Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, J

Percentage Accurate: 79.9% → 86.8%

Time: 8.6s

Alternatives: 21

Speedup: 0.8×

• 37.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

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, c)
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), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Initial Program: 79.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

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, c)
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), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Alternative 1: 86.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+47}:\\ \;\;\;\;\mathsf{fma}\left(\frac{9}{c}, \frac{y}{z}, \frac{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{b}{z}\right)}{c}}{x}\right) \cdot x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+112}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{c}, -4, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{t \cdot z}\right) \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -6.6e+47)
   (* (fma (/ 9.0 c) (/ y z) (/ (/ (fma (* -4.0 t) a (/ b z)) c) x)) x)
   (if (<= z 3.4e+112)
     (/ (/ (fma (* (* -4.0 z) a) t (fma (* y 9.0) x b)) c) z)
     (* (fma (/ a c) -4.0 (/ (/ (fma (* y x) 9.0 b) c) (* t z))) t))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -6.6e+47) {
		tmp = fma((9.0 / c), (y / z), ((fma((-4.0 * t), a, (b / z)) / c) / x)) * x;
	} else if (z <= 3.4e+112) {
		tmp = (fma(((-4.0 * z) * a), t, fma((y * 9.0), x, b)) / c) / z;
	} else {
		tmp = fma((a / c), -4.0, ((fma((y * x), 9.0, b) / c) / (t * z))) * t;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -6.6e+47)
		tmp = Float64(fma(Float64(9.0 / c), Float64(y / z), Float64(Float64(fma(Float64(-4.0 * t), a, Float64(b / z)) / c) / x)) * x);
	elseif (z <= 3.4e+112)
		tmp = Float64(Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * 9.0), x, b)) / c) / z);
	else
		tmp = Float64(fma(Float64(a / c), -4.0, Float64(Float64(fma(Float64(y * x), 9.0, b) / c) / Float64(t * z))) * t);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -6.6e+47], N[(N[(N[(9.0 / c), $MachinePrecision] * N[(y / z), $MachinePrecision] + N[(N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 3.4e+112], N[(N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * 9.0), $MachinePrecision] * x + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(a / c), $MachinePrecision] * -4.0 + N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / c), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5999999999999998e47

   1. Initial program 52.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(9 \cdot \frac{y}{c \cdot z} + \frac{b}{c \cdot \left(x \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot x}\right)} \]

   5. Applied rewrites 79.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{9}{c}, \frac{y}{z}, \frac{\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{b}{z}\right)}{c}}{x}\right) \cdot x} \]

   if -6.5999999999999998e47 < z < 3.39999999999999993e112

   1. Initial program 92.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{c \cdot z}} \]

      4. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

   4. Applied rewrites 96.3%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z}} \]

   if 3.39999999999999993e112 < z

   1. Initial program 51.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right) \cdot t} \]

   5. Applied rewrites 94.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{c}, -4, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{t \cdot z}\right) \cdot t} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 87.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := \frac{\mathsf{fma}\left(y \cdot 9, x, \mathsf{fma}\left(-4 \cdot z, a \cdot t, b\right)\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-207}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{\left(z \cdot a\right) \cdot c}\right) \cdot a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))
        (t_2 (/ (fma (* y 9.0) x (fma (* -4.0 z) (* a t) b)) (* z c))))
   (if (<= t_1 -5e-207)
     t_2
     (if (<= t_1 0.0)
       (/ (/ (fma (* y x) 9.0 b) z) c)
       (if (<= t_1 INFINITY)
         t_2
         (* (fma (/ t c) -4.0 (/ b (* (* z a) c))) a))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double t_2 = fma((y * 9.0), x, fma((-4.0 * z), (a * t), b)) / (z * c);
	double tmp;
	if (t_1 <= -5e-207) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = (fma((y * x), 9.0, b) / z) / c;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = fma((t / c), -4.0, (b / ((z * a) * c))) * a;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	t_2 = Float64(fma(Float64(y * 9.0), x, fma(Float64(-4.0 * z), Float64(a * t), b)) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -5e-207)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(fma(Float64(y * x), 9.0, b) / z) / c);
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(fma(Float64(t / c), -4.0, Float64(b / Float64(Float64(z * a) * c))) * a);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * 9.0), $MachinePrecision] * x + N[(N[(-4.0 * z), $MachinePrecision] * N[(a * t), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-207], t$95$2, If[LessEqual[t$95$1, 0.0], N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$2, N[(N[(N[(t / c), $MachinePrecision] * -4.0 + N[(b / N[(N[(z * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -5.00000000000000014e-207 or -0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 89.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z \cdot c} \]

      2. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}{z \cdot c} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

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

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a\right)} + b}{z \cdot c} \]

      5. associate-+l+ N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y + \left(\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}}{z \cdot c} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y} + \left(\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}{z \cdot c} \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right)} \cdot y + \left(\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}{z \cdot c} \]

      8. associate-*l* N/A

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + \left(\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}{z \cdot c} \]

      9. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x} + \left(\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}{z \cdot c} \]

      10. lower-fma.f64 N/A

          \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(9 \cdot y, x, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}}{z \cdot c} \]

      11. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot 9}, x, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}{z \cdot c} \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot 9}, x, \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}{z \cdot c} \]

      13. lift-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y \cdot 9, x, \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 4\right) \cdot t}\right)\right) \cdot a + b\right)}{z \cdot c} \]

      14. distribute-lft-neg-in N/A

          \[\leadsto \frac{\mathsf{fma}\left(y \cdot 9, x, \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot t\right)} \cdot a + b\right)}{z \cdot c} \]

      15. associate-*r* N/A

          \[\leadsto \frac{\mathsf{fma}\left(y \cdot 9, x, \color{blue}{\left(\mathsf{neg}\left(z \cdot 4\right)\right) \cdot \left(t \cdot a\right)} + b\right)}{z \cdot c} \]

      16. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(y \cdot 9, x, \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(z \cdot 4\right), t \cdot a, b\right)}\right)}{z \cdot c} \]

   4. Applied rewrites 89.7%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y \cdot 9, x, \mathsf{fma}\left(-4 \cdot z, a \cdot t, b\right)\right)}}{z \cdot c} \]

   if -5.00000000000000014e-207 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -0.0

   1. Initial program 34.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

         \[\leadsto \frac{b + 9 \cdot \left(x \cdot y\right)}{\color{blue}{z \cdot c}} \]

      2. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c}} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}}{c} \]

      5. +-commutative N/A

         \[\leadsto \frac{\frac{\color{blue}{9 \cdot \left(x \cdot y\right) + b}}{z}}{c} \]

      6. *-commutative N/A

         \[\leadsto \frac{\frac{\color{blue}{\left(x \cdot y\right) \cdot 9} + b}{z}}{c} \]

      7. lower-fma.f64 N/A

         \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(x \cdot y, 9, b\right)}}{z}}{c} \]

      8. *-commutative N/A

         \[\leadsto \frac{\frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, b\right)}{z}}{c} \]

      9. lower-*.f64 85.6

         \[\leadsto \frac{\frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, b\right)}{z}}{c} \]

   5. Applied rewrites 85.6%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z}}{c}} \]

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 52.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{c}, -4, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{a}}{c \cdot z}\right) \cdot a} \]

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{a \cdot \left(c \cdot z\right)}\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 69.0%

      \[\leadsto \mathsf{fma}\left(\frac{t}{c}, -4, \frac{\frac{b}{c \cdot z}}{a}\right) \cdot a \]
   9. Step-by-step derivation

   10. Applied rewrites 69.0%

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

Alternative 3: 87.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-318}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \mathsf{fma}\left(x, 9 \cdot y, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{\left(z \cdot a\right) \cdot c}\right) \cdot a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))))
   (if (<= t_1 -5e-318)
     t_1
     (if (<= t_1 INFINITY)
       (/ (/ (fma (* (* t a) z) -4.0 (fma x (* 9.0 y) b)) c) z)
       (* (fma (/ t c) -4.0 (/ b (* (* z a) c))) a)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_1 <= -5e-318) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (fma(((t * a) * z), -4.0, fma(x, (9.0 * y), b)) / c) / z;
	} else {
		tmp = fma((t / c), -4.0, (b / ((z * a) * c))) * a;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -5e-318)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(fma(Float64(Float64(t * a) * z), -4.0, fma(x, Float64(9.0 * y), b)) / c) / z);
	else
		tmp = Float64(fma(Float64(t / c), -4.0, Float64(b / Float64(Float64(z * a) * c))) * a);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-318], t$95$1, If[LessEqual[t$95$1, Infinity], N[(N[(N[(N[(N[(t * a), $MachinePrecision] * z), $MachinePrecision] * -4.0 + N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(t / c), $MachinePrecision] * -4.0 + N[(b / N[(N[(z * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -4.9999987e-318

   1. Initial program 89.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   if -4.9999987e-318 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 80.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{c \cdot z}} \]

      4. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

   4. Applied rewrites 86.4%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z}} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \frac{\frac{\color{blue}{\left(\left(-4 \cdot z\right) \cdot a\right) \cdot t + \mathsf{fma}\left(y \cdot 9, x, b\right)}}{c}}{z} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\color{blue}{\left(\left(-4 \cdot z\right) \cdot a\right)} \cdot t + \mathsf{fma}\left(y \cdot 9, x, b\right)}{c}}{z} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\frac{\color{blue}{\left(-4 \cdot z\right) \cdot \left(a \cdot t\right)} + \mathsf{fma}\left(y \cdot 9, x, b\right)}{c}}{z} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\left(-4 \cdot z\right) \cdot \color{blue}{\left(a \cdot t\right)} + \mathsf{fma}\left(y \cdot 9, x, b\right)}{c}}{z} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\color{blue}{\left(-4 \cdot z\right)} \cdot \left(a \cdot t\right) + \mathsf{fma}\left(y \cdot 9, x, b\right)}{c}}{z} \]

      6. associate-*l* N/A

         \[\leadsto \frac{\frac{\color{blue}{-4 \cdot \left(z \cdot \left(a \cdot t\right)\right)} + \mathsf{fma}\left(y \cdot 9, x, b\right)}{c}}{z} \]

      7. *-commutative N/A

         \[\leadsto \frac{\frac{\color{blue}{\left(z \cdot \left(a \cdot t\right)\right) \cdot -4} + \mathsf{fma}\left(y \cdot 9, x, b\right)}{c}}{z} \]

      8. lower-fma.f64 N/A

         \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(z \cdot \left(a \cdot t\right), -4, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}}{c}}{z} \]

      9. *-commutative N/A

         \[\leadsto \frac{\frac{\mathsf{fma}\left(\color{blue}{\left(a \cdot t\right) \cdot z}, -4, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z} \]

      10. lower-*.f64 90.9

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\color{blue}{\left(a \cdot t\right) \cdot z}, -4, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z} \]

      11. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\color{blue}{\left(a \cdot t\right)} \cdot z, -4, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z} \]

      12. *-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\color{blue}{\left(t \cdot a\right)} \cdot z, -4, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z} \]

      13. lower-*.f64 90.9

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\color{blue}{\left(t \cdot a\right)} \cdot z, -4, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z} \]

      14. lift-fma.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \color{blue}{\left(y \cdot 9\right) \cdot x + b}\right)}{c}}{z} \]

      15. +-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \color{blue}{b + \left(y \cdot 9\right) \cdot x}\right)}{c}}{z} \]

      16. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, b + \color{blue}{\left(y \cdot 9\right)} \cdot x\right)}{c}}{z} \]

      17. associate-*l* N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, b + \color{blue}{y \cdot \left(9 \cdot x\right)}\right)}{c}}{z} \]

      18. *-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, b + y \cdot \color{blue}{\left(x \cdot 9\right)}\right)}{c}}{z} \]

      19. associate-*l* N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, b + \color{blue}{\left(y \cdot x\right) \cdot 9}\right)}{c}}{z} \]

      20. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, b + \color{blue}{\left(y \cdot x\right)} \cdot 9\right)}{c}}{z} \]

      21. +-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \color{blue}{\left(y \cdot x\right) \cdot 9 + b}\right)}{c}}{z} \]

      22. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \color{blue}{\left(y \cdot x\right)} \cdot 9 + b\right)}{c}}{z} \]

      23. associate-*l* N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \color{blue}{y \cdot \left(x \cdot 9\right)} + b\right)}{c}}{z} \]

      24. *-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, y \cdot \color{blue}{\left(9 \cdot x\right)} + b\right)}{c}}{z} \]

      25. associate-*l* N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \color{blue}{\left(y \cdot 9\right) \cdot x} + b\right)}{c}}{z} \]

      26. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \color{blue}{\left(y \cdot 9\right)} \cdot x + b\right)}{c}}{z} \]

      27. *-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \color{blue}{x \cdot \left(y \cdot 9\right)} + b\right)}{c}}{z} \]

   6. Applied rewrites 90.9%

      \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \mathsf{fma}\left(x, 9 \cdot y, b\right)\right)}}{c}}{z} \]

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 52.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{c}, -4, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{a}}{c \cdot z}\right) \cdot a} \]

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{a \cdot \left(c \cdot z\right)}\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 69.0%

      \[\leadsto \mathsf{fma}\left(\frac{t}{c}, -4, \frac{\frac{b}{c \cdot z}}{a}\right) \cdot a \]
   9. Step-by-step derivation

   10. Applied rewrites 69.0%

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

Alternative 4: 53.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := -4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{+116}:\\ \;\;\;\;\left(x \cdot 9\right) \cdot \frac{y}{c \cdot z}\\ \mathbf{elif}\;t\_3 \leq -1 \cdot 10^{-39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{-189}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 10^{-300}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{-220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+100}:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{9}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ b c) z)) (t_2 (* -4.0 (/ (* a t) c))) (t_3 (* (* x 9.0) y)))
   (if (<= t_3 -2e+116)
     (* (* x 9.0) (/ y (* c z)))
     (if (<= t_3 -1e-39)
       t_2
       (if (<= t_3 -2e-189)
         t_1
         (if (<= t_3 1e-300)
           t_2
           (if (<= t_3 2e-220)
             t_1
             (if (<= t_3 5e+100)
               (* (* (/ t c) -4.0) a)
               (* (* x y) (/ 9.0 (* c z)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double t_2 = -4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double tmp;
	if (t_3 <= -2e+116) {
		tmp = (x * 9.0) * (y / (c * z));
	} else if (t_3 <= -1e-39) {
		tmp = t_2;
	} else if (t_3 <= -2e-189) {
		tmp = t_1;
	} else if (t_3 <= 1e-300) {
		tmp = t_2;
	} else if (t_3 <= 2e-220) {
		tmp = t_1;
	} else if (t_3 <= 5e+100) {
		tmp = ((t / c) * -4.0) * a;
	} else {
		tmp = (x * y) * (9.0 / (c * z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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, c)
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), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (b / c) / z
    t_2 = (-4.0d0) * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    if (t_3 <= (-2d+116)) then
        tmp = (x * 9.0d0) * (y / (c * z))
    else if (t_3 <= (-1d-39)) then
        tmp = t_2
    else if (t_3 <= (-2d-189)) then
        tmp = t_1
    else if (t_3 <= 1d-300) then
        tmp = t_2
    else if (t_3 <= 2d-220) then
        tmp = t_1
    else if (t_3 <= 5d+100) then
        tmp = ((t / c) * (-4.0d0)) * a
    else
        tmp = (x * y) * (9.0d0 / (c * z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double t_2 = -4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double tmp;
	if (t_3 <= -2e+116) {
		tmp = (x * 9.0) * (y / (c * z));
	} else if (t_3 <= -1e-39) {
		tmp = t_2;
	} else if (t_3 <= -2e-189) {
		tmp = t_1;
	} else if (t_3 <= 1e-300) {
		tmp = t_2;
	} else if (t_3 <= 2e-220) {
		tmp = t_1;
	} else if (t_3 <= 5e+100) {
		tmp = ((t / c) * -4.0) * a;
	} else {
		tmp = (x * y) * (9.0 / (c * z));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (b / c) / z
	t_2 = -4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	tmp = 0
	if t_3 <= -2e+116:
		tmp = (x * 9.0) * (y / (c * z))
	elif t_3 <= -1e-39:
		tmp = t_2
	elif t_3 <= -2e-189:
		tmp = t_1
	elif t_3 <= 1e-300:
		tmp = t_2
	elif t_3 <= 2e-220:
		tmp = t_1
	elif t_3 <= 5e+100:
		tmp = ((t / c) * -4.0) * a
	else:
		tmp = (x * y) * (9.0 / (c * z))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b / c) / z)
	t_2 = Float64(-4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_3 <= -2e+116)
		tmp = Float64(Float64(x * 9.0) * Float64(y / Float64(c * z)));
	elseif (t_3 <= -1e-39)
		tmp = t_2;
	elseif (t_3 <= -2e-189)
		tmp = t_1;
	elseif (t_3 <= 1e-300)
		tmp = t_2;
	elseif (t_3 <= 2e-220)
		tmp = t_1;
	elseif (t_3 <= 5e+100)
		tmp = Float64(Float64(Float64(t / c) * -4.0) * a);
	else
		tmp = Float64(Float64(x * y) * Float64(9.0 / Float64(c * z)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b / c) / z;
	t_2 = -4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	tmp = 0.0;
	if (t_3 <= -2e+116)
		tmp = (x * 9.0) * (y / (c * z));
	elseif (t_3 <= -1e-39)
		tmp = t_2;
	elseif (t_3 <= -2e-189)
		tmp = t_1;
	elseif (t_3 <= 1e-300)
		tmp = t_2;
	elseif (t_3 <= 2e-220)
		tmp = t_1;
	elseif (t_3 <= 5e+100)
		tmp = ((t / c) * -4.0) * a;
	else
		tmp = (x * y) * (9.0 / (c * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$3, -2e+116], N[(N[(x * 9.0), $MachinePrecision] * N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -1e-39], t$95$2, If[LessEqual[t$95$3, -2e-189], t$95$1, If[LessEqual[t$95$3, 1e-300], t$95$2, If[LessEqual[t$95$3, 2e-220], t$95$1, If[LessEqual[t$95$3, 5e+100], N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision], N[(N[(x * y), $MachinePrecision] * N[(9.0 / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.00000000000000003e116

   1. Initial program 78.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{9 \cdot \color{blue}{\left(y \cdot x\right)}}{c \cdot z} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{c \cdot z} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{9 \cdot y}{c} \cdot \frac{x}{z}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{9 \cdot y}{c} \cdot \frac{x}{z}} \]

      6. associate-*r/ N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c}\right)} \cdot \frac{x}{z} \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c}\right)} \cdot \frac{x}{z} \]

      8. lower-/.f64 N/A

         \[\leadsto \left(9 \cdot \color{blue}{\frac{y}{c}}\right) \cdot \frac{x}{z} \]

      9. lower-/.f64 83.3

         \[\leadsto \left(9 \cdot \frac{y}{c}\right) \cdot \color{blue}{\frac{x}{z}} \]

   5. Applied rewrites 83.3%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 80.1%

      \[\leadsto \left(x \cdot 9\right) \cdot \color{blue}{\frac{y}{c \cdot z}} \]

   if -2.00000000000000003e116 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999929e-40 or -2.00000000000000014e-189 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.00000000000000003e-300

   1. Initial program 75.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

      2. lower-/.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\frac{a \cdot t}{c}} \]

      3. lower-*.f64 63.3

         \[\leadsto -4 \cdot \frac{\color{blue}{a \cdot t}}{c} \]

   5. Applied rewrites 63.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

   if -9.99999999999999929e-40 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.00000000000000014e-189 or 1.00000000000000003e-300 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999998e-220

   1. Initial program 78.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{c \cdot z}} \]

      4. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

   4. Applied rewrites 94.7%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z}} \]

   5. Taylor expanded in b around inf

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

      1. lower-/.f64 77.7

         \[\leadsto \frac{\color{blue}{\frac{b}{c}}}{z} \]

   7. Applied rewrites 77.7%

      \[\leadsto \frac{\color{blue}{\frac{b}{c}}}{z} \]

   if 1.99999999999999998e-220 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999999e100

   1. Initial program 77.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 77.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{c}, -4, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{a}}{c \cdot z}\right) \cdot a} \]

   6. Taylor expanded in z around inf

      \[\leadsto \left(-4 \cdot \frac{t}{c}\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 55.2%

      \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]

   if 4.9999999999999999e100 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 83.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{9 \cdot \color{blue}{\left(y \cdot x\right)}}{c \cdot z} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{c \cdot z} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{9 \cdot y}{c} \cdot \frac{x}{z}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{9 \cdot y}{c} \cdot \frac{x}{z}} \]

      6. associate-*r/ N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c}\right)} \cdot \frac{x}{z} \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c}\right)} \cdot \frac{x}{z} \]

      8. lower-/.f64 N/A

         \[\leadsto \left(9 \cdot \color{blue}{\frac{y}{c}}\right) \cdot \frac{x}{z} \]

      9. lower-/.f64 65.6

         \[\leadsto \left(9 \cdot \frac{y}{c}\right) \cdot \color{blue}{\frac{x}{z}} \]

   5. Applied rewrites 65.6%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 65.4%

      \[\leadsto \left(x \cdot y\right) \cdot \color{blue}{\frac{9}{c \cdot z}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 5: 54.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := -4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{+116}:\\ \;\;\;\;\left(x \cdot 9\right) \cdot \frac{y}{c \cdot z}\\ \mathbf{elif}\;t\_3 \leq -1 \cdot 10^{-39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{-189}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 10^{-300}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{-220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+100}:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot y\right) \cdot \frac{x}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ b c) z)) (t_2 (* -4.0 (/ (* a t) c))) (t_3 (* (* x 9.0) y)))
   (if (<= t_3 -2e+116)
     (* (* x 9.0) (/ y (* c z)))
     (if (<= t_3 -1e-39)
       t_2
       (if (<= t_3 -2e-189)
         t_1
         (if (<= t_3 1e-300)
           t_2
           (if (<= t_3 2e-220)
             t_1
             (if (<= t_3 5e+100)
               (* (* (/ t c) -4.0) a)
               (* (* 9.0 y) (/ x (* c z)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double t_2 = -4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double tmp;
	if (t_3 <= -2e+116) {
		tmp = (x * 9.0) * (y / (c * z));
	} else if (t_3 <= -1e-39) {
		tmp = t_2;
	} else if (t_3 <= -2e-189) {
		tmp = t_1;
	} else if (t_3 <= 1e-300) {
		tmp = t_2;
	} else if (t_3 <= 2e-220) {
		tmp = t_1;
	} else if (t_3 <= 5e+100) {
		tmp = ((t / c) * -4.0) * a;
	} else {
		tmp = (9.0 * y) * (x / (c * z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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, c)
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), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (b / c) / z
    t_2 = (-4.0d0) * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    if (t_3 <= (-2d+116)) then
        tmp = (x * 9.0d0) * (y / (c * z))
    else if (t_3 <= (-1d-39)) then
        tmp = t_2
    else if (t_3 <= (-2d-189)) then
        tmp = t_1
    else if (t_3 <= 1d-300) then
        tmp = t_2
    else if (t_3 <= 2d-220) then
        tmp = t_1
    else if (t_3 <= 5d+100) then
        tmp = ((t / c) * (-4.0d0)) * a
    else
        tmp = (9.0d0 * y) * (x / (c * z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double t_2 = -4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double tmp;
	if (t_3 <= -2e+116) {
		tmp = (x * 9.0) * (y / (c * z));
	} else if (t_3 <= -1e-39) {
		tmp = t_2;
	} else if (t_3 <= -2e-189) {
		tmp = t_1;
	} else if (t_3 <= 1e-300) {
		tmp = t_2;
	} else if (t_3 <= 2e-220) {
		tmp = t_1;
	} else if (t_3 <= 5e+100) {
		tmp = ((t / c) * -4.0) * a;
	} else {
		tmp = (9.0 * y) * (x / (c * z));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (b / c) / z
	t_2 = -4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	tmp = 0
	if t_3 <= -2e+116:
		tmp = (x * 9.0) * (y / (c * z))
	elif t_3 <= -1e-39:
		tmp = t_2
	elif t_3 <= -2e-189:
		tmp = t_1
	elif t_3 <= 1e-300:
		tmp = t_2
	elif t_3 <= 2e-220:
		tmp = t_1
	elif t_3 <= 5e+100:
		tmp = ((t / c) * -4.0) * a
	else:
		tmp = (9.0 * y) * (x / (c * z))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b / c) / z)
	t_2 = Float64(-4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_3 <= -2e+116)
		tmp = Float64(Float64(x * 9.0) * Float64(y / Float64(c * z)));
	elseif (t_3 <= -1e-39)
		tmp = t_2;
	elseif (t_3 <= -2e-189)
		tmp = t_1;
	elseif (t_3 <= 1e-300)
		tmp = t_2;
	elseif (t_3 <= 2e-220)
		tmp = t_1;
	elseif (t_3 <= 5e+100)
		tmp = Float64(Float64(Float64(t / c) * -4.0) * a);
	else
		tmp = Float64(Float64(9.0 * y) * Float64(x / Float64(c * z)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b / c) / z;
	t_2 = -4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	tmp = 0.0;
	if (t_3 <= -2e+116)
		tmp = (x * 9.0) * (y / (c * z));
	elseif (t_3 <= -1e-39)
		tmp = t_2;
	elseif (t_3 <= -2e-189)
		tmp = t_1;
	elseif (t_3 <= 1e-300)
		tmp = t_2;
	elseif (t_3 <= 2e-220)
		tmp = t_1;
	elseif (t_3 <= 5e+100)
		tmp = ((t / c) * -4.0) * a;
	else
		tmp = (9.0 * y) * (x / (c * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$3, -2e+116], N[(N[(x * 9.0), $MachinePrecision] * N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -1e-39], t$95$2, If[LessEqual[t$95$3, -2e-189], t$95$1, If[LessEqual[t$95$3, 1e-300], t$95$2, If[LessEqual[t$95$3, 2e-220], t$95$1, If[LessEqual[t$95$3, 5e+100], N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision], N[(N[(9.0 * y), $MachinePrecision] * N[(x / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.00000000000000003e116

   1. Initial program 78.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{9 \cdot \color{blue}{\left(y \cdot x\right)}}{c \cdot z} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{c \cdot z} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{9 \cdot y}{c} \cdot \frac{x}{z}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{9 \cdot y}{c} \cdot \frac{x}{z}} \]

      6. associate-*r/ N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c}\right)} \cdot \frac{x}{z} \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c}\right)} \cdot \frac{x}{z} \]

      8. lower-/.f64 N/A

         \[\leadsto \left(9 \cdot \color{blue}{\frac{y}{c}}\right) \cdot \frac{x}{z} \]

      9. lower-/.f64 83.3

         \[\leadsto \left(9 \cdot \frac{y}{c}\right) \cdot \color{blue}{\frac{x}{z}} \]

   5. Applied rewrites 83.3%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 80.1%

      \[\leadsto \left(x \cdot 9\right) \cdot \color{blue}{\frac{y}{c \cdot z}} \]

   if -2.00000000000000003e116 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999929e-40 or -2.00000000000000014e-189 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.00000000000000003e-300

   1. Initial program 75.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

      2. lower-/.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\frac{a \cdot t}{c}} \]

      3. lower-*.f64 63.3

         \[\leadsto -4 \cdot \frac{\color{blue}{a \cdot t}}{c} \]

   5. Applied rewrites 63.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

   if -9.99999999999999929e-40 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.00000000000000014e-189 or 1.00000000000000003e-300 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999998e-220

   1. Initial program 78.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{c \cdot z}} \]

      4. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

   4. Applied rewrites 94.7%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z}} \]

   5. Taylor expanded in b around inf

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

      1. lower-/.f64 77.7

         \[\leadsto \frac{\color{blue}{\frac{b}{c}}}{z} \]

   7. Applied rewrites 77.7%

      \[\leadsto \frac{\color{blue}{\frac{b}{c}}}{z} \]

   if 1.99999999999999998e-220 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999999e100

   1. Initial program 77.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 77.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{c}, -4, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{a}}{c \cdot z}\right) \cdot a} \]

   6. Taylor expanded in z around inf

      \[\leadsto \left(-4 \cdot \frac{t}{c}\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 55.2%

      \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]

   if 4.9999999999999999e100 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 83.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{9 \cdot \color{blue}{\left(y \cdot x\right)}}{c \cdot z} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{c \cdot z} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{9 \cdot y}{c} \cdot \frac{x}{z}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{9 \cdot y}{c} \cdot \frac{x}{z}} \]

      6. associate-*r/ N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c}\right)} \cdot \frac{x}{z} \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c}\right)} \cdot \frac{x}{z} \]

      8. lower-/.f64 N/A

         \[\leadsto \left(9 \cdot \color{blue}{\frac{y}{c}}\right) \cdot \frac{x}{z} \]

      9. lower-/.f64 65.6

         \[\leadsto \left(9 \cdot \frac{y}{c}\right) \cdot \color{blue}{\frac{x}{z}} \]

   5. Applied rewrites 65.6%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 64.5%

      \[\leadsto \left(9 \cdot y\right) \cdot \color{blue}{\frac{x}{c \cdot z}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 6: 54.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := -4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(9 \cdot y\right) \cdot \frac{x}{c \cdot z}\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{+116}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq -1 \cdot 10^{-39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{-189}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 10^{-300}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{-220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+100}:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ b c) z))
        (t_2 (* -4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (* (* 9.0 y) (/ x (* c z)))))
   (if (<= t_3 -2e+116)
     t_4
     (if (<= t_3 -1e-39)
       t_2
       (if (<= t_3 -2e-189)
         t_1
         (if (<= t_3 1e-300)
           t_2
           (if (<= t_3 2e-220)
             t_1
             (if (<= t_3 5e+100) (* (* (/ t c) -4.0) a) t_4))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double t_2 = -4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (9.0 * y) * (x / (c * z));
	double tmp;
	if (t_3 <= -2e+116) {
		tmp = t_4;
	} else if (t_3 <= -1e-39) {
		tmp = t_2;
	} else if (t_3 <= -2e-189) {
		tmp = t_1;
	} else if (t_3 <= 1e-300) {
		tmp = t_2;
	} else if (t_3 <= 2e-220) {
		tmp = t_1;
	} else if (t_3 <= 5e+100) {
		tmp = ((t / c) * -4.0) * a;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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, c)
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), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (b / c) / z
    t_2 = (-4.0d0) * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (9.0d0 * y) * (x / (c * z))
    if (t_3 <= (-2d+116)) then
        tmp = t_4
    else if (t_3 <= (-1d-39)) then
        tmp = t_2
    else if (t_3 <= (-2d-189)) then
        tmp = t_1
    else if (t_3 <= 1d-300) then
        tmp = t_2
    else if (t_3 <= 2d-220) then
        tmp = t_1
    else if (t_3 <= 5d+100) then
        tmp = ((t / c) * (-4.0d0)) * a
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double t_2 = -4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (9.0 * y) * (x / (c * z));
	double tmp;
	if (t_3 <= -2e+116) {
		tmp = t_4;
	} else if (t_3 <= -1e-39) {
		tmp = t_2;
	} else if (t_3 <= -2e-189) {
		tmp = t_1;
	} else if (t_3 <= 1e-300) {
		tmp = t_2;
	} else if (t_3 <= 2e-220) {
		tmp = t_1;
	} else if (t_3 <= 5e+100) {
		tmp = ((t / c) * -4.0) * a;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (b / c) / z
	t_2 = -4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (9.0 * y) * (x / (c * z))
	tmp = 0
	if t_3 <= -2e+116:
		tmp = t_4
	elif t_3 <= -1e-39:
		tmp = t_2
	elif t_3 <= -2e-189:
		tmp = t_1
	elif t_3 <= 1e-300:
		tmp = t_2
	elif t_3 <= 2e-220:
		tmp = t_1
	elif t_3 <= 5e+100:
		tmp = ((t / c) * -4.0) * a
	else:
		tmp = t_4
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b / c) / z)
	t_2 = Float64(-4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(9.0 * y) * Float64(x / Float64(c * z)))
	tmp = 0.0
	if (t_3 <= -2e+116)
		tmp = t_4;
	elseif (t_3 <= -1e-39)
		tmp = t_2;
	elseif (t_3 <= -2e-189)
		tmp = t_1;
	elseif (t_3 <= 1e-300)
		tmp = t_2;
	elseif (t_3 <= 2e-220)
		tmp = t_1;
	elseif (t_3 <= 5e+100)
		tmp = Float64(Float64(Float64(t / c) * -4.0) * a);
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b / c) / z;
	t_2 = -4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (9.0 * y) * (x / (c * z));
	tmp = 0.0;
	if (t_3 <= -2e+116)
		tmp = t_4;
	elseif (t_3 <= -1e-39)
		tmp = t_2;
	elseif (t_3 <= -2e-189)
		tmp = t_1;
	elseif (t_3 <= 1e-300)
		tmp = t_2;
	elseif (t_3 <= 2e-220)
		tmp = t_1;
	elseif (t_3 <= 5e+100)
		tmp = ((t / c) * -4.0) * a;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(9.0 * y), $MachinePrecision] * N[(x / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -2e+116], t$95$4, If[LessEqual[t$95$3, -1e-39], t$95$2, If[LessEqual[t$95$3, -2e-189], t$95$1, If[LessEqual[t$95$3, 1e-300], t$95$2, If[LessEqual[t$95$3, 2e-220], t$95$1, If[LessEqual[t$95$3, 5e+100], N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision], t$95$4]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.00000000000000003e116 or 4.9999999999999999e100 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 80.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{9 \cdot \color{blue}{\left(y \cdot x\right)}}{c \cdot z} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{c \cdot z} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{9 \cdot y}{c} \cdot \frac{x}{z}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{9 \cdot y}{c} \cdot \frac{x}{z}} \]

      6. associate-*r/ N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c}\right)} \cdot \frac{x}{z} \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c}\right)} \cdot \frac{x}{z} \]

      8. lower-/.f64 N/A

         \[\leadsto \left(9 \cdot \color{blue}{\frac{y}{c}}\right) \cdot \frac{x}{z} \]

      9. lower-/.f64 75.1

         \[\leadsto \left(9 \cdot \frac{y}{c}\right) \cdot \color{blue}{\frac{x}{z}} \]

   5. Applied rewrites 75.1%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 72.9%

      \[\leadsto \left(9 \cdot y\right) \cdot \color{blue}{\frac{x}{c \cdot z}} \]

   if -2.00000000000000003e116 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999929e-40 or -2.00000000000000014e-189 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.00000000000000003e-300

   1. Initial program 75.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

      2. lower-/.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\frac{a \cdot t}{c}} \]

      3. lower-*.f64 63.3

         \[\leadsto -4 \cdot \frac{\color{blue}{a \cdot t}}{c} \]

   5. Applied rewrites 63.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

   if -9.99999999999999929e-40 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.00000000000000014e-189 or 1.00000000000000003e-300 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.99999999999999998e-220

   1. Initial program 78.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{c \cdot z}} \]

      4. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

   4. Applied rewrites 94.7%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z}} \]

   5. Taylor expanded in b around inf

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

      1. lower-/.f64 77.7

         \[\leadsto \frac{\color{blue}{\frac{b}{c}}}{z} \]

   7. Applied rewrites 77.7%

      \[\leadsto \frac{\color{blue}{\frac{b}{c}}}{z} \]

   if 1.99999999999999998e-220 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999999e100

   1. Initial program 77.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 77.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{c}, -4, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{a}}{c \cdot z}\right) \cdot a} \]

   6. Taylor expanded in z around inf

      \[\leadsto \left(-4 \cdot \frac{t}{c}\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 55.2%

      \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 7: 85.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y \cdot x, 9, b\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+158}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{c}, -4, \frac{t\_1}{\left(z \cdot t\right) \cdot c}\right) \cdot t\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-23}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{9 \cdot x}{c \cdot z}, \frac{\mathsf{fma}\left(-4 \cdot z, a \cdot t, b\right)}{c \cdot z}\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+112}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{c}, -4, \frac{\frac{t\_1}{c}}{t \cdot z}\right) \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (fma (* y x) 9.0 b)))
   (if (<= z -6.5e+158)
     (* (fma (/ a c) -4.0 (/ t_1 (* (* z t) c))) t)
     (if (<= z -1.8e-23)
       (fma y (/ (* 9.0 x) (* c z)) (/ (fma (* -4.0 z) (* a t) b) (* c z)))
       (if (<= z 3.4e+112)
         (/ (/ (fma (* (* -4.0 z) a) t (fma (* y 9.0) x b)) c) z)
         (* (fma (/ a c) -4.0 (/ (/ t_1 c) (* t z))) t))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((y * x), 9.0, b);
	double tmp;
	if (z <= -6.5e+158) {
		tmp = fma((a / c), -4.0, (t_1 / ((z * t) * c))) * t;
	} else if (z <= -1.8e-23) {
		tmp = fma(y, ((9.0 * x) / (c * z)), (fma((-4.0 * z), (a * t), b) / (c * z)));
	} else if (z <= 3.4e+112) {
		tmp = (fma(((-4.0 * z) * a), t, fma((y * 9.0), x, b)) / c) / z;
	} else {
		tmp = fma((a / c), -4.0, ((t_1 / c) / (t * z))) * t;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = fma(Float64(y * x), 9.0, b)
	tmp = 0.0
	if (z <= -6.5e+158)
		tmp = Float64(fma(Float64(a / c), -4.0, Float64(t_1 / Float64(Float64(z * t) * c))) * t);
	elseif (z <= -1.8e-23)
		tmp = fma(y, Float64(Float64(9.0 * x) / Float64(c * z)), Float64(fma(Float64(-4.0 * z), Float64(a * t), b) / Float64(c * z)));
	elseif (z <= 3.4e+112)
		tmp = Float64(Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * 9.0), x, b)) / c) / z);
	else
		tmp = Float64(fma(Float64(a / c), -4.0, Float64(Float64(t_1 / c) / Float64(t * z))) * t);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]}, If[LessEqual[z, -6.5e+158], N[(N[(N[(a / c), $MachinePrecision] * -4.0 + N[(t$95$1 / N[(N[(z * t), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, -1.8e-23], N[(y * N[(N[(9.0 * x), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(-4.0 * z), $MachinePrecision] * N[(a * t), $MachinePrecision] + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e+112], N[(N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * 9.0), $MachinePrecision] * x + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(a / c), $MachinePrecision] * -4.0 + N[(N[(t$95$1 / c), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.5000000000000001e158

   1. Initial program 44.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{c \cdot z}} \]

      4. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

   4. Applied rewrites 45.7%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z}} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \frac{\frac{\color{blue}{\left(\left(-4 \cdot z\right) \cdot a\right) \cdot t + \mathsf{fma}\left(y \cdot 9, x, b\right)}}{c}}{z} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\color{blue}{\left(\left(-4 \cdot z\right) \cdot a\right)} \cdot t + \mathsf{fma}\left(y \cdot 9, x, b\right)}{c}}{z} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\frac{\color{blue}{\left(-4 \cdot z\right) \cdot \left(a \cdot t\right)} + \mathsf{fma}\left(y \cdot 9, x, b\right)}{c}}{z} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\left(-4 \cdot z\right) \cdot \color{blue}{\left(a \cdot t\right)} + \mathsf{fma}\left(y \cdot 9, x, b\right)}{c}}{z} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\color{blue}{\left(-4 \cdot z\right)} \cdot \left(a \cdot t\right) + \mathsf{fma}\left(y \cdot 9, x, b\right)}{c}}{z} \]

      6. associate-*l* N/A

         \[\leadsto \frac{\frac{\color{blue}{-4 \cdot \left(z \cdot \left(a \cdot t\right)\right)} + \mathsf{fma}\left(y \cdot 9, x, b\right)}{c}}{z} \]

      7. *-commutative N/A

         \[\leadsto \frac{\frac{\color{blue}{\left(z \cdot \left(a \cdot t\right)\right) \cdot -4} + \mathsf{fma}\left(y \cdot 9, x, b\right)}{c}}{z} \]

      8. lower-fma.f64 N/A

         \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(z \cdot \left(a \cdot t\right), -4, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}}{c}}{z} \]

      9. *-commutative N/A

         \[\leadsto \frac{\frac{\mathsf{fma}\left(\color{blue}{\left(a \cdot t\right) \cdot z}, -4, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z} \]

      10. lower-*.f64 54.2

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\color{blue}{\left(a \cdot t\right) \cdot z}, -4, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z} \]

      11. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\color{blue}{\left(a \cdot t\right)} \cdot z, -4, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z} \]

      12. *-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\color{blue}{\left(t \cdot a\right)} \cdot z, -4, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z} \]

      13. lower-*.f64 54.2

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\color{blue}{\left(t \cdot a\right)} \cdot z, -4, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z} \]

      14. lift-fma.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \color{blue}{\left(y \cdot 9\right) \cdot x + b}\right)}{c}}{z} \]

      15. +-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \color{blue}{b + \left(y \cdot 9\right) \cdot x}\right)}{c}}{z} \]

      16. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, b + \color{blue}{\left(y \cdot 9\right)} \cdot x\right)}{c}}{z} \]

      17. associate-*l* N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, b + \color{blue}{y \cdot \left(9 \cdot x\right)}\right)}{c}}{z} \]

      18. *-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, b + y \cdot \color{blue}{\left(x \cdot 9\right)}\right)}{c}}{z} \]

      19. associate-*l* N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, b + \color{blue}{\left(y \cdot x\right) \cdot 9}\right)}{c}}{z} \]

      20. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, b + \color{blue}{\left(y \cdot x\right)} \cdot 9\right)}{c}}{z} \]

      21. +-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \color{blue}{\left(y \cdot x\right) \cdot 9 + b}\right)}{c}}{z} \]

      22. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \color{blue}{\left(y \cdot x\right)} \cdot 9 + b\right)}{c}}{z} \]

      23. associate-*l* N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \color{blue}{y \cdot \left(x \cdot 9\right)} + b\right)}{c}}{z} \]

      24. *-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, y \cdot \color{blue}{\left(9 \cdot x\right)} + b\right)}{c}}{z} \]

      25. associate-*l* N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \color{blue}{\left(y \cdot 9\right) \cdot x} + b\right)}{c}}{z} \]

      26. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \color{blue}{\left(y \cdot 9\right)} \cdot x + b\right)}{c}}{z} \]

      27. *-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \color{blue}{x \cdot \left(y \cdot 9\right)} + b\right)}{c}}{z} \]

   6. Applied rewrites 54.2%

      \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \mathsf{fma}\left(x, 9 \cdot y, b\right)\right)}}{c}}{z} \]

   7. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(-4 \cdot \frac{a \cdot t}{c \cdot y} + \left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \frac{a \cdot t}{c \cdot y} + \left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \frac{a \cdot t}{c \cdot y} + \left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right)\right) \cdot y} \]

   9. Applied rewrites 76.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{9}{c}, \frac{x}{z}, \frac{\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{b}{z}\right)}{c}}{y}\right) \cdot y} \]

   10. Taylor expanded in t around inf

       \[\leadsto \color{blue}{t \cdot \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \color{blue}{\left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right) \cdot t} \]

       2. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right) \cdot t} \]

   12. Applied rewrites 70.9%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{c}, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{\left(z \cdot t\right) \cdot c}\right) \cdot t} \]

   if -6.5000000000000001e158 < z < -1.7999999999999999e-23

   1. Initial program 78.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z \cdot c} \]

      3. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}{z \cdot c} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

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

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a\right)} + b}{z \cdot c} \]

      6. associate-+l+ N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y + \left(\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}}{z \cdot c} \]

      7. div-add N/A

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} + \frac{\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b}{z \cdot c}} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y}}{z \cdot c} + \frac{\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b}{z \cdot c} \]

      9. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(x \cdot 9\right)}}{z \cdot c} + \frac{\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b}{z \cdot c} \]

      10. associate-/l* N/A

          \[\leadsto \color{blue}{y \cdot \frac{x \cdot 9}{z \cdot c}} + \frac{\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b}{z \cdot c} \]

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{x \cdot 9}{z \cdot c}, \frac{\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b}{z \cdot c}\right)} \]

   4. Applied rewrites 86.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{9 \cdot x}{c \cdot z}, \frac{\mathsf{fma}\left(-4 \cdot z, a \cdot t, b\right)}{c \cdot z}\right)} \]

   if -1.7999999999999999e-23 < z < 3.39999999999999993e112

   1. Initial program 91.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{c \cdot z}} \]

      4. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

   4. Applied rewrites 96.5%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z}} \]

   if 3.39999999999999993e112 < z

   1. Initial program 51.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right) \cdot t} \]

   5. Applied rewrites 94.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{c}, -4, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{t \cdot z}\right) \cdot t} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 8: 71.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+116}:\\ \;\;\;\;\frac{\left(\frac{y}{c} \cdot 9\right) \cdot x}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+98}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{\left(z \cdot a\right) \cdot c}\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(-4 \cdot t\right) \cdot z, a, \left(y \cdot x\right) \cdot 9\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -2e+116)
     (/ (* (* (/ y c) 9.0) x) z)
     (if (<= t_1 5e+98)
       (* (fma (/ t c) -4.0 (/ b (* (* z a) c))) a)
       (/ (fma (* (* -4.0 t) z) a (* (* y x) 9.0)) (* z c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -2e+116) {
		tmp = (((y / c) * 9.0) * x) / z;
	} else if (t_1 <= 5e+98) {
		tmp = fma((t / c), -4.0, (b / ((z * a) * c))) * a;
	} else {
		tmp = fma(((-4.0 * t) * z), a, ((y * x) * 9.0)) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_1 <= -2e+116)
		tmp = Float64(Float64(Float64(Float64(y / c) * 9.0) * x) / z);
	elseif (t_1 <= 5e+98)
		tmp = Float64(fma(Float64(t / c), -4.0, Float64(b / Float64(Float64(z * a) * c))) * a);
	else
		tmp = Float64(fma(Float64(Float64(-4.0 * t) * z), a, Float64(Float64(y * x) * 9.0)) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+116], N[(N[(N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 5e+98], N[(N[(N[(t / c), $MachinePrecision] * -4.0 + N[(b / N[(N[(z * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], N[(N[(N[(N[(-4.0 * t), $MachinePrecision] * z), $MachinePrecision] * a + N[(N[(y * x), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.00000000000000003e116

   1. Initial program 78.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{9 \cdot \color{blue}{\left(y \cdot x\right)}}{c \cdot z} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{c \cdot z} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{9 \cdot y}{c} \cdot \frac{x}{z}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{9 \cdot y}{c} \cdot \frac{x}{z}} \]

      6. associate-*r/ N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c}\right)} \cdot \frac{x}{z} \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c}\right)} \cdot \frac{x}{z} \]

      8. lower-/.f64 N/A

         \[\leadsto \left(9 \cdot \color{blue}{\frac{y}{c}}\right) \cdot \frac{x}{z} \]

      9. lower-/.f64 83.3

         \[\leadsto \left(9 \cdot \frac{y}{c}\right) \cdot \color{blue}{\frac{x}{z}} \]

   5. Applied rewrites 83.3%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 85.1%

      \[\leadsto \frac{\left(\frac{y}{c} \cdot 9\right) \cdot x}{\color{blue}{z}} \]

   if -2.00000000000000003e116 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999998e98

   1. Initial program 76.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 78.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{c}, -4, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{a}}{c \cdot z}\right) \cdot a} \]

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{a \cdot \left(c \cdot z\right)}\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 78.1%

      \[\leadsto \mathsf{fma}\left(\frac{t}{c}, -4, \frac{\frac{b}{c \cdot z}}{a}\right) \cdot a \]
   9. Step-by-step derivation

   10. Applied rewrites 79.9%

       \[\leadsto \mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{\left(z \cdot a\right) \cdot c}\right) \cdot a \]

   if 4.9999999999999998e98 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 84.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right) + b}}{z \cdot c} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot y\right) \cdot 9} + b}{z \cdot c} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x \cdot y, 9, b\right)}}{z \cdot c} \]

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, b\right)}{z \cdot c} \]

      5. lower-*.f64 71.1

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, b\right)}{z \cdot c} \]

   5. Applied rewrites 71.1%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y \cdot x, 9, b\right)}}{z \cdot c} \]

   6. Taylor expanded in b around 0

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z \cdot c} \]
   7. Step-by-step derivation

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

         \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z \cdot c} \]

      2. metadata-eval N/A

         \[\leadsto \frac{9 \cdot \left(x \cdot y\right) + \color{blue}{-4} \cdot \left(a \cdot \left(t \cdot z\right)\right)}{z \cdot c} \]

      3. +-commutative N/A

         \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot \left(t \cdot z\right)\right) + 9 \cdot \left(x \cdot y\right)}}{z \cdot c} \]

      4. *-commutative N/A

         \[\leadsto \frac{-4 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot a\right)} + 9 \cdot \left(x \cdot y\right)}{z \cdot c} \]

      5. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(-4 \cdot \left(t \cdot z\right)\right) \cdot a} + 9 \cdot \left(x \cdot y\right)}{z \cdot c} \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-4 \cdot \left(t \cdot z\right), a, 9 \cdot \left(x \cdot y\right)\right)}}{z \cdot c} \]

      7. associate-*r* N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\left(-4 \cdot t\right) \cdot z}, a, 9 \cdot \left(x \cdot y\right)\right)}{z \cdot c} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\left(-4 \cdot t\right) \cdot z}, a, 9 \cdot \left(x \cdot y\right)\right)}{z \cdot c} \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\left(-4 \cdot t\right)} \cdot z, a, 9 \cdot \left(x \cdot y\right)\right)}{z \cdot c} \]

      10. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(\left(-4 \cdot t\right) \cdot z, a, \color{blue}{\left(x \cdot y\right) \cdot 9}\right)}{z \cdot c} \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\left(-4 \cdot t\right) \cdot z, a, \color{blue}{\left(x \cdot y\right) \cdot 9}\right)}{z \cdot c} \]

      12. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(\left(-4 \cdot t\right) \cdot z, a, \color{blue}{\left(y \cdot x\right)} \cdot 9\right)}{z \cdot c} \]

      13. lower-*.f64 75.7

          \[\leadsto \frac{\mathsf{fma}\left(\left(-4 \cdot t\right) \cdot z, a, \color{blue}{\left(y \cdot x\right)} \cdot 9\right)}{z \cdot c} \]

   8. Applied rewrites 75.7%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\left(-4 \cdot t\right) \cdot z, a, \left(y \cdot x\right) \cdot 9\right)}}{z \cdot c} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 71.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+116}:\\ \;\;\;\;\frac{\left(\frac{y}{c} \cdot 9\right) \cdot x}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+98}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(-4 \cdot t\right) \cdot z, a, \left(y \cdot x\right) \cdot 9\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -2e+116)
     (/ (* (* (/ y c) 9.0) x) z)
     (if (<= t_1 5e+98)
       (/ (fma -4.0 (* (* t z) a) b) (* z c))
       (/ (fma (* (* -4.0 t) z) a (* (* y x) 9.0)) (* z c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -2e+116) {
		tmp = (((y / c) * 9.0) * x) / z;
	} else if (t_1 <= 5e+98) {
		tmp = fma(-4.0, ((t * z) * a), b) / (z * c);
	} else {
		tmp = fma(((-4.0 * t) * z), a, ((y * x) * 9.0)) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_1 <= -2e+116)
		tmp = Float64(Float64(Float64(Float64(y / c) * 9.0) * x) / z);
	elseif (t_1 <= 5e+98)
		tmp = Float64(fma(-4.0, Float64(Float64(t * z) * a), b) / Float64(z * c));
	else
		tmp = Float64(fma(Float64(Float64(-4.0 * t) * z), a, Float64(Float64(y * x) * 9.0)) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+116], N[(N[(N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 5e+98], N[(N[(-4.0 * N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(-4.0 * t), $MachinePrecision] * z), $MachinePrecision] * a + N[(N[(y * x), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.00000000000000003e116

   1. Initial program 78.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{9 \cdot \color{blue}{\left(y \cdot x\right)}}{c \cdot z} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{c \cdot z} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{9 \cdot y}{c} \cdot \frac{x}{z}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{9 \cdot y}{c} \cdot \frac{x}{z}} \]

      6. associate-*r/ N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c}\right)} \cdot \frac{x}{z} \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c}\right)} \cdot \frac{x}{z} \]

      8. lower-/.f64 N/A

         \[\leadsto \left(9 \cdot \color{blue}{\frac{y}{c}}\right) \cdot \frac{x}{z} \]

      9. lower-/.f64 83.3

         \[\leadsto \left(9 \cdot \frac{y}{c}\right) \cdot \color{blue}{\frac{x}{z}} \]

   5. Applied rewrites 83.3%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 85.1%

      \[\leadsto \frac{\left(\frac{y}{c} \cdot 9\right) \cdot x}{\color{blue}{z}} \]

   if -2.00000000000000003e116 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.9999999999999998e98

   1. Initial program 76.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

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

         \[\leadsto \frac{\color{blue}{b + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z \cdot c} \]

      2. metadata-eval N/A

         \[\leadsto \frac{b + \color{blue}{-4} \cdot \left(a \cdot \left(t \cdot z\right)\right)}{z \cdot c} \]

      3. +-commutative N/A

         \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot \left(t \cdot z\right)\right) + b}}{z \cdot c} \]

      4. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-4, a \cdot \left(t \cdot z\right), b\right)}}{z \cdot c} \]

      5. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(-4, \color{blue}{\left(t \cdot z\right) \cdot a}, b\right)}{z \cdot c} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(-4, \color{blue}{\left(t \cdot z\right) \cdot a}, b\right)}{z \cdot c} \]

      7. lower-*.f64 71.0

         \[\leadsto \frac{\mathsf{fma}\left(-4, \color{blue}{\left(t \cdot z\right)} \cdot a, b\right)}{z \cdot c} \]

   5. Applied rewrites 71.0%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, b\right)}}{z \cdot c} \]

   if 4.9999999999999998e98 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 84.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right) + b}}{z \cdot c} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot y\right) \cdot 9} + b}{z \cdot c} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x \cdot y, 9, b\right)}}{z \cdot c} \]

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, b\right)}{z \cdot c} \]

      5. lower-*.f64 71.1

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, b\right)}{z \cdot c} \]

   5. Applied rewrites 71.1%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y \cdot x, 9, b\right)}}{z \cdot c} \]

   6. Taylor expanded in b around 0

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z \cdot c} \]
   7. Step-by-step derivation

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

         \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z \cdot c} \]

      2. metadata-eval N/A

         \[\leadsto \frac{9 \cdot \left(x \cdot y\right) + \color{blue}{-4} \cdot \left(a \cdot \left(t \cdot z\right)\right)}{z \cdot c} \]

      3. +-commutative N/A

         \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot \left(t \cdot z\right)\right) + 9 \cdot \left(x \cdot y\right)}}{z \cdot c} \]

      4. *-commutative N/A

         \[\leadsto \frac{-4 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot a\right)} + 9 \cdot \left(x \cdot y\right)}{z \cdot c} \]

      5. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(-4 \cdot \left(t \cdot z\right)\right) \cdot a} + 9 \cdot \left(x \cdot y\right)}{z \cdot c} \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-4 \cdot \left(t \cdot z\right), a, 9 \cdot \left(x \cdot y\right)\right)}}{z \cdot c} \]

      7. associate-*r* N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\left(-4 \cdot t\right) \cdot z}, a, 9 \cdot \left(x \cdot y\right)\right)}{z \cdot c} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\left(-4 \cdot t\right) \cdot z}, a, 9 \cdot \left(x \cdot y\right)\right)}{z \cdot c} \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\left(-4 \cdot t\right)} \cdot z, a, 9 \cdot \left(x \cdot y\right)\right)}{z \cdot c} \]

      10. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(\left(-4 \cdot t\right) \cdot z, a, \color{blue}{\left(x \cdot y\right) \cdot 9}\right)}{z \cdot c} \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\left(-4 \cdot t\right) \cdot z, a, \color{blue}{\left(x \cdot y\right) \cdot 9}\right)}{z \cdot c} \]

      12. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(\left(-4 \cdot t\right) \cdot z, a, \color{blue}{\left(y \cdot x\right)} \cdot 9\right)}{z \cdot c} \]

      13. lower-*.f64 75.7

          \[\leadsto \frac{\mathsf{fma}\left(\left(-4 \cdot t\right) \cdot z, a, \color{blue}{\left(y \cdot x\right)} \cdot 9\right)}{z \cdot c} \]

   8. Applied rewrites 75.7%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\left(-4 \cdot t\right) \cdot z, a, \left(y \cdot x\right) \cdot 9\right)}}{z \cdot c} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 85.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+158}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{c}, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{\left(z \cdot t\right) \cdot c}\right) \cdot t\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-23}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{9 \cdot x}{c \cdot z}, \frac{\mathsf{fma}\left(-4 \cdot z, a \cdot t, b\right)}{c \cdot z}\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+110}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{\left(z \cdot a\right) \cdot c}\right) \cdot a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -6.5e+158)
   (* (fma (/ a c) -4.0 (/ (fma (* y x) 9.0 b) (* (* z t) c))) t)
   (if (<= z -1.8e-23)
     (fma y (/ (* 9.0 x) (* c z)) (/ (fma (* -4.0 z) (* a t) b) (* c z)))
     (if (<= z 1.1e+110)
       (/ (/ (fma (* (* -4.0 z) a) t (fma (* y 9.0) x b)) c) z)
       (* (fma (/ t c) -4.0 (/ b (* (* z a) c))) a)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -6.5e+158) {
		tmp = fma((a / c), -4.0, (fma((y * x), 9.0, b) / ((z * t) * c))) * t;
	} else if (z <= -1.8e-23) {
		tmp = fma(y, ((9.0 * x) / (c * z)), (fma((-4.0 * z), (a * t), b) / (c * z)));
	} else if (z <= 1.1e+110) {
		tmp = (fma(((-4.0 * z) * a), t, fma((y * 9.0), x, b)) / c) / z;
	} else {
		tmp = fma((t / c), -4.0, (b / ((z * a) * c))) * a;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -6.5e+158)
		tmp = Float64(fma(Float64(a / c), -4.0, Float64(fma(Float64(y * x), 9.0, b) / Float64(Float64(z * t) * c))) * t);
	elseif (z <= -1.8e-23)
		tmp = fma(y, Float64(Float64(9.0 * x) / Float64(c * z)), Float64(fma(Float64(-4.0 * z), Float64(a * t), b) / Float64(c * z)));
	elseif (z <= 1.1e+110)
		tmp = Float64(Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * 9.0), x, b)) / c) / z);
	else
		tmp = Float64(fma(Float64(t / c), -4.0, Float64(b / Float64(Float64(z * a) * c))) * a);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -6.5e+158], N[(N[(N[(a / c), $MachinePrecision] * -4.0 + N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, -1.8e-23], N[(y * N[(N[(9.0 * x), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(-4.0 * z), $MachinePrecision] * N[(a * t), $MachinePrecision] + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+110], N[(N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * 9.0), $MachinePrecision] * x + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(t / c), $MachinePrecision] * -4.0 + N[(b / N[(N[(z * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.5000000000000001e158

   1. Initial program 44.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{c \cdot z}} \]

      4. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

   4. Applied rewrites 45.7%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z}} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \frac{\frac{\color{blue}{\left(\left(-4 \cdot z\right) \cdot a\right) \cdot t + \mathsf{fma}\left(y \cdot 9, x, b\right)}}{c}}{z} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\color{blue}{\left(\left(-4 \cdot z\right) \cdot a\right)} \cdot t + \mathsf{fma}\left(y \cdot 9, x, b\right)}{c}}{z} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\frac{\color{blue}{\left(-4 \cdot z\right) \cdot \left(a \cdot t\right)} + \mathsf{fma}\left(y \cdot 9, x, b\right)}{c}}{z} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\left(-4 \cdot z\right) \cdot \color{blue}{\left(a \cdot t\right)} + \mathsf{fma}\left(y \cdot 9, x, b\right)}{c}}{z} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\frac{\color{blue}{\left(-4 \cdot z\right)} \cdot \left(a \cdot t\right) + \mathsf{fma}\left(y \cdot 9, x, b\right)}{c}}{z} \]

      6. associate-*l* N/A

         \[\leadsto \frac{\frac{\color{blue}{-4 \cdot \left(z \cdot \left(a \cdot t\right)\right)} + \mathsf{fma}\left(y \cdot 9, x, b\right)}{c}}{z} \]

      7. *-commutative N/A

         \[\leadsto \frac{\frac{\color{blue}{\left(z \cdot \left(a \cdot t\right)\right) \cdot -4} + \mathsf{fma}\left(y \cdot 9, x, b\right)}{c}}{z} \]

      8. lower-fma.f64 N/A

         \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(z \cdot \left(a \cdot t\right), -4, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}}{c}}{z} \]

      9. *-commutative N/A

         \[\leadsto \frac{\frac{\mathsf{fma}\left(\color{blue}{\left(a \cdot t\right) \cdot z}, -4, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z} \]

      10. lower-*.f64 54.2

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\color{blue}{\left(a \cdot t\right) \cdot z}, -4, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z} \]

      11. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\color{blue}{\left(a \cdot t\right)} \cdot z, -4, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z} \]

      12. *-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\color{blue}{\left(t \cdot a\right)} \cdot z, -4, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z} \]

      13. lower-*.f64 54.2

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\color{blue}{\left(t \cdot a\right)} \cdot z, -4, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z} \]

      14. lift-fma.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \color{blue}{\left(y \cdot 9\right) \cdot x + b}\right)}{c}}{z} \]

      15. +-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \color{blue}{b + \left(y \cdot 9\right) \cdot x}\right)}{c}}{z} \]

      16. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, b + \color{blue}{\left(y \cdot 9\right)} \cdot x\right)}{c}}{z} \]

      17. associate-*l* N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, b + \color{blue}{y \cdot \left(9 \cdot x\right)}\right)}{c}}{z} \]

      18. *-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, b + y \cdot \color{blue}{\left(x \cdot 9\right)}\right)}{c}}{z} \]

      19. associate-*l* N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, b + \color{blue}{\left(y \cdot x\right) \cdot 9}\right)}{c}}{z} \]

      20. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, b + \color{blue}{\left(y \cdot x\right)} \cdot 9\right)}{c}}{z} \]

      21. +-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \color{blue}{\left(y \cdot x\right) \cdot 9 + b}\right)}{c}}{z} \]

      22. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \color{blue}{\left(y \cdot x\right)} \cdot 9 + b\right)}{c}}{z} \]

      23. associate-*l* N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \color{blue}{y \cdot \left(x \cdot 9\right)} + b\right)}{c}}{z} \]

      24. *-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, y \cdot \color{blue}{\left(9 \cdot x\right)} + b\right)}{c}}{z} \]

      25. associate-*l* N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \color{blue}{\left(y \cdot 9\right) \cdot x} + b\right)}{c}}{z} \]

      26. lift-*.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \color{blue}{\left(y \cdot 9\right)} \cdot x + b\right)}{c}}{z} \]

      27. *-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \color{blue}{x \cdot \left(y \cdot 9\right)} + b\right)}{c}}{z} \]

   6. Applied rewrites 54.2%

      \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(\left(t \cdot a\right) \cdot z, -4, \mathsf{fma}\left(x, 9 \cdot y, b\right)\right)}}{c}}{z} \]

   7. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(-4 \cdot \frac{a \cdot t}{c \cdot y} + \left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \frac{a \cdot t}{c \cdot y} + \left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \frac{a \cdot t}{c \cdot y} + \left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right)\right) \cdot y} \]

   9. Applied rewrites 76.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{9}{c}, \frac{x}{z}, \frac{\frac{\mathsf{fma}\left(-4 \cdot a, t, \frac{b}{z}\right)}{c}}{y}\right) \cdot y} \]

   10. Taylor expanded in t around inf

       \[\leadsto \color{blue}{t \cdot \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \color{blue}{\left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right) \cdot t} \]

       2. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right) \cdot t} \]

   12. Applied rewrites 70.9%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{c}, -4, \frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{\left(z \cdot t\right) \cdot c}\right) \cdot t} \]

   if -6.5000000000000001e158 < z < -1.7999999999999999e-23

   1. Initial program 78.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z \cdot c} \]

      3. lift--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)} + b}{z \cdot c} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

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

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a\right)} + b}{z \cdot c} \]

      6. associate-+l+ N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y + \left(\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b\right)}}{z \cdot c} \]

      7. div-add N/A

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} + \frac{\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b}{z \cdot c}} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y}}{z \cdot c} + \frac{\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b}{z \cdot c} \]

      9. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(x \cdot 9\right)}}{z \cdot c} + \frac{\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b}{z \cdot c} \]

      10. associate-/l* N/A

          \[\leadsto \color{blue}{y \cdot \frac{x \cdot 9}{z \cdot c}} + \frac{\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b}{z \cdot c} \]

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{x \cdot 9}{z \cdot c}, \frac{\left(\mathsf{neg}\left(\left(z \cdot 4\right) \cdot t\right)\right) \cdot a + b}{z \cdot c}\right)} \]

   4. Applied rewrites 86.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{9 \cdot x}{c \cdot z}, \frac{\mathsf{fma}\left(-4 \cdot z, a \cdot t, b\right)}{c \cdot z}\right)} \]

   if -1.7999999999999999e-23 < z < 1.09999999999999996e110

   1. Initial program 91.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{c \cdot z}} \]

      4. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

   4. Applied rewrites 97.1%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z}} \]

   if 1.09999999999999996e110 < z

   1. Initial program 52.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 78.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{c}, -4, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{a}}{c \cdot z}\right) \cdot a} \]

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{a \cdot \left(c \cdot z\right)}\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 79.6%

      \[\leadsto \mathsf{fma}\left(\frac{t}{c}, -4, \frac{\frac{b}{c \cdot z}}{a}\right) \cdot a \]
   9. Step-by-step derivation

   10. Applied rewrites 79.6%

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

Alternative 11: 70.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+116} \lor \neg \left(t\_1 \leq 6 \cdot 10^{+193}\right):\\ \;\;\;\;\frac{\left(\frac{y}{c} \cdot 9\right) \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, b\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (or (<= t_1 -2e+116) (not (<= t_1 6e+193)))
     (/ (* (* (/ y c) 9.0) x) z)
     (/ (fma -4.0 (* (* t z) a) b) (* z c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if ((t_1 <= -2e+116) || !(t_1 <= 6e+193)) {
		tmp = (((y / c) * 9.0) * x) / z;
	} else {
		tmp = fma(-4.0, ((t * z) * a), b) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if ((t_1 <= -2e+116) || !(t_1 <= 6e+193))
		tmp = Float64(Float64(Float64(Float64(y / c) * 9.0) * x) / z);
	else
		tmp = Float64(fma(-4.0, Float64(Float64(t * z) * a), b) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+116], N[Not[LessEqual[t$95$1, 6e+193]], $MachinePrecision]], N[(N[(N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision], N[(N[(-4.0 * N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.00000000000000003e116 or 6e193 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 78.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{9 \cdot \color{blue}{\left(y \cdot x\right)}}{c \cdot z} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{c \cdot z} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{9 \cdot y}{c} \cdot \frac{x}{z}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{9 \cdot y}{c} \cdot \frac{x}{z}} \]

      6. associate-*r/ N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c}\right)} \cdot \frac{x}{z} \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c}\right)} \cdot \frac{x}{z} \]

      8. lower-/.f64 N/A

         \[\leadsto \left(9 \cdot \color{blue}{\frac{y}{c}}\right) \cdot \frac{x}{z} \]

      9. lower-/.f64 79.5

         \[\leadsto \left(9 \cdot \frac{y}{c}\right) \cdot \color{blue}{\frac{x}{z}} \]

   5. Applied rewrites 79.5%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 84.4%

      \[\leadsto \frac{\left(\frac{y}{c} \cdot 9\right) \cdot x}{\color{blue}{z}} \]

   if -2.00000000000000003e116 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 6e193

   1. Initial program 78.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

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

         \[\leadsto \frac{\color{blue}{b + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z \cdot c} \]

      2. metadata-eval N/A

         \[\leadsto \frac{b + \color{blue}{-4} \cdot \left(a \cdot \left(t \cdot z\right)\right)}{z \cdot c} \]

      3. +-commutative N/A

         \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot \left(t \cdot z\right)\right) + b}}{z \cdot c} \]

      4. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-4, a \cdot \left(t \cdot z\right), b\right)}}{z \cdot c} \]

      5. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(-4, \color{blue}{\left(t \cdot z\right) \cdot a}, b\right)}{z \cdot c} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(-4, \color{blue}{\left(t \cdot z\right) \cdot a}, b\right)}{z \cdot c} \]

      7. lower-*.f64 70.3

         \[\leadsto \frac{\mathsf{fma}\left(-4, \color{blue}{\left(t \cdot z\right)} \cdot a, b\right)}{z \cdot c} \]

   5. Applied rewrites 70.3%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 9\right) \cdot y \leq -2 \cdot 10^{+116} \lor \neg \left(\left(x \cdot 9\right) \cdot y \leq 6 \cdot 10^{+193}\right):\\ \;\;\;\;\frac{\left(\frac{y}{c} \cdot 9\right) \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, b\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+141} \lor \neg \left(z \leq 1.1 \cdot 10^{+110}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{\left(z \cdot a\right) \cdot c}\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -5.5e+141) (not (<= z 1.1e+110)))
   (* (fma (/ t c) -4.0 (/ b (* (* z a) c))) a)
   (/ (/ (fma (* (* -4.0 z) a) t (fma (* y 9.0) x b)) c) z)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -5.5e+141) || !(z <= 1.1e+110)) {
		tmp = fma((t / c), -4.0, (b / ((z * a) * c))) * a;
	} else {
		tmp = (fma(((-4.0 * z) * a), t, fma((y * 9.0), x, b)) / c) / z;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -5.5e+141) || !(z <= 1.1e+110))
		tmp = Float64(fma(Float64(t / c), -4.0, Float64(b / Float64(Float64(z * a) * c))) * a);
	else
		tmp = Float64(Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * 9.0), x, b)) / c) / z);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -5.5e+141], N[Not[LessEqual[z, 1.1e+110]], $MachinePrecision]], N[(N[(N[(t / c), $MachinePrecision] * -4.0 + N[(b / N[(N[(z * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], N[(N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * 9.0), $MachinePrecision] * x + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.49999999999999967e141 or 1.09999999999999996e110 < z

   1. Initial program 49.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 72.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{c}, -4, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{a}}{c \cdot z}\right) \cdot a} \]

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{a \cdot \left(c \cdot z\right)}\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 76.1%

      \[\leadsto \mathsf{fma}\left(\frac{t}{c}, -4, \frac{\frac{b}{c \cdot z}}{a}\right) \cdot a \]
   9. Step-by-step derivation

   10. Applied rewrites 77.5%

       \[\leadsto \mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{\left(z \cdot a\right) \cdot c}\right) \cdot a \]

   if -5.49999999999999967e141 < z < 1.09999999999999996e110

   1. Initial program 88.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{c \cdot z}} \]

      4. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

   4. Applied rewrites 92.6%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+141} \lor \neg \left(z \leq 1.1 \cdot 10^{+110}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{\left(z \cdot a\right) \cdot c}\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{c}, -4, \frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{\left(c \cdot z\right) \cdot t}\right) \cdot t\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+110}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{\left(z \cdot a\right) \cdot c}\right) \cdot a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.4e+84)
   (* (fma (/ a c) -4.0 (/ (fma (* x y) 9.0 b) (* (* c z) t))) t)
   (if (<= z 1.1e+110)
     (/ (/ (fma (* (* -4.0 z) a) t (fma (* y 9.0) x b)) c) z)
     (* (fma (/ t c) -4.0 (/ b (* (* z a) c))) a))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.4e+84) {
		tmp = fma((a / c), -4.0, (fma((x * y), 9.0, b) / ((c * z) * t))) * t;
	} else if (z <= 1.1e+110) {
		tmp = (fma(((-4.0 * z) * a), t, fma((y * 9.0), x, b)) / c) / z;
	} else {
		tmp = fma((t / c), -4.0, (b / ((z * a) * c))) * a;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.4e+84)
		tmp = Float64(fma(Float64(a / c), -4.0, Float64(fma(Float64(x * y), 9.0, b) / Float64(Float64(c * z) * t))) * t);
	elseif (z <= 1.1e+110)
		tmp = Float64(Float64(fma(Float64(Float64(-4.0 * z) * a), t, fma(Float64(y * 9.0), x, b)) / c) / z);
	else
		tmp = Float64(fma(Float64(t / c), -4.0, Float64(b / Float64(Float64(z * a) * c))) * a);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.4e+84], N[(N[(N[(a / c), $MachinePrecision] * -4.0 + N[(N[(N[(x * y), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 1.1e+110], N[(N[(N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + N[(N[(y * 9.0), $MachinePrecision] * x + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(t / c), $MachinePrecision] * -4.0 + N[(b / N[(N[(z * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.39999999999999991e84

   1. Initial program 49.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{c \cdot z}} \]

      4. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

   4. Applied rewrites 43.6%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z}} \]

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right) \cdot t} \]

   7. Applied rewrites 58.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{c}, -4, \frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{\left(c \cdot z\right) \cdot t}\right) \cdot t} \]

   if -1.39999999999999991e84 < z < 1.09999999999999996e110

   1. Initial program 90.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{c \cdot z}} \]

      4. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

   4. Applied rewrites 96.4%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z}} \]

   if 1.09999999999999996e110 < z

   1. Initial program 52.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 78.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{c}, -4, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{a}}{c \cdot z}\right) \cdot a} \]

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{a \cdot \left(c \cdot z\right)}\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 79.6%

      \[\leadsto \mathsf{fma}\left(\frac{t}{c}, -4, \frac{\frac{b}{c \cdot z}}{a}\right) \cdot a \]
   9. Step-by-step derivation

   10. Applied rewrites 79.6%

       \[\leadsto \mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{\left(z \cdot a\right) \cdot c}\right) \cdot a \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{c}, -4, \frac{\mathsf{fma}\left(x \cdot y, 9, b\right)}{\left(c \cdot z\right) \cdot t}\right) \cdot t\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+110}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{\left(z \cdot a\right) \cdot c}\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+134} \lor \neg \left(z \leq 3.2 \cdot 10^{+77}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{\left(z \cdot a\right) \cdot c}\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -2.05e+134) (not (<= z 3.2e+77)))
   (* (fma (/ t c) -4.0 (/ b (* (* z a) c))) a)
   (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2.05e+134) || !(z <= 3.2e+77)) {
		tmp = fma((t / c), -4.0, (b / ((z * a) * c))) * a;
	} else {
		tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -2.05e+134) || !(z <= 3.2e+77))
		tmp = Float64(fma(Float64(t / c), -4.0, Float64(b / Float64(Float64(z * a) * c))) * a);
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -2.05e+134], N[Not[LessEqual[z, 3.2e+77]], $MachinePrecision]], N[(N[(N[(t / c), $MachinePrecision] * -4.0 + N[(b / N[(N[(z * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0500000000000002e134 or 3.2000000000000002e77 < z

   1. Initial program 47.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 68.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{c}, -4, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{a}}{c \cdot z}\right) \cdot a} \]

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{a \cdot \left(c \cdot z\right)}\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 72.5%

      \[\leadsto \mathsf{fma}\left(\frac{t}{c}, -4, \frac{\frac{b}{c \cdot z}}{a}\right) \cdot a \]
   9. Step-by-step derivation

   10. Applied rewrites 73.8%

       \[\leadsto \mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{\left(z \cdot a\right) \cdot c}\right) \cdot a \]

   if -2.0500000000000002e134 < z < 3.2000000000000002e77

   1. Initial program 90.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+134} \lor \neg \left(z \leq 3.2 \cdot 10^{+77}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{c}, -4, \frac{b}{\left(z \cdot a\right) \cdot c}\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 70.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+93}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+71}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{-4}{c}\right) \cdot a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -3e+93)
   (* -4.0 (/ (* a t) c))
   (if (<= z 5.8e+71) (/ (fma (* y x) 9.0 b) (* z c)) (* (* t (/ -4.0 c)) a))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3e+93) {
		tmp = -4.0 * ((a * t) / c);
	} else if (z <= 5.8e+71) {
		tmp = fma((y * x), 9.0, b) / (z * c);
	} else {
		tmp = (t * (-4.0 / c)) * a;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -3e+93)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	elseif (z <= 5.8e+71)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c));
	else
		tmp = Float64(Float64(t * Float64(-4.0 / c)) * a);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -3e+93], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+71], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.99999999999999978e93

   1. Initial program 49.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

      2. lower-/.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\frac{a \cdot t}{c}} \]

      3. lower-*.f64 58.4

         \[\leadsto -4 \cdot \frac{\color{blue}{a \cdot t}}{c} \]

   5. Applied rewrites 58.4%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

   if -2.99999999999999978e93 < z < 5.80000000000000014e71

   1. Initial program 91.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right) + b}}{z \cdot c} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot y\right) \cdot 9} + b}{z \cdot c} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x \cdot y, 9, b\right)}}{z \cdot c} \]

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, b\right)}{z \cdot c} \]

      5. lower-*.f64 76.1

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, b\right)}{z \cdot c} \]

   5. Applied rewrites 76.1%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y \cdot x, 9, b\right)}}{z \cdot c} \]

   if 5.80000000000000014e71 < z

   1. Initial program 52.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 75.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{c}, -4, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{a}}{c \cdot z}\right) \cdot a} \]

   6. Taylor expanded in z around inf

      \[\leadsto \left(-4 \cdot \frac{t}{c}\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 66.7%

      \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]
   9. Step-by-step derivation

   10. Applied rewrites 66.7%

       \[\leadsto \left(t \cdot \frac{-4}{c}\right) \cdot a \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 53.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+89} \lor \neg \left(b \leq 4.5 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -9.5e+89) (not (<= b 4.5e+19)))
   (/ (/ b c) z)
   (* (* (/ t c) -4.0) a)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -9.5e+89) || !(b <= 4.5e+19)) {
		tmp = (b / c) / z;
	} else {
		tmp = ((t / c) * -4.0) * a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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, c)
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), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-9.5d+89)) .or. (.not. (b <= 4.5d+19))) then
        tmp = (b / c) / z
    else
        tmp = ((t / c) * (-4.0d0)) * a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -9.5e+89) || !(b <= 4.5e+19)) {
		tmp = (b / c) / z;
	} else {
		tmp = ((t / c) * -4.0) * a;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -9.5e+89) or not (b <= 4.5e+19):
		tmp = (b / c) / z
	else:
		tmp = ((t / c) * -4.0) * a
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -9.5e+89) || !(b <= 4.5e+19))
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(Float64(Float64(t / c) * -4.0) * a);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -9.5e+89) || ~((b <= 4.5e+19)))
		tmp = (b / c) / z;
	else
		tmp = ((t / c) * -4.0) * a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -9.5e+89], N[Not[LessEqual[b, 4.5e+19]], $MachinePrecision]], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.5000000000000003e89 or 4.5e19 < b

   1. Initial program 79.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{z \cdot c}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{\color{blue}{c \cdot z}} \]

      4. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c}}{z}} \]

   4. Applied rewrites 83.3%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, \mathsf{fma}\left(y \cdot 9, x, b\right)\right)}{c}}{z}} \]

   5. Taylor expanded in b around inf

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

      1. lower-/.f64 61.3

         \[\leadsto \frac{\color{blue}{\frac{b}{c}}}{z} \]

   7. Applied rewrites 61.3%

      \[\leadsto \frac{\color{blue}{\frac{b}{c}}}{z} \]

   if -9.5000000000000003e89 < b < 4.5e19

   1. Initial program 77.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 77.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{c}, -4, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{a}}{c \cdot z}\right) \cdot a} \]

   6. Taylor expanded in z around inf

      \[\leadsto \left(-4 \cdot \frac{t}{c}\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 52.9%

      \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+89} \lor \neg \left(b \leq 4.5 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+90} \lor \neg \left(b \leq 4.5 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -1.6e+90) (not (<= b 4.5e+19)))
   (/ (/ b z) c)
   (* (* (/ t c) -4.0) a)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.6e+90) || !(b <= 4.5e+19)) {
		tmp = (b / z) / c;
	} else {
		tmp = ((t / c) * -4.0) * a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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, c)
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), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-1.6d+90)) .or. (.not. (b <= 4.5d+19))) then
        tmp = (b / z) / c
    else
        tmp = ((t / c) * (-4.0d0)) * a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.6e+90) || !(b <= 4.5e+19)) {
		tmp = (b / z) / c;
	} else {
		tmp = ((t / c) * -4.0) * a;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -1.6e+90) or not (b <= 4.5e+19):
		tmp = (b / z) / c
	else:
		tmp = ((t / c) * -4.0) * a
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -1.6e+90) || !(b <= 4.5e+19))
		tmp = Float64(Float64(b / z) / c);
	else
		tmp = Float64(Float64(Float64(t / c) * -4.0) * a);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -1.6e+90) || ~((b <= 4.5e+19)))
		tmp = (b / z) / c;
	else
		tmp = ((t / c) * -4.0) * a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -1.6e+90], N[Not[LessEqual[b, 4.5e+19]], $MachinePrecision]], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.59999999999999999e90 or 4.5e19 < b

   1. Initial program 79.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      2. lower-*.f64 58.6

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 58.6%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 59.3%

      \[\leadsto \frac{\frac{b}{z}}{\color{blue}{c}} \]

   if -1.59999999999999999e90 < b < 4.5e19

   1. Initial program 77.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 77.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{c}, -4, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{a}}{c \cdot z}\right) \cdot a} \]

   6. Taylor expanded in z around inf

      \[\leadsto \left(-4 \cdot \frac{t}{c}\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 52.9%

      \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+90} \lor \neg \left(b \leq 4.5 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+94} \lor \neg \left(b \leq 4.5 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -3e+94) (not (<= b 4.5e+19)))
   (/ b (* c z))
   (* (* (/ t c) -4.0) a)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -3e+94) || !(b <= 4.5e+19)) {
		tmp = b / (c * z);
	} else {
		tmp = ((t / c) * -4.0) * a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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, c)
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), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-3d+94)) .or. (.not. (b <= 4.5d+19))) then
        tmp = b / (c * z)
    else
        tmp = ((t / c) * (-4.0d0)) * a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -3e+94) || !(b <= 4.5e+19)) {
		tmp = b / (c * z);
	} else {
		tmp = ((t / c) * -4.0) * a;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -3e+94) or not (b <= 4.5e+19):
		tmp = b / (c * z)
	else:
		tmp = ((t / c) * -4.0) * a
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -3e+94) || !(b <= 4.5e+19))
		tmp = Float64(b / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(t / c) * -4.0) * a);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -3e+94) || ~((b <= 4.5e+19)))
		tmp = b / (c * z);
	else
		tmp = ((t / c) * -4.0) * a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -3e+94], N[Not[LessEqual[b, 4.5e+19]], $MachinePrecision]], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t / c), $MachinePrecision] * -4.0), $MachinePrecision] * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.0000000000000001e94 or 4.5e19 < b

   1. Initial program 80.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      2. lower-*.f64 59.0

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 59.0%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

   if -3.0000000000000001e94 < b < 4.5e19

   1. Initial program 76.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 76.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{c}, -4, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{a}}{c \cdot z}\right) \cdot a} \]

   6. Taylor expanded in z around inf

      \[\leadsto \left(-4 \cdot \frac{t}{c}\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 52.6%

      \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+94} \lor \neg \left(b \leq 4.5 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{c} \cdot -4\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 52.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+94} \lor \neg \left(b \leq 4.5 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{-4}{c}\right) \cdot a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -3e+94) (not (<= b 4.5e+19)))
   (/ b (* c z))
   (* (* t (/ -4.0 c)) a)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -3e+94) || !(b <= 4.5e+19)) {
		tmp = b / (c * z);
	} else {
		tmp = (t * (-4.0 / c)) * a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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, c)
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), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-3d+94)) .or. (.not. (b <= 4.5d+19))) then
        tmp = b / (c * z)
    else
        tmp = (t * ((-4.0d0) / c)) * a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -3e+94) || !(b <= 4.5e+19)) {
		tmp = b / (c * z);
	} else {
		tmp = (t * (-4.0 / c)) * a;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -3e+94) or not (b <= 4.5e+19):
		tmp = b / (c * z)
	else:
		tmp = (t * (-4.0 / c)) * a
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -3e+94) || !(b <= 4.5e+19))
		tmp = Float64(b / Float64(c * z));
	else
		tmp = Float64(Float64(t * Float64(-4.0 / c)) * a);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -3e+94) || ~((b <= 4.5e+19)))
		tmp = b / (c * z);
	else
		tmp = (t * (-4.0 / c)) * a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -3e+94], N[Not[LessEqual[b, 4.5e+19]], $MachinePrecision]], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.0000000000000001e94 or 4.5e19 < b

   1. Initial program 80.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      2. lower-*.f64 59.0

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 59.0%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

   if -3.0000000000000001e94 < b < 4.5e19

   1. Initial program 76.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 76.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{c}, -4, \frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{a}}{c \cdot z}\right) \cdot a} \]

   6. Taylor expanded in z around inf

      \[\leadsto \left(-4 \cdot \frac{t}{c}\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 52.6%

      \[\leadsto \left(\frac{t}{c} \cdot -4\right) \cdot a \]
   9. Step-by-step derivation

   10. Applied rewrites 52.6%

       \[\leadsto \left(t \cdot \frac{-4}{c}\right) \cdot a \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+94} \lor \neg \left(b \leq 4.5 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{-4}{c}\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 51.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+90} \lor \neg \left(b \leq 8.2 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -1.15e+90) (not (<= b 8.2e+18)))
   (/ b (* c z))
   (* -4.0 (/ (* a t) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.15e+90) || !(b <= 8.2e+18)) {
		tmp = b / (c * z);
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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, c)
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), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-1.15d+90)) .or. (.not. (b <= 8.2d+18))) then
        tmp = b / (c * z)
    else
        tmp = (-4.0d0) * ((a * t) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.15e+90) || !(b <= 8.2e+18)) {
		tmp = b / (c * z);
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -1.15e+90) or not (b <= 8.2e+18):
		tmp = b / (c * z)
	else:
		tmp = -4.0 * ((a * t) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -1.15e+90) || !(b <= 8.2e+18))
		tmp = Float64(b / Float64(c * z));
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -1.15e+90) || ~((b <= 8.2e+18)))
		tmp = b / (c * z);
	else
		tmp = -4.0 * ((a * t) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -1.15e+90], N[Not[LessEqual[b, 8.2e+18]], $MachinePrecision]], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.15e90 or 8.2e18 < b

   1. Initial program 79.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      2. lower-*.f64 58.6

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 58.6%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

   if -1.15e90 < b < 8.2e18

   1. Initial program 77.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

      2. lower-/.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\frac{a \cdot t}{c}} \]

      3. lower-*.f64 50.4

         \[\leadsto -4 \cdot \frac{\color{blue}{a \cdot t}}{c} \]

   5. Applied rewrites 50.4%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+90} \lor \neg \left(b \leq 8.2 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 35.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{c \cdot z} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ b (* c z)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (c * z);
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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, c)
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), intent (in) :: c
    code = b / (c * z)
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (c * z);
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	return b / (c * z)

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(c * z))
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (c * z);
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.3%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Add Preprocessing

3. Taylor expanded in b around inf

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

   1. lower-/.f64 N/A

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

   2. lower-*.f64 37.4

      \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

5. Applied rewrites 37.4%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Add Preprocessing

Developer Target 1: 80.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t\_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t\_4}{z \cdot c}\\ t_6 := \frac{\left(t\_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 0:\\ \;\;\;\;\frac{\frac{t\_4}{z}}{c}\\ \mathbf{elif}\;t\_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t\_1\right) - t\_2\\ \mathbf{elif}\;t\_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	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, c)
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), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2025017 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) -220031348160821/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 0) (/ (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 365902434742109/31250000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 28768236795461370000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ (* (* 9 (/ y c)) (/ x z)) (/ b (* c z))) (* 4 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 138385150424563190000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (- (+ (* 9 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4 (/ (* a t) c)))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))