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

Percentage Accurate: 79.4% → 90.5%

Time: 19.4s

Alternatives: 15

Speedup: 0.7×

• 36.6% 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: 79.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot \left(\frac{t \cdot \left(-4 \cdot a\right) + \frac{b}{z}}{x} - -9 \cdot \frac{y}{z}\right)}{c}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{\frac{\left(b + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + x \cdot \left(y \cdot 9\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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
         (/ (* x (- (/ (+ (* t (* -4.0 a)) (/ b z)) x) (* -9.0 (/ y z)))) c)))
   (if (<= z -1.5e+21)
     t_1
     (if (<= z 2.8e-22)
       (/ (/ (+ (+ b (* t (* a (* z -4.0)))) (* x (* y 9.0))) 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 = (x * ((((t * (-4.0 * a)) + (b / z)) / x) - (-9.0 * (y / z)))) / c;
	double tmp;
	if (z <= -1.5e+21) {
		tmp = t_1;
	} else if (z <= 2.8e-22) {
		tmp = (((b + (t * (a * (z * -4.0)))) + (x * (y * 9.0))) / 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 = (x * ((((t * ((-4.0d0) * a)) + (b / z)) / x) - ((-9.0d0) * (y / z)))) / c
    if (z <= (-1.5d+21)) then
        tmp = t_1
    else if (z <= 2.8d-22) then
        tmp = (((b + (t * (a * (z * (-4.0d0))))) + (x * (y * 9.0d0))) / 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 = (x * ((((t * (-4.0 * a)) + (b / z)) / x) - (-9.0 * (y / z)))) / c;
	double tmp;
	if (z <= -1.5e+21) {
		tmp = t_1;
	} else if (z <= 2.8e-22) {
		tmp = (((b + (t * (a * (z * -4.0)))) + (x * (y * 9.0))) / 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 = (x * ((((t * (-4.0 * a)) + (b / z)) / x) - (-9.0 * (y / z)))) / c
	tmp = 0
	if z <= -1.5e+21:
		tmp = t_1
	elif z <= 2.8e-22:
		tmp = (((b + (t * (a * (z * -4.0)))) + (x * (y * 9.0))) / 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(x * Float64(Float64(Float64(Float64(t * Float64(-4.0 * a)) + Float64(b / z)) / x) - Float64(-9.0 * Float64(y / z)))) / c)
	tmp = 0.0
	if (z <= -1.5e+21)
		tmp = t_1;
	elseif (z <= 2.8e-22)
		tmp = Float64(Float64(Float64(Float64(b + Float64(t * Float64(a * Float64(z * -4.0)))) + Float64(x * Float64(y * 9.0))) / 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 = (x * ((((t * (-4.0 * a)) + (b / z)) / x) - (-9.0 * (y / z)))) / c;
	tmp = 0.0;
	if (z <= -1.5e+21)
		tmp = t_1;
	elseif (z <= 2.8e-22)
		tmp = (((b + (t * (a * (z * -4.0)))) + (x * (y * 9.0))) / 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[(x * N[(N[(N[(N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - N[(-9.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.5e+21], t$95$1, If[LessEqual[z, 2.8e-22], N[(N[(N[(N[(b + N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5e21 or 2.79999999999999995e-22 < z

   1. Initial program 57.6%

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

      1. associate-/r* N/A

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

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

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

   4. Applied egg-rr 70.0%

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

   5. Taylor expanded in x around -inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(-1 \cdot \left(x \cdot \left(-9 \cdot \frac{y}{z} + -1 \cdot \frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{x}\right)\right)\right)}, c\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

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

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

   7. Simplified 89.4%

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

   if -1.5e21 < z < 2.79999999999999995e-22

   1. Initial program 93.2%

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

      1. associate-/l/ N/A

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

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

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

   4. Applied egg-rr 96.6%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{x \cdot \left(\frac{t \cdot \left(-4 \cdot a\right) + \frac{b}{z}}{x} - -9 \cdot \frac{y}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{\frac{\left(b + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + x \cdot \left(y \cdot 9\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(\frac{t \cdot \left(-4 \cdot a\right) + \frac{b}{z}}{x} - -9 \cdot \frac{y}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+298}:\\ \;\;\;\;\frac{y \cdot 9}{z} \cdot \frac{x}{c}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-163}:\\ \;\;\;\;\frac{\frac{\left(b + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + x \cdot \left(y \cdot 9\right)}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-106}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+286}:\\ \;\;\;\;\frac{b + \left(t\_1 - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{c} \cdot \frac{9}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))))
   (if (<= t_1 -2e+298)
     (* (/ (* y 9.0) z) (/ x c))
     (if (<= t_1 -5e-163)
       (/ (/ (+ (+ b (* t (* a (* z -4.0)))) (* x (* y 9.0))) c) z)
       (if (<= t_1 5e-106)
         (/ (+ (/ b z) (* -4.0 (* t a))) c)
         (if (<= t_1 2e+286)
           (/ (+ b (- t_1 (* a (* t (* z 4.0))))) (* z c))
           (* (/ x c) (/ 9.0 (/ z y)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -2e+298) {
		tmp = ((y * 9.0) / z) * (x / c);
	} else if (t_1 <= -5e-163) {
		tmp = (((b + (t * (a * (z * -4.0)))) + (x * (y * 9.0))) / c) / z;
	} else if (t_1 <= 5e-106) {
		tmp = ((b / z) + (-4.0 * (t * a))) / c;
	} else if (t_1 <= 2e+286) {
		tmp = (b + (t_1 - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = (x / c) * (9.0 / (z / y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x * 9.0d0)
    if (t_1 <= (-2d+298)) then
        tmp = ((y * 9.0d0) / z) * (x / c)
    else if (t_1 <= (-5d-163)) then
        tmp = (((b + (t * (a * (z * (-4.0d0))))) + (x * (y * 9.0d0))) / c) / z
    else if (t_1 <= 5d-106) then
        tmp = ((b / z) + ((-4.0d0) * (t * a))) / c
    else if (t_1 <= 2d+286) then
        tmp = (b + (t_1 - (a * (t * (z * 4.0d0))))) / (z * c)
    else
        tmp = (x / c) * (9.0d0 / (z / y))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -2e+298) {
		tmp = ((y * 9.0) / z) * (x / c);
	} else if (t_1 <= -5e-163) {
		tmp = (((b + (t * (a * (z * -4.0)))) + (x * (y * 9.0))) / c) / z;
	} else if (t_1 <= 5e-106) {
		tmp = ((b / z) + (-4.0 * (t * a))) / c;
	} else if (t_1 <= 2e+286) {
		tmp = (b + (t_1 - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = (x / c) * (9.0 / (z / y));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = y * (x * 9.0)
	tmp = 0
	if t_1 <= -2e+298:
		tmp = ((y * 9.0) / z) * (x / c)
	elif t_1 <= -5e-163:
		tmp = (((b + (t * (a * (z * -4.0)))) + (x * (y * 9.0))) / c) / z
	elif t_1 <= 5e-106:
		tmp = ((b / z) + (-4.0 * (t * a))) / c
	elif t_1 <= 2e+286:
		tmp = (b + (t_1 - (a * (t * (z * 4.0))))) / (z * c)
	else:
		tmp = (x / c) * (9.0 / (z / y))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -2e+298)
		tmp = Float64(Float64(Float64(y * 9.0) / z) * Float64(x / c));
	elseif (t_1 <= -5e-163)
		tmp = Float64(Float64(Float64(Float64(b + Float64(t * Float64(a * Float64(z * -4.0)))) + Float64(x * Float64(y * 9.0))) / c) / z);
	elseif (t_1 <= 5e-106)
		tmp = Float64(Float64(Float64(b / z) + Float64(-4.0 * Float64(t * a))) / c);
	elseif (t_1 <= 2e+286)
		tmp = Float64(Float64(b + Float64(t_1 - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(Float64(x / c) * Float64(9.0 / Float64(z / y)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y * (x * 9.0);
	tmp = 0.0;
	if (t_1 <= -2e+298)
		tmp = ((y * 9.0) / z) * (x / c);
	elseif (t_1 <= -5e-163)
		tmp = (((b + (t * (a * (z * -4.0)))) + (x * (y * 9.0))) / c) / z;
	elseif (t_1 <= 5e-106)
		tmp = ((b / z) + (-4.0 * (t * a))) / c;
	elseif (t_1 <= 2e+286)
		tmp = (b + (t_1 - (a * (t * (z * 4.0))))) / (z * c);
	else
		tmp = (x / c) * (9.0 / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+298], N[(N[(N[(y * 9.0), $MachinePrecision] / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-163], N[(N[(N[(N[(b + N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 5e-106], N[(N[(N[(b / z), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 2e+286], 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[(x / c), $MachinePrecision] * N[(9.0 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.9999999999999999e298

   1. Initial program 35.7%

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

      1. clear-num N/A

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

      2. associate-/l* N/A

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

      3. associate-/r* N/A

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

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

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

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

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

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

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. associate-+r+ N/A

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

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

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

   4. Applied egg-rr 41.2%

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

   5. Taylor expanded in x around inf

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

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

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

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

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

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

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

      8. *-lowering-*.f64 72.5%

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

   7. Simplified 72.5%

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

      1. associate-*r/ N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. times-frac N/A

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

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

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

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

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

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

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

      9. /-lowering-/.f64 88.5%

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

   9. Applied egg-rr 88.5%

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

   if -1.9999999999999999e298 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.99999999999999977e-163

   1. Initial program 82.1%

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

      1. associate-/l/ N/A

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

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

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

   4. Applied egg-rr 90.1%

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

   if -4.99999999999999977e-163 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 4.99999999999999983e-106

   1. Initial program 73.4%

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

      1. associate-/r* N/A

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

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

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

   4. Applied egg-rr 83.2%

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

   5. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 78.3%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in b around 0

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

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

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

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

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

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

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

      4. /-lowering-/.f64 93.5%

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

   10. Simplified 93.5%

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

   if 4.99999999999999983e-106 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2.00000000000000007e286

   1. Initial program 88.7%

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

   if 2.00000000000000007e286 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 61.8%

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

      1. clear-num N/A

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

      2. associate-/l* N/A

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

      3. associate-/r* N/A

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

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

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

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

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

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

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. associate-+r+ N/A

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

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

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

   4. Applied egg-rr 61.9%

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

   5. Taylor expanded in x around inf

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

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

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

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

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

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

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

      8. *-lowering-*.f64 86.6%

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

   7. Simplified 86.6%

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

      1. associate-*r* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. associate-/l* N/A

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

      5. times-frac N/A

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

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

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

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

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

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

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

      9. /-lowering-/.f64 87.1%

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

   9. Applied egg-rr 87.1%

      \[\leadsto \color{blue}{\frac{x}{c} \cdot \frac{9}{\frac{z}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -2 \cdot 10^{+298}:\\ \;\;\;\;\frac{y \cdot 9}{z} \cdot \frac{x}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -5 \cdot 10^{-163}:\\ \;\;\;\;\frac{\frac{\left(b + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + x \cdot \left(y \cdot 9\right)}{c}}{z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{-106}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+286}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{c} \cdot \frac{9}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ t_2 := x \cdot \left(y \cdot 9\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-32}:\\ \;\;\;\;\frac{b + \left(t\_2 + \left(z \cdot -4\right) \cdot \left(t \cdot a\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+84}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{\left(b + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + t\_2}{c}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (/ (+ (/ b z) (* -4.0 (* t a))) c)) (t_2 (* x (* y 9.0))))
   (if (<= z -1.6e+200)
     t_1
     (if (<= z -3.6e-32)
       (* (/ (+ b (+ t_2 (* (* z -4.0) (* t a)))) z) (/ 1.0 c))
       (if (<= z 3.7e+84)
         (/ 1.0 (/ z (/ (+ (+ b (* t (* a (* z -4.0)))) t_2) 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 = ((b / z) + (-4.0 * (t * a))) / c;
	double t_2 = x * (y * 9.0);
	double tmp;
	if (z <= -1.6e+200) {
		tmp = t_1;
	} else if (z <= -3.6e-32) {
		tmp = ((b + (t_2 + ((z * -4.0) * (t * a)))) / z) * (1.0 / c);
	} else if (z <= 3.7e+84) {
		tmp = 1.0 / (z / (((b + (t * (a * (z * -4.0)))) + t_2) / 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) :: t_2
    real(8) :: tmp
    t_1 = ((b / z) + ((-4.0d0) * (t * a))) / c
    t_2 = x * (y * 9.0d0)
    if (z <= (-1.6d+200)) then
        tmp = t_1
    else if (z <= (-3.6d-32)) then
        tmp = ((b + (t_2 + ((z * (-4.0d0)) * (t * a)))) / z) * (1.0d0 / c)
    else if (z <= 3.7d+84) then
        tmp = 1.0d0 / (z / (((b + (t * (a * (z * (-4.0d0))))) + t_2) / 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 = ((b / z) + (-4.0 * (t * a))) / c;
	double t_2 = x * (y * 9.0);
	double tmp;
	if (z <= -1.6e+200) {
		tmp = t_1;
	} else if (z <= -3.6e-32) {
		tmp = ((b + (t_2 + ((z * -4.0) * (t * a)))) / z) * (1.0 / c);
	} else if (z <= 3.7e+84) {
		tmp = 1.0 / (z / (((b + (t * (a * (z * -4.0)))) + t_2) / 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 = ((b / z) + (-4.0 * (t * a))) / c
	t_2 = x * (y * 9.0)
	tmp = 0
	if z <= -1.6e+200:
		tmp = t_1
	elif z <= -3.6e-32:
		tmp = ((b + (t_2 + ((z * -4.0) * (t * a)))) / z) * (1.0 / c)
	elif z <= 3.7e+84:
		tmp = 1.0 / (z / (((b + (t * (a * (z * -4.0)))) + t_2) / 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(b / z) + Float64(-4.0 * Float64(t * a))) / c)
	t_2 = Float64(x * Float64(y * 9.0))
	tmp = 0.0
	if (z <= -1.6e+200)
		tmp = t_1;
	elseif (z <= -3.6e-32)
		tmp = Float64(Float64(Float64(b + Float64(t_2 + Float64(Float64(z * -4.0) * Float64(t * a)))) / z) * Float64(1.0 / c));
	elseif (z <= 3.7e+84)
		tmp = Float64(1.0 / Float64(z / Float64(Float64(Float64(b + Float64(t * Float64(a * Float64(z * -4.0)))) + t_2) / 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 = ((b / z) + (-4.0 * (t * a))) / c;
	t_2 = x * (y * 9.0);
	tmp = 0.0;
	if (z <= -1.6e+200)
		tmp = t_1;
	elseif (z <= -3.6e-32)
		tmp = ((b + (t_2 + ((z * -4.0) * (t * a)))) / z) * (1.0 / c);
	elseif (z <= 3.7e+84)
		tmp = 1.0 / (z / (((b + (t * (a * (z * -4.0)))) + t_2) / 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[(b / z), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+200], t$95$1, If[LessEqual[z, -3.6e-32], N[(N[(N[(b + N[(t$95$2 + N[(N[(z * -4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e+84], N[(1.0 / N[(z / N[(N[(N[(b + N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.60000000000000016e200 or 3.7e84 < z

   1. Initial program 46.0%

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

      1. 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

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

   4. Applied egg-rr 56.0%

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

   5. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 49.4%

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

   7. Simplified 49.4%

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

   8. Taylor expanded in b around 0

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

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

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

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

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

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

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

      4. /-lowering-/.f64 78.5%

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

   10. Simplified 78.5%

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

   if -1.60000000000000016e200 < z < -3.59999999999999993e-32

   1. Initial program 71.5%

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

      1. clear-num N/A

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

      2. associate-/l* N/A

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

      3. associate-/r* N/A

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

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

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

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

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

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

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. associate-+r+ N/A

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

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

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

   4. Applied egg-rr 79.4%

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

      1. associate-/l/ N/A

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

      2. associate-/r/ N/A

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

      3. clear-num N/A

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

      4. div-inv N/A

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

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

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

   6. Applied egg-rr 87.6%

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

   if -3.59999999999999993e-32 < z < 3.7e84

   1. Initial program 92.1%

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

      1. associate-/l/ N/A

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

      2. clear-num N/A

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

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

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

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

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

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

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

   4. Applied egg-rr 96.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{\frac{\left(b + t \cdot \left(\left(z \cdot -4\right) \cdot a\right)\right) + x \cdot \left(9 \cdot y\right)}{c}}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+200}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-32}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(y \cdot 9\right) + \left(z \cdot -4\right) \cdot \left(t \cdot a\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+84}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{\left(b + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + x \cdot \left(y \cdot 9\right)}{c}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ t_2 := x \cdot \left(y \cdot 9\right)\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+201}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-13}:\\ \;\;\;\;\frac{b + \left(t\_2 + \left(z \cdot -4\right) \cdot \left(t \cdot a\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+98}:\\ \;\;\;\;\frac{\frac{\left(b + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + t\_2}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (/ (+ (/ b z) (* -4.0 (* t a))) c)) (t_2 (* x (* y 9.0))))
   (if (<= z -2.7e+201)
     t_1
     (if (<= z -1e-13)
       (* (/ (+ b (+ t_2 (* (* z -4.0) (* t a)))) z) (/ 1.0 c))
       (if (<= z 5.2e+98)
         (/ (/ (+ (+ b (* t (* a (* z -4.0)))) t_2) 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 = ((b / z) + (-4.0 * (t * a))) / c;
	double t_2 = x * (y * 9.0);
	double tmp;
	if (z <= -2.7e+201) {
		tmp = t_1;
	} else if (z <= -1e-13) {
		tmp = ((b + (t_2 + ((z * -4.0) * (t * a)))) / z) * (1.0 / c);
	} else if (z <= 5.2e+98) {
		tmp = (((b + (t * (a * (z * -4.0)))) + t_2) / 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) :: t_2
    real(8) :: tmp
    t_1 = ((b / z) + ((-4.0d0) * (t * a))) / c
    t_2 = x * (y * 9.0d0)
    if (z <= (-2.7d+201)) then
        tmp = t_1
    else if (z <= (-1d-13)) then
        tmp = ((b + (t_2 + ((z * (-4.0d0)) * (t * a)))) / z) * (1.0d0 / c)
    else if (z <= 5.2d+98) then
        tmp = (((b + (t * (a * (z * (-4.0d0))))) + t_2) / 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 = ((b / z) + (-4.0 * (t * a))) / c;
	double t_2 = x * (y * 9.0);
	double tmp;
	if (z <= -2.7e+201) {
		tmp = t_1;
	} else if (z <= -1e-13) {
		tmp = ((b + (t_2 + ((z * -4.0) * (t * a)))) / z) * (1.0 / c);
	} else if (z <= 5.2e+98) {
		tmp = (((b + (t * (a * (z * -4.0)))) + t_2) / 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 = ((b / z) + (-4.0 * (t * a))) / c
	t_2 = x * (y * 9.0)
	tmp = 0
	if z <= -2.7e+201:
		tmp = t_1
	elif z <= -1e-13:
		tmp = ((b + (t_2 + ((z * -4.0) * (t * a)))) / z) * (1.0 / c)
	elif z <= 5.2e+98:
		tmp = (((b + (t * (a * (z * -4.0)))) + t_2) / 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(Float64(b / z) + Float64(-4.0 * Float64(t * a))) / c)
	t_2 = Float64(x * Float64(y * 9.0))
	tmp = 0.0
	if (z <= -2.7e+201)
		tmp = t_1;
	elseif (z <= -1e-13)
		tmp = Float64(Float64(Float64(b + Float64(t_2 + Float64(Float64(z * -4.0) * Float64(t * a)))) / z) * Float64(1.0 / c));
	elseif (z <= 5.2e+98)
		tmp = Float64(Float64(Float64(Float64(b + Float64(t * Float64(a * Float64(z * -4.0)))) + t_2) / 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 = ((b / z) + (-4.0 * (t * a))) / c;
	t_2 = x * (y * 9.0);
	tmp = 0.0;
	if (z <= -2.7e+201)
		tmp = t_1;
	elseif (z <= -1e-13)
		tmp = ((b + (t_2 + ((z * -4.0) * (t * a)))) / z) * (1.0 / c);
	elseif (z <= 5.2e+98)
		tmp = (((b + (t * (a * (z * -4.0)))) + t_2) / 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[(N[(b / z), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e+201], t$95$1, If[LessEqual[z, -1e-13], N[(N[(N[(b + N[(t$95$2 + N[(N[(z * -4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+98], N[(N[(N[(N[(b + N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7e201 or 5.1999999999999999e98 < z

   1. Initial program 45.2%

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

      1. 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

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

   4. Applied egg-rr 55.4%

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

   5. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 48.6%

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

   7. Simplified 48.6%

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

   8. Taylor expanded in b around 0

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

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

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

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

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

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

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

      4. /-lowering-/.f64 78.2%

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

   10. Simplified 78.2%

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

   if -2.7e201 < z < -1e-13

   1. Initial program 71.7%

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

      1. clear-num N/A

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

      2. associate-/l* N/A

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

      3. associate-/r* N/A

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

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

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

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

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

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

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. associate-+r+ N/A

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

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

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

   4. Applied egg-rr 80.1%

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

      1. associate-/l/ N/A

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

      2. associate-/r/ N/A

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

      3. clear-num N/A

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

      4. div-inv N/A

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

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

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

   6. Applied egg-rr 88.9%

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

   if -1e-13 < z < 5.1999999999999999e98

   1. Initial program 91.7%

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

      1. associate-/l/ N/A

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

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

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

   4. Applied egg-rr 95.5%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+201}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-13}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(y \cdot 9\right) + \left(z \cdot -4\right) \cdot \left(t \cdot a\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+98}:\\ \;\;\;\;\frac{\frac{\left(b + t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + x \cdot \left(y \cdot 9\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+182}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (/ b z) (* -4.0 (* t a))) c)))
   (if (<= z -4.8e+182)
     t_1
     (if (<= z 3.5e+19)
       (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((b / z) + (-4.0 * (t * a))) / c;
	double tmp;
	if (z <= -4.8e+182) {
		tmp = t_1;
	} else if (z <= 3.5e+19) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((b / z) + ((-4.0d0) * (t * a))) / c
    if (z <= (-4.8d+182)) then
        tmp = t_1
    else if (z <= 3.5d+19) then
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (z * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((b / z) + (-4.0 * (t * a))) / c;
	double tmp;
	if (z <= -4.8e+182) {
		tmp = t_1;
	} else if (z <= 3.5e+19) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = ((b / z) + (-4.0 * (t * a))) / c
	tmp = 0
	if z <= -4.8e+182:
		tmp = t_1
	elif z <= 3.5e+19:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(b / z) + Float64(-4.0 * Float64(t * a))) / c)
	tmp = 0.0
	if (z <= -4.8e+182)
		tmp = t_1;
	elseif (z <= 3.5e+19)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((b / z) + (-4.0 * (t * a))) / c;
	tmp = 0.0;
	if (z <= -4.8e+182)
		tmp = t_1;
	elseif (z <= 3.5e+19)
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(b / z), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -4.8e+182], t$95$1, If[LessEqual[z, 3.5e+19], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.80000000000000019e182 or 3.5e19 < z

   1. Initial program 50.5%

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

      1. 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

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

   4. Applied egg-rr 63.3%

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

   5. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 53.2%

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

   7. Simplified 53.2%

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

   8. Taylor expanded in b around 0

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

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

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

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

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

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

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

      4. /-lowering-/.f64 79.7%

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

   10. Simplified 79.7%

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

   if -4.80000000000000019e182 < z < 3.5e19

   1. Initial program 88.2%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+182}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{b + \left(t \cdot \left(a \cdot \left(z \cdot -4\right)\right) + x \cdot \left(y \cdot 9\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (/ b z) (* -4.0 (* t a))) c)))
   (if (<= z -3.7e+94)
     t_1
     (if (<= z 9.5e+99)
       (/ (+ b (+ (* t (* a (* z -4.0))) (* x (* y 9.0)))) (* z c))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((b / z) + (-4.0 * (t * a))) / c;
	double tmp;
	if (z <= -3.7e+94) {
		tmp = t_1;
	} else if (z <= 9.5e+99) {
		tmp = (b + ((t * (a * (z * -4.0))) + (x * (y * 9.0)))) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((b / z) + ((-4.0d0) * (t * a))) / c
    if (z <= (-3.7d+94)) then
        tmp = t_1
    else if (z <= 9.5d+99) then
        tmp = (b + ((t * (a * (z * (-4.0d0)))) + (x * (y * 9.0d0)))) / (z * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((b / z) + (-4.0 * (t * a))) / c;
	double tmp;
	if (z <= -3.7e+94) {
		tmp = t_1;
	} else if (z <= 9.5e+99) {
		tmp = (b + ((t * (a * (z * -4.0))) + (x * (y * 9.0)))) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = ((b / z) + (-4.0 * (t * a))) / c
	tmp = 0
	if z <= -3.7e+94:
		tmp = t_1
	elif z <= 9.5e+99:
		tmp = (b + ((t * (a * (z * -4.0))) + (x * (y * 9.0)))) / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(b / z) + Float64(-4.0 * Float64(t * a))) / c)
	tmp = 0.0
	if (z <= -3.7e+94)
		tmp = t_1;
	elseif (z <= 9.5e+99)
		tmp = Float64(Float64(b + Float64(Float64(t * Float64(a * Float64(z * -4.0))) + Float64(x * Float64(y * 9.0)))) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((b / z) + (-4.0 * (t * a))) / c;
	tmp = 0.0;
	if (z <= -3.7e+94)
		tmp = t_1;
	elseif (z <= 9.5e+99)
		tmp = (b + ((t * (a * (z * -4.0))) + (x * (y * 9.0)))) / (z * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(b / z), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -3.7e+94], t$95$1, If[LessEqual[z, 9.5e+99], N[(N[(b + N[(N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7000000000000001e94 or 9.49999999999999908e99 < z

   1. Initial program 47.9%

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

      1. associate-/r* N/A

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

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

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

   4. Applied egg-rr 63.0%

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

   5. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 49.5%

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

   7. Simplified 49.5%

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

   8. Taylor expanded in b around 0

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

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

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

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

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

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

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

      4. /-lowering-/.f64 74.9%

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

   10. Simplified 74.9%

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

   if -3.7000000000000001e94 < z < 9.49999999999999908e99

   1. Initial program 91.1%

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

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

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

      2. sub-neg N/A

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

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

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

      4. associate-*l* N/A

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

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

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

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

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

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

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

      8. *-commutative N/A

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

      9. distribute-rgt-neg-in N/A

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

      10. associate-*l* N/A

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

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

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

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

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

      13. distribute-rgt-neg-in N/A

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

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

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

      15. metadata-eval 91.9%

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

   4. Applied egg-rr 91.9%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+94}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{b + \left(t \cdot \left(a \cdot \left(z \cdot -4\right)\right) + x \cdot \left(y \cdot 9\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+96}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-246}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right)}{c}\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+93}:\\ \;\;\;\;\frac{\frac{9}{\frac{\frac{c}{y}}{x}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \end{array} \end{array} \]

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 (<= b -8.2e+96)
   (/ (/ b c) z)
   (if (<= b 1.5e-246)
     (/ (* t (* -4.0 a)) c)
     (if (<= b 1.95e+93) (/ (/ 9.0 (/ (/ c y) x)) z) (* (/ b c) (/ 1.0 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 (b <= -8.2e+96) {
		tmp = (b / c) / z;
	} else if (b <= 1.5e-246) {
		tmp = (t * (-4.0 * a)) / c;
	} else if (b <= 1.95e+93) {
		tmp = (9.0 / ((c / y) / x)) / z;
	} else {
		tmp = (b / c) * (1.0 / 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 (b <= (-8.2d+96)) then
        tmp = (b / c) / z
    else if (b <= 1.5d-246) then
        tmp = (t * ((-4.0d0) * a)) / c
    else if (b <= 1.95d+93) then
        tmp = (9.0d0 / ((c / y) / x)) / z
    else
        tmp = (b / c) * (1.0d0 / 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 (b <= -8.2e+96) {
		tmp = (b / c) / z;
	} else if (b <= 1.5e-246) {
		tmp = (t * (-4.0 * a)) / c;
	} else if (b <= 1.95e+93) {
		tmp = (9.0 / ((c / y) / x)) / z;
	} else {
		tmp = (b / c) * (1.0 / 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 b <= -8.2e+96:
		tmp = (b / c) / z
	elif b <= 1.5e-246:
		tmp = (t * (-4.0 * a)) / c
	elif b <= 1.95e+93:
		tmp = (9.0 / ((c / y) / x)) / z
	else:
		tmp = (b / c) * (1.0 / 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 (b <= -8.2e+96)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= 1.5e-246)
		tmp = Float64(Float64(t * Float64(-4.0 * a)) / c);
	elseif (b <= 1.95e+93)
		tmp = Float64(Float64(9.0 / Float64(Float64(c / y) / x)) / z);
	else
		tmp = Float64(Float64(b / c) * Float64(1.0 / 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 (b <= -8.2e+96)
		tmp = (b / c) / z;
	elseif (b <= 1.5e-246)
		tmp = (t * (-4.0 * a)) / c;
	elseif (b <= 1.95e+93)
		tmp = (9.0 / ((c / y) / x)) / z;
	else
		tmp = (b / c) * (1.0 / 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[b, -8.2e+96], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, 1.5e-246], N[(N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[b, 1.95e+93], N[(N[(9.0 / N[(N[(c / y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(b / c), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.19999999999999996e96

   1. Initial program 88.3%

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

   3. Taylor expanded in b around inf

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 70.8%

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

   5. Simplified 70.8%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

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

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

      4. /-lowering-/.f64 72.0%

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

   7. Applied egg-rr 72.0%

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

   if -8.19999999999999996e96 < b < 1.5e-246

   1. Initial program 69.4%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

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

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 51.8%

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

   5. Simplified 51.8%

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

   if 1.5e-246 < b < 1.9500000000000001e93

   1. Initial program 75.6%

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

      1. clear-num N/A

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

      2. associate-/l* N/A

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

      3. associate-/r* N/A

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

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

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

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

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

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

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. associate-+r+ N/A

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

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

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

   4. Applied egg-rr 82.4%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, z\right), \color{blue}{\left(\frac{1}{9} \cdot \frac{c}{x \cdot y}\right)}\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{*.f64}\left(\frac{1}{9}, \color{blue}{\left(\frac{c}{x \cdot y}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{*.f64}\left(\frac{1}{9}, \mathsf{/.f64}\left(c, \color{blue}{\left(x \cdot y\right)}\right)\right)\right) \]

      3. *-lowering-*.f64 46.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{*.f64}\left(\frac{1}{9}, \mathsf{/.f64}\left(c, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right)\right) \]

   7. Simplified 46.8%

      \[\leadsto \frac{\frac{1}{z}}{\color{blue}{0.1111111111111111 \cdot \frac{c}{x \cdot y}}} \]
   8. Step-by-step derivation

      1. associate-/l/ N/A

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

      2. associate-/r* N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{\frac{1}{9} \cdot \frac{c}{x \cdot y}}\right), \color{blue}{z}\right) \]

      4. associate-/r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\frac{1}{\frac{1}{9}}}{\frac{c}{x \cdot y}}\right), z\right) \]

      5. metadata-eval N/A

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

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

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

      7. *-commutative N/A

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

      8. associate-/r* N/A

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

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

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

      10. /-lowering-/.f64 46.9%

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

   9. Applied egg-rr 46.9%

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

   if 1.9500000000000001e93 < b

   1. Initial program 76.2%

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

   3. Taylor expanded in b around inf

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 54.7%

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

   5. Simplified 54.7%

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

      1. div-inv N/A

         \[\leadsto b \cdot \color{blue}{\frac{1}{z \cdot c}} \]

      2. associate-*r/ N/A

         \[\leadsto \frac{b \cdot 1}{\color{blue}{z \cdot c}} \]

      3. *-commutative N/A

         \[\leadsto \frac{b \cdot 1}{c \cdot \color{blue}{z}} \]

      4. times-frac N/A

         \[\leadsto \frac{b}{c} \cdot \color{blue}{\frac{1}{z}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{b}{c}\right), \color{blue}{\left(\frac{1}{z}\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(b, c\right), \left(\frac{\color{blue}{1}}{z}\right)\right) \]

      7. /-lowering-/.f64 60.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(b, c\right), \mathsf{/.f64}\left(1, \color{blue}{z}\right)\right) \]

   7. Applied egg-rr 60.9%

      \[\leadsto \color{blue}{\frac{b}{c} \cdot \frac{1}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+96}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-246}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right)}{c}\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+93}:\\ \;\;\;\;\frac{\frac{9}{\frac{\frac{c}{y}}{x}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+96}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-280}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right)}{c}\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \frac{\frac{9}{z}}{\frac{c}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \end{array} \end{array} \]

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 (<= b -8.2e+96)
   (/ (/ b c) z)
   (if (<= b 6.8e-280)
     (/ (* t (* -4.0 a)) c)
     (if (<= b 1.25e+92) (* x (/ (/ 9.0 z) (/ c y))) (* (/ b c) (/ 1.0 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 (b <= -8.2e+96) {
		tmp = (b / c) / z;
	} else if (b <= 6.8e-280) {
		tmp = (t * (-4.0 * a)) / c;
	} else if (b <= 1.25e+92) {
		tmp = x * ((9.0 / z) / (c / y));
	} else {
		tmp = (b / c) * (1.0 / 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 (b <= (-8.2d+96)) then
        tmp = (b / c) / z
    else if (b <= 6.8d-280) then
        tmp = (t * ((-4.0d0) * a)) / c
    else if (b <= 1.25d+92) then
        tmp = x * ((9.0d0 / z) / (c / y))
    else
        tmp = (b / c) * (1.0d0 / 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 (b <= -8.2e+96) {
		tmp = (b / c) / z;
	} else if (b <= 6.8e-280) {
		tmp = (t * (-4.0 * a)) / c;
	} else if (b <= 1.25e+92) {
		tmp = x * ((9.0 / z) / (c / y));
	} else {
		tmp = (b / c) * (1.0 / 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 b <= -8.2e+96:
		tmp = (b / c) / z
	elif b <= 6.8e-280:
		tmp = (t * (-4.0 * a)) / c
	elif b <= 1.25e+92:
		tmp = x * ((9.0 / z) / (c / y))
	else:
		tmp = (b / c) * (1.0 / 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 (b <= -8.2e+96)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= 6.8e-280)
		tmp = Float64(Float64(t * Float64(-4.0 * a)) / c);
	elseif (b <= 1.25e+92)
		tmp = Float64(x * Float64(Float64(9.0 / z) / Float64(c / y)));
	else
		tmp = Float64(Float64(b / c) * Float64(1.0 / 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 (b <= -8.2e+96)
		tmp = (b / c) / z;
	elseif (b <= 6.8e-280)
		tmp = (t * (-4.0 * a)) / c;
	elseif (b <= 1.25e+92)
		tmp = x * ((9.0 / z) / (c / y));
	else
		tmp = (b / c) * (1.0 / 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[b, -8.2e+96], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, 6.8e-280], N[(N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[b, 1.25e+92], N[(x * N[(N[(9.0 / z), $MachinePrecision] / N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.19999999999999996e96

   1. Initial program 88.3%

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

   3. Taylor expanded in b around inf

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 70.8%

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

   5. Simplified 70.8%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

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

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

      4. /-lowering-/.f64 72.0%

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

   7. Applied egg-rr 72.0%

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

   if -8.19999999999999996e96 < b < 6.7999999999999995e-280

   1. Initial program 69.9%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

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

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 53.6%

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

   5. Simplified 53.6%

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

   if 6.7999999999999995e-280 < b < 1.25000000000000005e92

   1. Initial program 74.7%

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

      1. clear-num N/A

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

      2. associate-/l* N/A

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

      3. associate-/r* N/A

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

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

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

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

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

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

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. associate-+r+ N/A

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

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

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

   4. Applied egg-rr 81.0%

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

   5. Taylor expanded in x around inf

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

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

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

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

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

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

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

      8. *-lowering-*.f64 40.6%

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

   7. Simplified 40.6%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. times-frac N/A

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

      4. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{9}{z} \cdot \frac{1}{\color{blue}{\frac{c}{y}}}\right)\right) \]

      5. un-div-inv N/A

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

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

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

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

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

      8. /-lowering-/.f64 44.2%

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

   9. Applied egg-rr 44.2%

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

   if 1.25000000000000005e92 < b

   1. Initial program 76.2%

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

   3. Taylor expanded in b around inf

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 54.7%

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

   5. Simplified 54.7%

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

      1. div-inv N/A

         \[\leadsto b \cdot \color{blue}{\frac{1}{z \cdot c}} \]

      2. associate-*r/ N/A

         \[\leadsto \frac{b \cdot 1}{\color{blue}{z \cdot c}} \]

      3. *-commutative N/A

         \[\leadsto \frac{b \cdot 1}{c \cdot \color{blue}{z}} \]

      4. times-frac N/A

         \[\leadsto \frac{b}{c} \cdot \color{blue}{\frac{1}{z}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{b}{c}\right), \color{blue}{\left(\frac{1}{z}\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(b, c\right), \left(\frac{\color{blue}{1}}{z}\right)\right) \]

      7. /-lowering-/.f64 60.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(b, c\right), \mathsf{/.f64}\left(1, \color{blue}{z}\right)\right) \]

   7. Applied egg-rr 60.9%

      \[\leadsto \color{blue}{\frac{b}{c} \cdot \frac{1}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+96}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-280}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right)}{c}\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \frac{\frac{9}{z}}{\frac{c}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{-4 \cdot a}{c}\\ \mathbf{if}\;a \leq -4.3 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 10^{-36}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{elif}\;a \leq 102000:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (/ (* -4.0 a) c))))
   (if (<= a -4.3e-128)
     t_1
     (if (<= a 1e-36)
       (* (/ b c) (/ 1.0 z))
       (if (<= a 102000.0) (* x (* 9.0 (/ y (* z c)))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * ((-4.0 * a) / c);
	double tmp;
	if (a <= -4.3e-128) {
		tmp = t_1;
	} else if (a <= 1e-36) {
		tmp = (b / c) * (1.0 / z);
	} else if (a <= 102000.0) {
		tmp = x * (9.0 * (y / (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (((-4.0d0) * a) / c)
    if (a <= (-4.3d-128)) then
        tmp = t_1
    else if (a <= 1d-36) then
        tmp = (b / c) * (1.0d0 / z)
    else if (a <= 102000.0d0) then
        tmp = x * (9.0d0 * (y / (z * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * ((-4.0 * a) / c);
	double tmp;
	if (a <= -4.3e-128) {
		tmp = t_1;
	} else if (a <= 1e-36) {
		tmp = (b / c) * (1.0 / z);
	} else if (a <= 102000.0) {
		tmp = x * (9.0 * (y / (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = t * ((-4.0 * a) / c)
	tmp = 0
	if a <= -4.3e-128:
		tmp = t_1
	elif a <= 1e-36:
		tmp = (b / c) * (1.0 / z)
	elif a <= 102000.0:
		tmp = x * (9.0 * (y / (z * c)))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(Float64(-4.0 * a) / c))
	tmp = 0.0
	if (a <= -4.3e-128)
		tmp = t_1;
	elseif (a <= 1e-36)
		tmp = Float64(Float64(b / c) * Float64(1.0 / z));
	elseif (a <= 102000.0)
		tmp = Float64(x * Float64(9.0 * Float64(y / Float64(z * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * ((-4.0 * a) / c);
	tmp = 0.0;
	if (a <= -4.3e-128)
		tmp = t_1;
	elseif (a <= 1e-36)
		tmp = (b / c) * (1.0 / z);
	elseif (a <= 102000.0)
		tmp = x * (9.0 * (y / (z * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(N[(-4.0 * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.3e-128], t$95$1, If[LessEqual[a, 1e-36], N[(N[(b / c), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 102000.0], N[(x * N[(9.0 * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.29999999999999994e-128 or 102000 < a

   1. Initial program 79.1%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 42.5%

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

   5. Simplified 42.5%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. times-frac N/A

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

      6. *-inverses N/A

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

      7. clear-num N/A

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

      8. div-inv N/A

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

      9. clear-num N/A

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

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

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

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

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 54.7%

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

   7. Applied egg-rr 54.7%

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

   if -4.29999999999999994e-128 < a < 9.9999999999999994e-37

   1. Initial program 70.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 42.7%

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

   5. Simplified 42.7%

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

      1. div-inv N/A

         \[\leadsto b \cdot \color{blue}{\frac{1}{z \cdot c}} \]

      2. associate-*r/ N/A

         \[\leadsto \frac{b \cdot 1}{\color{blue}{z \cdot c}} \]

      3. *-commutative N/A

         \[\leadsto \frac{b \cdot 1}{c \cdot \color{blue}{z}} \]

      4. times-frac N/A

         \[\leadsto \frac{b}{c} \cdot \color{blue}{\frac{1}{z}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{b}{c}\right), \color{blue}{\left(\frac{1}{z}\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(b, c\right), \left(\frac{\color{blue}{1}}{z}\right)\right) \]

      7. /-lowering-/.f64 48.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(b, c\right), \mathsf{/.f64}\left(1, \color{blue}{z}\right)\right) \]

   7. Applied egg-rr 48.3%

      \[\leadsto \color{blue}{\frac{b}{c} \cdot \frac{1}{z}} \]

   if 9.9999999999999994e-37 < a < 102000

   1. Initial program 82.7%

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

      1. clear-num N/A

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

      2. associate-/l* N/A

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

      3. associate-/r* N/A

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

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

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

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

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

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

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. associate-+r+ N/A

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

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

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

   4. Applied egg-rr 82.0%

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

   5. Taylor expanded in x around inf

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

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

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

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

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

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

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

      8. *-lowering-*.f64 55.9%

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

   7. Simplified 55.9%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{-128}:\\ \;\;\;\;t \cdot \frac{-4 \cdot a}{c}\\ \mathbf{elif}\;a \leq 10^{-36}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{elif}\;a \leq 102000:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-4 \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;z \leq -9 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-171}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (/ b z) (* -4.0 (* t a))) c)))
   (if (<= z -9e-30)
     t_1
     (if (<= z 4.6e-171) (/ (+ b (* 9.0 (* y x))) (* 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 = ((b / z) + (-4.0 * (t * a))) / c;
	double tmp;
	if (z <= -9e-30) {
		tmp = t_1;
	} else if (z <= 4.6e-171) {
		tmp = (b + (9.0 * (y * x))) / (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 = ((b / z) + ((-4.0d0) * (t * a))) / c
    if (z <= (-9d-30)) then
        tmp = t_1
    else if (z <= 4.6d-171) then
        tmp = (b + (9.0d0 * (y * x))) / (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 = ((b / z) + (-4.0 * (t * a))) / c;
	double tmp;
	if (z <= -9e-30) {
		tmp = t_1;
	} else if (z <= 4.6e-171) {
		tmp = (b + (9.0 * (y * x))) / (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 = ((b / z) + (-4.0 * (t * a))) / c
	tmp = 0
	if z <= -9e-30:
		tmp = t_1
	elif z <= 4.6e-171:
		tmp = (b + (9.0 * (y * x))) / (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(b / z) + Float64(-4.0 * Float64(t * a))) / c)
	tmp = 0.0
	if (z <= -9e-30)
		tmp = t_1;
	elseif (z <= 4.6e-171)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / 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 = ((b / z) + (-4.0 * (t * a))) / c;
	tmp = 0.0;
	if (z <= -9e-30)
		tmp = t_1;
	elseif (z <= 4.6e-171)
		tmp = (b + (9.0 * (y * x))) / (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[(b / z), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -9e-30], t$95$1, If[LessEqual[z, 4.6e-171], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999935e-30 or 4.59999999999999956e-171 < z

   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. 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

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

   4. Applied egg-rr 75.8%

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

   5. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 63.0%

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

   7. Simplified 63.0%

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

   8. Taylor expanded in b around 0

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

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

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

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

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

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

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

      4. /-lowering-/.f64 77.4%

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

   10. Simplified 77.4%

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

   if -8.99999999999999935e-30 < z < 4.59999999999999956e-171

   1. Initial program 91.3%

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

   3. 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 82.6%

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

   5. Simplified 82.6%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-30}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-171}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 70.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \frac{\frac{y \cdot 9}{c}}{z}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+193}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{9}{z}}{\frac{c}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -3.5e-7)
   (* x (/ (/ (* y 9.0) c) z))
   (if (<= y 1.12e+193)
     (/ (+ (/ b z) (* -4.0 (* t a))) c)
     (* x (/ (/ 9.0 z) (/ c y))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -3.5e-7) {
		tmp = x * (((y * 9.0) / c) / z);
	} else if (y <= 1.12e+193) {
		tmp = ((b / z) + (-4.0 * (t * a))) / c;
	} else {
		tmp = x * ((9.0 / z) / (c / y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= (-3.5d-7)) then
        tmp = x * (((y * 9.0d0) / c) / z)
    else if (y <= 1.12d+193) then
        tmp = ((b / z) + ((-4.0d0) * (t * a))) / c
    else
        tmp = x * ((9.0d0 / z) / (c / y))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -3.5e-7) {
		tmp = x * (((y * 9.0) / c) / z);
	} else if (y <= 1.12e+193) {
		tmp = ((b / z) + (-4.0 * (t * a))) / c;
	} else {
		tmp = x * ((9.0 / z) / (c / y));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -3.5e-7:
		tmp = x * (((y * 9.0) / c) / z)
	elif y <= 1.12e+193:
		tmp = ((b / z) + (-4.0 * (t * a))) / c
	else:
		tmp = x * ((9.0 / z) / (c / y))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -3.5e-7)
		tmp = Float64(x * Float64(Float64(Float64(y * 9.0) / c) / z));
	elseif (y <= 1.12e+193)
		tmp = Float64(Float64(Float64(b / z) + Float64(-4.0 * Float64(t * a))) / c);
	else
		tmp = Float64(x * Float64(Float64(9.0 / z) / Float64(c / y)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -3.5e-7)
		tmp = x * (((y * 9.0) / c) / z);
	elseif (y <= 1.12e+193)
		tmp = ((b / z) + (-4.0 * (t * a))) / c;
	else
		tmp = x * ((9.0 / z) / (c / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -3.5e-7], N[(x * N[(N[(N[(y * 9.0), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.12e+193], N[(N[(N[(b / z), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(x * N[(N[(9.0 / z), $MachinePrecision] / N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.49999999999999984e-7

   1. Initial program 77.0%

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

   3. Taylor expanded in x around inf

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

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

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

      2. associate--l+ N/A

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

      3. associate-/r* N/A

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

      4. associate-/l/ N/A

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

      5. associate-/r* N/A

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

      6. associate-/r* N/A

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

      7. associate-*r/ N/A

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

      8. div-sub N/A

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

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

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

      10. associate-*r/ N/A

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

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

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

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

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

      13. *-commutative N/A

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

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

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

      15. /-lowering-/.f64 N/A

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

   5. Simplified 73.5%

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

   6. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 64.6%

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

   8. Simplified 64.6%

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

   9. Taylor expanded in y around inf

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

       1. associate-/r* N/A

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

       2. associate-*r/ N/A

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

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

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

       4. associate-*r/ N/A

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

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

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

       6. *-lowering-*.f64 50.7%

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

   11. Simplified 50.7%

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

   if -3.49999999999999984e-7 < y < 1.1199999999999999e193

   1. Initial program 76.3%

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

      1. 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

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

   4. Applied egg-rr 79.8%

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

   5. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 65.6%

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

   7. Simplified 65.6%

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

   8. Taylor expanded in b around 0

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

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

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

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

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

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

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

      4. /-lowering-/.f64 76.4%

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

   10. Simplified 76.4%

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

   if 1.1199999999999999e193 < y

   1. Initial program 72.0%

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

      1. clear-num N/A

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

      2. associate-/l* N/A

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

      3. associate-/r* N/A

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

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

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

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

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

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

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. associate-+r+ N/A

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

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

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

   4. Applied egg-rr 68.3%

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

   5. Taylor expanded in x around inf

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

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

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

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

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

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

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

      8. *-lowering-*.f64 71.8%

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

   7. Simplified 71.8%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. times-frac N/A

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

      4. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{9}{z} \cdot \frac{1}{\color{blue}{\frac{c}{y}}}\right)\right) \]

      5. un-div-inv N/A

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

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

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

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

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

      8. /-lowering-/.f64 72.0%

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

   9. Applied egg-rr 72.0%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \frac{\frac{y \cdot 9}{c}}{z}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+193}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{9}{z}}{\frac{c}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 47.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{-4 \cdot a}{c}\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{+92}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* t (/ (* -4.0 a) c))))
   (if (<= a -2.3e-128) t_1 (if (<= a 1.26e+92) (* (/ b c) (/ 1.0 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 = t * ((-4.0 * a) / c);
	double tmp;
	if (a <= -2.3e-128) {
		tmp = t_1;
	} else if (a <= 1.26e+92) {
		tmp = (b / c) * (1.0 / 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 = t * (((-4.0d0) * a) / c)
    if (a <= (-2.3d-128)) then
        tmp = t_1
    else if (a <= 1.26d+92) then
        tmp = (b / c) * (1.0d0 / 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 = t * ((-4.0 * a) / c);
	double tmp;
	if (a <= -2.3e-128) {
		tmp = t_1;
	} else if (a <= 1.26e+92) {
		tmp = (b / c) * (1.0 / 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 = t * ((-4.0 * a) / c)
	tmp = 0
	if a <= -2.3e-128:
		tmp = t_1
	elif a <= 1.26e+92:
		tmp = (b / c) * (1.0 / 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(t * Float64(Float64(-4.0 * a) / c))
	tmp = 0.0
	if (a <= -2.3e-128)
		tmp = t_1;
	elseif (a <= 1.26e+92)
		tmp = Float64(Float64(b / c) * Float64(1.0 / 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 = t * ((-4.0 * a) / c);
	tmp = 0.0;
	if (a <= -2.3e-128)
		tmp = t_1;
	elseif (a <= 1.26e+92)
		tmp = (b / c) * (1.0 / 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[(t * N[(N[(-4.0 * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.3e-128], t$95$1, If[LessEqual[a, 1.26e+92], N[(N[(b / c), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.3000000000000001e-128 or 1.26e92 < a

   1. Initial program 78.8%

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

   3. Taylor expanded in 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. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 41.7%

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

   5. Simplified 41.7%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. times-frac N/A

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

      6. *-inverses N/A

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

      7. clear-num N/A

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

      8. div-inv N/A

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

      9. clear-num N/A

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

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

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

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

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 54.7%

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

   7. Applied egg-rr 54.7%

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

   if -2.3000000000000001e-128 < a < 1.26e92

   1. Initial program 73.3%

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

   3. Taylor expanded in b around inf

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 42.6%

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

   5. Simplified 42.6%

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

      1. div-inv N/A

         \[\leadsto b \cdot \color{blue}{\frac{1}{z \cdot c}} \]

      2. associate-*r/ N/A

         \[\leadsto \frac{b \cdot 1}{\color{blue}{z \cdot c}} \]

      3. *-commutative N/A

         \[\leadsto \frac{b \cdot 1}{c \cdot \color{blue}{z}} \]

      4. times-frac N/A

         \[\leadsto \frac{b}{c} \cdot \color{blue}{\frac{1}{z}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{b}{c}\right), \color{blue}{\left(\frac{1}{z}\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(b, c\right), \left(\frac{\color{blue}{1}}{z}\right)\right) \]

      7. /-lowering-/.f64 47.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(b, c\right), \mathsf{/.f64}\left(1, \color{blue}{z}\right)\right) \]

   7. Applied egg-rr 47.8%

      \[\leadsto \color{blue}{\frac{b}{c} \cdot \frac{1}{z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 47.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{-4 \cdot a}{c}\\ \mathbf{if}\;a \leq -4.3 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+92}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* t (/ (* -4.0 a) c))))
   (if (<= a -4.3e-128) t_1 (if (<= a 1.75e+92) (/ (/ 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 = t * ((-4.0 * a) / c);
	double tmp;
	if (a <= -4.3e-128) {
		tmp = t_1;
	} else if (a <= 1.75e+92) {
		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 = t * (((-4.0d0) * a) / c)
    if (a <= (-4.3d-128)) then
        tmp = t_1
    else if (a <= 1.75d+92) 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 = t * ((-4.0 * a) / c);
	double tmp;
	if (a <= -4.3e-128) {
		tmp = t_1;
	} else if (a <= 1.75e+92) {
		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 = t * ((-4.0 * a) / c)
	tmp = 0
	if a <= -4.3e-128:
		tmp = t_1
	elif a <= 1.75e+92:
		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(t * Float64(Float64(-4.0 * a) / c))
	tmp = 0.0
	if (a <= -4.3e-128)
		tmp = t_1;
	elseif (a <= 1.75e+92)
		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 = t * ((-4.0 * a) / c);
	tmp = 0.0;
	if (a <= -4.3e-128)
		tmp = t_1;
	elseif (a <= 1.75e+92)
		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[(t * N[(N[(-4.0 * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.3e-128], t$95$1, If[LessEqual[a, 1.75e+92], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -4.29999999999999994e-128 or 1.74999999999999993e92 < a

   1. Initial program 78.8%

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

   3. Taylor expanded in 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. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 41.7%

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

   5. Simplified 41.7%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. times-frac N/A

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

      6. *-inverses N/A

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

      7. clear-num N/A

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

      8. div-inv N/A

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

      9. clear-num N/A

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

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

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

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

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 54.7%

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

   7. Applied egg-rr 54.7%

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

   if -4.29999999999999994e-128 < a < 1.74999999999999993e92

   1. Initial program 73.3%

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

   3. Taylor expanded in b around inf

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 42.6%

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

   5. Simplified 42.6%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   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 47.8%

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

   7. Applied egg-rr 47.8%

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

Alternative 14: 35.3% accurate, 3.8× speedup

Math

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

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 76.1%

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

3. Taylor expanded in 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 36.9%

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

5. Simplified 36.9%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
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 38.6%

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

7. Applied egg-rr 38.6%

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

Alternative 15: 35.5% 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 76.1%

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

3. Taylor expanded in 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 36.9%

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

5. Simplified 36.9%

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

Developer Target 1: 80.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t\_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t\_4}{z \cdot c}\\ t_6 := \frac{\left(t\_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 0:\\ \;\;\;\;\frac{\frac{t\_4}{z}}{c}\\ \mathbf{elif}\;t\_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t\_1\right) - t\_2\\ \mathbf{elif}\;t\_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

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 2024191 
(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)))