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

Percentage Accurate: 61.3% → 88.5%

Time: 7.8s

Alternatives: 13

Speedup: 1.3×

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: 61.3% 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: 88.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 2 \cdot 10^{+242}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+242))) (- (+ a z) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+242)) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	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 tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+242)) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+242):
		tmp = (a + z) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+242))
		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 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+242)))
		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[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+242]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], t$95$1]]

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 2.0000000000000001e242 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.9%

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

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

      2. lower-+.f64 80.5

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

   5. Applied rewrites 80.5%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e242

   1. Initial program 99.8%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 2 \cdot 10^{+242}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 66.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := \left(a + z\right) - b\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+262}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-45}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, x, y \cdot \left(z - b\right)\right)}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+35}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+242}:\\ \;\;\;\;\frac{t\_3 \cdot y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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 -1e+262)
     t_3
     (if (<= t_2 -5e-45)
       (/ (fma z x (* y (- z b))) t_1)
       (if (<= t_2 2e+35)
         (/ (fma a t (* z x)) (+ t x))
         (if (<= t_2 2e+242) (/ (* t_3 y) 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 <= -1e+262) {
		tmp = t_3;
	} else if (t_2 <= -5e-45) {
		tmp = fma(z, x, (y * (z - b))) / t_1;
	} else if (t_2 <= 2e+35) {
		tmp = fma(a, t, (z * x)) / (t + x);
	} else if (t_2 <= 2e+242) {
		tmp = (t_3 * y) / 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 <= -1e+262)
		tmp = t_3;
	elseif (t_2 <= -5e-45)
		tmp = Float64(fma(z, x, Float64(y * Float64(z - b))) / t_1);
	elseif (t_2 <= 2e+35)
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	elseif (t_2 <= 2e+242)
		tmp = Float64(Float64(t_3 * 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[(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, -1e+262], t$95$3, If[LessEqual[t$95$2, -5e-45], N[(N[(z * x + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 2e+35], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+242], N[(N[(t$95$3 * y), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -1e262 or 2.0000000000000001e242 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 11.4%

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

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

      2. lower-+.f64 80.2

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

   5. Applied rewrites 80.2%

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

   if -1e262 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -4.99999999999999976e-45

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. distribute-rgt-in N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. distribute-lft-out-- N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 78.2

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

   5. Applied rewrites 78.2%

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

   if -4.99999999999999976e-45 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.9999999999999999e35

   1. Initial program 99.8%

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

   3. Taylor expanded in 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

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 69.4

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

   5. Applied rewrites 69.4%

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

   if 1.9999999999999999e35 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e242

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 77.4

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

   5. Applied rewrites 77.4%

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

Alternative 3: 66.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := \left(a + z\right) - b\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+114}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t + y, a, y \cdot \left(z - b\right)\right)}{t + y}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+35}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+242}:\\ \;\;\;\;\frac{t\_3 \cdot y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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 -5e+114)
       (/ (fma (+ t y) a (* y (- z b))) (+ t y))
       (if (<= t_2 2e+35)
         (/ (fma a t (* z x)) (+ t x))
         (if (<= t_2 2e+242) (/ (* t_3 y) 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 <= -5e+114) {
		tmp = fma((t + y), a, (y * (z - b))) / (t + y);
	} else if (t_2 <= 2e+35) {
		tmp = fma(a, t, (z * x)) / (t + x);
	} else if (t_2 <= 2e+242) {
		tmp = (t_3 * y) / 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 <= -5e+114)
		tmp = Float64(fma(Float64(t + y), a, Float64(y * Float64(z - b))) / Float64(t + y));
	elseif (t_2 <= 2e+35)
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	elseif (t_2 <= 2e+242)
		tmp = Float64(Float64(t_3 * 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[(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, -5e+114], N[(N[(N[(t + y), $MachinePrecision] * a + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+35], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+242], N[(N[(t$95$3 * y), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 2.0000000000000001e242 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.9%

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

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

      2. lower-+.f64 80.5

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

   5. Applied rewrites 80.5%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -5.0000000000000001e114

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 77.3

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

   5. Applied rewrites 77.3%

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

   if -5.0000000000000001e114 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.9999999999999999e35

   1. Initial program 99.8%

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

   3. Taylor expanded in 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

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 69.2

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

   5. Applied rewrites 69.2%

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

   if 1.9999999999999999e35 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e242

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 77.4

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

   5. Applied rewrites 77.4%

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

Alternative 4: 65.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := \left(a + z\right) - b\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+114}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+35}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+242}:\\ \;\;\;\;\frac{t\_3 \cdot y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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 -5e+114)
     t_3
     (if (<= t_2 2e+35)
       (/ (fma a t (* z x)) (+ t x))
       (if (<= t_2 2e+242) (/ (* t_3 y) 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 <= -5e+114) {
		tmp = t_3;
	} else if (t_2 <= 2e+35) {
		tmp = fma(a, t, (z * x)) / (t + x);
	} else if (t_2 <= 2e+242) {
		tmp = (t_3 * y) / 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 <= -5e+114)
		tmp = t_3;
	elseif (t_2 <= 2e+35)
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	elseif (t_2 <= 2e+242)
		tmp = Float64(Float64(t_3 * 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[(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, -5e+114], t$95$3, If[LessEqual[t$95$2, 2e+35], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+242], N[(N[(t$95$3 * y), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -5.0000000000000001e114 or 2.0000000000000001e242 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 29.4%

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

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

      2. lower-+.f64 74.9

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

   5. Applied rewrites 74.9%

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

   if -5.0000000000000001e114 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.9999999999999999e35

   1. Initial program 99.8%

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

   3. Taylor expanded in 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

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 69.2

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

   5. Applied rewrites 69.2%

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

   if 1.9999999999999999e35 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e242

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 77.4

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

   5. Applied rewrites 77.4%

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

Alternative 5: 73.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) \cdot a\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + t\_1\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 5 \cdot 10^{+94}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, t\_1\right)}{\left(y + x\right) + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ t y) a))
        (t_2 (/ (- (+ (* (+ x y) z) t_1) (* y b)) (+ (+ x t) y))))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 5e+94)))
     (- (+ a z) b)
     (/ (fma (+ y x) z t_1) (+ (+ y x) t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) * a;
	double t_2 = ((((x + y) * z) + t_1) - (y * b)) / ((x + t) + y);
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 5e+94)) {
		tmp = (a + z) - b;
	} else {
		tmp = fma((y + x), z, t_1) / ((y + x) + t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) * a)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + t_1) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 5e+94))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(fma(Float64(y + x), z, t_1) / Float64(Float64(y + x) + t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 5e+94]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(y + x), $MachinePrecision] * z + t$95$1), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]]]]

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 5.0000000000000001e94 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 22.4%

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

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

      2. lower-+.f64 78.0

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

   5. Applied rewrites 78.0%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000001e94

   1. Initial program 99.8%

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

   3. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 82.0

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

   5. Applied rewrites 82.0%

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

4. Final simplification 80.1%

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

Alternative 6: 65.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+114} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+94}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (or (<= t_1 -5e+114) (not (<= t_1 5e+94)))
     (- (+ a z) b)
     (/ (fma a t (* z x)) (+ t x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if ((t_1 <= -5e+114) || !(t_1 <= 5e+94)) {
		tmp = (a + z) - b;
	} else {
		tmp = fma(a, t, (z * x)) / (t + x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if ((t_1 <= -5e+114) || !(t_1 <= 5e+94))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+114], N[Not[LessEqual[t$95$1, 5e+94]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]]]

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)) < -5.0000000000000001e114 or 5.0000000000000001e94 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 37.7%

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

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

      2. lower-+.f64 73.5

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

   5. Applied rewrites 73.5%

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

   if -5.0000000000000001e114 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000001e94

   1. Initial program 99.8%

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

   3. Taylor expanded in 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

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 67.8

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

   5. Applied rewrites 67.8%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -5 \cdot 10^{+114} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 5 \cdot 10^{+94}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+151} \lor \neg \left(x \leq 6.4 \cdot 10^{+127}\right):\\ \;\;\;\;z - \frac{b - a}{x} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -2.4e+151) (not (<= x 6.4e+127)))
   (- z (* (/ (- b a) x) y))
   (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -2.4e+151) || !(x <= 6.4e+127)) {
		tmp = z - (((b - a) / x) * y);
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-2.4d+151)) .or. (.not. (x <= 6.4d+127))) then
        tmp = z - (((b - a) / x) * y)
    else
        tmp = (a + z) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -2.4e+151) || !(x <= 6.4e+127)) {
		tmp = z - (((b - a) / x) * y);
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -2.4e+151) or not (x <= 6.4e+127):
		tmp = z - (((b - a) / x) * y)
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -2.4e+151) || !(x <= 6.4e+127))
		tmp = Float64(z - Float64(Float64(Float64(b - a) / x) * y));
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -2.4e+151) || ~((x <= 6.4e+127)))
		tmp = z - (((b - a) / x) * y);
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -2.4e+151], N[Not[LessEqual[x, 6.4e+127]], $MachinePrecision]], N[(z - N[(N[(N[(b - a), $MachinePrecision] / x), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4000000000000001e151 or 6.39999999999999952e127 < x

   1. Initial program 60.8%

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

   3. Taylor expanded in x around -inf

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 58.4%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 69.3%

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

   if -2.4000000000000001e151 < x < 6.39999999999999952e127

   1. Initial program 64.0%

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

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

      2. lower-+.f64 64.7

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

   5. Applied rewrites 64.7%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+151} \lor \neg \left(x \leq 6.4 \cdot 10^{+127}\right):\\ \;\;\;\;z - \frac{b - a}{x} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -9.1 \cdot 10^{-125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-194}:\\ \;\;\;\;\frac{x}{t + x} \cdot z\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-9}:\\ \;\;\;\;\frac{a}{z} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a z) b)))
   (if (<= y -9.1e-125)
     t_1
     (if (<= y 5.4e-194)
       (* (/ x (+ t x)) z)
       (if (<= y 1.1e-9) (* (/ a z) z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -9.1e-125) {
		tmp = t_1;
	} else if (y <= 5.4e-194) {
		tmp = (x / (t + x)) * z;
	} else if (y <= 1.1e-9) {
		tmp = (a / z) * z;
	} 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 + z) - b
    if (y <= (-9.1d-125)) then
        tmp = t_1
    else if (y <= 5.4d-194) then
        tmp = (x / (t + x)) * z
    else if (y <= 1.1d-9) then
        tmp = (a / z) * z
    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 + z) - b;
	double tmp;
	if (y <= -9.1e-125) {
		tmp = t_1;
	} else if (y <= 5.4e-194) {
		tmp = (x / (t + x)) * z;
	} else if (y <= 1.1e-9) {
		tmp = (a / z) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + z) - b
	tmp = 0
	if y <= -9.1e-125:
		tmp = t_1
	elif y <= 5.4e-194:
		tmp = (x / (t + x)) * z
	elif y <= 1.1e-9:
		tmp = (a / z) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (y <= -9.1e-125)
		tmp = t_1;
	elseif (y <= 5.4e-194)
		tmp = Float64(Float64(x / Float64(t + x)) * z);
	elseif (y <= 1.1e-9)
		tmp = Float64(Float64(a / z) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + z) - b;
	tmp = 0.0;
	if (y <= -9.1e-125)
		tmp = t_1;
	elseif (y <= 5.4e-194)
		tmp = (x / (t + x)) * z;
	elseif (y <= 1.1e-9)
		tmp = (a / z) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -9.1e-125], t$95$1, If[LessEqual[y, 5.4e-194], N[(N[(x / N[(t + x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[y, 1.1e-9], N[(N[(a / z), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.10000000000000046e-125 or 1.0999999999999999e-9 < y

   1. Initial program 55.2%

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

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

      2. lower-+.f64 70.5

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

   5. Applied rewrites 70.5%

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

   if -9.10000000000000046e-125 < y < 5.4e-194

   1. Initial program 80.7%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

   5. Applied rewrites 83.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 58.8%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 53.1%

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

   if 5.4e-194 < y < 1.0999999999999999e-9

   1. Initial program 73.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

   5. Applied rewrites 56.5%

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

   6. Taylor expanded in t around inf

      \[\leadsto \frac{a}{z} \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 61.6%

      \[\leadsto \frac{a}{z} \cdot z \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 56.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+191} \lor \neg \left(t \leq 1.5 \cdot 10^{+233}\right):\\ \;\;\;\;\frac{a}{z} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -7.2e+191) (not (<= t 1.5e+233))) (* (/ a z) z) (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7.2e+191) || !(t <= 1.5e+233)) {
		tmp = (a / z) * z;
	} else {
		tmp = (a + z) - b;
	}
	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 <= (-7.2d+191)) .or. (.not. (t <= 1.5d+233))) then
        tmp = (a / z) * z
    else
        tmp = (a + z) - b
    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 <= -7.2e+191) || !(t <= 1.5e+233)) {
		tmp = (a / z) * z;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -7.2e+191) or not (t <= 1.5e+233):
		tmp = (a / z) * z
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -7.2e+191) || !(t <= 1.5e+233))
		tmp = Float64(Float64(a / z) * z);
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -7.2e+191) || ~((t <= 1.5e+233)))
		tmp = (a / z) * z;
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -7.2e+191], N[Not[LessEqual[t, 1.5e+233]], $MachinePrecision]], N[(N[(a / z), $MachinePrecision] * z), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.1999999999999999e191 or 1.50000000000000007e233 < t

   1. Initial program 64.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

   5. Applied rewrites 41.6%

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

   6. Taylor expanded in t around inf

      \[\leadsto \frac{a}{z} \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 61.7%

      \[\leadsto \frac{a}{z} \cdot z \]

   if -7.1999999999999999e191 < t < 1.50000000000000007e233

   1. Initial program 63.0%

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

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

      2. lower-+.f64 64.1

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

   5. Applied rewrites 64.1%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+191} \lor \neg \left(t \leq 1.5 \cdot 10^{+233}\right):\\ \;\;\;\;\frac{a}{z} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+125} \lor \neg \left(b \leq 4 \cdot 10^{+92}\right):\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.9e+125) (not (<= b 4e+92))) (- a b) (+ a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.9e+125) || !(b <= 4e+92)) {
		tmp = a - b;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.9d+125)) .or. (.not. (b <= 4d+92))) then
        tmp = a - b
    else
        tmp = a + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.9e+125) || !(b <= 4e+92)) {
		tmp = a - b;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.9e+125) or not (b <= 4e+92):
		tmp = a - b
	else:
		tmp = a + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.9e+125) || !(b <= 4e+92))
		tmp = Float64(a - b);
	else
		tmp = Float64(a + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.9e+125) || ~((b <= 4e+92)))
		tmp = a - b;
	else
		tmp = a + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.9e+125], N[Not[LessEqual[b, 4e+92]], $MachinePrecision]], N[(a - b), $MachinePrecision], N[(a + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.89999999999999993e125 or 4.0000000000000002e92 < b

   1. Initial program 49.4%

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

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

      2. lower-+.f64 47.8

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

   5. Applied rewrites 47.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 43.8%

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

   if -2.89999999999999993e125 < b < 4.0000000000000002e92

   1. Initial program 70.0%

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

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

      2. lower-+.f64 63.6

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

   5. Applied rewrites 63.6%

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

   6. Taylor expanded in b around inf

      \[\leadsto -1 \cdot \color{blue}{b} \]
   7. Step-by-step derivation

   8. Applied rewrites 6.0%

      \[\leadsto -b \]

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 63.3%

       \[\leadsto a + \color{blue}{z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+125} \lor \neg \left(b \leq 4 \cdot 10^{+92}\right):\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+224} \lor \neg \left(b \leq 3.8 \cdot 10^{+146}\right):\\ \;\;\;\;-b\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.2e+224) (not (<= b 3.8e+146))) (- b) (+ a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.2e+224) || !(b <= 3.8e+146)) {
		tmp = -b;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.2d+224)) .or. (.not. (b <= 3.8d+146))) then
        tmp = -b
    else
        tmp = a + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.2e+224) || !(b <= 3.8e+146)) {
		tmp = -b;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.2e+224) or not (b <= 3.8e+146):
		tmp = -b
	else:
		tmp = a + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.2e+224) || !(b <= 3.8e+146))
		tmp = Float64(-b);
	else
		tmp = Float64(a + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.2e+224) || ~((b <= 3.8e+146)))
		tmp = -b;
	else
		tmp = a + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.2e+224], N[Not[LessEqual[b, 3.8e+146]], $MachinePrecision]], (-b), N[(a + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.2e224 or 3.79999999999999979e146 < b

   1. Initial program 43.9%

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

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

      2. lower-+.f64 42.9

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

   5. Applied rewrites 42.9%

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

   6. Taylor expanded in b around inf

      \[\leadsto -1 \cdot \color{blue}{b} \]
   7. Step-by-step derivation

   8. Applied rewrites 37.3%

      \[\leadsto -b \]

   if -2.2e224 < b < 3.79999999999999979e146

   1. Initial program 69.2%

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

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

      2. lower-+.f64 63.2

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

   5. Applied rewrites 63.2%

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

   6. Taylor expanded in b around inf

      \[\leadsto -1 \cdot \color{blue}{b} \]
   7. Step-by-step derivation

   8. Applied rewrites 8.8%

      \[\leadsto -b \]

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 60.3%

       \[\leadsto a + \color{blue}{z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+224} \lor \neg \left(b \leq 3.8 \cdot 10^{+146}\right):\\ \;\;\;\;-b\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 56.9% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+157}:\\ \;\;\;\;1 \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -5e+157) (* 1.0 z) (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5e+157) {
		tmp = 1.0 * z;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-5d+157)) then
        tmp = 1.0d0 * z
    else
        tmp = (a + z) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5e+157) {
		tmp = 1.0 * z;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -5e+157:
		tmp = 1.0 * z
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -5e+157)
		tmp = Float64(1.0 * z);
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -5e+157)
		tmp = 1.0 * z;
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -5e+157], N[(1.0 * z), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.99999999999999976e157

   1. Initial program 63.1%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

   5. Applied rewrites 77.8%

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

   6. Taylor expanded in x around inf

      \[\leadsto 1 \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 60.2%

      \[\leadsto 1 \cdot z \]

   if -4.99999999999999976e157 < x

   1. Initial program 63.2%

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

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

      2. lower-+.f64 61.5

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

   5. Applied rewrites 61.5%

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

Alternative 13: 13.5% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ -b \end{array} \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := (-b)

Derivation

1. Initial program 63.2%

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

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

   2. lower-+.f64 58.3

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

5. Applied rewrites 58.3%

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

6. Taylor expanded in b around inf

   \[\leadsto -1 \cdot \color{blue}{b} \]
7. Step-by-step derivation

8. Applied rewrites 15.6%

   \[\leadsto -b \]
9. Add Preprocessing

Developer Target 1: 82.6% 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 2025016 
(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)))