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

Percentage Accurate: 80.6% → 92.1%

Time: 15.7s

Alternatives: 15

Speedup: 0.9×

• 39.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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: 80.6% 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: 92.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+65}:\\ \;\;\;\;\frac{\frac{1}{\frac{z}{9 \cdot \left(x \cdot y\right) + b}} + t\_1}{c}\\ \mathbf{elif}\;z \leq 13000000000000:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1 + y \cdot \left(\frac{9 \cdot x}{z} + \frac{b}{z \cdot y}\right)}{c}\\ \end{array} \end{array} \]

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 (<= z -3.5e+65)
     (/ (+ (/ 1.0 (/ z (+ (* 9.0 (* x y)) b))) t_1) c)
     (if (<= z 13000000000000.0)
       (/ (+ b (- (* x (* 9.0 y)) (* a (* t (* z 4.0))))) (* z c))
       (/ (+ t_1 (* y (+ (/ (* 9.0 x) z) (/ b (* 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);
	double tmp;
	if (z <= -3.5e+65) {
		tmp = ((1.0 / (z / ((9.0 * (x * y)) + b))) + t_1) / c;
	} else if (z <= 13000000000000.0) {
		tmp = (b + ((x * (9.0 * y)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = (t_1 + (y * (((9.0 * x) / z) + (b / (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))
    if (z <= (-3.5d+65)) then
        tmp = ((1.0d0 / (z / ((9.0d0 * (x * y)) + b))) + t_1) / c
    else if (z <= 13000000000000.0d0) then
        tmp = (b + ((x * (9.0d0 * y)) - (a * (t * (z * 4.0d0))))) / (z * c)
    else
        tmp = (t_1 + (y * (((9.0d0 * x) / z) + (b / (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);
	double tmp;
	if (z <= -3.5e+65) {
		tmp = ((1.0 / (z / ((9.0 * (x * y)) + b))) + t_1) / c;
	} else if (z <= 13000000000000.0) {
		tmp = (b + ((x * (9.0 * y)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = (t_1 + (y * (((9.0 * x) / z) + (b / (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)
	tmp = 0
	if z <= -3.5e+65:
		tmp = ((1.0 / (z / ((9.0 * (x * y)) + b))) + t_1) / c
	elif z <= 13000000000000.0:
		tmp = (b + ((x * (9.0 * y)) - (a * (t * (z * 4.0))))) / (z * c)
	else:
		tmp = (t_1 + (y * (((9.0 * x) / z) + (b / (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 * -4.0))
	tmp = 0.0
	if (z <= -3.5e+65)
		tmp = Float64(Float64(Float64(1.0 / Float64(z / Float64(Float64(9.0 * Float64(x * y)) + b))) + t_1) / c);
	elseif (z <= 13000000000000.0)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(Float64(t_1 + Float64(y * Float64(Float64(Float64(9.0 * x) / z) + Float64(b / Float64(z * 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);
	tmp = 0.0;
	if (z <= -3.5e+65)
		tmp = ((1.0 / (z / ((9.0 * (x * y)) + b))) + t_1) / c;
	elseif (z <= 13000000000000.0)
		tmp = (b + ((x * (9.0 * y)) - (a * (t * (z * 4.0))))) / (z * c);
	else
		tmp = (t_1 + (y * (((9.0 * x) / z) + (b / (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 * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+65], N[(N[(N[(1.0 / N[(z / N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 13000000000000.0], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 + N[(y * N[(N[(N[(9.0 * x), $MachinePrecision] / z), $MachinePrecision] + N[(b / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5000000000000001e65

   1. Initial program 59.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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 89.9%

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

      1. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{\frac{z}{x \cdot \left(9 \cdot y\right) + b}}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{z}{x \cdot \left(9 \cdot y\right) + b}\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \left(x \cdot \left(9 \cdot y\right) + b\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \left(\left(x \cdot 9\right) \cdot y + b\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\left(\left(x \cdot 9\right) \cdot y\right), b\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), b\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), b\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      9. *-lowering-*.f64 90.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   6. Applied egg-rr 90.0%

      \[\leadsto \frac{\color{blue}{\frac{1}{\frac{z}{9 \cdot \left(x \cdot y\right) + b}}} + t \cdot \left(a \cdot -4\right)}{c} \]

   if -3.5000000000000001e65 < z < 1.3e13

   1. Initial program 95.6%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. *-lowering-*.f64 95.5%

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

   4. Applied egg-rr 95.5%

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

   if 1.3e13 < z

   1. Initial program 43.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 78.5%

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

   5. Taylor expanded in y around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 85.1%

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

   7. Simplified 85.1%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+65}:\\ \;\;\;\;\frac{\frac{1}{\frac{z}{9 \cdot \left(x \cdot y\right) + b}} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 13000000000000:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + y \cdot \left(\frac{9 \cdot x}{z} + \frac{b}{z \cdot y}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := x \cdot \left(9 \cdot y\right)\\ t_2 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+65}:\\ \;\;\;\;\frac{\frac{1}{\frac{z}{9 \cdot \left(x \cdot y\right) + b}} + t\_2}{c}\\ \mathbf{elif}\;z \leq 10^{-39}:\\ \;\;\;\;\frac{b + \left(t\_1 - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_2 + \frac{b + t\_1}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* x (* 9.0 y))) (t_2 (* t (* a -4.0))))
   (if (<= z -3.5e+65)
     (/ (+ (/ 1.0 (/ z (+ (* 9.0 (* x y)) b))) t_2) c)
     (if (<= z 1e-39)
       (/ (+ b (- t_1 (* a (* t (* z 4.0))))) (* z c))
       (/ (+ t_2 (/ (+ b t_1) z)) c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x * (9.0 * y);
	double t_2 = t * (a * -4.0);
	double tmp;
	if (z <= -3.5e+65) {
		tmp = ((1.0 / (z / ((9.0 * (x * y)) + b))) + t_2) / c;
	} else if (z <= 1e-39) {
		tmp = (b + (t_1 - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = (t_2 + ((b + t_1) / 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) :: t_2
    real(8) :: tmp
    t_1 = x * (9.0d0 * y)
    t_2 = t * (a * (-4.0d0))
    if (z <= (-3.5d+65)) then
        tmp = ((1.0d0 / (z / ((9.0d0 * (x * y)) + b))) + t_2) / c
    else if (z <= 1d-39) then
        tmp = (b + (t_1 - (a * (t * (z * 4.0d0))))) / (z * c)
    else
        tmp = (t_2 + ((b + t_1) / 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 = x * (9.0 * y);
	double t_2 = t * (a * -4.0);
	double tmp;
	if (z <= -3.5e+65) {
		tmp = ((1.0 / (z / ((9.0 * (x * y)) + b))) + t_2) / c;
	} else if (z <= 1e-39) {
		tmp = (b + (t_1 - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = (t_2 + ((b + t_1) / 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 = x * (9.0 * y)
	t_2 = t * (a * -4.0)
	tmp = 0
	if z <= -3.5e+65:
		tmp = ((1.0 / (z / ((9.0 * (x * y)) + b))) + t_2) / c
	elif z <= 1e-39:
		tmp = (b + (t_1 - (a * (t * (z * 4.0))))) / (z * c)
	else:
		tmp = (t_2 + ((b + t_1) / 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(x * Float64(9.0 * y))
	t_2 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (z <= -3.5e+65)
		tmp = Float64(Float64(Float64(1.0 / Float64(z / Float64(Float64(9.0 * Float64(x * y)) + b))) + t_2) / c);
	elseif (z <= 1e-39)
		tmp = Float64(Float64(b + Float64(t_1 - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(Float64(t_2 + Float64(Float64(b + t_1) / 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 = x * (9.0 * y);
	t_2 = t * (a * -4.0);
	tmp = 0.0;
	if (z <= -3.5e+65)
		tmp = ((1.0 / (z / ((9.0 * (x * y)) + b))) + t_2) / c;
	elseif (z <= 1e-39)
		tmp = (b + (t_1 - (a * (t * (z * 4.0))))) / (z * c);
	else
		tmp = (t_2 + ((b + t_1) / 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[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+65], N[(N[(N[(1.0 / N[(z / N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 1e-39], N[(N[(b + N[(t$95$1 - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$2 + N[(N[(b + t$95$1), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5000000000000001e65

   1. Initial program 59.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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 89.9%

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

      1. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{\frac{z}{x \cdot \left(9 \cdot y\right) + b}}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{z}{x \cdot \left(9 \cdot y\right) + b}\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \left(x \cdot \left(9 \cdot y\right) + b\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \left(\left(x \cdot 9\right) \cdot y + b\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\left(\left(x \cdot 9\right) \cdot y\right), b\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), b\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), b\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      9. *-lowering-*.f64 90.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   6. Applied egg-rr 90.0%

      \[\leadsto \frac{\color{blue}{\frac{1}{\frac{z}{9 \cdot \left(x \cdot y\right) + b}}} + t \cdot \left(a \cdot -4\right)}{c} \]

   if -3.5000000000000001e65 < z < 9.99999999999999929e-40

   1. Initial program 95.4%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. *-lowering-*.f64 95.4%

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

   4. Applied egg-rr 95.4%

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

   if 9.99999999999999929e-40 < z

   1. Initial program 47.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 80.0%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+65}:\\ \;\;\;\;\frac{\frac{1}{\frac{z}{9 \cdot \left(x \cdot y\right) + b}} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 10^{-39}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := x \cdot \left(9 \cdot y\right)\\ t_2 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b + t\_1}{z}}{c}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-10}:\\ \;\;\;\;\frac{b + \left(t\_1 - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* x (* 9.0 y))) (t_2 (/ (+ (* t (* a -4.0)) (/ (+ b t_1) z)) c)))
   (if (<= z -2e+33)
     t_2
     (if (<= z 2e-10) (/ (+ b (- t_1 (* a (* t (* z 4.0))))) (* z c)) 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 = x * (9.0 * y);
	double t_2 = ((t * (a * -4.0)) + ((b + t_1) / z)) / c;
	double tmp;
	if (z <= -2e+33) {
		tmp = t_2;
	} else if (z <= 2e-10) {
		tmp = (b + (t_1 - (a * (t * (z * 4.0))))) / (z * c);
	} 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 = x * (9.0d0 * y)
    t_2 = ((t * (a * (-4.0d0))) + ((b + t_1) / z)) / c
    if (z <= (-2d+33)) then
        tmp = t_2
    else if (z <= 2d-10) then
        tmp = (b + (t_1 - (a * (t * (z * 4.0d0))))) / (z * c)
    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 = x * (9.0 * y);
	double t_2 = ((t * (a * -4.0)) + ((b + t_1) / z)) / c;
	double tmp;
	if (z <= -2e+33) {
		tmp = t_2;
	} else if (z <= 2e-10) {
		tmp = (b + (t_1 - (a * (t * (z * 4.0))))) / (z * c);
	} 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 = x * (9.0 * y)
	t_2 = ((t * (a * -4.0)) + ((b + t_1) / z)) / c
	tmp = 0
	if z <= -2e+33:
		tmp = t_2
	elif z <= 2e-10:
		tmp = (b + (t_1 - (a * (t * (z * 4.0))))) / (z * c)
	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(x * Float64(9.0 * y))
	t_2 = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(Float64(b + t_1) / z)) / c)
	tmp = 0.0
	if (z <= -2e+33)
		tmp = t_2;
	elseif (z <= 2e-10)
		tmp = Float64(Float64(b + Float64(t_1 - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	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 = x * (9.0 * y);
	t_2 = ((t * (a * -4.0)) + ((b + t_1) / z)) / c;
	tmp = 0.0;
	if (z <= -2e+33)
		tmp = t_2;
	elseif (z <= 2e-10)
		tmp = (b + (t_1 - (a * (t * (z * 4.0))))) / (z * c);
	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[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(b + t$95$1), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -2e+33], t$95$2, If[LessEqual[z, 2e-10], N[(N[(b + N[(t$95$1 - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9999999999999999e33 or 2.00000000000000007e-10 < z

   1. Initial program 55.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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 84.9%

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

   if -1.9999999999999999e33 < z < 2.00000000000000007e-10

   1. Initial program 95.9%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. *-lowering-*.f64 95.9%

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

   4. Applied egg-rr 95.9%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+33}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-10}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \left(9 \cdot x\right) \cdot \frac{y}{z}}{c}\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-46}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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)) (* (* 9.0 x) (/ y z))) c)))
   (if (<= z -1.15e-46)
     t_1
     (if (<= z 3.3e-46) (/ (+ (* 9.0 (* x y)) 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)) + ((9.0 * x) * (y / z))) / c;
	double tmp;
	if (z <= -1.15e-46) {
		tmp = t_1;
	} else if (z <= 3.3e-46) {
		tmp = ((9.0 * (x * y)) + 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))) + ((9.0d0 * x) * (y / z))) / c
    if (z <= (-1.15d-46)) then
        tmp = t_1
    else if (z <= 3.3d-46) then
        tmp = ((9.0d0 * (x * y)) + 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)) + ((9.0 * x) * (y / z))) / c;
	double tmp;
	if (z <= -1.15e-46) {
		tmp = t_1;
	} else if (z <= 3.3e-46) {
		tmp = ((9.0 * (x * y)) + 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)) + ((9.0 * x) * (y / z))) / c
	tmp = 0
	if z <= -1.15e-46:
		tmp = t_1
	elif z <= 3.3e-46:
		tmp = ((9.0 * (x * y)) + 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(Float64(Float64(t * Float64(a * -4.0)) + Float64(Float64(9.0 * x) * Float64(y / z))) / c)
	tmp = 0.0
	if (z <= -1.15e-46)
		tmp = t_1;
	elseif (z <= 3.3e-46)
		tmp = Float64(Float64(Float64(9.0 * Float64(x * y)) + 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)) + ((9.0 * x) * (y / z))) / c;
	tmp = 0.0;
	if (z <= -1.15e-46)
		tmp = t_1;
	elseif (z <= 3.3e-46)
		tmp = ((9.0 * (x * y)) + 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[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * x), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.15e-46], t$95$1, If[LessEqual[z, 3.3e-46], N[(N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e-46 or 3.30000000000000013e-46 < z

   1. Initial program 62.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 86.6%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   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 73.6%

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

   7. Simplified 73.6%

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

      1. associate-*r* N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. /-lowering-/.f64 75.8%

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

   9. Applied egg-rr 75.8%

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

   if -1.15e-46 < z < 3.30000000000000013e-46

   1. Initial program 95.9%

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

   3. Taylor expanded in 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 85.9%

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

   5. Simplified 85.9%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-46}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \left(9 \cdot x\right) \cdot \frac{y}{z}}{c}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-46}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \left(9 \cdot x\right) \cdot \frac{y}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{if}\;z \leq -9 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-32}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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)) (* 9.0 (/ (* x y) z))) c)))
   (if (<= z -9e-50)
     t_1
     (if (<= z 3e-32) (/ (+ (* 9.0 (* x y)) 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)) + (9.0 * ((x * y) / z))) / c;
	double tmp;
	if (z <= -9e-50) {
		tmp = t_1;
	} else if (z <= 3e-32) {
		tmp = ((9.0 * (x * y)) + 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))) + (9.0d0 * ((x * y) / z))) / c
    if (z <= (-9d-50)) then
        tmp = t_1
    else if (z <= 3d-32) then
        tmp = ((9.0d0 * (x * y)) + 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)) + (9.0 * ((x * y) / z))) / c;
	double tmp;
	if (z <= -9e-50) {
		tmp = t_1;
	} else if (z <= 3e-32) {
		tmp = ((9.0 * (x * y)) + 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)) + (9.0 * ((x * y) / z))) / c
	tmp = 0
	if z <= -9e-50:
		tmp = t_1
	elif z <= 3e-32:
		tmp = ((9.0 * (x * y)) + 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(Float64(Float64(t * Float64(a * -4.0)) + Float64(9.0 * Float64(Float64(x * y) / z))) / c)
	tmp = 0.0
	if (z <= -9e-50)
		tmp = t_1;
	elseif (z <= 3e-32)
		tmp = Float64(Float64(Float64(9.0 * Float64(x * y)) + 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)) + (9.0 * ((x * y) / z))) / c;
	tmp = 0.0;
	if (z <= -9e-50)
		tmp = t_1;
	elseif (z <= 3e-32)
		tmp = ((9.0 * (x * y)) + 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[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -9e-50], t$95$1, If[LessEqual[z, 3e-32], N[(N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999924e-50 or 3e-32 < z

   1. Initial program 62.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 86.6%

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

   5. Taylor expanded in x around inf

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

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

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

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

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

      3. *-lowering-*.f64 73.6%

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

   7. Simplified 73.6%

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

   if -8.99999999999999924e-50 < z < 3e-32

   1. Initial program 95.9%

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

   3. Taylor expanded in 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 85.9%

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

   5. Simplified 85.9%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-50}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-32}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 46.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-23}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot \frac{y}{z}\right)}{c}\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-119}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{c}}{z}\\ \end{array} \end{array} \]

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 (<= t -3.6e+58)
   (* a (/ (* t -4.0) c))
   (if (<= t -8e-23)
     (/ (* 9.0 (* x (/ y z))) c)
     (if (<= t -6.8e-119) (/ (/ b c) z) (/ (* 9.0 (/ (* x y) 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 (t <= -3.6e+58) {
		tmp = a * ((t * -4.0) / c);
	} else if (t <= -8e-23) {
		tmp = (9.0 * (x * (y / z))) / c;
	} else if (t <= -6.8e-119) {
		tmp = (b / c) / z;
	} else {
		tmp = (9.0 * ((x * y) / 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 (t <= (-3.6d+58)) then
        tmp = a * ((t * (-4.0d0)) / c)
    else if (t <= (-8d-23)) then
        tmp = (9.0d0 * (x * (y / z))) / c
    else if (t <= (-6.8d-119)) then
        tmp = (b / c) / z
    else
        tmp = (9.0d0 * ((x * y) / 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 (t <= -3.6e+58) {
		tmp = a * ((t * -4.0) / c);
	} else if (t <= -8e-23) {
		tmp = (9.0 * (x * (y / z))) / c;
	} else if (t <= -6.8e-119) {
		tmp = (b / c) / z;
	} else {
		tmp = (9.0 * ((x * y) / 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 t <= -3.6e+58:
		tmp = a * ((t * -4.0) / c)
	elif t <= -8e-23:
		tmp = (9.0 * (x * (y / z))) / c
	elif t <= -6.8e-119:
		tmp = (b / c) / z
	else:
		tmp = (9.0 * ((x * y) / 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 (t <= -3.6e+58)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	elseif (t <= -8e-23)
		tmp = Float64(Float64(9.0 * Float64(x * Float64(y / z))) / c);
	elseif (t <= -6.8e-119)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(Float64(9.0 * Float64(Float64(x * y) / 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 (t <= -3.6e+58)
		tmp = a * ((t * -4.0) / c);
	elseif (t <= -8e-23)
		tmp = (9.0 * (x * (y / z))) / c;
	elseif (t <= -6.8e-119)
		tmp = (b / c) / z;
	else
		tmp = (9.0 * ((x * y) / 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[t, -3.6e+58], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8e-23], N[(N[(9.0 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, -6.8e-119], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.59999999999999996e58

   1. Initial program 67.6%

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

      1. *-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 79.6%

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

   4. Applied egg-rr 79.6%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 67.4%

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

   7. Simplified 67.4%

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

   if -3.59999999999999996e58 < t < -7.99999999999999968e-23

   1. Initial program 85.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 85.3%

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

   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 75.3%

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

   7. Simplified 75.3%

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

   8. Taylor expanded in x around inf

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

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

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 49.7%

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

   10. Simplified 49.7%

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

   if -7.99999999999999968e-23 < t < -6.80000000000000047e-119

   1. Initial program 81.9%

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

   3. Taylor expanded in b around inf

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

      1. /-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 49.6%

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

   5. Simplified 49.6%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   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 56.8%

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

   7. Applied egg-rr 56.8%

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

   if -6.80000000000000047e-119 < t

   1. Initial program 79.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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 86.9%

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

      1. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{\frac{z}{x \cdot \left(9 \cdot y\right) + b}}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{z}{x \cdot \left(9 \cdot y\right) + b}\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \left(x \cdot \left(9 \cdot y\right) + b\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \left(\left(x \cdot 9\right) \cdot y + b\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\left(\left(x \cdot 9\right) \cdot y\right), b\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), b\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), b\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      9. *-lowering-*.f64 86.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   6. Applied egg-rr 86.9%

      \[\leadsto \frac{\color{blue}{\frac{1}{\frac{z}{9 \cdot \left(x \cdot y\right) + b}}} + t \cdot \left(a \cdot -4\right)}{c} \]

   7. Taylor expanded in x around inf

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

      1. associate-/r* N/A

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

      2. associate-*r/ N/A

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

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

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

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

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

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

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

      6. *-lowering-*.f64 46.3%

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

   9. Simplified 46.3%

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

Alternative 7: 46.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-54}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot \frac{y}{z}\right)}{c}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-121}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-8}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -1.2e-54)
   (/ (* 9.0 (* x (/ y z))) c)
   (if (<= y 2.4e-121)
     (* a (/ (* t -4.0) c))
     (if (<= y 3.7e-8) (/ (/ b z) c) (/ (* 9.0 (* x y)) (* 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 <= -1.2e-54) {
		tmp = (9.0 * (x * (y / z))) / c;
	} else if (y <= 2.4e-121) {
		tmp = a * ((t * -4.0) / c);
	} else if (y <= 3.7e-8) {
		tmp = (b / z) / c;
	} else {
		tmp = (9.0 * (x * y)) / (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 <= (-1.2d-54)) then
        tmp = (9.0d0 * (x * (y / z))) / c
    else if (y <= 2.4d-121) then
        tmp = a * ((t * (-4.0d0)) / c)
    else if (y <= 3.7d-8) then
        tmp = (b / z) / c
    else
        tmp = (9.0d0 * (x * y)) / (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 <= -1.2e-54) {
		tmp = (9.0 * (x * (y / z))) / c;
	} else if (y <= 2.4e-121) {
		tmp = a * ((t * -4.0) / c);
	} else if (y <= 3.7e-8) {
		tmp = (b / z) / c;
	} else {
		tmp = (9.0 * (x * y)) / (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 <= -1.2e-54:
		tmp = (9.0 * (x * (y / z))) / c
	elif y <= 2.4e-121:
		tmp = a * ((t * -4.0) / c)
	elif y <= 3.7e-8:
		tmp = (b / z) / c
	else:
		tmp = (9.0 * (x * y)) / (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 <= -1.2e-54)
		tmp = Float64(Float64(9.0 * Float64(x * Float64(y / z))) / c);
	elseif (y <= 2.4e-121)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	elseif (y <= 3.7e-8)
		tmp = Float64(Float64(b / z) / c);
	else
		tmp = Float64(Float64(9.0 * Float64(x * y)) / Float64(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 <= -1.2e-54)
		tmp = (9.0 * (x * (y / z))) / c;
	elseif (y <= 2.4e-121)
		tmp = a * ((t * -4.0) / c);
	elseif (y <= 3.7e-8)
		tmp = (b / z) / c;
	else
		tmp = (9.0 * (x * y)) / (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, -1.2e-54], N[(N[(9.0 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[y, 2.4e-121], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e-8], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.20000000000000007e-54

   1. Initial program 78.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 76.5%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   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 65.3%

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

   7. Simplified 65.3%

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

   8. Taylor expanded in x around inf

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

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

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 54.2%

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

   10. Simplified 54.2%

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

   if -1.20000000000000007e-54 < y < 2.40000000000000003e-121

   1. Initial program 79.8%

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

      1. *-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 80.8%

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

   4. Applied egg-rr 80.8%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 55.8%

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

   7. Simplified 55.8%

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

   if 2.40000000000000003e-121 < y < 3.7e-8

   1. Initial program 88.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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 88.6%

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

   5. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 47.5%

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

   7. Simplified 47.5%

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

   if 3.7e-8 < y

   1. Initial program 70.3%

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

   3. Taylor expanded in x around inf

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

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

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

      2. *-lowering-*.f64 57.3%

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

   5. Simplified 57.3%

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

Alternative 8: 46.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;t \leq -1.08 \cdot 10^{+68}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-119}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (/ (* 9.0 (* x y)) (* z c))))
   (if (<= t -1.08e+68)
     (* a (/ (* t -4.0) c))
     (if (<= t -6e-9) t_1 (if (<= t -9.8e-119) (/ (/ b c) z) 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 = (9.0 * (x * y)) / (z * c);
	double tmp;
	if (t <= -1.08e+68) {
		tmp = a * ((t * -4.0) / c);
	} else if (t <= -6e-9) {
		tmp = t_1;
	} else if (t <= -9.8e-119) {
		tmp = (b / c) / z;
	} 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 = (9.0d0 * (x * y)) / (z * c)
    if (t <= (-1.08d+68)) then
        tmp = a * ((t * (-4.0d0)) / c)
    else if (t <= (-6d-9)) then
        tmp = t_1
    else if (t <= (-9.8d-119)) then
        tmp = (b / c) / z
    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 = (9.0 * (x * y)) / (z * c);
	double tmp;
	if (t <= -1.08e+68) {
		tmp = a * ((t * -4.0) / c);
	} else if (t <= -6e-9) {
		tmp = t_1;
	} else if (t <= -9.8e-119) {
		tmp = (b / c) / z;
	} 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 = (9.0 * (x * y)) / (z * c)
	tmp = 0
	if t <= -1.08e+68:
		tmp = a * ((t * -4.0) / c)
	elif t <= -6e-9:
		tmp = t_1
	elif t <= -9.8e-119:
		tmp = (b / c) / z
	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(9.0 * Float64(x * y)) / Float64(z * c))
	tmp = 0.0
	if (t <= -1.08e+68)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	elseif (t <= -6e-9)
		tmp = t_1;
	elseif (t <= -9.8e-119)
		tmp = Float64(Float64(b / c) / z);
	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 = (9.0 * (x * y)) / (z * c);
	tmp = 0.0;
	if (t <= -1.08e+68)
		tmp = a * ((t * -4.0) / c);
	elseif (t <= -6e-9)
		tmp = t_1;
	elseif (t <= -9.8e-119)
		tmp = (b / c) / z;
	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[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.08e+68], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6e-9], t$95$1, If[LessEqual[t, -9.8e-119], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.08e68

   1. Initial program 66.5%

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

      1. *-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 78.9%

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

   4. Applied egg-rr 78.9%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 69.7%

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

   7. Simplified 69.7%

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

   if -1.08e68 < t < -5.99999999999999996e-9 or -9.8e-119 < t

   1. Initial program 80.9%

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

   3. Taylor expanded in x around inf

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

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

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

      2. *-lowering-*.f64 47.2%

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

   5. Simplified 47.2%

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

   if -5.99999999999999996e-9 < t < -9.8e-119

   1. Initial program 81.7%

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

   3. Taylor expanded in 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 48.3%

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

   5. Simplified 48.3%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   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 52.5%

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

   7. Applied egg-rr 52.5%

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

Alternative 9: 49.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := a \cdot \frac{t \cdot -4}{c}\\ \mathbf{if}\;a \leq -6 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-162}:\\ \;\;\;\;9 \cdot \frac{\frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{+20}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* a (/ (* t -4.0) c))))
   (if (<= a -6e-29)
     t_1
     (if (<= a 1.9e-162)
       (* 9.0 (/ (/ (* x y) z) c))
       (if (<= a 5.4e+20) (/ (/ b c) z) 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 = a * ((t * -4.0) / c);
	double tmp;
	if (a <= -6e-29) {
		tmp = t_1;
	} else if (a <= 1.9e-162) {
		tmp = 9.0 * (((x * y) / z) / c);
	} else if (a <= 5.4e+20) {
		tmp = (b / c) / z;
	} 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 = a * ((t * (-4.0d0)) / c)
    if (a <= (-6d-29)) then
        tmp = t_1
    else if (a <= 1.9d-162) then
        tmp = 9.0d0 * (((x * y) / z) / c)
    else if (a <= 5.4d+20) then
        tmp = (b / c) / z
    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 = a * ((t * -4.0) / c);
	double tmp;
	if (a <= -6e-29) {
		tmp = t_1;
	} else if (a <= 1.9e-162) {
		tmp = 9.0 * (((x * y) / z) / c);
	} else if (a <= 5.4e+20) {
		tmp = (b / c) / z;
	} 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 = a * ((t * -4.0) / c)
	tmp = 0
	if a <= -6e-29:
		tmp = t_1
	elif a <= 1.9e-162:
		tmp = 9.0 * (((x * y) / z) / c)
	elif a <= 5.4e+20:
		tmp = (b / c) / z
	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(a * Float64(Float64(t * -4.0) / c))
	tmp = 0.0
	if (a <= -6e-29)
		tmp = t_1;
	elseif (a <= 1.9e-162)
		tmp = Float64(9.0 * Float64(Float64(Float64(x * y) / z) / c));
	elseif (a <= 5.4e+20)
		tmp = Float64(Float64(b / c) / z);
	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 = a * ((t * -4.0) / c);
	tmp = 0.0;
	if (a <= -6e-29)
		tmp = t_1;
	elseif (a <= 1.9e-162)
		tmp = 9.0 * (((x * y) / z) / c);
	elseif (a <= 5.4e+20)
		tmp = (b / c) / z;
	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[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6e-29], t$95$1, If[LessEqual[a, 1.9e-162], N[(9.0 * N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.4e+20], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.0000000000000005e-29 or 5.4e20 < a

   1. Initial program 78.5%

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

      1. *-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 76.7%

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

   4. Applied egg-rr 76.7%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 60.0%

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

   7. Simplified 60.0%

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

   if -6.0000000000000005e-29 < a < 1.90000000000000002e-162

   1. Initial program 78.6%

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

   3. Taylor expanded in x around inf

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

      1. *-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 42.9%

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

   5. Simplified 42.9%

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

   if 1.90000000000000002e-162 < a < 5.4e20

   1. Initial program 74.6%

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

   3. Taylor expanded in 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 32.1%

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

   5. Simplified 32.1%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   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 35.0%

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

   7. Applied egg-rr 35.0%

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

Alternative 10: 86.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{t}{c} \cdot \frac{a \cdot \left(z \cdot -4\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -4.5e+16)
   (* (/ t c) (/ (* a (* z -4.0)) z))
   (/ (+ (* t (* a -4.0)) (/ (+ b (* x (* 9.0 y))) 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 (a <= -4.5e+16) {
		tmp = (t / c) * ((a * (z * -4.0)) / z);
	} else {
		tmp = ((t * (a * -4.0)) + ((b + (x * (9.0 * y))) / 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 (a <= (-4.5d+16)) then
        tmp = (t / c) * ((a * (z * (-4.0d0))) / z)
    else
        tmp = ((t * (a * (-4.0d0))) + ((b + (x * (9.0d0 * y))) / 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 (a <= -4.5e+16) {
		tmp = (t / c) * ((a * (z * -4.0)) / z);
	} else {
		tmp = ((t * (a * -4.0)) + ((b + (x * (9.0 * y))) / 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 a <= -4.5e+16:
		tmp = (t / c) * ((a * (z * -4.0)) / z)
	else:
		tmp = ((t * (a * -4.0)) + ((b + (x * (9.0 * y))) / 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 (a <= -4.5e+16)
		tmp = Float64(Float64(t / c) * Float64(Float64(a * Float64(z * -4.0)) / z));
	else
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(Float64(b + Float64(x * Float64(9.0 * y))) / 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 (a <= -4.5e+16)
		tmp = (t / c) * ((a * (z * -4.0)) / z);
	else
		tmp = ((t * (a * -4.0)) + ((b + (x * (9.0 * y))) / 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[a, -4.5e+16], N[(N[(t / c), $MachinePrecision] * N[(N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.5e16

   1. Initial program 73.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-lowering-*.f64 42.1%

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

   5. Simplified 42.1%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. times-frac N/A

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

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

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

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

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

      8. /-lowering-/.f64 N/A

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

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

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

      10. *-lowering-*.f64 58.1%

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

   7. Applied egg-rr 58.1%

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

   if -4.5e16 < a

   1. Initial program 79.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 86.6%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{t}{c} \cdot \frac{a \cdot \left(z \cdot -4\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-74}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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)) (/ b z)) c)))
   (if (<= z -1.8e-57)
     t_1
     (if (<= z 4e-74) (/ (+ (* 9.0 (* x y)) 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)) + (b / z)) / c;
	double tmp;
	if (z <= -1.8e-57) {
		tmp = t_1;
	} else if (z <= 4e-74) {
		tmp = ((9.0 * (x * y)) + 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))) + (b / z)) / c
    if (z <= (-1.8d-57)) then
        tmp = t_1
    else if (z <= 4d-74) then
        tmp = ((9.0d0 * (x * y)) + 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)) + (b / z)) / c;
	double tmp;
	if (z <= -1.8e-57) {
		tmp = t_1;
	} else if (z <= 4e-74) {
		tmp = ((9.0 * (x * y)) + 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)) + (b / z)) / c
	tmp = 0
	if z <= -1.8e-57:
		tmp = t_1
	elif z <= 4e-74:
		tmp = ((9.0 * (x * y)) + 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(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -1.8e-57)
		tmp = t_1;
	elseif (z <= 4e-74)
		tmp = Float64(Float64(Float64(9.0 * Float64(x * y)) + 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)) + (b / z)) / c;
	tmp = 0.0;
	if (z <= -1.8e-57)
		tmp = t_1;
	elseif (z <= 4e-74)
		tmp = ((9.0 * (x * y)) + 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[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.8e-57], t$95$1, If[LessEqual[z, 4e-74], N[(N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8000000000000001e-57 or 3.99999999999999983e-74 < z

   1. Initial program 65.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 87.1%

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

   5. Taylor expanded in x around 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 65.2%

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

   7. Simplified 65.2%

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

   if -1.8000000000000001e-57 < z < 3.99999999999999983e-74

   1. Initial program 95.5%

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

   3. Taylor expanded in 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 88.9%

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

   5. Simplified 88.9%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-57}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-74}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{-26}:\\ \;\;\;\;\frac{t}{c} \cdot \frac{a \cdot \left(z \cdot -4\right)}{z}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+241}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t \cdot -4\right)}{c} \cdot \frac{a}{z}\\ \end{array} \end{array} \]

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 (<= a -5.2e-26)
   (* (/ t c) (/ (* a (* z -4.0)) z))
   (if (<= a 3.5e+241)
     (/ (+ (* 9.0 (* x y)) b) (* z c))
     (* (/ (* z (* t -4.0)) c) (/ a 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 (a <= -5.2e-26) {
		tmp = (t / c) * ((a * (z * -4.0)) / z);
	} else if (a <= 3.5e+241) {
		tmp = ((9.0 * (x * y)) + b) / (z * c);
	} else {
		tmp = ((z * (t * -4.0)) / c) * (a / 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 (a <= (-5.2d-26)) then
        tmp = (t / c) * ((a * (z * (-4.0d0))) / z)
    else if (a <= 3.5d+241) then
        tmp = ((9.0d0 * (x * y)) + b) / (z * c)
    else
        tmp = ((z * (t * (-4.0d0))) / c) * (a / 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 (a <= -5.2e-26) {
		tmp = (t / c) * ((a * (z * -4.0)) / z);
	} else if (a <= 3.5e+241) {
		tmp = ((9.0 * (x * y)) + b) / (z * c);
	} else {
		tmp = ((z * (t * -4.0)) / c) * (a / 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 a <= -5.2e-26:
		tmp = (t / c) * ((a * (z * -4.0)) / z)
	elif a <= 3.5e+241:
		tmp = ((9.0 * (x * y)) + b) / (z * c)
	else:
		tmp = ((z * (t * -4.0)) / c) * (a / 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 (a <= -5.2e-26)
		tmp = Float64(Float64(t / c) * Float64(Float64(a * Float64(z * -4.0)) / z));
	elseif (a <= 3.5e+241)
		tmp = Float64(Float64(Float64(9.0 * Float64(x * y)) + b) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(z * Float64(t * -4.0)) / c) * Float64(a / 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 (a <= -5.2e-26)
		tmp = (t / c) * ((a * (z * -4.0)) / z);
	elseif (a <= 3.5e+241)
		tmp = ((9.0 * (x * y)) + b) / (z * c);
	else
		tmp = ((z * (t * -4.0)) / c) * (a / 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[a, -5.2e-26], N[(N[(t / c), $MachinePrecision] * N[(N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e+241], N[(N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.2000000000000002e-26

   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

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-lowering-*.f64 44.6%

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

   5. Simplified 44.6%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. times-frac N/A

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

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

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

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

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

      8. /-lowering-/.f64 N/A

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

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

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

      10. *-lowering-*.f64 57.5%

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

   7. Applied egg-rr 57.5%

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

   if -5.2000000000000002e-26 < a < 3.5e241

   1. Initial program 78.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)}, b\right), \mathsf{*.f64}\left(z, c\right)\right) \]
   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 70.4%

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

   5. Simplified 70.4%

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

   if 3.5e241 < a

   1. Initial program 77.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-lowering-*.f64 60.3%

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

   5. Simplified 60.3%

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

      1. times-frac N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

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

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

      9. /-lowering-/.f64 77.4%

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

   7. Applied egg-rr 77.4%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{-26}:\\ \;\;\;\;\frac{t}{c} \cdot \frac{a \cdot \left(z \cdot -4\right)}{z}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+241}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t \cdot -4\right)}{c} \cdot \frac{a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := a \cdot \frac{t \cdot -4}{c}\\ \mathbf{if}\;t \leq -5 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-86}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* a (/ (* t -4.0) c))))
   (if (<= t -5e-18) t_1 (if (<= t 2.2e-86) (/ (/ b c) z) 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 = a * ((t * -4.0) / c);
	double tmp;
	if (t <= -5e-18) {
		tmp = t_1;
	} else if (t <= 2.2e-86) {
		tmp = (b / c) / z;
	} 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 = a * ((t * (-4.0d0)) / c)
    if (t <= (-5d-18)) then
        tmp = t_1
    else if (t <= 2.2d-86) then
        tmp = (b / c) / z
    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 = a * ((t * -4.0) / c);
	double tmp;
	if (t <= -5e-18) {
		tmp = t_1;
	} else if (t <= 2.2e-86) {
		tmp = (b / c) / z;
	} 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 = a * ((t * -4.0) / c)
	tmp = 0
	if t <= -5e-18:
		tmp = t_1
	elif t <= 2.2e-86:
		tmp = (b / c) / z
	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(a * Float64(Float64(t * -4.0) / c))
	tmp = 0.0
	if (t <= -5e-18)
		tmp = t_1;
	elseif (t <= 2.2e-86)
		tmp = Float64(Float64(b / c) / z);
	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 = a * ((t * -4.0) / c);
	tmp = 0.0;
	if (t <= -5e-18)
		tmp = t_1;
	elseif (t <= 2.2e-86)
		tmp = (b / c) / z;
	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[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e-18], t$95$1, If[LessEqual[t, 2.2e-86], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.00000000000000036e-18 or 2.2000000000000002e-86 < t

   1. Initial program 74.3%

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

      1. *-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 80.4%

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

   4. Applied egg-rr 80.4%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*r/ N/A

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 51.1%

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

   7. Simplified 51.1%

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

   if -5.00000000000000036e-18 < t < 2.2000000000000002e-86

   1. Initial program 83.8%

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

   3. Taylor expanded in 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 41.4%

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

   5. Simplified 41.4%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   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 45.3%

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

   7. Applied egg-rr 45.3%

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

Alternative 14: 35.7% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	return (b / c) / z

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(Float64(b / c) / z)
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = (b / c) / z;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]

Derivation

1. Initial program 77.9%

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

3. Taylor expanded in b around inf

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

   1. /-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 33.1%

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

5. Simplified 33.1%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
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 34.4%

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

7. Applied egg-rr 34.4%

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

Alternative 15: 36.2% 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 77.9%

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

3. Taylor expanded in b around inf

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

   1. /-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 33.1%

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

5. Simplified 33.1%

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

Developer Target 1: 81.7% 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 2024155 
(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)))