * y) / t))
	tmp = 0.0
	if (t <= -1.15e+129)
		tmp = t_1;
	elseif (t <= 2.35e+151)
		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 = a - ((b * y) / t);
	tmp = 0.0;
	if (t <= -1.15e+129)
		tmp = t_1;
	elseif (t <= 2.35e+151)
		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[(a - N[(N[(b * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+129], t$95$1, If[LessEqual[t, 2.35e+151], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.14999999999999995e129 or 2.34999999999999995e151 < t

   1. Initial program 49.0%

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

   4. Applied rewrites 52.5%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 66.7%

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

   8. Taylor expanded in t around inf

      \[\leadsto a - \color{blue}{\frac{b \cdot y}{t}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto a - \frac{b \cdot y}{\color{blue}{t}} \]

      2. lower-*.f64 57.5

         \[\leadsto a - \frac{b \cdot y}{t} \]

   10. Applied rewrites 57.5%

       \[\leadsto a - \color{blue}{\frac{b \cdot y}{t}} \]

   if -1.14999999999999995e129 < t < 2.34999999999999995e151

   1. Initial program 66.0%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 61.4

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

   5. Applied rewrites 61.4%

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

Alternative 13: 59.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+207}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+151}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.5e+207) a (if (<= t 7e+151) (- (+ a z) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.5e+207) {
		tmp = a;
	} else if (t <= 7e+151) {
		tmp = (a + z) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-7.5d+207)) then
        tmp = a
    else if (t <= 7d+151) then
        tmp = (a + z) - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.5e+207) {
		tmp = a;
	} else if (t <= 7e+151) {
		tmp = (a + z) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.5e+207:
		tmp = a
	elif t <= 7e+151:
		tmp = (a + z) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.5e+207)
		tmp = a;
	elseif (t <= 7e+151)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7.5e+207)
		tmp = a;
	elseif (t <= 7e+151)
		tmp = (a + z) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.5e+207], a, If[LessEqual[t, 7e+151], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -7.49999999999999986e207 or 7.0000000000000006e151 < t

   1. Initial program 46.4%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 56.0%

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

   if -7.49999999999999986e207 < t < 7.0000000000000006e151

   1. Initial program 65.4%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 60.0

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

   5. Applied rewrites 60.0%

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

Alternative 14: 47.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+23}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+151}:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.45e+23) a (if (<= t 2.6e+151) (- z b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.45e+23) {
		tmp = a;
	} else if (t <= 2.6e+151) {
		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 (t <= (-1.45d+23)) then
        tmp = a
    else if (t <= 2.6d+151) 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 (t <= -1.45e+23) {
		tmp = a;
	} else if (t <= 2.6e+151) {
		tmp = z - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.45e+23:
		tmp = a
	elif t <= 2.6e+151:
		tmp = z - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.45e+23)
		tmp = a;
	elseif (t <= 2.6e+151)
		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 (t <= -1.45e+23)
		tmp = a;
	elseif (t <= 2.6e+151)
		tmp = z - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.45e+23], a, If[LessEqual[t, 2.6e+151], N[(z - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -1.45000000000000006e23 or 2.60000000000000013e151 < t

   1. Initial program 52.3%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 48.7%

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

   if -1.45000000000000006e23 < t < 2.60000000000000013e151

   1. Initial program 66.6%

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

   4. Applied rewrites 71.5%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 45.5%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 36.6%

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

   11. Taylor expanded in x around inf

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

   13. Applied rewrites 46.4%

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

Alternative 15: 47.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.65 \cdot 10^{-53}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+51}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.65e-53) z (if (<= z 3e+51) (- a b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.65e-53) {
		tmp = z;
	} else if (z <= 3e+51) {
		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 (z <= (-3.65d-53)) then
        tmp = z
    else if (z <= 3d+51) 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 (z <= -3.65e-53) {
		tmp = z;
	} else if (z <= 3e+51) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.65e-53:
		tmp = z
	elif z <= 3e+51:
		tmp = a - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.65e-53)
		tmp = z;
	elseif (z <= 3e+51)
		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 (z <= -3.65e-53)
		tmp = z;
	elseif (z <= 3e+51)
		tmp = a - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.65e-53], z, If[LessEqual[z, 3e+51], N[(a - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -3.65000000000000008e-53 or 3e51 < z

   1. Initial program 50.4%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 46.9%

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

   if -3.65000000000000008e-53 < z < 3e51

   1. Initial program 72.4%

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

   4. Applied rewrites 78.9%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 67.4%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 47.5%

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

Alternative 16: 43.7% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -105000000000:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+151}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -105000000000.0) a (if (<= t 2.35e+151) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -105000000000.0) {
		tmp = a;
	} else if (t <= 2.35e+151) {
		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 (t <= (-105000000000.0d0)) then
        tmp = a
    else if (t <= 2.35d+151) 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 (t <= -105000000000.0) {
		tmp = a;
	} else if (t <= 2.35e+151) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -105000000000.0:
		tmp = a
	elif t <= 2.35e+151:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -105000000000.0)
		tmp = a;
	elseif (t <= 2.35e+151)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -105000000000.0)
		tmp = a;
	elseif (t <= 2.35e+151)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -105000000000.0], a, If[LessEqual[t, 2.35e+151], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e11 or 2.34999999999999995e151 < t

   1. Initial program 52.7%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 48.5%

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

   if -1.05e11 < t < 2.34999999999999995e151

   1. Initial program 66.6%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 40.9%

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

Alternative 17: 33.5% accurate, 45.0× 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 61.4%

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

3. Taylor expanded in t around inf

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

5. Applied rewrites 33.5%

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

Developer Target 1: 82.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\\ t_3 := \frac{t\_2}{t\_1}\\ t_4 := \left(z + a\right) - b\\ \mathbf{if}\;t\_3 < -3.5813117084150564 \cdot 10^{+153}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 < 1.2285964308315609 \cdot 10^{+82}:\\ \;\;\;\;\frac{1}{\frac{t\_1}{t\_2}}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

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_3 (/ t_2 t_1))
        (t_4 (- (+ z a) b)))
   (if (< t_3 -3.5813117084150564e+153)
     t_4
     (if (< t_3 1.2285964308315609e+82) (/ 1.0 (/ t_1 t_2)) t_4))))

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);
	double t_3 = t_2 / t_1;
	double t_4 = (z + a) - b;
	double tmp;
	if (t_3 < -3.5813117084150564e+153) {
		tmp = t_4;
	} else if (t_3 < 1.2285964308315609e+82) {
		tmp = 1.0 / (t_1 / t_2);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (x + t) + y
    t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b)
    t_3 = t_2 / t_1
    t_4 = (z + a) - b
    if (t_3 < (-3.5813117084150564d+153)) then
        tmp = t_4
    else if (t_3 < 1.2285964308315609d+82) then
        tmp = 1.0d0 / (t_1 / t_2)
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	double t_3 = t_2 / t_1;
	double t_4 = (z + a) - b;
	double tmp;
	if (t_3 < -3.5813117084150564e+153) {
		tmp = t_4;
	} else if (t_3 < 1.2285964308315609e+82) {
		tmp = 1.0 / (t_1 / t_2);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + t) + y
	t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b)
	t_3 = t_2 / t_1
	t_4 = (z + a) - b
	tmp = 0
	if t_3 < -3.5813117084150564e+153:
		tmp = t_4
	elif t_3 < 1.2285964308315609e+82:
		tmp = 1.0 / (t_1 / t_2)
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b))
	t_3 = Float64(t_2 / t_1)
	t_4 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_3 < -3.5813117084150564e+153)
		tmp = t_4;
	elseif (t_3 < 1.2285964308315609e+82)
		tmp = Float64(1.0 / Float64(t_1 / t_2));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + t) + y;
	t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	t_3 = t_2 / t_1;
	t_4 = (z + a) - b;
	tmp = 0.0;
	if (t_3 < -3.5813117084150564e+153)
		tmp = t_4;
	elseif (t_3 < 1.2285964308315609e+82)
		tmp = 1.0 / (t_1 / t_2);
	else
		tmp = t_4;
	end
	tmp_2 = 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[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[Less[t$95$3, -3.5813117084150564e+153], t$95$4, If[Less[t$95$3, 1.2285964308315609e+82], N[(1.0 / N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]

Reproduce

herbie shell --seed 2025089 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3581311708415056400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 12285964308315609000000000000000000000000000000000000000000000000000000000000000000) (/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (- (+ z a) b))))

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