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

Percentage Accurate: 59.0% → 87.6%

Time: 7.3s

Alternatives: 14

Speedup: 1.4×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 59.0% 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: 87.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{t + y}\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_3 := {\left(t + y\right)}^{2}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\frac{y}{t\_3}, b, t\_1 - \mathsf{fma}\left(\frac{z}{t\_3}, y, \frac{a}{t + y}\right)\right), x, \mathsf{fma}\left(t\_1, y, a\right)\right) - \frac{y}{t + y} \cdot b\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+251}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ z (+ t y)))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_3 (pow (+ t y) 2.0)))
   (if (<= t_2 (- INFINITY))
     (-
      (fma
       (fma (/ y t_3) b (- t_1 (fma (/ z t_3) y (/ a (+ t y)))))
       x
       (fma t_1 y a))
      (* (/ y (+ t y)) b))
     (if (<= t_2 2e+251) t_2 (- (+ a z) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z / (t + y);
	double t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double t_3 = pow((t + y), 2.0);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = fma(fma((y / t_3), b, (t_1 - fma((z / t_3), y, (a / (t + y))))), x, fma(t_1, y, a)) - ((y / (t + y)) * b);
	} else if (t_2 <= 2e+251) {
		tmp = t_2;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z / Float64(t + y))
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	t_3 = Float64(t + y) ^ 2.0
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(fma(fma(Float64(y / t_3), b, Float64(t_1 - fma(Float64(z / t_3), y, Float64(a / Float64(t + y))))), x, fma(t_1, y, a)) - Float64(Float64(y / Float64(t + y)) * b));
	elseif (t_2 <= 2e+251)
		tmp = t_2;
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z / N[(t + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Power[N[(t + y), $MachinePrecision], 2.0], $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(N[(y / t$95$3), $MachinePrecision] * b + N[(t$95$1 - N[(N[(z / t$95$3), $MachinePrecision] * y + N[(a / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x + N[(t$95$1 * y + a), $MachinePrecision]), $MachinePrecision] - N[(N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+251], t$95$2, N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.0%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 88.0%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e251

   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

   if 2.0000000000000001e251 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.9%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 76.9

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

   5. Applied rewrites 76.9%

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

Alternative 2: 75.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) \cdot a\\ t_2 := \left(x + t\right) + y\\ t_3 := \frac{\left(\left(x + y\right) \cdot z + t\_1\right) - y \cdot b}{t\_2}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t + y}, z - b, a\right)\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+98}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, t\_1\right)}{\left(y + x\right) + t}\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+243}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, x, y \cdot \left(z - b\right)\right)}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ t y) a))
        (t_2 (+ (+ x t) y))
        (t_3 (/ (- (+ (* (+ x y) z) t_1) (* y b)) t_2)))
   (if (<= t_3 (- INFINITY))
     (fma (/ y (+ t y)) (- z b) a)
     (if (<= t_3 2e+98)
       (/ (fma (+ y x) z t_1) (+ (+ y x) t))
       (if (<= t_3 2e+243) (/ (fma z x (* y (- z b))) t_2) (- (+ a z) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) * a;
	double t_2 = (x + t) + y;
	double t_3 = ((((x + y) * z) + t_1) - (y * b)) / t_2;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = fma((y / (t + y)), (z - b), a);
	} else if (t_3 <= 2e+98) {
		tmp = fma((y + x), z, t_1) / ((y + x) + t);
	} else if (t_3 <= 2e+243) {
		tmp = fma(z, x, (y * (z - b))) / t_2;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) * a)
	t_2 = Float64(Float64(x + t) + y)
	t_3 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + t_1) - Float64(y * b)) / t_2)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = fma(Float64(y / Float64(t + y)), Float64(z - b), a);
	elseif (t_3 <= 2e+98)
		tmp = Float64(fma(Float64(y + x), z, t_1) / Float64(Float64(y + x) + t));
	elseif (t_3 <= 2e+243)
		tmp = Float64(fma(z, x, Float64(y * Float64(z - b))) / t_2);
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision] * N[(z - b), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t$95$3, 2e+98], N[(N[(N[(y + x), $MachinePrecision] * z + t$95$1), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+243], N[(N[(z * x + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 6.0%

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

   3. Taylor expanded in 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. distribute-lft-in N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. distribute-lft-in N/A

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

      9. associate--l+ N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower-+.f64 N/A

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

      15. lower-+.f64 8.2

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

   5. Applied rewrites 8.2%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 87.5%

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

   10. Applied rewrites 87.6%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2e98

   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 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 78.9

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

   5. Applied rewrites 78.9%

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

   if 2e98 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e243

   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 83.3

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

   5. Applied rewrites 83.3%

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

   if 2.0000000000000001e243 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 9.3%

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

   3. Taylor expanded in 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 76.6

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

   5. Applied rewrites 76.6%

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

Alternative 3: 88.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t + y}, z - b, a\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+251}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (<= t_1 (- INFINITY))
     (fma (/ y (+ t y)) (- z b) a)
     (if (<= t_1 2e+251) t_1 (- (+ a z) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = fma((y / (t + y)), (z - b), a);
	} else if (t_1 <= 2e+251) {
		tmp = t_1;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = fma(Float64(y / Float64(t + y)), Float64(z - b), a);
	elseif (t_1 <= 2e+251)
		tmp = t_1;
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision] * N[(z - b), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t$95$1, 2e+251], t$95$1, N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.0%

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

   3. Taylor expanded in 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. distribute-lft-in N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. distribute-lft-in N/A

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

      9. associate--l+ N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower-+.f64 N/A

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

      15. lower-+.f64 8.2

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

   5. Applied rewrites 8.2%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 87.5%

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

   10. Applied rewrites 87.6%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e251

   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

   if 2.0000000000000001e251 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.9%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 76.9

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

   5. Applied rewrites 76.9%

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

Alternative 4: 73.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-108} \lor \neg \left(y \leq 4.8 \cdot 10^{-147}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t + y}, z - b, a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9e-108) (not (<= y 4.8e-147)))
   (fma (/ y (+ t y)) (- z b) a)
   (/ (fma a t (* z x)) (+ t x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9e-108) || !(y <= 4.8e-147)) {
		tmp = fma((y / (t + y)), (z - b), a);
	} else {
		tmp = fma(a, t, (z * x)) / (t + x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9e-108) || !(y <= 4.8e-147))
		tmp = fma(Float64(y / Float64(t + y)), Float64(z - b), a);
	else
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9e-108], N[Not[LessEqual[y, 4.8e-147]], $MachinePrecision]], N[(N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision] * N[(z - b), $MachinePrecision] + a), $MachinePrecision], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.99999999999999941e-108 or 4.79999999999999997e-147 < y

   1. Initial program 55.7%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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. distribute-lft-in N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. distribute-lft-in N/A

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

      9. associate--l+ N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower-+.f64 N/A

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

      15. lower-+.f64 43.3

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

   5. Applied rewrites 43.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 76.4%

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

   10. Applied rewrites 79.2%

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

   if -8.99999999999999941e-108 < y < 4.79999999999999997e-147

   1. Initial program 82.4%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      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 67.4

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

   5. Applied rewrites 67.4%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-108} \lor \neg \left(y \leq 4.8 \cdot 10^{-147}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t + y}, z - b, a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.72 \cdot 10^{+161} \lor \neg \left(x \leq 2.9 \cdot 10^{+166}\right):\\ \;\;\;\;\frac{y + x}{t + \left(y + x\right)} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t + y}, z - b, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.72e+161) (not (<= x 2.9e+166)))
   (* (/ (+ y x) (+ t (+ y x))) z)
   (fma (/ y (+ t y)) (- z b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.72e+161) || !(x <= 2.9e+166)) {
		tmp = ((y + x) / (t + (y + x))) * z;
	} else {
		tmp = fma((y / (t + y)), (z - b), a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.72e+161) || !(x <= 2.9e+166))
		tmp = Float64(Float64(Float64(y + x) / Float64(t + Float64(y + x))) * z);
	else
		tmp = fma(Float64(y / Float64(t + y)), Float64(z - b), a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.72e+161], N[Not[LessEqual[x, 2.9e+166]], $MachinePrecision]], N[(N[(N[(y + x), $MachinePrecision] / N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision] * N[(z - b), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.71999999999999996e161 or 2.9000000000000001e166 < x

   1. Initial program 56.1%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 80.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 60.6%

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

   if -1.71999999999999996e161 < x < 2.9000000000000001e166

   1. Initial program 65.5%

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

   3. Taylor expanded in 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. distribute-lft-in N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. distribute-lft-in N/A

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

      9. associate--l+ N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower-+.f64 N/A

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

      15. lower-+.f64 46.6

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

   5. Applied rewrites 46.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 72.7%

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

   10. Applied rewrites 77.9%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.72 \cdot 10^{+161} \lor \neg \left(x \leq 2.9 \cdot 10^{+166}\right):\\ \;\;\;\;\frac{y + x}{t + \left(y + x\right)} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t + y}, z - b, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.72 \cdot 10^{+161} \lor \neg \left(x \leq 5.2 \cdot 10^{+170}\right):\\ \;\;\;\;1 \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t + y}, z - b, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.72e+161) (not (<= x 5.2e+170)))
   (* 1.0 z)
   (fma (/ y (+ t y)) (- z b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.72e+161) || !(x <= 5.2e+170)) {
		tmp = 1.0 * z;
	} else {
		tmp = fma((y / (t + y)), (z - b), a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.72e+161) || !(x <= 5.2e+170))
		tmp = Float64(1.0 * z);
	else
		tmp = fma(Float64(y / Float64(t + y)), Float64(z - b), a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.72e+161], N[Not[LessEqual[x, 5.2e+170]], $MachinePrecision]], N[(1.0 * z), $MachinePrecision], N[(N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision] * N[(z - b), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.71999999999999996e161 or 5.1999999999999996e170 < x

   1. Initial program 56.1%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 80.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 54.2%

      \[\leadsto 1 \cdot z \]

   if -1.71999999999999996e161 < x < 5.1999999999999996e170

   1. Initial program 65.5%

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

   3. Taylor expanded in 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. distribute-lft-in N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. distribute-lft-in N/A

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

      9. associate--l+ N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower-+.f64 N/A

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

      15. lower-+.f64 46.6

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

   5. Applied rewrites 46.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 72.7%

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

   10. Applied rewrites 77.9%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.72 \cdot 10^{+161} \lor \neg \left(x \leq 5.2 \cdot 10^{+170}\right):\\ \;\;\;\;1 \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t + y}, z - b, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.72 \cdot 10^{+161} \lor \neg \left(x \leq 5.2 \cdot 10^{+170}\right):\\ \;\;\;\;1 \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{t + y}, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.72e+161) (not (<= x 5.2e+170)))
   (* 1.0 z)
   (fma y (/ (- z b) (+ t y)) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.72e+161) || !(x <= 5.2e+170)) {
		tmp = 1.0 * z;
	} else {
		tmp = fma(y, ((z - b) / (t + y)), a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.72e+161) || !(x <= 5.2e+170))
		tmp = Float64(1.0 * z);
	else
		tmp = fma(y, Float64(Float64(z - b) / Float64(t + y)), a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.72e+161], N[Not[LessEqual[x, 5.2e+170]], $MachinePrecision]], N[(1.0 * z), $MachinePrecision], N[(y * N[(N[(z - b), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.71999999999999996e161 or 5.1999999999999996e170 < x

   1. Initial program 56.1%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 80.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 54.2%

      \[\leadsto 1 \cdot z \]

   if -1.71999999999999996e161 < x < 5.1999999999999996e170

   1. Initial program 65.5%

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

   3. Taylor expanded in 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. distribute-lft-in N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. distribute-lft-in N/A

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

      9. associate--l+ N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower-+.f64 N/A

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

      15. lower-+.f64 46.6

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

   5. Applied rewrites 46.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 72.7%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.72 \cdot 10^{+161} \lor \neg \left(x \leq 5.2 \cdot 10^{+170}\right):\\ \;\;\;\;1 \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{t + y}, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+132}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - b}{t}, y, a\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+96}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t + y}, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.7e+132)
   (fma (/ (- z b) t) y a)
   (if (<= t 6e+96) (- (+ a z) b) (fma y (/ z (+ t y)) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.7e+132) {
		tmp = fma(((z - b) / t), y, a);
	} else if (t <= 6e+96) {
		tmp = (a + z) - b;
	} else {
		tmp = fma(y, (z / (t + y)), a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.7e+132)
		tmp = fma(Float64(Float64(z - b) / t), y, a);
	elseif (t <= 6e+96)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = fma(y, Float64(z / Float64(t + y)), a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.7e+132], N[(N[(N[(z - b), $MachinePrecision] / t), $MachinePrecision] * y + a), $MachinePrecision], If[LessEqual[t, 6e+96], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(y * N[(z / N[(t + y), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.70000000000000013e132

   1. Initial program 57.5%

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

   3. Taylor expanded in 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. distribute-lft-in N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. distribute-lft-in N/A

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

      9. associate--l+ N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower-+.f64 N/A

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

      15. lower-+.f64 37.7

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

   5. Applied rewrites 37.7%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 73.3%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 68.2%

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

   if -1.70000000000000013e132 < t < 6.0000000000000001e96

   1. Initial program 68.2%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 60.6

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

   5. Applied rewrites 60.6%

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

   if 6.0000000000000001e96 < t

   1. Initial program 44.8%

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

   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. distribute-lft-in N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. distribute-lft-in N/A

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

      9. associate--l+ N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower-+.f64 N/A

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

      15. lower-+.f64 39.4

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

   5. Applied rewrites 39.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 82.1%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 69.9%

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

Alternative 9: 61.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+132}:\\ \;\;\;\;a \cdot \frac{t}{t + x}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+96}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t + y}, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2e+132)
   (* a (/ t (+ t x)))
   (if (<= t 6e+96) (- (+ a z) b) (fma y (/ z (+ t y)) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2e+132) {
		tmp = a * (t / (t + x));
	} else if (t <= 6e+96) {
		tmp = (a + z) - b;
	} else {
		tmp = fma(y, (z / (t + y)), a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2e+132)
		tmp = Float64(a * Float64(t / Float64(t + x)));
	elseif (t <= 6e+96)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = fma(y, Float64(z / Float64(t + y)), a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2e+132], N[(a * N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+96], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(y * N[(z / N[(t + y), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.99999999999999998e132

   1. Initial program 57.5%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 60.3

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

   5. Applied rewrites 60.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 66.4%

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

   if -1.99999999999999998e132 < t < 6.0000000000000001e96

   1. Initial program 68.2%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 60.6

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

   5. Applied rewrites 60.6%

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

   if 6.0000000000000001e96 < t

   1. Initial program 44.8%

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

   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. distribute-lft-in N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. distribute-lft-in N/A

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

      9. associate--l+ N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower-+.f64 N/A

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

      15. lower-+.f64 39.4

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

   5. Applied rewrites 39.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 82.1%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 69.9%

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

Alternative 10: 60.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+132} \lor \neg \left(t \leq 1.02 \cdot 10^{+102}\right):\\ \;\;\;\;a \cdot \frac{t}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2e+132) (not (<= t 1.02e+102)))
   (* a (/ t (+ t x)))
   (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2e+132) || !(t <= 1.02e+102)) {
		tmp = a * (t / (t + x));
	} 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 <= (-2d+132)) .or. (.not. (t <= 1.02d+102))) then
        tmp = a * (t / (t + x))
    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 <= -2e+132) || !(t <= 1.02e+102)) {
		tmp = a * (t / (t + x));
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2e+132) or not (t <= 1.02e+102):
		tmp = a * (t / (t + x))
	else:
		tmp = (a + z) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2e+132) || !(t <= 1.02e+102))
		tmp = Float64(a * Float64(t / Float64(t + x)));
	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 <= -2e+132) || ~((t <= 1.02e+102)))
		tmp = a * (t / (t + x));
	else
		tmp = (a + z) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2e+132], N[Not[LessEqual[t, 1.02e+102]], $MachinePrecision]], N[(a * N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.99999999999999998e132 or 1.01999999999999999e102 < t

   1. Initial program 50.3%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 57.1

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

   5. Applied rewrites 57.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 62.6%

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

   if -1.99999999999999998e132 < t < 1.01999999999999999e102

   1. Initial program 68.2%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 60.6

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

   5. Applied rewrites 60.6%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+132} \lor \neg \left(t \leq 1.02 \cdot 10^{+102}\right):\\ \;\;\;\;a \cdot \frac{t}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+60} \lor \neg \left(z \leq 7 \cdot 10^{+152}\right):\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.1e+60) (not (<= z 7e+152))) (- z b) (- a b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.1e+60) || !(z <= 7e+152)) {
		tmp = z - b;
	} else {
		tmp = a - 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 ((z <= (-2.1d+60)) .or. (.not. (z <= 7d+152))) then
        tmp = z - b
    else
        tmp = a - 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 ((z <= -2.1e+60) || !(z <= 7e+152)) {
		tmp = z - b;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.1e+60) or not (z <= 7e+152):
		tmp = z - b
	else:
		tmp = a - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.1e+60) || !(z <= 7e+152))
		tmp = Float64(z - b);
	else
		tmp = Float64(a - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.1e+60) || ~((z <= 7e+152)))
		tmp = z - b;
	else
		tmp = a - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.1e+60], N[Not[LessEqual[z, 7e+152]], $MachinePrecision]], N[(z - b), $MachinePrecision], N[(a - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1000000000000001e60 or 6.99999999999999963e152 < z

   1. Initial program 44.7%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 60.2

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

   5. Applied rewrites 60.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 19.2%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 60.0%

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

   if -2.1000000000000001e60 < z < 6.99999999999999963e152

   1. Initial program 73.1%

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

   3. Taylor expanded in 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 54.1

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

   5. Applied rewrites 54.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 53.0%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+60} \lor \neg \left(z \leq 7 \cdot 10^{+152}\right):\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+164}:\\ \;\;\;\;1 \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9e+164) (* 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 <= -9e+164) {
		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 <= (-9d+164)) 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 <= -9e+164) {
		tmp = 1.0 * z;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -9e+164:
		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 <= -9e+164)
		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 <= -9e+164)
		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, -9e+164], N[(1.0 * z), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.9999999999999995e164

   1. Initial program 53.9%

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

   3. Taylor expanded in 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 79.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 54.5%

      \[\leadsto 1 \cdot z \]

   if -8.9999999999999995e164 < x

   1. Initial program 64.9%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 59.5

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

   5. Applied rewrites 59.5%

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

Alternative 13: 37.8% accurate, 11.3× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return a - 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 = a - b
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 63.5%

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

3. Taylor expanded in 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 56.2

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

5. Applied rewrites 56.2%

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

6. Taylor expanded in z around 0

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

8. Applied rewrites 41.6%

   \[\leadsto a - \color{blue}{b} \]
9. Add Preprocessing

Alternative 14: 13.7% 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 63.5%

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

3. Taylor expanded in 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 56.2

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

5. Applied rewrites 56.2%

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

6. Taylor expanded in z around 0

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

8. Applied rewrites 41.6%

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

9. Taylor expanded in a around 0

   \[\leadsto -1 \cdot b \]
10. Step-by-step derivation

11. Applied rewrites 16.8%

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

Developer Target 1: 82.9% 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 2025017 
(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)))