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

Percentage Accurate: 78.8% → 90.9%

Time: 14.5s

Alternatives: 14

Speedup: 1.1×

• 36.8% 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

real(8) function code(x, y, z, t, a, b, c)
    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: 78.8% 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

real(8) function code(x, y, z, t, a, b, c)
    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: 90.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{if}\;z \leq -1 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-95}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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)) b) z) (* t (* a -4.0))) c)))
   (if (<= z -1e-85)
     t_1
     (if (<= z 2.75e-95)
       (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))
       t_1))))

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)) + b) / z) + (t * (a * -4.0))) / c;
	double tmp;
	if (z <= -1e-85) {
		tmp = t_1;
	} else if (z <= 2.75e-95) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    t_1 = ((((x * (9.0d0 * y)) + b) / z) + (t * (a * (-4.0d0)))) / c
    if (z <= (-1d-85)) then
        tmp = t_1
    else if (z <= 2.75d-95) then
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (z * c)
    else
        tmp = t_1
    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 = ((((x * (9.0 * y)) + b) / z) + (t * (a * -4.0))) / c;
	double tmp;
	if (z <= -1e-85) {
		tmp = t_1;
	} else if (z <= 2.75e-95) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = t_1;
	}
	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 = ((((x * (9.0 * y)) + b) / z) + (t * (a * -4.0))) / c
	tmp = 0
	if z <= -1e-85:
		tmp = t_1
	elif z <= 2.75e-95:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)
	else:
		tmp = t_1
	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 * Float64(9.0 * y)) + b) / z) + Float64(t * Float64(a * -4.0))) / c)
	tmp = 0.0
	if (z <= -1e-85)
		tmp = t_1;
	elseif (z <= 2.75e-95)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = t_1;
	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 = ((((x * (9.0 * y)) + b) / z) + (t * (a * -4.0))) / c;
	tmp = 0.0;
	if (z <= -1e-85)
		tmp = t_1;
	elseif (z <= 2.75e-95)
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	else
		tmp = t_1;
	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[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1e-85], t$95$1, If[LessEqual[z, 2.75e-95], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999998e-86 or 2.75000000000000001e-95 < z

   1. Initial program 69.1%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 92.3%

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

   if -9.9999999999999998e-86 < z < 2.75000000000000001e-95

   1. Initial program 97.8%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-85}:\\ \;\;\;\;\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-95}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := \frac{t\_1 + y \cdot \left(x \cdot \frac{9}{z}\right)}{c}\\ t_3 := \frac{t\_1 + \frac{b}{z}}{c}\\ \mathbf{if}\;z \leq -1 \cdot 10^{+103}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-12}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+26}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+191}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* t (* a -4.0)))
        (t_2 (/ (+ t_1 (* y (* x (/ 9.0 z)))) c))
        (t_3 (/ (+ t_1 (/ b z)) c)))
   (if (<= z -1e+103)
     t_2
     (if (<= z -9e-12)
       t_3
       (if (<= z 9e+26)
         (/ (+ b (* 9.0 (* x y))) (* z c))
         (if (<= z 1.9e+191) t_3 t_2))))))

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 = t * (a * -4.0);
	double t_2 = (t_1 + (y * (x * (9.0 / z)))) / c;
	double t_3 = (t_1 + (b / z)) / c;
	double tmp;
	if (z <= -1e+103) {
		tmp = t_2;
	} else if (z <= -9e-12) {
		tmp = t_3;
	} else if (z <= 9e+26) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (z <= 1.9e+191) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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 = t * (a * (-4.0d0))
    t_2 = (t_1 + (y * (x * (9.0d0 / z)))) / c
    t_3 = (t_1 + (b / z)) / c
    if (z <= (-1d+103)) then
        tmp = t_2
    else if (z <= (-9d-12)) then
        tmp = t_3
    else if (z <= 9d+26) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else if (z <= 1.9d+191) then
        tmp = t_3
    else
        tmp = t_2
    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 = t * (a * -4.0);
	double t_2 = (t_1 + (y * (x * (9.0 / z)))) / c;
	double t_3 = (t_1 + (b / z)) / c;
	double tmp;
	if (z <= -1e+103) {
		tmp = t_2;
	} else if (z <= -9e-12) {
		tmp = t_3;
	} else if (z <= 9e+26) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (z <= 1.9e+191) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	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 = t * (a * -4.0)
	t_2 = (t_1 + (y * (x * (9.0 / z)))) / c
	t_3 = (t_1 + (b / z)) / c
	tmp = 0
	if z <= -1e+103:
		tmp = t_2
	elif z <= -9e-12:
		tmp = t_3
	elif z <= 9e+26:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	elif z <= 1.9e+191:
		tmp = t_3
	else:
		tmp = t_2
	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(t * Float64(a * -4.0))
	t_2 = Float64(Float64(t_1 + Float64(y * Float64(x * Float64(9.0 / z)))) / c)
	t_3 = Float64(Float64(t_1 + Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -1e+103)
		tmp = t_2;
	elseif (z <= -9e-12)
		tmp = t_3;
	elseif (z <= 9e+26)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	elseif (z <= 1.9e+191)
		tmp = t_3;
	else
		tmp = t_2;
	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 = t * (a * -4.0);
	t_2 = (t_1 + (y * (x * (9.0 / z)))) / c;
	t_3 = (t_1 + (b / z)) / c;
	tmp = 0.0;
	if (z <= -1e+103)
		tmp = t_2;
	elseif (z <= -9e-12)
		tmp = t_3;
	elseif (z <= 9e+26)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	elseif (z <= 1.9e+191)
		tmp = t_3;
	else
		tmp = t_2;
	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[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(y * N[(x * N[(9.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1e+103], t$95$2, If[LessEqual[z, -9e-12], t$95$3, If[LessEqual[z, 9e+26], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+191], t$95$3, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e103 or 1.8999999999999999e191 < z

   1. Initial program 46.4%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 86.1%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)}, z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. *-lowering-*.f64 75.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 75.4%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{\left(x \cdot y\right) \cdot 9}{z}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(x \cdot y\right) \cdot \frac{9}{z}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(y \cdot x\right) \cdot \frac{9}{z}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      4. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \left(x \cdot \frac{9}{z}\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(x \cdot \frac{9}{z}\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \left(\frac{9}{z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      7. /-lowering-/.f64 82.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(9, z\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   9. Applied egg-rr 82.3%

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

   if -1e103 < z < -8.99999999999999962e-12 or 8.99999999999999957e26 < z < 1.8999999999999999e191

   1. Initial program 82.3%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 98.2%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{b}{z}\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 87.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 87.0%

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

   if -8.99999999999999962e-12 < z < 8.99999999999999957e26

   1. Initial program 96.1%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)}, b\right), \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      2. *-lowering-*.f64 83.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   5. Simplified 83.3%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+103}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + y \cdot \left(x \cdot \frac{9}{z}\right)}{c}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-12}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+26}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+191}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + y \cdot \left(x \cdot \frac{9}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 48.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{+56}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-224}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9}{\frac{c}{y}}\\ \end{array} \end{array} \]

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 (* t (* a (/ -4.0 c)))))
   (if (<= x -1.65e+56)
     (* 9.0 (* y (/ x (* z c))))
     (if (<= x -7.6e-147)
       t_1
       (if (<= x -4.5e-224)
         (/ (/ b c) z)
         (if (<= x 1.2e-89) t_1 (* (/ x z) (/ 9.0 (/ c y)))))))))

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 = t * (a * (-4.0 / c));
	double tmp;
	if (x <= -1.65e+56) {
		tmp = 9.0 * (y * (x / (z * c)));
	} else if (x <= -7.6e-147) {
		tmp = t_1;
	} else if (x <= -4.5e-224) {
		tmp = (b / c) / z;
	} else if (x <= 1.2e-89) {
		tmp = t_1;
	} else {
		tmp = (x / z) * (9.0 / (c / y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    t_1 = t * (a * ((-4.0d0) / c))
    if (x <= (-1.65d+56)) then
        tmp = 9.0d0 * (y * (x / (z * c)))
    else if (x <= (-7.6d-147)) then
        tmp = t_1
    else if (x <= (-4.5d-224)) then
        tmp = (b / c) / z
    else if (x <= 1.2d-89) then
        tmp = t_1
    else
        tmp = (x / z) * (9.0d0 / (c / y))
    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 = t * (a * (-4.0 / c));
	double tmp;
	if (x <= -1.65e+56) {
		tmp = 9.0 * (y * (x / (z * c)));
	} else if (x <= -7.6e-147) {
		tmp = t_1;
	} else if (x <= -4.5e-224) {
		tmp = (b / c) / z;
	} else if (x <= 1.2e-89) {
		tmp = t_1;
	} else {
		tmp = (x / z) * (9.0 / (c / y));
	}
	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 = t * (a * (-4.0 / c))
	tmp = 0
	if x <= -1.65e+56:
		tmp = 9.0 * (y * (x / (z * c)))
	elif x <= -7.6e-147:
		tmp = t_1
	elif x <= -4.5e-224:
		tmp = (b / c) / z
	elif x <= 1.2e-89:
		tmp = t_1
	else:
		tmp = (x / z) * (9.0 / (c / y))
	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(t * Float64(a * Float64(-4.0 / c)))
	tmp = 0.0
	if (x <= -1.65e+56)
		tmp = Float64(9.0 * Float64(y * Float64(x / Float64(z * c))));
	elseif (x <= -7.6e-147)
		tmp = t_1;
	elseif (x <= -4.5e-224)
		tmp = Float64(Float64(b / c) / z);
	elseif (x <= 1.2e-89)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / z) * Float64(9.0 / Float64(c / y)));
	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 = t * (a * (-4.0 / c));
	tmp = 0.0;
	if (x <= -1.65e+56)
		tmp = 9.0 * (y * (x / (z * c)));
	elseif (x <= -7.6e-147)
		tmp = t_1;
	elseif (x <= -4.5e-224)
		tmp = (b / c) / z;
	elseif (x <= 1.2e-89)
		tmp = t_1;
	else
		tmp = (x / z) * (9.0 / (c / y));
	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[(t * N[(a * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.65e+56], N[(9.0 * N[(y * N[(x / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.6e-147], t$95$1, If[LessEqual[x, -4.5e-224], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, 1.2e-89], t$95$1, N[(N[(x / z), $MachinePrecision] * N[(9.0 / N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.65000000000000001e56

   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 x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \color{blue}{\left(\frac{x \cdot y}{c \cdot z}\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(9, \left(\frac{x \cdot y}{z \cdot \color{blue}{c}}\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \mathsf{*.f64}\left(9, \left(\frac{\frac{x \cdot y}{z}}{\color{blue}{c}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\left(\frac{x \cdot y}{z}\right), \color{blue}{c}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot y\right), z\right), c\right)\right) \]

      6. *-lowering-*.f64 56.4%

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), c\right)\right) \]

   5. Simplified 56.4%

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

      1. associate-/r* N/A

         \[\leadsto \mathsf{*.f64}\left(9, \left(\frac{x \cdot y}{\color{blue}{z \cdot c}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(9, \left(\frac{y \cdot x}{\color{blue}{z} \cdot c}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(9, \left(y \cdot \color{blue}{\frac{x}{z \cdot c}}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{x}{z \cdot c}\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{\left(z \cdot c\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 61.5%

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right)\right)\right) \]

   7. Applied egg-rr 61.5%

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

   if -1.65000000000000001e56 < x < -7.60000000000000055e-147 or -4.5000000000000004e-224 < x < 1.20000000000000008e-89

   1. Initial program 80.2%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot t\right)\right), \color{blue}{c}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot t\right) \cdot -4\right), c\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(t \cdot -4\right)\right), c\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(-4 \cdot t\right)\right), c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(-4 \cdot t\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(t \cdot -4\right)\right), c\right) \]

      8. *-lowering-*.f64 48.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, -4\right)\right), c\right) \]

   5. Simplified 48.0%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-*l* N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{-4}{c} \cdot a\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\left(\frac{-4}{c}\right), \color{blue}{a}\right)\right) \]

      7. /-lowering-/.f64 48.3%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(-4, c\right), a\right)\right) \]

   7. Applied egg-rr 48.3%

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

   if -7.60000000000000055e-147 < x < -4.5000000000000004e-224

   1. Initial program 82.0%

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

   3. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 57.8%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 57.8%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{b}{c}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 63.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, c\right), z\right) \]

   7. Applied egg-rr 63.8%

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

   if 1.20000000000000008e-89 < x

   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. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \color{blue}{\left(\frac{x \cdot y}{c \cdot z}\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(9, \left(\frac{x \cdot y}{z \cdot \color{blue}{c}}\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \mathsf{*.f64}\left(9, \left(\frac{\frac{x \cdot y}{z}}{\color{blue}{c}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\left(\frac{x \cdot y}{z}\right), \color{blue}{c}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot y\right), z\right), c\right)\right) \]

      6. *-lowering-*.f64 44.9%

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), c\right)\right) \]

   5. Simplified 44.9%

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

      1. associate-*r/ N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*r/ N/A

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

      6. associate-/r* N/A

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

      7. clear-num N/A

         \[\leadsto \left(x \cdot 9\right) \cdot \frac{1}{\color{blue}{\frac{z \cdot c}{y}}} \]

      8. un-div-inv N/A

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

      9. associate-/l* N/A

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

      10. times-frac N/A

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

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{z}\right), \color{blue}{\left(\frac{9}{\frac{c}{y}}\right)}\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\frac{\color{blue}{9}}{\frac{c}{y}}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{/.f64}\left(9, \color{blue}{\left(\frac{c}{y}\right)}\right)\right) \]

      14. /-lowering-/.f64 49.4%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{/.f64}\left(9, \mathsf{/.f64}\left(c, \color{blue}{y}\right)\right)\right) \]

   7. Applied egg-rr 49.4%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{9}{\frac{c}{y}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+56}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-147}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-224}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-89}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9}{\frac{c}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{if}\;x \leq -4.3 \cdot 10^{+55}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-224}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \end{array} \end{array} \]

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 (* t (* a (/ -4.0 c)))))
   (if (<= x -4.3e+55)
     (* 9.0 (* y (/ x (* z c))))
     (if (<= x -7.2e-147)
       t_1
       (if (<= x -6.5e-224)
         (/ (/ b c) z)
         (if (<= x 4.8e-89) t_1 (* 9.0 (* (/ x z) (/ y 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 = t * (a * (-4.0 / c));
	double tmp;
	if (x <= -4.3e+55) {
		tmp = 9.0 * (y * (x / (z * c)));
	} else if (x <= -7.2e-147) {
		tmp = t_1;
	} else if (x <= -6.5e-224) {
		tmp = (b / c) / z;
	} else if (x <= 4.8e-89) {
		tmp = t_1;
	} else {
		tmp = 9.0 * ((x / z) * (y / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    t_1 = t * (a * ((-4.0d0) / c))
    if (x <= (-4.3d+55)) then
        tmp = 9.0d0 * (y * (x / (z * c)))
    else if (x <= (-7.2d-147)) then
        tmp = t_1
    else if (x <= (-6.5d-224)) then
        tmp = (b / c) / z
    else if (x <= 4.8d-89) then
        tmp = t_1
    else
        tmp = 9.0d0 * ((x / z) * (y / 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 t_1 = t * (a * (-4.0 / c));
	double tmp;
	if (x <= -4.3e+55) {
		tmp = 9.0 * (y * (x / (z * c)));
	} else if (x <= -7.2e-147) {
		tmp = t_1;
	} else if (x <= -6.5e-224) {
		tmp = (b / c) / z;
	} else if (x <= 4.8e-89) {
		tmp = t_1;
	} else {
		tmp = 9.0 * ((x / z) * (y / 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):
	t_1 = t * (a * (-4.0 / c))
	tmp = 0
	if x <= -4.3e+55:
		tmp = 9.0 * (y * (x / (z * c)))
	elif x <= -7.2e-147:
		tmp = t_1
	elif x <= -6.5e-224:
		tmp = (b / c) / z
	elif x <= 4.8e-89:
		tmp = t_1
	else:
		tmp = 9.0 * ((x / z) * (y / 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(t * Float64(a * Float64(-4.0 / c)))
	tmp = 0.0
	if (x <= -4.3e+55)
		tmp = Float64(9.0 * Float64(y * Float64(x / Float64(z * c))));
	elseif (x <= -7.2e-147)
		tmp = t_1;
	elseif (x <= -6.5e-224)
		tmp = Float64(Float64(b / c) / z);
	elseif (x <= 4.8e-89)
		tmp = t_1;
	else
		tmp = Float64(9.0 * Float64(Float64(x / z) * Float64(y / 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)
	t_1 = t * (a * (-4.0 / c));
	tmp = 0.0;
	if (x <= -4.3e+55)
		tmp = 9.0 * (y * (x / (z * c)));
	elseif (x <= -7.2e-147)
		tmp = t_1;
	elseif (x <= -6.5e-224)
		tmp = (b / c) / z;
	elseif (x <= 4.8e-89)
		tmp = t_1;
	else
		tmp = 9.0 * ((x / z) * (y / 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_] := Block[{t$95$1 = N[(t * N[(a * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.3e+55], N[(9.0 * N[(y * N[(x / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.2e-147], t$95$1, If[LessEqual[x, -6.5e-224], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, 4.8e-89], t$95$1, N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.2999999999999999e55

   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 x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \color{blue}{\left(\frac{x \cdot y}{c \cdot z}\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(9, \left(\frac{x \cdot y}{z \cdot \color{blue}{c}}\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \mathsf{*.f64}\left(9, \left(\frac{\frac{x \cdot y}{z}}{\color{blue}{c}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\left(\frac{x \cdot y}{z}\right), \color{blue}{c}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot y\right), z\right), c\right)\right) \]

      6. *-lowering-*.f64 56.4%

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), c\right)\right) \]

   5. Simplified 56.4%

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

      1. associate-/r* N/A

         \[\leadsto \mathsf{*.f64}\left(9, \left(\frac{x \cdot y}{\color{blue}{z \cdot c}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(9, \left(\frac{y \cdot x}{\color{blue}{z} \cdot c}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(9, \left(y \cdot \color{blue}{\frac{x}{z \cdot c}}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{x}{z \cdot c}\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{\left(z \cdot c\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 61.5%

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right)\right)\right) \]

   7. Applied egg-rr 61.5%

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

   if -4.2999999999999999e55 < x < -7.20000000000000023e-147 or -6.5e-224 < x < 4.80000000000000032e-89

   1. Initial program 80.2%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot t\right)\right), \color{blue}{c}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot t\right) \cdot -4\right), c\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(t \cdot -4\right)\right), c\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(-4 \cdot t\right)\right), c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(-4 \cdot t\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(t \cdot -4\right)\right), c\right) \]

      8. *-lowering-*.f64 48.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, -4\right)\right), c\right) \]

   5. Simplified 48.0%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-*l* N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{-4}{c} \cdot a\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\left(\frac{-4}{c}\right), \color{blue}{a}\right)\right) \]

      7. /-lowering-/.f64 48.3%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(-4, c\right), a\right)\right) \]

   7. Applied egg-rr 48.3%

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

   if -7.20000000000000023e-147 < x < -6.5e-224

   1. Initial program 82.0%

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

   3. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 57.8%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 57.8%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{b}{c}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 63.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, c\right), z\right) \]

   7. Applied egg-rr 63.8%

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

   if 4.80000000000000032e-89 < x

   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. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \color{blue}{\left(\frac{x \cdot y}{c \cdot z}\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(9, \left(\frac{x \cdot y}{z \cdot \color{blue}{c}}\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \mathsf{*.f64}\left(9, \left(\frac{\frac{x \cdot y}{z}}{\color{blue}{c}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\left(\frac{x \cdot y}{z}\right), \color{blue}{c}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot y\right), z\right), c\right)\right) \]

      6. *-lowering-*.f64 44.9%

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), c\right)\right) \]

   5. Simplified 44.9%

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

      1. associate-/l/ N/A

         \[\leadsto \mathsf{*.f64}\left(9, \left(\frac{x \cdot y}{\color{blue}{c \cdot z}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(9, \left(\frac{y \cdot x}{\color{blue}{c} \cdot z}\right)\right) \]

      3. times-frac N/A

         \[\leadsto \mathsf{*.f64}\left(9, \left(\frac{y}{c} \cdot \color{blue}{\frac{x}{z}}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(\left(\frac{y}{c}\right), \color{blue}{\left(\frac{x}{z}\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, c\right), \left(\frac{\color{blue}{x}}{z}\right)\right)\right) \]

      6. /-lowering-/.f64 49.4%

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, c\right), \mathsf{/.f64}\left(x, \color{blue}{z}\right)\right)\right) \]

   7. Applied egg-rr 49.4%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+55}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-147}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-224}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-89}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 48.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot \frac{-4}{c}\right)\\ t_2 := 9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{if}\;x \leq -1.06 \cdot 10^{+57}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-224}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* t (* a (/ -4.0 c)))) (t_2 (* 9.0 (* y (/ x (* z c))))))
   (if (<= x -1.06e+57)
     t_2
     (if (<= x -2.9e-146)
       t_1
       (if (<= x -7.5e-224) (/ (/ b c) z) (if (<= x 2.9e-89) t_1 t_2))))))

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 = t * (a * (-4.0 / c));
	double t_2 = 9.0 * (y * (x / (z * c)));
	double tmp;
	if (x <= -1.06e+57) {
		tmp = t_2;
	} else if (x <= -2.9e-146) {
		tmp = t_1;
	} else if (x <= -7.5e-224) {
		tmp = (b / c) / z;
	} else if (x <= 2.9e-89) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    t_1 = t * (a * ((-4.0d0) / c))
    t_2 = 9.0d0 * (y * (x / (z * c)))
    if (x <= (-1.06d+57)) then
        tmp = t_2
    else if (x <= (-2.9d-146)) then
        tmp = t_1
    else if (x <= (-7.5d-224)) then
        tmp = (b / c) / z
    else if (x <= 2.9d-89) then
        tmp = t_1
    else
        tmp = t_2
    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 = t * (a * (-4.0 / c));
	double t_2 = 9.0 * (y * (x / (z * c)));
	double tmp;
	if (x <= -1.06e+57) {
		tmp = t_2;
	} else if (x <= -2.9e-146) {
		tmp = t_1;
	} else if (x <= -7.5e-224) {
		tmp = (b / c) / z;
	} else if (x <= 2.9e-89) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = t * (a * (-4.0 / c))
	t_2 = 9.0 * (y * (x / (z * c)))
	tmp = 0
	if x <= -1.06e+57:
		tmp = t_2
	elif x <= -2.9e-146:
		tmp = t_1
	elif x <= -7.5e-224:
		tmp = (b / c) / z
	elif x <= 2.9e-89:
		tmp = t_1
	else:
		tmp = t_2
	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(t * Float64(a * Float64(-4.0 / c)))
	t_2 = Float64(9.0 * Float64(y * Float64(x / Float64(z * c))))
	tmp = 0.0
	if (x <= -1.06e+57)
		tmp = t_2;
	elseif (x <= -2.9e-146)
		tmp = t_1;
	elseif (x <= -7.5e-224)
		tmp = Float64(Float64(b / c) / z);
	elseif (x <= 2.9e-89)
		tmp = t_1;
	else
		tmp = t_2;
	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 = t * (a * (-4.0 / c));
	t_2 = 9.0 * (y * (x / (z * c)));
	tmp = 0.0;
	if (x <= -1.06e+57)
		tmp = t_2;
	elseif (x <= -2.9e-146)
		tmp = t_1;
	elseif (x <= -7.5e-224)
		tmp = (b / c) / z;
	elseif (x <= 2.9e-89)
		tmp = t_1;
	else
		tmp = t_2;
	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[(t * N[(a * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(y * N[(x / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.06e+57], t$95$2, If[LessEqual[x, -2.9e-146], t$95$1, If[LessEqual[x, -7.5e-224], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, 2.9e-89], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.06e57 or 2.89999999999999992e-89 < x

   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 inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \color{blue}{\left(\frac{x \cdot y}{c \cdot z}\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(9, \left(\frac{x \cdot y}{z \cdot \color{blue}{c}}\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \mathsf{*.f64}\left(9, \left(\frac{\frac{x \cdot y}{z}}{\color{blue}{c}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\left(\frac{x \cdot y}{z}\right), \color{blue}{c}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot y\right), z\right), c\right)\right) \]

      6. *-lowering-*.f64 49.5%

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), c\right)\right) \]

   5. Simplified 49.5%

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

      1. associate-/r* N/A

         \[\leadsto \mathsf{*.f64}\left(9, \left(\frac{x \cdot y}{\color{blue}{z \cdot c}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(9, \left(\frac{y \cdot x}{\color{blue}{z} \cdot c}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(9, \left(y \cdot \color{blue}{\frac{x}{z \cdot c}}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{x}{z \cdot c}\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{\left(z \cdot c\right)}\right)\right)\right) \]

      6. *-lowering-*.f64 55.1%

         \[\leadsto \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right)\right)\right) \]

   7. Applied egg-rr 55.1%

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

   if -1.06e57 < x < -2.90000000000000011e-146 or -7.49999999999999978e-224 < x < 2.89999999999999992e-89

   1. Initial program 80.2%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot t\right)\right), \color{blue}{c}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot t\right) \cdot -4\right), c\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(t \cdot -4\right)\right), c\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(-4 \cdot t\right)\right), c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(-4 \cdot t\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(t \cdot -4\right)\right), c\right) \]

      8. *-lowering-*.f64 48.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, -4\right)\right), c\right) \]

   5. Simplified 48.0%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-*l* N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{-4}{c} \cdot a\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\left(\frac{-4}{c}\right), \color{blue}{a}\right)\right) \]

      7. /-lowering-/.f64 48.3%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(-4, c\right), a\right)\right) \]

   7. Applied egg-rr 48.3%

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

   if -2.90000000000000011e-146 < x < -7.49999999999999978e-224

   1. Initial program 82.0%

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

   3. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 57.8%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 57.8%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{b}{c}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 63.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, c\right), z\right) \]

   7. Applied egg-rr 63.8%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{+57}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-146}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-224}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-89}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{if}\;z \leq -4 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-56}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - t \cdot \left(a \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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)) b) z) (* t (* a -4.0))) c)))
   (if (<= z -4e-85)
     t_1
     (if (<= z 1.25e-56)
       (/ (+ b (- (* y (* x 9.0)) (* t (* a (* z 4.0))))) (* z c))
       t_1))))

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)) + b) / z) + (t * (a * -4.0))) / c;
	double tmp;
	if (z <= -4e-85) {
		tmp = t_1;
	} else if (z <= 1.25e-56) {
		tmp = (b + ((y * (x * 9.0)) - (t * (a * (z * 4.0))))) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    t_1 = ((((x * (9.0d0 * y)) + b) / z) + (t * (a * (-4.0d0)))) / c
    if (z <= (-4d-85)) then
        tmp = t_1
    else if (z <= 1.25d-56) then
        tmp = (b + ((y * (x * 9.0d0)) - (t * (a * (z * 4.0d0))))) / (z * c)
    else
        tmp = t_1
    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 = ((((x * (9.0 * y)) + b) / z) + (t * (a * -4.0))) / c;
	double tmp;
	if (z <= -4e-85) {
		tmp = t_1;
	} else if (z <= 1.25e-56) {
		tmp = (b + ((y * (x * 9.0)) - (t * (a * (z * 4.0))))) / (z * c);
	} else {
		tmp = t_1;
	}
	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 = ((((x * (9.0 * y)) + b) / z) + (t * (a * -4.0))) / c
	tmp = 0
	if z <= -4e-85:
		tmp = t_1
	elif z <= 1.25e-56:
		tmp = (b + ((y * (x * 9.0)) - (t * (a * (z * 4.0))))) / (z * c)
	else:
		tmp = t_1
	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 * Float64(9.0 * y)) + b) / z) + Float64(t * Float64(a * -4.0))) / c)
	tmp = 0.0
	if (z <= -4e-85)
		tmp = t_1;
	elseif (z <= 1.25e-56)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(t * Float64(a * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = t_1;
	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 = ((((x * (9.0 * y)) + b) / z) + (t * (a * -4.0))) / c;
	tmp = 0.0;
	if (z <= -4e-85)
		tmp = t_1;
	elseif (z <= 1.25e-56)
		tmp = (b + ((y * (x * 9.0)) - (t * (a * (z * 4.0))))) / (z * c);
	else
		tmp = t_1;
	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[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -4e-85], t$95$1, If[LessEqual[z, 1.25e-56], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9999999999999999e-85 or 1.24999999999999999e-56 < z

   1. Initial program 68.1%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 91.9%

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

   if -3.9999999999999999e-85 < z < 1.24999999999999999e-56

   1. Initial program 97.0%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 9\right), y\right), \left(a \cdot \left(\left(z \cdot 4\right) \cdot t\right)\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 9\right), y\right), \left(\left(a \cdot \left(z \cdot 4\right)\right) \cdot t\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 9\right), y\right), \mathsf{*.f64}\left(\left(a \cdot \left(z \cdot 4\right)\right), t\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 9\right), y\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \left(z \cdot 4\right)\right), t\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      5. *-lowering-*.f64 98.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 9\right), y\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(z, 4\right)\right), t\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   4. Applied egg-rr 98.0%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-85}:\\ \;\;\;\;\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-56}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - t \cdot \left(a \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;x \leq -5 \cdot 10^{+68}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c} + x \cdot \left(9 \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-104}:\\ \;\;\;\;\frac{t\_1 + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1 + y \cdot \left(x \cdot \frac{9}{z}\right)}{c}\\ \end{array} \end{array} \]

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 (* t (* a -4.0))))
   (if (<= x -5e+68)
     (+ (* -4.0 (/ (* t a) c)) (* x (* 9.0 (/ y (* z c)))))
     (if (<= x 7.2e-104)
       (/ (+ t_1 (/ b z)) c)
       (/ (+ t_1 (* 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 = t * (a * -4.0);
	double tmp;
	if (x <= -5e+68) {
		tmp = (-4.0 * ((t * a) / c)) + (x * (9.0 * (y / (z * c))));
	} else if (x <= 7.2e-104) {
		tmp = (t_1 + (b / z)) / c;
	} else {
		tmp = (t_1 + (y * (x * (9.0 / z)))) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    t_1 = t * (a * (-4.0d0))
    if (x <= (-5d+68)) then
        tmp = ((-4.0d0) * ((t * a) / c)) + (x * (9.0d0 * (y / (z * c))))
    else if (x <= 7.2d-104) then
        tmp = (t_1 + (b / z)) / c
    else
        tmp = (t_1 + (y * (x * (9.0d0 / z)))) / 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 t_1 = t * (a * -4.0);
	double tmp;
	if (x <= -5e+68) {
		tmp = (-4.0 * ((t * a) / c)) + (x * (9.0 * (y / (z * c))));
	} else if (x <= 7.2e-104) {
		tmp = (t_1 + (b / z)) / c;
	} else {
		tmp = (t_1 + (y * (x * (9.0 / z)))) / 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):
	t_1 = t * (a * -4.0)
	tmp = 0
	if x <= -5e+68:
		tmp = (-4.0 * ((t * a) / c)) + (x * (9.0 * (y / (z * c))))
	elif x <= 7.2e-104:
		tmp = (t_1 + (b / z)) / c
	else:
		tmp = (t_1 + (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(t * Float64(a * -4.0))
	tmp = 0.0
	if (x <= -5e+68)
		tmp = Float64(Float64(-4.0 * Float64(Float64(t * a) / c)) + Float64(x * Float64(9.0 * Float64(y / Float64(z * c)))));
	elseif (x <= 7.2e-104)
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(t_1 + Float64(y * Float64(x * Float64(9.0 / z)))) / 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)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (x <= -5e+68)
		tmp = (-4.0 * ((t * a) / c)) + (x * (9.0 * (y / (z * c))));
	elseif (x <= 7.2e-104)
		tmp = (t_1 + (b / z)) / c;
	else
		tmp = (t_1 + (y * (x * (9.0 / z)))) / 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_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5e+68], N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(x * N[(9.0 * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.2e-104], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(t$95$1 + N[(y * N[(x * N[(9.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.0000000000000004e68

   1. Initial program 76.5%

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

   3. Taylor expanded in b around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right), \color{blue}{\left(c \cdot z\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(9 \cdot \left(x \cdot y\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot \left(t \cdot z\right)\right)\right), \left(\color{blue}{c} \cdot z\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(9 \cdot \left(x \cdot y\right) + -4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right), \left(c \cdot z\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), \left(-4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)\right), \left(\color{blue}{c} \cdot z\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), \left(-4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)\right), \left(c \cdot z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \left(-4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)\right), \left(c \cdot z\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \left(\left(a \cdot \left(t \cdot z\right)\right) \cdot -4\right)\right), \left(c \cdot z\right)\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \left(a \cdot \left(\left(t \cdot z\right) \cdot -4\right)\right)\right), \left(c \cdot z\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \left(a \cdot \left(-4 \cdot \left(t \cdot z\right)\right)\right)\right), \left(c \cdot z\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, \left(-4 \cdot \left(t \cdot z\right)\right)\right)\right), \left(c \cdot z\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, \left(\left(t \cdot z\right) \cdot -4\right)\right)\right), \left(c \cdot z\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\left(t \cdot z\right), -4\right)\right)\right), \left(c \cdot z\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), -4\right)\right)\right), \left(c \cdot z\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), -4\right)\right)\right), \left(z \cdot \color{blue}{c}\right)\right) \]

      15. *-lowering-*.f64 69.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), -4\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 69.3%

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

   6. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-4 \cdot \frac{a \cdot t}{c}\right), \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z}\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \left(\frac{a \cdot t}{c}\right)\right), \left(\color{blue}{9} \cdot \frac{x \cdot y}{c \cdot z}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\left(a \cdot t\right), c\right)\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right)\right), \left(9 \cdot \frac{x \cdot y}{c \cdot z}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right)\right), \left(\frac{x \cdot y}{c \cdot z} \cdot \color{blue}{9}\right)\right) \]

      6. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right)\right), \left(\left(x \cdot \frac{y}{c \cdot z}\right) \cdot 9\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right)\right), \left(x \cdot \color{blue}{\left(\frac{y}{c \cdot z} \cdot 9\right)}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right)\right), \left(x \cdot \left(9 \cdot \color{blue}{\frac{y}{c \cdot z}}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right)\right), \mathsf{*.f64}\left(x, \color{blue}{\left(9 \cdot \frac{y}{c \cdot z}\right)}\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right)\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(9, \color{blue}{\left(\frac{y}{c \cdot z}\right)}\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right)\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(9, \mathsf{/.f64}\left(y, \color{blue}{\left(c \cdot z\right)}\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right)\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(9, \mathsf{/.f64}\left(y, \left(z \cdot \color{blue}{c}\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 83.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right)\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(9, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right)\right)\right)\right) \]

   8. Simplified 83.8%

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

   if -5.0000000000000004e68 < x < 7.1999999999999996e-104

   1. Initial program 81.2%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 91.8%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{b}{z}\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 78.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 78.7%

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

   if 7.1999999999999996e-104 < x

   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. Step-by-step derivation

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 85.1%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)}, z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. *-lowering-*.f64 66.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 66.8%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{\left(x \cdot y\right) \cdot 9}{z}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(x \cdot y\right) \cdot \frac{9}{z}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(y \cdot x\right) \cdot \frac{9}{z}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      4. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \left(x \cdot \frac{9}{z}\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(x \cdot \frac{9}{z}\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \left(\frac{9}{z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      7. /-lowering-/.f64 68.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(9, z\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   9. Applied egg-rr 68.7%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+68}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c} + x \cdot \left(9 \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-104}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + y \cdot \left(x \cdot \frac{9}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 3.3 \cdot 10^{+217}:\\ \;\;\;\;\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-4 \cdot \frac{\frac{t \cdot a}{c}}{y} + \frac{9 \cdot \frac{x}{z}}{c}\right)\\ \end{array} \end{array} \]

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 (<= y 3.3e+217)
   (/ (+ (/ (+ (* x (* 9.0 y)) b) z) (* t (* a -4.0))) c)
   (* y (+ (* -4.0 (/ (/ (* t a) c) y)) (/ (* 9.0 (/ x 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 (y <= 3.3e+217) {
		tmp = ((((x * (9.0 * y)) + b) / z) + (t * (a * -4.0))) / c;
	} else {
		tmp = y * ((-4.0 * (((t * a) / c) / y)) + ((9.0 * (x / z)) / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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 (y <= 3.3d+217) then
        tmp = ((((x * (9.0d0 * y)) + b) / z) + (t * (a * (-4.0d0)))) / c
    else
        tmp = y * (((-4.0d0) * (((t * a) / c) / y)) + ((9.0d0 * (x / z)) / 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 (y <= 3.3e+217) {
		tmp = ((((x * (9.0 * y)) + b) / z) + (t * (a * -4.0))) / c;
	} else {
		tmp = y * ((-4.0 * (((t * a) / c) / y)) + ((9.0 * (x / z)) / 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 y <= 3.3e+217:
		tmp = ((((x * (9.0 * y)) + b) / z) + (t * (a * -4.0))) / c
	else:
		tmp = y * ((-4.0 * (((t * a) / c) / y)) + ((9.0 * (x / 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 (y <= 3.3e+217)
		tmp = Float64(Float64(Float64(Float64(Float64(x * Float64(9.0 * y)) + b) / z) + Float64(t * Float64(a * -4.0))) / c);
	else
		tmp = Float64(y * Float64(Float64(-4.0 * Float64(Float64(Float64(t * a) / c) / y)) + Float64(Float64(9.0 * Float64(x / z)) / 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 (y <= 3.3e+217)
		tmp = ((((x * (9.0 * y)) + b) / z) + (t * (a * -4.0))) / c;
	else
		tmp = y * ((-4.0 * (((t * a) / c) / y)) + ((9.0 * (x / z)) / 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[LessEqual[y, 3.3e+217], N[(N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(y * N[(N[(-4.0 * N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.3e217

   1. Initial program 79.5%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 88.7%

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

   if 3.3e217 < y

   1. Initial program 76.5%

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

   3. Taylor expanded in b around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right), \color{blue}{\left(c \cdot z\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(9 \cdot \left(x \cdot y\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot \left(t \cdot z\right)\right)\right), \left(\color{blue}{c} \cdot z\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(9 \cdot \left(x \cdot y\right) + -4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right), \left(c \cdot z\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), \left(-4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)\right), \left(\color{blue}{c} \cdot z\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), \left(-4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)\right), \left(c \cdot z\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \left(-4 \cdot \left(a \cdot \left(t \cdot z\right)\right)\right)\right), \left(c \cdot z\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \left(\left(a \cdot \left(t \cdot z\right)\right) \cdot -4\right)\right), \left(c \cdot z\right)\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \left(a \cdot \left(\left(t \cdot z\right) \cdot -4\right)\right)\right), \left(c \cdot z\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \left(a \cdot \left(-4 \cdot \left(t \cdot z\right)\right)\right)\right), \left(c \cdot z\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, \left(-4 \cdot \left(t \cdot z\right)\right)\right)\right), \left(c \cdot z\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, \left(\left(t \cdot z\right) \cdot -4\right)\right)\right), \left(c \cdot z\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\left(t \cdot z\right), -4\right)\right)\right), \left(c \cdot z\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), -4\right)\right)\right), \left(c \cdot z\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), -4\right)\right)\right), \left(z \cdot \color{blue}{c}\right)\right) \]

      15. *-lowering-*.f64 76.6%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, z\right), -4\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 76.6%

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

   6. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(-4 \cdot \frac{a \cdot t}{c \cdot y} + 9 \cdot \frac{x}{c \cdot z}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(-4 \cdot \frac{a \cdot t}{c \cdot y}\right), \color{blue}{\left(9 \cdot \frac{x}{c \cdot z}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \left(\frac{a \cdot t}{c \cdot y}\right)\right), \left(\color{blue}{9} \cdot \frac{x}{c \cdot z}\right)\right)\right) \]

      4. associate-/r* N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \left(\frac{\frac{a \cdot t}{c}}{y}\right)\right), \left(9 \cdot \frac{x}{c \cdot z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\left(\frac{a \cdot t}{c}\right), y\right)\right), \left(9 \cdot \frac{x}{c \cdot z}\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(a \cdot t\right), c\right), y\right)\right), \left(9 \cdot \frac{x}{c \cdot z}\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right), y\right)\right), \left(9 \cdot \frac{x}{c \cdot z}\right)\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right), y\right)\right), \left(\frac{9 \cdot x}{\color{blue}{c \cdot z}}\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right), y\right)\right), \left(\frac{9 \cdot x}{z \cdot \color{blue}{c}}\right)\right)\right) \]

      10. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right), y\right)\right), \left(\frac{\frac{9 \cdot x}{z}}{\color{blue}{c}}\right)\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right), y\right)\right), \left(\frac{9 \cdot \frac{x}{z}}{c}\right)\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right), y\right)\right), \mathsf{/.f64}\left(\left(9 \cdot \frac{x}{z}\right), \color{blue}{c}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right), y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(9, \left(\frac{x}{z}\right)\right), c\right)\right)\right) \]

      14. /-lowering-/.f64 93.2%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right), y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(9, \mathsf{/.f64}\left(x, z\right)\right), c\right)\right)\right) \]

   8. Simplified 93.2%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.3 \cdot 10^{+217}:\\ \;\;\;\;\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-4 \cdot \frac{\frac{t \cdot a}{c}}{y} + \frac{9 \cdot \frac{x}{z}}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+28}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (/ (+ (* t (* a -4.0)) (/ b z)) c)))
   (if (<= z -1.55e-13)
     t_1
     (if (<= z 1.26e+28) (/ (+ b (* 9.0 (* x y))) (* z c)) t_1))))

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 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -1.55e-13) {
		tmp = t_1;
	} else if (z <= 1.26e+28) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    t_1 = ((t * (a * (-4.0d0))) + (b / z)) / c
    if (z <= (-1.55d-13)) then
        tmp = t_1
    else if (z <= 1.26d+28) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else
        tmp = t_1
    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 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -1.55e-13) {
		tmp = t_1;
	} else if (z <= 1.26e+28) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = t_1;
	}
	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 = ((t * (a * -4.0)) + (b / z)) / c
	tmp = 0
	if z <= -1.55e-13:
		tmp = t_1
	elif z <= 1.26e+28:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = t_1
	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(t * Float64(a * -4.0)) + Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -1.55e-13)
		tmp = t_1;
	elseif (z <= 1.26e+28)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	else
		tmp = t_1;
	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 = ((t * (a * -4.0)) + (b / z)) / c;
	tmp = 0.0;
	if (z <= -1.55e-13)
		tmp = t_1;
	elseif (z <= 1.26e+28)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = t_1;
	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[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.55e-13], t$95$1, If[LessEqual[z, 1.26e+28], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.55e-13 or 1.26e28 < z

   1. Initial program 63.0%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 91.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{b}{z}\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 75.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 75.5%

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

   if -1.55e-13 < z < 1.26e28

   1. Initial program 96.1%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)}, b\right), \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      2. *-lowering-*.f64 83.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   5. Simplified 83.3%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-13}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+28}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+48}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+138}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c}{t \cdot -4}}\\ \end{array} \end{array} \]

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
 (if (<= z -4.2e+48)
   (/ (* a (* t -4.0)) c)
   (if (<= z 2.1e+138)
     (/ (+ b (* 9.0 (* x y))) (* z c))
     (/ a (/ c (* t -4.0))))))

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 <= -4.2e+48) {
		tmp = (a * (t * -4.0)) / c;
	} else if (z <= 2.1e+138) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = a / (c / (t * -4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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 (z <= (-4.2d+48)) then
        tmp = (a * (t * (-4.0d0))) / c
    else if (z <= 2.1d+138) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else
        tmp = a / (c / (t * (-4.0d0)))
    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 (z <= -4.2e+48) {
		tmp = (a * (t * -4.0)) / c;
	} else if (z <= 2.1e+138) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = a / (c / (t * -4.0));
	}
	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 z <= -4.2e+48:
		tmp = (a * (t * -4.0)) / c
	elif z <= 2.1e+138:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = a / (c / (t * -4.0))
	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 <= -4.2e+48)
		tmp = Float64(Float64(a * Float64(t * -4.0)) / c);
	elseif (z <= 2.1e+138)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	else
		tmp = Float64(a / Float64(c / Float64(t * -4.0)));
	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 (z <= -4.2e+48)
		tmp = (a * (t * -4.0)) / c;
	elseif (z <= 2.1e+138)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = a / (c / (t * -4.0));
	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[LessEqual[z, -4.2e+48], N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 2.1e+138], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(a / N[(c / N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.1999999999999997e48

   1. Initial program 58.9%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot t\right)\right), \color{blue}{c}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot t\right) \cdot -4\right), c\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(t \cdot -4\right)\right), c\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(-4 \cdot t\right)\right), c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(-4 \cdot t\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(t \cdot -4\right)\right), c\right) \]

      8. *-lowering-*.f64 60.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, -4\right)\right), c\right) \]

   5. Simplified 60.6%

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

   if -4.1999999999999997e48 < z < 2.10000000000000007e138

   1. Initial program 94.7%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)}, b\right), \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      2. *-lowering-*.f64 78.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   5. Simplified 78.7%

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

   if 2.10000000000000007e138 < z

   1. Initial program 41.9%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot t\right)\right), \color{blue}{c}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot t\right) \cdot -4\right), c\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(t \cdot -4\right)\right), c\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(-4 \cdot t\right)\right), c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(-4 \cdot t\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(t \cdot -4\right)\right), c\right) \]

      8. *-lowering-*.f64 54.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, -4\right)\right), c\right) \]

   5. Simplified 54.9%

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

      1. associate-*r/ N/A

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

      2. clear-num N/A

         \[\leadsto a \cdot \frac{1}{\color{blue}{\frac{c}{t \cdot -4}}} \]

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(a, \color{blue}{\left(\frac{c}{t \cdot -4}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(c, \color{blue}{\left(t \cdot -4\right)}\right)\right) \]

      6. *-lowering-*.f64 54.9%

         \[\leadsto \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(c, \mathsf{*.f64}\left(t, \color{blue}{-4}\right)\right)\right) \]

   7. Applied egg-rr 54.9%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+48}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+138}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c}{t \cdot -4}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{-185}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+50}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* t (* a (/ -4.0 c)))))
   (if (<= a -2.5e-185) t_1 (if (<= a 2.6e+50) (/ b (* z c)) t_1))))

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 = t * (a * (-4.0 / c));
	double tmp;
	if (a <= -2.5e-185) {
		tmp = t_1;
	} else if (a <= 2.6e+50) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    t_1 = t * (a * ((-4.0d0) / c))
    if (a <= (-2.5d-185)) then
        tmp = t_1
    else if (a <= 2.6d+50) then
        tmp = b / (z * c)
    else
        tmp = t_1
    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 = t * (a * (-4.0 / c));
	double tmp;
	if (a <= -2.5e-185) {
		tmp = t_1;
	} else if (a <= 2.6e+50) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	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 = t * (a * (-4.0 / c))
	tmp = 0
	if a <= -2.5e-185:
		tmp = t_1
	elif a <= 2.6e+50:
		tmp = b / (z * c)
	else:
		tmp = t_1
	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(t * Float64(a * Float64(-4.0 / c)))
	tmp = 0.0
	if (a <= -2.5e-185)
		tmp = t_1;
	elseif (a <= 2.6e+50)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = t_1;
	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 = t * (a * (-4.0 / c));
	tmp = 0.0;
	if (a <= -2.5e-185)
		tmp = t_1;
	elseif (a <= 2.6e+50)
		tmp = b / (z * c);
	else
		tmp = t_1;
	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[(t * N[(a * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.5e-185], t$95$1, If[LessEqual[a, 2.6e+50], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.5000000000000001e-185 or 2.6000000000000002e50 < a

   1. Initial program 76.5%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot t\right)\right), \color{blue}{c}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot t\right) \cdot -4\right), c\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(t \cdot -4\right)\right), c\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(-4 \cdot t\right)\right), c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(-4 \cdot t\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(t \cdot -4\right)\right), c\right) \]

      8. *-lowering-*.f64 45.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, -4\right)\right), c\right) \]

   5. Simplified 45.8%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-*l* N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{-4}{c} \cdot a\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\left(\frac{-4}{c}\right), \color{blue}{a}\right)\right) \]

      7. /-lowering-/.f64 48.7%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(-4, c\right), a\right)\right) \]

   7. Applied egg-rr 48.7%

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

   if -2.5000000000000001e-185 < a < 2.6000000000000002e50

   1. Initial program 84.5%

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

   3. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 44.0%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 44.0%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-185}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+50}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 85.9% accurate, 1.1× speedup

Math

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

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

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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)) + b) / z) + (t * (a * (-4.0d0)))) / c
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 ((((x * (9.0 * y)) + b) / z) + (t * (a * -4.0))) / c;
}

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 ((((x * (9.0 * y)) + b) / z) + (t * (a * -4.0))) / c

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(Float64(Float64(Float64(Float64(x * Float64(9.0 * y)) + b) / z) + Float64(t * Float64(a * -4.0))) / c)
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 = ((((x * (9.0 * y)) + b) / z) + (t * (a * -4.0))) / c;
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[(N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]

Derivation

1. Initial program 79.3%

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

   1. associate-/r* N/A

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

   2. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

3. Simplified 88.0%

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

Alternative 13: 35.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq 4 \cdot 10^{+25}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

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 (<= c 4e+25) (/ b (* z c)) (/ (/ 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 (c <= 4e+25) {
		tmp = b / (z * c);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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 (c <= 4d+25) then
        tmp = b / (z * c)
    else
        tmp = (b / 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 tmp;
	if (c <= 4e+25) {
		tmp = b / (z * c);
	} else {
		tmp = (b / 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):
	tmp = 0
	if c <= 4e+25:
		tmp = b / (z * c)
	else:
		tmp = (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 (c <= 4e+25)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(Float64(b / 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)
	tmp = 0.0;
	if (c <= 4e+25)
		tmp = b / (z * c);
	else
		tmp = (b / 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_] := If[LessEqual[c, 4e+25], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 4.00000000000000036e25

   1. Initial program 83.2%

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

   3. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 35.1%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 35.1%

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

   if 4.00000000000000036e25 < c

   1. Initial program 64.0%

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

   3. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 17.2%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 17.2%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{b}{c}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 23.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, c\right), z\right) \]

   7. Applied egg-rr 23.3%

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

Alternative 14: 35.3% accurate, 3.8× speedup

Math

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

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 (* 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) {
	return b / (z * c);
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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 / (z * c)
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 / (z * c);
}

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 / (z * c)

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(z * c))
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 / (z * c);
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[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.3%

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

3. Taylor expanded in b around inf

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

   1. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

   3. *-lowering-*.f64 31.4%

      \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

5. Simplified 31.4%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
6. Add Preprocessing

Developer Target 1: 79.6% 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

real(8) function code(x, y, z, t, a, b, c)
    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 2024145 
(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)))