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

Percentage Accurate: 79.9% → 91.6%

Time: 15.6s

Alternatives: 18

Speedup: 1.1×

• 37.5% 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: 79.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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: 91.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+26}:\\ \;\;\;\;\frac{y \cdot \left(\frac{9 \cdot x}{z} + \frac{b}{z \cdot y}\right) + t\_1}{c}\\ \mathbf{elif}\;z \leq 10^{-50}:\\ \;\;\;\;\frac{\frac{\left(b + x \cdot \left(y \cdot 9\right)\right) - a \cdot \left(z \cdot \left(t \cdot 4\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{c}{t\_1 + \frac{b + 9 \cdot \left(y \cdot x\right)}{z}}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= z -4.8e+26)
     (/ (+ (* y (+ (/ (* 9.0 x) z) (/ b (* z y)))) t_1) c)
     (if (<= z 1e-50)
       (/ (/ (- (+ b (* x (* y 9.0))) (* a (* z (* t 4.0)))) c) z)
       (/ 1.0 (/ c (+ t_1 (/ (+ b (* 9.0 (* y x))) z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (z <= -4.8e+26) {
		tmp = ((y * (((9.0 * x) / z) + (b / (z * y)))) + t_1) / c;
	} else if (z <= 1e-50) {
		tmp = (((b + (x * (y * 9.0))) - (a * (z * (t * 4.0)))) / c) / z;
	} else {
		tmp = 1.0 / (c / (t_1 + ((b + (9.0 * (y * x))) / 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) :: t_1
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    if (z <= (-4.8d+26)) then
        tmp = ((y * (((9.0d0 * x) / z) + (b / (z * y)))) + t_1) / c
    else if (z <= 1d-50) then
        tmp = (((b + (x * (y * 9.0d0))) - (a * (z * (t * 4.0d0)))) / c) / z
    else
        tmp = 1.0d0 / (c / (t_1 + ((b + (9.0d0 * (y * x))) / z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (z <= -4.8e+26) {
		tmp = ((y * (((9.0 * x) / z) + (b / (z * y)))) + t_1) / c;
	} else if (z <= 1e-50) {
		tmp = (((b + (x * (y * 9.0))) - (a * (z * (t * 4.0)))) / c) / z;
	} else {
		tmp = 1.0 / (c / (t_1 + ((b + (9.0 * (y * x))) / z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = t * (a * -4.0)
	tmp = 0
	if z <= -4.8e+26:
		tmp = ((y * (((9.0 * x) / z) + (b / (z * y)))) + t_1) / c
	elif z <= 1e-50:
		tmp = (((b + (x * (y * 9.0))) - (a * (z * (t * 4.0)))) / c) / z
	else:
		tmp = 1.0 / (c / (t_1 + ((b + (9.0 * (y * x))) / z)))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (z <= -4.8e+26)
		tmp = Float64(Float64(Float64(y * Float64(Float64(Float64(9.0 * x) / z) + Float64(b / Float64(z * y)))) + t_1) / c);
	elseif (z <= 1e-50)
		tmp = Float64(Float64(Float64(Float64(b + Float64(x * Float64(y * 9.0))) - Float64(a * Float64(z * Float64(t * 4.0)))) / c) / z);
	else
		tmp = Float64(1.0 / Float64(c / Float64(t_1 + Float64(Float64(b + Float64(9.0 * Float64(y * x))) / z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (z <= -4.8e+26)
		tmp = ((y * (((9.0 * x) / z) + (b / (z * y)))) + t_1) / c;
	elseif (z <= 1e-50)
		tmp = (((b + (x * (y * 9.0))) - (a * (z * (t * 4.0)))) / c) / z;
	else
		tmp = 1.0 / (c / (t_1 + ((b + (9.0 * (y * x))) / z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e+26], N[(N[(N[(y * N[(N[(N[(9.0 * x), $MachinePrecision] / z), $MachinePrecision] + N[(b / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 1e-50], N[(N[(N[(N[(b + N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(z * N[(t * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(1.0 / N[(c / N[(t$95$1 + N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.80000000000000009e26

   1. Initial program 57.3%

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

      1. associate-/r* N/A

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

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

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

   3. Simplified 84.4%

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

   5. Taylor expanded in y around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 90.2%

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

   7. Simplified 90.2%

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

   if -4.80000000000000009e26 < z < 1.00000000000000001e-50

   1. Initial program 95.6%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

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

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

      5. *-lowering-*.f64 95.0%

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

   4. Applied egg-rr 95.0%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

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

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

   6. Applied egg-rr 96.8%

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

   if 1.00000000000000001e-50 < z

   1. Initial program 71.0%

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

      1. associate-/r* N/A

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

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

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

   3. Simplified 93.1%

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

      1. clear-num N/A

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

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

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

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

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

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

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

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

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

      6. associate-*r* N/A

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

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

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

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

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

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

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

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

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

      13. *-lowering-*.f64 93.1%

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

   6. Applied egg-rr 93.1%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+26}:\\ \;\;\;\;\frac{y \cdot \left(\frac{9 \cdot x}{z} + \frac{b}{z \cdot y}\right) + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 10^{-50}:\\ \;\;\;\;\frac{\frac{\left(b + x \cdot \left(y \cdot 9\right)\right) - a \cdot \left(z \cdot \left(t \cdot 4\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{c}{t \cdot \left(a \cdot -4\right) + \frac{b + 9 \cdot \left(y \cdot x\right)}{z}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 49.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+214}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+103}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-102}:\\ \;\;\;\;\frac{y \cdot 9}{c} \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-187}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-284}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-162}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -3.3e+214)
   (* a (* -4.0 (/ t c)))
   (if (<= t -1.2e+103)
     (* -4.0 (/ (* t a) c))
     (if (<= t -7.5e-102)
       (* (/ (* y 9.0) c) (/ x z))
       (if (<= t -1.75e-187)
         (* b (/ (/ 1.0 z) c))
         (if (<= t -5.8e-284)
           (/ (* 9.0 (* y x)) (* z c))
           (if (<= t 2.1e-162) (/ b (* z c)) (* (* t -4.0) (/ a c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -3.3e+214) {
		tmp = a * (-4.0 * (t / c));
	} else if (t <= -1.2e+103) {
		tmp = -4.0 * ((t * a) / c);
	} else if (t <= -7.5e-102) {
		tmp = ((y * 9.0) / c) * (x / z);
	} else if (t <= -1.75e-187) {
		tmp = b * ((1.0 / z) / c);
	} else if (t <= -5.8e-284) {
		tmp = (9.0 * (y * x)) / (z * c);
	} else if (t <= 2.1e-162) {
		tmp = b / (z * c);
	} else {
		tmp = (t * -4.0) * (a / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-3.3d+214)) then
        tmp = a * ((-4.0d0) * (t / c))
    else if (t <= (-1.2d+103)) then
        tmp = (-4.0d0) * ((t * a) / c)
    else if (t <= (-7.5d-102)) then
        tmp = ((y * 9.0d0) / c) * (x / z)
    else if (t <= (-1.75d-187)) then
        tmp = b * ((1.0d0 / z) / c)
    else if (t <= (-5.8d-284)) then
        tmp = (9.0d0 * (y * x)) / (z * c)
    else if (t <= 2.1d-162) then
        tmp = b / (z * c)
    else
        tmp = (t * (-4.0d0)) * (a / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -3.3e+214) {
		tmp = a * (-4.0 * (t / c));
	} else if (t <= -1.2e+103) {
		tmp = -4.0 * ((t * a) / c);
	} else if (t <= -7.5e-102) {
		tmp = ((y * 9.0) / c) * (x / z);
	} else if (t <= -1.75e-187) {
		tmp = b * ((1.0 / z) / c);
	} else if (t <= -5.8e-284) {
		tmp = (9.0 * (y * x)) / (z * c);
	} else if (t <= 2.1e-162) {
		tmp = b / (z * c);
	} else {
		tmp = (t * -4.0) * (a / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -3.3e+214:
		tmp = a * (-4.0 * (t / c))
	elif t <= -1.2e+103:
		tmp = -4.0 * ((t * a) / c)
	elif t <= -7.5e-102:
		tmp = ((y * 9.0) / c) * (x / z)
	elif t <= -1.75e-187:
		tmp = b * ((1.0 / z) / c)
	elif t <= -5.8e-284:
		tmp = (9.0 * (y * x)) / (z * c)
	elif t <= 2.1e-162:
		tmp = b / (z * c)
	else:
		tmp = (t * -4.0) * (a / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -3.3e+214)
		tmp = Float64(a * Float64(-4.0 * Float64(t / c)));
	elseif (t <= -1.2e+103)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c));
	elseif (t <= -7.5e-102)
		tmp = Float64(Float64(Float64(y * 9.0) / c) * Float64(x / z));
	elseif (t <= -1.75e-187)
		tmp = Float64(b * Float64(Float64(1.0 / z) / c));
	elseif (t <= -5.8e-284)
		tmp = Float64(Float64(9.0 * Float64(y * x)) / Float64(z * c));
	elseif (t <= 2.1e-162)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(Float64(t * -4.0) * Float64(a / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -3.3e+214)
		tmp = a * (-4.0 * (t / c));
	elseif (t <= -1.2e+103)
		tmp = -4.0 * ((t * a) / c);
	elseif (t <= -7.5e-102)
		tmp = ((y * 9.0) / c) * (x / z);
	elseif (t <= -1.75e-187)
		tmp = b * ((1.0 / z) / c);
	elseif (t <= -5.8e-284)
		tmp = (9.0 * (y * x)) / (z * c);
	elseif (t <= 2.1e-162)
		tmp = b / (z * c);
	else
		tmp = (t * -4.0) * (a / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -3.3e+214], N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.2e+103], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.5e-102], N[(N[(N[(y * 9.0), $MachinePrecision] / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.75e-187], N[(b * N[(N[(1.0 / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.8e-284], N[(N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e-162], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(t * -4.0), $MachinePrecision] * N[(a / c), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -3.30000000000000011e214

   1. Initial program 70.6%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 66.4%

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

   5. Simplified 66.4%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

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

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

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

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

      7. /-lowering-/.f64 80.5%

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

   7. Applied egg-rr 80.5%

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

   if -3.30000000000000011e214 < t < -1.1999999999999999e103

   1. Initial program 73.6%

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

      1. associate-/r* N/A

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

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

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

   3. Simplified 91.2%

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

      1. clear-num N/A

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

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

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

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

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

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

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

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

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

      6. associate-*r* N/A

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

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

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

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

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

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

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

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

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

      13. *-lowering-*.f64 91.0%

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

   6. Applied egg-rr 91.0%

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

   7. Taylor expanded in z around inf

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

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

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

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

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

      3. *-lowering-*.f64 77.5%

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

   9. Simplified 77.5%

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

   if -1.1999999999999999e103 < t < -7.5000000000000008e-102

   1. Initial program 77.1%

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

      1. associate-/r* N/A

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

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

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

   3. Simplified 89.3%

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

   5. Taylor expanded in x around inf

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

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

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

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

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

      3. *-lowering-*.f64 51.4%

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

   7. Simplified 51.4%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-/l/ N/A

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

      6. *-commutative N/A

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

      7. times-frac N/A

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

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

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

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

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

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

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

      11. /-lowering-/.f64 47.3%

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

   9. Applied egg-rr 47.3%

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

   if -7.5000000000000008e-102 < t < -1.74999999999999989e-187

   1. Initial program 82.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 58.1%

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

   5. Simplified 58.1%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

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

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

      4. associate-/r* N/A

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

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

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

      6. /-lowering-/.f64 58.1%

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

   7. Applied egg-rr 58.1%

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

   if -1.74999999999999989e-187 < t < -5.8000000000000002e-284

   1. Initial program 87.6%

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

   3. Taylor expanded in x around inf

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

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

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

      2. *-lowering-*.f64 63.7%

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

   5. Simplified 63.7%

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

   if -5.8000000000000002e-284 < t < 2.1e-162

   1. Initial program 88.7%

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

   3. 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 52.4%

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

   5. Simplified 52.4%

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

      1. frac-2neg N/A

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

      2. distribute-frac-neg N/A

         \[\leadsto \mathsf{neg}\left(\frac{b}{\mathsf{neg}\left(z \cdot c\right)}\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\left(\frac{b}{\mathsf{neg}\left(z \cdot c\right)}\right)\right) \]

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

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

      5. neg-sub0 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{/.f64}\left(b, \left(0 - z \cdot c\right)\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{/.f64}\left(b, \mathsf{\_.f64}\left(0, \left(z \cdot c\right)\right)\right)\right) \]

      7. *-lowering-*.f64 52.4%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{/.f64}\left(b, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, c\right)\right)\right)\right) \]

   7. Applied egg-rr 52.4%

      \[\leadsto \color{blue}{-\frac{b}{0 - z \cdot c}} \]

   if 2.1e-162 < t

   1. Initial program 83.0%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 40.6%

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

   5. Simplified 40.6%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. /-lowering-/.f64 42.7%

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

   7. Applied egg-rr 42.7%

      \[\leadsto \color{blue}{\left(t \cdot -4\right) \cdot \frac{a}{c}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+214}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+103}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-102}:\\ \;\;\;\;\frac{y \cdot 9}{c} \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-187}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-284}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-162}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+213}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+108}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-102}:\\ \;\;\;\;\frac{y \cdot 9}{c} \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -5.7 \cdot 10^{-187}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-284}:\\ \;\;\;\;9 \cdot \frac{\frac{y \cdot x}{z}}{c}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-163}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -9.5e+213)
   (* a (* -4.0 (/ t c)))
   (if (<= t -8e+108)
     (* -4.0 (/ (* t a) c))
     (if (<= t -6.8e-102)
       (* (/ (* y 9.0) c) (/ x z))
       (if (<= t -5.7e-187)
         (* b (/ (/ 1.0 z) c))
         (if (<= t -4.7e-284)
           (* 9.0 (/ (/ (* y x) z) c))
           (if (<= t 9.8e-163) (/ b (* z c)) (* (* t -4.0) (/ a c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -9.5e+213) {
		tmp = a * (-4.0 * (t / c));
	} else if (t <= -8e+108) {
		tmp = -4.0 * ((t * a) / c);
	} else if (t <= -6.8e-102) {
		tmp = ((y * 9.0) / c) * (x / z);
	} else if (t <= -5.7e-187) {
		tmp = b * ((1.0 / z) / c);
	} else if (t <= -4.7e-284) {
		tmp = 9.0 * (((y * x) / z) / c);
	} else if (t <= 9.8e-163) {
		tmp = b / (z * c);
	} else {
		tmp = (t * -4.0) * (a / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-9.5d+213)) then
        tmp = a * ((-4.0d0) * (t / c))
    else if (t <= (-8d+108)) then
        tmp = (-4.0d0) * ((t * a) / c)
    else if (t <= (-6.8d-102)) then
        tmp = ((y * 9.0d0) / c) * (x / z)
    else if (t <= (-5.7d-187)) then
        tmp = b * ((1.0d0 / z) / c)
    else if (t <= (-4.7d-284)) then
        tmp = 9.0d0 * (((y * x) / z) / c)
    else if (t <= 9.8d-163) then
        tmp = b / (z * c)
    else
        tmp = (t * (-4.0d0)) * (a / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -9.5e+213) {
		tmp = a * (-4.0 * (t / c));
	} else if (t <= -8e+108) {
		tmp = -4.0 * ((t * a) / c);
	} else if (t <= -6.8e-102) {
		tmp = ((y * 9.0) / c) * (x / z);
	} else if (t <= -5.7e-187) {
		tmp = b * ((1.0 / z) / c);
	} else if (t <= -4.7e-284) {
		tmp = 9.0 * (((y * x) / z) / c);
	} else if (t <= 9.8e-163) {
		tmp = b / (z * c);
	} else {
		tmp = (t * -4.0) * (a / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -9.5e+213:
		tmp = a * (-4.0 * (t / c))
	elif t <= -8e+108:
		tmp = -4.0 * ((t * a) / c)
	elif t <= -6.8e-102:
		tmp = ((y * 9.0) / c) * (x / z)
	elif t <= -5.7e-187:
		tmp = b * ((1.0 / z) / c)
	elif t <= -4.7e-284:
		tmp = 9.0 * (((y * x) / z) / c)
	elif t <= 9.8e-163:
		tmp = b / (z * c)
	else:
		tmp = (t * -4.0) * (a / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -9.5e+213)
		tmp = Float64(a * Float64(-4.0 * Float64(t / c)));
	elseif (t <= -8e+108)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c));
	elseif (t <= -6.8e-102)
		tmp = Float64(Float64(Float64(y * 9.0) / c) * Float64(x / z));
	elseif (t <= -5.7e-187)
		tmp = Float64(b * Float64(Float64(1.0 / z) / c));
	elseif (t <= -4.7e-284)
		tmp = Float64(9.0 * Float64(Float64(Float64(y * x) / z) / c));
	elseif (t <= 9.8e-163)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(Float64(t * -4.0) * Float64(a / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -9.5e+213)
		tmp = a * (-4.0 * (t / c));
	elseif (t <= -8e+108)
		tmp = -4.0 * ((t * a) / c);
	elseif (t <= -6.8e-102)
		tmp = ((y * 9.0) / c) * (x / z);
	elseif (t <= -5.7e-187)
		tmp = b * ((1.0 / z) / c);
	elseif (t <= -4.7e-284)
		tmp = 9.0 * (((y * x) / z) / c);
	elseif (t <= 9.8e-163)
		tmp = b / (z * c);
	else
		tmp = (t * -4.0) * (a / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -9.5e+213], N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8e+108], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.8e-102], N[(N[(N[(y * 9.0), $MachinePrecision] / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.7e-187], N[(b * N[(N[(1.0 / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.7e-284], N[(9.0 * N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.8e-163], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(t * -4.0), $MachinePrecision] * N[(a / c), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -9.49999999999999993e213

   1. Initial program 70.6%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 66.4%

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

   5. Simplified 66.4%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

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

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

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

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

      7. /-lowering-/.f64 80.5%

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

   7. Applied egg-rr 80.5%

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

   if -9.49999999999999993e213 < t < -8.0000000000000003e108

   1. Initial program 73.6%

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

      1. associate-/r* N/A

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

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

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

   3. Simplified 91.2%

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

      1. clear-num N/A

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

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

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

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

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

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

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

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

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

      6. associate-*r* N/A

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

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

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

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

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

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

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

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

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

      13. *-lowering-*.f64 91.0%

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

   6. Applied egg-rr 91.0%

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

   7. Taylor expanded in z around inf

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

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

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

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

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

      3. *-lowering-*.f64 77.5%

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

   9. Simplified 77.5%

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

   if -8.0000000000000003e108 < t < -6.80000000000000026e-102

   1. Initial program 77.1%

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

      1. associate-/r* N/A

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

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

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

   3. Simplified 89.3%

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

   5. Taylor expanded in x around inf

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

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

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

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

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

      3. *-lowering-*.f64 51.4%

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

   7. Simplified 51.4%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-/l/ N/A

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

      6. *-commutative N/A

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

      7. times-frac N/A

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

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

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

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

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

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

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

      11. /-lowering-/.f64 47.3%

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

   9. Applied egg-rr 47.3%

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

   if -6.80000000000000026e-102 < t < -5.6999999999999996e-187

   1. Initial program 82.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 58.1%

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

   5. Simplified 58.1%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

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

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

      4. associate-/r* N/A

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

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

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

      6. /-lowering-/.f64 58.1%

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

   7. Applied egg-rr 58.1%

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

   if -5.6999999999999996e-187 < t < -4.70000000000000022e-284

   1. Initial program 87.6%

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

   3. Taylor expanded in x around inf

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

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

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

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

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

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

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

      6. *-lowering-*.f64 67.3%

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

   5. Simplified 67.3%

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

   if -4.70000000000000022e-284 < t < 9.8000000000000005e-163

   1. Initial program 88.7%

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

   3. 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 52.4%

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

   5. Simplified 52.4%

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

      1. frac-2neg N/A

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

      2. distribute-frac-neg N/A

         \[\leadsto \mathsf{neg}\left(\frac{b}{\mathsf{neg}\left(z \cdot c\right)}\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\left(\frac{b}{\mathsf{neg}\left(z \cdot c\right)}\right)\right) \]

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

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

      5. neg-sub0 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{/.f64}\left(b, \left(0 - z \cdot c\right)\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{/.f64}\left(b, \mathsf{\_.f64}\left(0, \left(z \cdot c\right)\right)\right)\right) \]

      7. *-lowering-*.f64 52.4%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{/.f64}\left(b, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, c\right)\right)\right)\right) \]

   7. Applied egg-rr 52.4%

      \[\leadsto \color{blue}{-\frac{b}{0 - z \cdot c}} \]

   if 9.8000000000000005e-163 < t

   1. Initial program 83.0%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 40.6%

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

   5. Simplified 40.6%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. /-lowering-/.f64 42.7%

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

   7. Applied egg-rr 42.7%

      \[\leadsto \color{blue}{\left(t \cdot -4\right) \cdot \frac{a}{c}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+213}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+108}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-102}:\\ \;\;\;\;\frac{y \cdot 9}{c} \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -5.7 \cdot 10^{-187}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-284}:\\ \;\;\;\;9 \cdot \frac{\frac{y \cdot x}{z}}{c}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-163}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+126}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-102}:\\ \;\;\;\;\frac{\frac{y \cdot \left(9 \cdot x\right)}{c}}{z}\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-188}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-284}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-163}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.35e+126)
   (* a (* -4.0 (/ t c)))
   (if (<= t -6.8e-102)
     (/ (/ (* y (* 9.0 x)) c) z)
     (if (<= t -2.25e-188)
       (* b (/ (/ 1.0 z) c))
       (if (<= t -5.5e-284)
         (/ (* 9.0 (* y x)) (* z c))
         (if (<= t 7e-163) (/ b (* z c)) (* (* t -4.0) (/ a c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.35e+126) {
		tmp = a * (-4.0 * (t / c));
	} else if (t <= -6.8e-102) {
		tmp = ((y * (9.0 * x)) / c) / z;
	} else if (t <= -2.25e-188) {
		tmp = b * ((1.0 / z) / c);
	} else if (t <= -5.5e-284) {
		tmp = (9.0 * (y * x)) / (z * c);
	} else if (t <= 7e-163) {
		tmp = b / (z * c);
	} else {
		tmp = (t * -4.0) * (a / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-1.35d+126)) then
        tmp = a * ((-4.0d0) * (t / c))
    else if (t <= (-6.8d-102)) then
        tmp = ((y * (9.0d0 * x)) / c) / z
    else if (t <= (-2.25d-188)) then
        tmp = b * ((1.0d0 / z) / c)
    else if (t <= (-5.5d-284)) then
        tmp = (9.0d0 * (y * x)) / (z * c)
    else if (t <= 7d-163) then
        tmp = b / (z * c)
    else
        tmp = (t * (-4.0d0)) * (a / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.35e+126) {
		tmp = a * (-4.0 * (t / c));
	} else if (t <= -6.8e-102) {
		tmp = ((y * (9.0 * x)) / c) / z;
	} else if (t <= -2.25e-188) {
		tmp = b * ((1.0 / z) / c);
	} else if (t <= -5.5e-284) {
		tmp = (9.0 * (y * x)) / (z * c);
	} else if (t <= 7e-163) {
		tmp = b / (z * c);
	} else {
		tmp = (t * -4.0) * (a / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -1.35e+126:
		tmp = a * (-4.0 * (t / c))
	elif t <= -6.8e-102:
		tmp = ((y * (9.0 * x)) / c) / z
	elif t <= -2.25e-188:
		tmp = b * ((1.0 / z) / c)
	elif t <= -5.5e-284:
		tmp = (9.0 * (y * x)) / (z * c)
	elif t <= 7e-163:
		tmp = b / (z * c)
	else:
		tmp = (t * -4.0) * (a / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.35e+126)
		tmp = Float64(a * Float64(-4.0 * Float64(t / c)));
	elseif (t <= -6.8e-102)
		tmp = Float64(Float64(Float64(y * Float64(9.0 * x)) / c) / z);
	elseif (t <= -2.25e-188)
		tmp = Float64(b * Float64(Float64(1.0 / z) / c));
	elseif (t <= -5.5e-284)
		tmp = Float64(Float64(9.0 * Float64(y * x)) / Float64(z * c));
	elseif (t <= 7e-163)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(Float64(t * -4.0) * Float64(a / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -1.35e+126)
		tmp = a * (-4.0 * (t / c));
	elseif (t <= -6.8e-102)
		tmp = ((y * (9.0 * x)) / c) / z;
	elseif (t <= -2.25e-188)
		tmp = b * ((1.0 / z) / c);
	elseif (t <= -5.5e-284)
		tmp = (9.0 * (y * x)) / (z * c);
	elseif (t <= 7e-163)
		tmp = b / (z * c);
	else
		tmp = (t * -4.0) * (a / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -1.35e+126], N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.8e-102], N[(N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, -2.25e-188], N[(b * N[(N[(1.0 / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.5e-284], N[(N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-163], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(t * -4.0), $MachinePrecision] * N[(a / c), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.35000000000000001e126

   1. Initial program 73.0%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 70.8%

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

   5. Simplified 70.8%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

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

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

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

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

      7. /-lowering-/.f64 70.7%

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

   7. Applied egg-rr 70.7%

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

   if -1.35000000000000001e126 < t < -6.80000000000000026e-102

   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. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

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

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

      5. *-lowering-*.f64 78.1%

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

   4. Applied egg-rr 78.1%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

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

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

   6. Applied egg-rr 78.1%

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

   7. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

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

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 51.3%

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

   9. Simplified 51.3%

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

   if -6.80000000000000026e-102 < t < -2.24999999999999997e-188

   1. Initial program 83.6%

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

   3. Taylor expanded in 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 59.8%

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

   5. Simplified 59.8%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

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

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

      4. associate-/r* N/A

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

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

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

      6. /-lowering-/.f64 59.9%

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

   7. Applied egg-rr 59.9%

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

   if -2.24999999999999997e-188 < t < -5.4999999999999995e-284

   1. Initial program 87.1%

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

   3. Taylor expanded in x around inf

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

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

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

      2. *-lowering-*.f64 62.1%

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

   5. Simplified 62.1%

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

   if -5.4999999999999995e-284 < t < 7.00000000000000054e-163

   1. Initial program 88.7%

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

   3. 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 52.4%

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

   5. Simplified 52.4%

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

      1. frac-2neg N/A

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

      2. distribute-frac-neg N/A

         \[\leadsto \mathsf{neg}\left(\frac{b}{\mathsf{neg}\left(z \cdot c\right)}\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\left(\frac{b}{\mathsf{neg}\left(z \cdot c\right)}\right)\right) \]

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

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

      5. neg-sub0 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{/.f64}\left(b, \left(0 - z \cdot c\right)\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{/.f64}\left(b, \mathsf{\_.f64}\left(0, \left(z \cdot c\right)\right)\right)\right) \]

      7. *-lowering-*.f64 52.4%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{/.f64}\left(b, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, c\right)\right)\right)\right) \]

   7. Applied egg-rr 52.4%

      \[\leadsto \color{blue}{-\frac{b}{0 - z \cdot c}} \]

   if 7.00000000000000054e-163 < t

   1. Initial program 83.0%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 40.6%

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

   5. Simplified 40.6%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. /-lowering-/.f64 42.7%

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

   7. Applied egg-rr 42.7%

      \[\leadsto \color{blue}{\left(t \cdot -4\right) \cdot \frac{a}{c}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+126}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-102}:\\ \;\;\;\;\frac{\frac{y \cdot \left(9 \cdot x\right)}{c}}{z}\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-188}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-284}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-163}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{y \cdot x}{z}}{c}\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+226}:\\ \;\;\;\;\frac{z \cdot -4}{z} \cdot \frac{\frac{t}{c}}{\frac{1}{a}}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-162}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(y \cdot x\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (* t (* a -4.0)) (* 9.0 (/ (* y x) z))) c)))
   (if (<= t -3.7e+226)
     (* (/ (* z -4.0) z) (/ (/ t c) (/ 1.0 a)))
     (if (<= t -1.3e-68)
       t_1
       (if (<= t 1.95e-162) (/ (/ (+ 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 = ((t * (a * -4.0)) + (9.0 * ((y * x) / z))) / c;
	double tmp;
	if (t <= -3.7e+226) {
		tmp = ((z * -4.0) / z) * ((t / c) / (1.0 / a));
	} else if (t <= -1.3e-68) {
		tmp = t_1;
	} else if (t <= 1.95e-162) {
		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 = ((t * (a * (-4.0d0))) + (9.0d0 * ((y * x) / z))) / c
    if (t <= (-3.7d+226)) then
        tmp = ((z * (-4.0d0)) / z) * ((t / c) / (1.0d0 / a))
    else if (t <= (-1.3d-68)) then
        tmp = t_1
    else if (t <= 1.95d-162) 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 = ((t * (a * -4.0)) + (9.0 * ((y * x) / z))) / c;
	double tmp;
	if (t <= -3.7e+226) {
		tmp = ((z * -4.0) / z) * ((t / c) / (1.0 / a));
	} else if (t <= -1.3e-68) {
		tmp = t_1;
	} else if (t <= 1.95e-162) {
		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 = ((t * (a * -4.0)) + (9.0 * ((y * x) / z))) / c
	tmp = 0
	if t <= -3.7e+226:
		tmp = ((z * -4.0) / z) * ((t / c) / (1.0 / a))
	elif t <= -1.3e-68:
		tmp = t_1
	elif t <= 1.95e-162:
		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(t * Float64(a * -4.0)) + Float64(9.0 * Float64(Float64(y * x) / z))) / c)
	tmp = 0.0
	if (t <= -3.7e+226)
		tmp = Float64(Float64(Float64(z * -4.0) / z) * Float64(Float64(t / c) / Float64(1.0 / a)));
	elseif (t <= -1.3e-68)
		tmp = t_1;
	elseif (t <= 1.95e-162)
		tmp = Float64(Float64(Float64(b + Float64(9.0 * Float64(y * x))) / z) / c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((t * (a * -4.0)) + (9.0 * ((y * x) / z))) / c;
	tmp = 0.0;
	if (t <= -3.7e+226)
		tmp = ((z * -4.0) / z) * ((t / c) / (1.0 / a));
	elseif (t <= -1.3e-68)
		tmp = t_1;
	elseif (t <= 1.95e-162)
		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[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[t, -3.7e+226], N[(N[(N[(z * -4.0), $MachinePrecision] / z), $MachinePrecision] * N[(N[(t / c), $MachinePrecision] / N[(1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.3e-68], t$95$1, If[LessEqual[t, 1.95e-162], N[(N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.69999999999999982e226

   1. Initial program 67.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-lowering-*.f64 51.1%

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

   5. Simplified 51.1%

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

      1. times-frac N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. associate-*l* N/A

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

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

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

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

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

      8. /-lowering-/.f64 68.0%

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

   7. Applied egg-rr 68.0%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. div-inv N/A

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

      6. times-frac N/A

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

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

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, -4\right), z\right), \left(\frac{\frac{\color{blue}{t}}{c}}{\frac{1}{a}}\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, -4\right), z\right), \mathsf{/.f64}\left(\left(\frac{t}{c}\right), \color{blue}{\left(\frac{1}{a}\right)}\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, -4\right), z\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(t, c\right), \left(\frac{\color{blue}{1}}{a}\right)\right)\right) \]

      12. /-lowering-/.f64 84.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, -4\right), z\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(t, c\right), \mathsf{/.f64}\left(1, \color{blue}{a}\right)\right)\right) \]

   9. Applied egg-rr 84.2%

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

   if -3.69999999999999982e226 < t < -1.2999999999999999e-68 or 1.95e-162 < t

   1. Initial program 79.4%

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

      1. associate-/r* N/A

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

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

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

   3. Simplified 89.4%

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

   5. Taylor expanded in x around inf

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

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

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

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

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

      3. *-lowering-*.f64 74.1%

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

   7. Simplified 74.1%

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

   if -1.2999999999999999e-68 < t < 1.95e-162

   1. Initial program 87.2%

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

      1. associate-/r* N/A

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

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

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

   3. Simplified 87.3%

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

   5. Taylor expanded in z around 0

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

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

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

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

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

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

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

      4. *-lowering-*.f64 79.2%

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

   7. Simplified 79.2%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+226}:\\ \;\;\;\;\frac{z \cdot -4}{z} \cdot \frac{\frac{t}{c}}{\frac{1}{a}}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-68}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{y \cdot x}{z}}{c}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-162}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(y \cdot x\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{y \cdot x}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := b + 9 \cdot \left(y \cdot x\right)\\ t_2 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -5 \cdot 10^{-40}:\\ \;\;\;\;\frac{t\_2 + \frac{1}{\frac{z}{t\_1}}}{c}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{\frac{\left(b + x \cdot \left(y \cdot 9\right)\right) - a \cdot \left(z \cdot \left(t \cdot 4\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{c}{t\_2 + \frac{t\_1}{z}}}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (+ b (* 9.0 (* y x)))) (t_2 (* t (* a -4.0))))
   (if (<= z -5e-40)
     (/ (+ t_2 (/ 1.0 (/ z t_1))) c)
     (if (<= z 1.5e-50)
       (/ (/ (- (+ b (* x (* y 9.0))) (* a (* z (* t 4.0)))) c) z)
       (/ 1.0 (/ c (+ t_2 (/ t_1 z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b + (9.0 * (y * x));
	double t_2 = t * (a * -4.0);
	double tmp;
	if (z <= -5e-40) {
		tmp = (t_2 + (1.0 / (z / t_1))) / c;
	} else if (z <= 1.5e-50) {
		tmp = (((b + (x * (y * 9.0))) - (a * (z * (t * 4.0)))) / c) / z;
	} else {
		tmp = 1.0 / (c / (t_2 + (t_1 / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b + (9.0d0 * (y * x))
    t_2 = t * (a * (-4.0d0))
    if (z <= (-5d-40)) then
        tmp = (t_2 + (1.0d0 / (z / t_1))) / c
    else if (z <= 1.5d-50) then
        tmp = (((b + (x * (y * 9.0d0))) - (a * (z * (t * 4.0d0)))) / c) / z
    else
        tmp = 1.0d0 / (c / (t_2 + (t_1 / z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b + (9.0 * (y * x));
	double t_2 = t * (a * -4.0);
	double tmp;
	if (z <= -5e-40) {
		tmp = (t_2 + (1.0 / (z / t_1))) / c;
	} else if (z <= 1.5e-50) {
		tmp = (((b + (x * (y * 9.0))) - (a * (z * (t * 4.0)))) / c) / z;
	} else {
		tmp = 1.0 / (c / (t_2 + (t_1 / z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = b + (9.0 * (y * x))
	t_2 = t * (a * -4.0)
	tmp = 0
	if z <= -5e-40:
		tmp = (t_2 + (1.0 / (z / t_1))) / c
	elif z <= 1.5e-50:
		tmp = (((b + (x * (y * 9.0))) - (a * (z * (t * 4.0)))) / c) / z
	else:
		tmp = 1.0 / (c / (t_2 + (t_1 / z)))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(b + Float64(9.0 * Float64(y * x)))
	t_2 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (z <= -5e-40)
		tmp = Float64(Float64(t_2 + Float64(1.0 / Float64(z / t_1))) / c);
	elseif (z <= 1.5e-50)
		tmp = Float64(Float64(Float64(Float64(b + Float64(x * Float64(y * 9.0))) - Float64(a * Float64(z * Float64(t * 4.0)))) / c) / z);
	else
		tmp = Float64(1.0 / Float64(c / Float64(t_2 + Float64(t_1 / z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b + (9.0 * (y * x));
	t_2 = t * (a * -4.0);
	tmp = 0.0;
	if (z <= -5e-40)
		tmp = (t_2 + (1.0 / (z / t_1))) / c;
	elseif (z <= 1.5e-50)
		tmp = (((b + (x * (y * 9.0))) - (a * (z * (t * 4.0)))) / c) / z;
	else
		tmp = 1.0 / (c / (t_2 + (t_1 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e-40], N[(N[(t$95$2 + N[(1.0 / N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 1.5e-50], N[(N[(N[(N[(b + N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(z * N[(t * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(1.0 / N[(c / N[(t$95$2 + N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.99999999999999965e-40

   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. Step-by-step derivation

      1. associate-/r* N/A

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

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

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

   3. Simplified 88.1%

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

      1. clear-num N/A

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

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

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

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

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

      4. associate-*r* N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

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

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

      9. *-lowering-*.f64 88.1%

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

   6. Applied egg-rr 88.1%

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

   if -4.99999999999999965e-40 < z < 1.49999999999999995e-50

   1. Initial program 95.1%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

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

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

      5. *-lowering-*.f64 94.4%

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

   4. Applied egg-rr 94.4%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

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

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

   6. Applied egg-rr 97.1%

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

   if 1.49999999999999995e-50 < z

   1. Initial program 71.0%

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

      1. associate-/r* N/A

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

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

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

   3. Simplified 93.1%

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

      1. clear-num N/A

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

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

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

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

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

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

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

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

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

      6. associate-*r* N/A

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

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

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

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

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

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

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

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

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

      13. *-lowering-*.f64 93.1%

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

   6. Applied egg-rr 93.1%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-40}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{1}{\frac{z}{b + 9 \cdot \left(y \cdot x\right)}}}{c}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{\frac{\left(b + x \cdot \left(y \cdot 9\right)\right) - a \cdot \left(z \cdot \left(t \cdot 4\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{c}{t \cdot \left(a \cdot -4\right) + \frac{b + 9 \cdot \left(y \cdot x\right)}{z}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(y \cdot x\right)\\ t_2 := b + t\_1\\ t_3 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{-40}:\\ \;\;\;\;\frac{t\_3 + \frac{1}{\frac{z}{t\_2}}}{c}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{\frac{b + \left(t\_1 - z \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{c}{t\_3 + \frac{t\_2}{z}}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (* y x))) (t_2 (+ b t_1)) (t_3 (* t (* a -4.0))))
   (if (<= z -6e-40)
     (/ (+ t_3 (/ 1.0 (/ z t_2))) c)
     (if (<= z 6.5e-50)
       (/ (/ (+ b (- t_1 (* z (* 4.0 (* t a))))) c) z)
       (/ 1.0 (/ c (+ t_3 (/ t_2 z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * (y * x);
	double t_2 = b + t_1;
	double t_3 = t * (a * -4.0);
	double tmp;
	if (z <= -6e-40) {
		tmp = (t_3 + (1.0 / (z / t_2))) / c;
	} else if (z <= 6.5e-50) {
		tmp = ((b + (t_1 - (z * (4.0 * (t * a))))) / c) / z;
	} else {
		tmp = 1.0 / (c / (t_3 + (t_2 / 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 9.0d0 * (y * x)
    t_2 = b + t_1
    t_3 = t * (a * (-4.0d0))
    if (z <= (-6d-40)) then
        tmp = (t_3 + (1.0d0 / (z / t_2))) / c
    else if (z <= 6.5d-50) then
        tmp = ((b + (t_1 - (z * (4.0d0 * (t * a))))) / c) / z
    else
        tmp = 1.0d0 / (c / (t_3 + (t_2 / z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * (y * x);
	double t_2 = b + t_1;
	double t_3 = t * (a * -4.0);
	double tmp;
	if (z <= -6e-40) {
		tmp = (t_3 + (1.0 / (z / t_2))) / c;
	} else if (z <= 6.5e-50) {
		tmp = ((b + (t_1 - (z * (4.0 * (t * a))))) / c) / z;
	} else {
		tmp = 1.0 / (c / (t_3 + (t_2 / z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * (y * x)
	t_2 = b + t_1
	t_3 = t * (a * -4.0)
	tmp = 0
	if z <= -6e-40:
		tmp = (t_3 + (1.0 / (z / t_2))) / c
	elif z <= 6.5e-50:
		tmp = ((b + (t_1 - (z * (4.0 * (t * a))))) / c) / z
	else:
		tmp = 1.0 / (c / (t_3 + (t_2 / z)))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(y * x))
	t_2 = Float64(b + t_1)
	t_3 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (z <= -6e-40)
		tmp = Float64(Float64(t_3 + Float64(1.0 / Float64(z / t_2))) / c);
	elseif (z <= 6.5e-50)
		tmp = Float64(Float64(Float64(b + Float64(t_1 - Float64(z * Float64(4.0 * Float64(t * a))))) / c) / z);
	else
		tmp = Float64(1.0 / Float64(c / Float64(t_3 + Float64(t_2 / z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * (y * x);
	t_2 = b + t_1;
	t_3 = t * (a * -4.0);
	tmp = 0.0;
	if (z <= -6e-40)
		tmp = (t_3 + (1.0 / (z / t_2))) / c;
	elseif (z <= 6.5e-50)
		tmp = ((b + (t_1 - (z * (4.0 * (t * a))))) / c) / z;
	else
		tmp = 1.0 / (c / (t_3 + (t_2 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e-40], N[(N[(t$95$3 + N[(1.0 / N[(z / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 6.5e-50], N[(N[(N[(b + N[(t$95$1 - N[(z * N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], N[(1.0 / N[(c / N[(t$95$3 + N[(t$95$2 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.00000000000000039e-40

   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. Step-by-step derivation

      1. associate-/r* N/A

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

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

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

   3. Simplified 88.1%

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

      1. clear-num N/A

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

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

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

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

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

      4. associate-*r* N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

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

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

      9. *-lowering-*.f64 88.1%

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

   6. Applied egg-rr 88.1%

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

   if -6.00000000000000039e-40 < z < 6.49999999999999987e-50

   1. Initial program 95.1%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

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

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

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

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

      11. associate-*l* N/A

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

      12. associate-*l* N/A

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

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

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

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

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

      15. *-lowering-*.f64 95.6%

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

   4. Applied egg-rr 95.6%

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

   if 6.49999999999999987e-50 < z

   1. Initial program 71.0%

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

      1. associate-/r* N/A

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

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

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

   3. Simplified 93.1%

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

      1. clear-num N/A

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

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

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

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

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

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

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

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

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

      6. associate-*r* N/A

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

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

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

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

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

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

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

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

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

      13. *-lowering-*.f64 93.1%

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

   6. Applied egg-rr 93.1%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-40}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{1}{\frac{z}{b + 9 \cdot \left(y \cdot x\right)}}}{c}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{\frac{b + \left(9 \cdot \left(y \cdot x\right) - z \cdot \left(4 \cdot \left(t \cdot a\right)\right)\right)}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{c}{t \cdot \left(a \cdot -4\right) + \frac{b + 9 \cdot \left(y \cdot x\right)}{z}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 91.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := b + 9 \cdot \left(y \cdot x\right)\\ t_2 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -1.46 \cdot 10^{+81}:\\ \;\;\;\;\frac{t\_2 + \frac{1}{\frac{z}{t\_1}}}{c}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{b - \left(t \cdot \left(a \cdot \left(z \cdot 4\right)\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{c}{t\_2 + \frac{t\_1}{z}}}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (+ b (* 9.0 (* y x)))) (t_2 (* t (* a -4.0))))
   (if (<= z -1.46e+81)
     (/ (+ t_2 (/ 1.0 (/ z t_1))) c)
     (if (<= z 6.5e-50)
       (/ (- b (- (* t (* a (* z 4.0))) (* y (* 9.0 x)))) (* z c))
       (/ 1.0 (/ c (+ t_2 (/ t_1 z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b + (9.0 * (y * x));
	double t_2 = t * (a * -4.0);
	double tmp;
	if (z <= -1.46e+81) {
		tmp = (t_2 + (1.0 / (z / t_1))) / c;
	} else if (z <= 6.5e-50) {
		tmp = (b - ((t * (a * (z * 4.0))) - (y * (9.0 * x)))) / (z * c);
	} else {
		tmp = 1.0 / (c / (t_2 + (t_1 / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b + (9.0d0 * (y * x))
    t_2 = t * (a * (-4.0d0))
    if (z <= (-1.46d+81)) then
        tmp = (t_2 + (1.0d0 / (z / t_1))) / c
    else if (z <= 6.5d-50) then
        tmp = (b - ((t * (a * (z * 4.0d0))) - (y * (9.0d0 * x)))) / (z * c)
    else
        tmp = 1.0d0 / (c / (t_2 + (t_1 / z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b + (9.0 * (y * x));
	double t_2 = t * (a * -4.0);
	double tmp;
	if (z <= -1.46e+81) {
		tmp = (t_2 + (1.0 / (z / t_1))) / c;
	} else if (z <= 6.5e-50) {
		tmp = (b - ((t * (a * (z * 4.0))) - (y * (9.0 * x)))) / (z * c);
	} else {
		tmp = 1.0 / (c / (t_2 + (t_1 / z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = b + (9.0 * (y * x))
	t_2 = t * (a * -4.0)
	tmp = 0
	if z <= -1.46e+81:
		tmp = (t_2 + (1.0 / (z / t_1))) / c
	elif z <= 6.5e-50:
		tmp = (b - ((t * (a * (z * 4.0))) - (y * (9.0 * x)))) / (z * c)
	else:
		tmp = 1.0 / (c / (t_2 + (t_1 / z)))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(b + Float64(9.0 * Float64(y * x)))
	t_2 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (z <= -1.46e+81)
		tmp = Float64(Float64(t_2 + Float64(1.0 / Float64(z / t_1))) / c);
	elseif (z <= 6.5e-50)
		tmp = Float64(Float64(b - Float64(Float64(t * Float64(a * Float64(z * 4.0))) - Float64(y * Float64(9.0 * x)))) / Float64(z * c));
	else
		tmp = Float64(1.0 / Float64(c / Float64(t_2 + Float64(t_1 / z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b + (9.0 * (y * x));
	t_2 = t * (a * -4.0);
	tmp = 0.0;
	if (z <= -1.46e+81)
		tmp = (t_2 + (1.0 / (z / t_1))) / c;
	elseif (z <= 6.5e-50)
		tmp = (b - ((t * (a * (z * 4.0))) - (y * (9.0 * x)))) / (z * c);
	else
		tmp = 1.0 / (c / (t_2 + (t_1 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.46e+81], N[(N[(t$95$2 + N[(1.0 / N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 6.5e-50], N[(N[(b - N[(N[(t * N[(a * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(c / N[(t$95$2 + N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45999999999999998e81

   1. Initial program 51.5%

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

      1. associate-/r* N/A

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

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

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

   3. Simplified 82.2%

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

      1. clear-num N/A

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

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

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

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

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

      4. associate-*r* N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

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

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

      9. *-lowering-*.f64 82.4%

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

   6. Applied egg-rr 82.4%

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

   if -1.45999999999999998e81 < z < 6.49999999999999987e-50

   1. Initial program 95.8%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

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

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

      5. *-lowering-*.f64 95.2%

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

   4. Applied egg-rr 95.2%

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

   if 6.49999999999999987e-50 < z

   1. Initial program 71.0%

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

      1. associate-/r* N/A

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

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

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

   3. Simplified 93.1%

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

      1. clear-num N/A

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

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

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

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

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

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

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

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

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

      6. associate-*r* N/A

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

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

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

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

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

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

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

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

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

      13. *-lowering-*.f64 93.1%

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

   6. Applied egg-rr 93.1%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{+81}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{1}{\frac{z}{b + 9 \cdot \left(y \cdot x\right)}}}{c}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{b - \left(t \cdot \left(a \cdot \left(z \cdot 4\right)\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{c}{t \cdot \left(a \cdot -4\right) + \frac{b + 9 \cdot \left(y \cdot x\right)}{z}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 91.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -0.0004:\\ \;\;\;\;\frac{t\_1 + \frac{b + x \cdot \left(y \cdot 9\right)}{z}}{c}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{b - \left(t \cdot \left(a \cdot \left(z \cdot 4\right)\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{c}{t\_1 + \frac{b + 9 \cdot \left(y \cdot x\right)}{z}}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= z -0.0004)
     (/ (+ t_1 (/ (+ b (* x (* y 9.0))) z)) c)
     (if (<= z 6.5e-50)
       (/ (- b (- (* t (* a (* z 4.0))) (* y (* 9.0 x)))) (* z c))
       (/ 1.0 (/ c (+ t_1 (/ (+ b (* 9.0 (* y x))) z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (z <= -0.0004) {
		tmp = (t_1 + ((b + (x * (y * 9.0))) / z)) / c;
	} else if (z <= 6.5e-50) {
		tmp = (b - ((t * (a * (z * 4.0))) - (y * (9.0 * x)))) / (z * c);
	} else {
		tmp = 1.0 / (c / (t_1 + ((b + (9.0 * (y * x))) / 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) :: t_1
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    if (z <= (-0.0004d0)) then
        tmp = (t_1 + ((b + (x * (y * 9.0d0))) / z)) / c
    else if (z <= 6.5d-50) then
        tmp = (b - ((t * (a * (z * 4.0d0))) - (y * (9.0d0 * x)))) / (z * c)
    else
        tmp = 1.0d0 / (c / (t_1 + ((b + (9.0d0 * (y * x))) / z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (z <= -0.0004) {
		tmp = (t_1 + ((b + (x * (y * 9.0))) / z)) / c;
	} else if (z <= 6.5e-50) {
		tmp = (b - ((t * (a * (z * 4.0))) - (y * (9.0 * x)))) / (z * c);
	} else {
		tmp = 1.0 / (c / (t_1 + ((b + (9.0 * (y * x))) / z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = t * (a * -4.0)
	tmp = 0
	if z <= -0.0004:
		tmp = (t_1 + ((b + (x * (y * 9.0))) / z)) / c
	elif z <= 6.5e-50:
		tmp = (b - ((t * (a * (z * 4.0))) - (y * (9.0 * x)))) / (z * c)
	else:
		tmp = 1.0 / (c / (t_1 + ((b + (9.0 * (y * x))) / z)))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (z <= -0.0004)
		tmp = Float64(Float64(t_1 + Float64(Float64(b + Float64(x * Float64(y * 9.0))) / z)) / c);
	elseif (z <= 6.5e-50)
		tmp = Float64(Float64(b - Float64(Float64(t * Float64(a * Float64(z * 4.0))) - Float64(y * Float64(9.0 * x)))) / Float64(z * c));
	else
		tmp = Float64(1.0 / Float64(c / Float64(t_1 + Float64(Float64(b + Float64(9.0 * Float64(y * x))) / z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (z <= -0.0004)
		tmp = (t_1 + ((b + (x * (y * 9.0))) / z)) / c;
	elseif (z <= 6.5e-50)
		tmp = (b - ((t * (a * (z * 4.0))) - (y * (9.0 * x)))) / (z * c);
	else
		tmp = 1.0 / (c / (t_1 + ((b + (9.0 * (y * x))) / z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0004], N[(N[(t$95$1 + N[(N[(b + N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 6.5e-50], N[(N[(b - N[(N[(t * N[(a * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(c / N[(t$95$1 + N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.00000000000000019e-4

   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. Step-by-step derivation

      1. associate-/r* N/A

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

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

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

   3. Simplified 86.0%

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

   if -4.00000000000000019e-4 < z < 6.49999999999999987e-50

   1. Initial program 95.5%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

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

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

      5. *-lowering-*.f64 94.8%

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

   4. Applied egg-rr 94.8%

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

   if 6.49999999999999987e-50 < z

   1. Initial program 71.0%

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

      1. associate-/r* N/A

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

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

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

   3. Simplified 93.1%

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

      1. clear-num N/A

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

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

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

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

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

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

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

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

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

      6. associate-*r* N/A

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

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

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

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

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

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

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

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

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

      13. *-lowering-*.f64 93.1%

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

   6. Applied egg-rr 93.1%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0004:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + x \cdot \left(y \cdot 9\right)}{z}}{c}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{b - \left(t \cdot \left(a \cdot \left(z \cdot 4\right)\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{c}{t \cdot \left(a \cdot -4\right) + \frac{b + 9 \cdot \left(y \cdot x\right)}{z}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+125}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-284}:\\ \;\;\;\;9 \cdot \frac{\frac{y \cdot x}{z}}{c}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-162}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -9.5e+125)
   (* a (* -4.0 (/ t c)))
   (if (<= t -4.8e-284)
     (* 9.0 (/ (/ (* y x) z) c))
     (if (<= t 1.2e-162) (/ b (* z c)) (* (* t -4.0) (/ a c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -9.5e+125) {
		tmp = a * (-4.0 * (t / c));
	} else if (t <= -4.8e-284) {
		tmp = 9.0 * (((y * x) / z) / c);
	} else if (t <= 1.2e-162) {
		tmp = b / (z * c);
	} else {
		tmp = (t * -4.0) * (a / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-9.5d+125)) then
        tmp = a * ((-4.0d0) * (t / c))
    else if (t <= (-4.8d-284)) then
        tmp = 9.0d0 * (((y * x) / z) / c)
    else if (t <= 1.2d-162) then
        tmp = b / (z * c)
    else
        tmp = (t * (-4.0d0)) * (a / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -9.5e+125) {
		tmp = a * (-4.0 * (t / c));
	} else if (t <= -4.8e-284) {
		tmp = 9.0 * (((y * x) / z) / c);
	} else if (t <= 1.2e-162) {
		tmp = b / (z * c);
	} else {
		tmp = (t * -4.0) * (a / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -9.5e+125:
		tmp = a * (-4.0 * (t / c))
	elif t <= -4.8e-284:
		tmp = 9.0 * (((y * x) / z) / c)
	elif t <= 1.2e-162:
		tmp = b / (z * c)
	else:
		tmp = (t * -4.0) * (a / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -9.5e+125)
		tmp = Float64(a * Float64(-4.0 * Float64(t / c)));
	elseif (t <= -4.8e-284)
		tmp = Float64(9.0 * Float64(Float64(Float64(y * x) / z) / c));
	elseif (t <= 1.2e-162)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(Float64(t * -4.0) * Float64(a / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -9.5e+125)
		tmp = a * (-4.0 * (t / c));
	elseif (t <= -4.8e-284)
		tmp = 9.0 * (((y * x) / z) / c);
	elseif (t <= 1.2e-162)
		tmp = b / (z * c);
	else
		tmp = (t * -4.0) * (a / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -9.5e+125], N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.8e-284], N[(9.0 * N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-162], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(t * -4.0), $MachinePrecision] * N[(a / c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.50000000000000041e125

   1. Initial program 73.0%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 70.8%

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

   5. Simplified 70.8%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

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

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

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

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

      7. /-lowering-/.f64 70.7%

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

   7. Applied egg-rr 70.7%

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

   if -9.50000000000000041e125 < t < -4.80000000000000006e-284

   1. Initial program 80.7%

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

   3. Taylor expanded in x around inf

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

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

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

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

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

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

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

      6. *-lowering-*.f64 49.9%

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

   5. Simplified 49.9%

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

   if -4.80000000000000006e-284 < t < 1.2000000000000001e-162

   1. Initial program 88.7%

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

   3. 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 52.4%

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

   5. Simplified 52.4%

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

      1. frac-2neg N/A

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

      2. distribute-frac-neg N/A

         \[\leadsto \mathsf{neg}\left(\frac{b}{\mathsf{neg}\left(z \cdot c\right)}\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\left(\frac{b}{\mathsf{neg}\left(z \cdot c\right)}\right)\right) \]

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

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

      5. neg-sub0 N/A

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{/.f64}\left(b, \left(0 - z \cdot c\right)\right)\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{/.f64}\left(b, \mathsf{\_.f64}\left(0, \left(z \cdot c\right)\right)\right)\right) \]

      7. *-lowering-*.f64 52.4%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{/.f64}\left(b, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, c\right)\right)\right)\right) \]

   7. Applied egg-rr 52.4%

      \[\leadsto \color{blue}{-\frac{b}{0 - z \cdot c}} \]

   if 1.2000000000000001e-162 < t

   1. Initial program 83.0%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 40.6%

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

   5. Simplified 40.6%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. /-lowering-/.f64 42.7%

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

   7. Applied egg-rr 42.7%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+125}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-284}:\\ \;\;\;\;9 \cdot \frac{\frac{y \cdot x}{z}}{c}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-162}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;t \leq -1.75 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-134}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(y \cdot x\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (* t (* a -4.0)) (/ b z)) c)))
   (if (<= t -1.75e+31)
     t_1
     (if (<= t 3.6e-134) (/ (/ (+ 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 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (t <= -1.75e+31) {
		tmp = t_1;
	} else if (t <= 3.6e-134) {
		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 = ((t * (a * (-4.0d0))) + (b / z)) / c
    if (t <= (-1.75d+31)) then
        tmp = t_1
    else if (t <= 3.6d-134) 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 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (t <= -1.75e+31) {
		tmp = t_1;
	} else if (t <= 3.6e-134) {
		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 = ((t * (a * -4.0)) + (b / z)) / c
	tmp = 0
	if t <= -1.75e+31:
		tmp = t_1
	elif t <= 3.6e-134:
		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(t * Float64(a * -4.0)) + Float64(b / z)) / c)
	tmp = 0.0
	if (t <= -1.75e+31)
		tmp = t_1;
	elseif (t <= 3.6e-134)
		tmp = Float64(Float64(Float64(b + Float64(9.0 * Float64(y * x))) / z) / c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	tmp = 0.0;
	if (t <= -1.75e+31)
		tmp = t_1;
	elseif (t <= 3.6e-134)
		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[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[t, -1.75e+31], t$95$1, If[LessEqual[t, 3.6e-134], N[(N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.75e31 or 3.5999999999999999e-134 < t

   1. Initial program 78.3%

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

      1. associate-/r* N/A

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

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

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

   3. Simplified 87.6%

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

   5. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 71.0%

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

   7. Simplified 71.0%

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

   if -1.75e31 < t < 3.5999999999999999e-134

   1. Initial program 85.0%

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

      1. associate-/r* N/A

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

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

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

   3. Simplified 88.3%

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

   5. Taylor expanded in z around 0

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

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

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

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

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

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

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

      4. *-lowering-*.f64 77.8%

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

   7. Simplified 77.8%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+31}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-134}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(y \cdot x\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{y \cdot 9}{c} \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{-69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+190}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* (/ (* y 9.0) c) (/ x z))))
   (if (<= y -5.6e-69)
     t_1
     (if (<= y 2.8e+190) (/ (+ (* t (* a -4.0)) (/ b z)) c) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((y * 9.0) / c) * (x / z);
	double tmp;
	if (y <= -5.6e-69) {
		tmp = t_1;
	} else if (y <= 2.8e+190) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y * 9.0d0) / c) * (x / z)
    if (y <= (-5.6d-69)) then
        tmp = t_1
    else if (y <= 2.8d+190) then
        tmp = ((t * (a * (-4.0d0))) + (b / z)) / c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((y * 9.0) / c) * (x / z);
	double tmp;
	if (y <= -5.6e-69) {
		tmp = t_1;
	} else if (y <= 2.8e+190) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = ((y * 9.0) / c) * (x / z)
	tmp = 0
	if y <= -5.6e-69:
		tmp = t_1
	elif y <= 2.8e+190:
		tmp = ((t * (a * -4.0)) + (b / z)) / c
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(y * 9.0) / c) * Float64(x / z))
	tmp = 0.0
	if (y <= -5.6e-69)
		tmp = t_1;
	elseif (y <= 2.8e+190)
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / 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 = ((y * 9.0) / c) * (x / z);
	tmp = 0.0;
	if (y <= -5.6e-69)
		tmp = t_1;
	elseif (y <= 2.8e+190)
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.6e-69], t$95$1, If[LessEqual[y, 2.8e+190], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.59999999999999959e-69 or 2.79999999999999997e190 < y

   1. Initial program 79.0%

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

      1. associate-/r* N/A

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

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

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

   3. Simplified 84.0%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(9, \left(\frac{x \cdot y}{z}\right)\right), c\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\left(x \cdot y\right), z\right)\right), c\right) \]

      3. *-lowering-*.f64 56.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(9, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), c\right) \]

   7. Simplified 56.5%

      \[\leadsto \frac{\color{blue}{9 \cdot \frac{x \cdot y}{z}}}{c} \]
   8. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{9 \cdot \left(x \cdot y\right)}{z}}{c} \]

      2. *-commutative N/A

         \[\leadsto \frac{\frac{9 \cdot \left(y \cdot x\right)}{z}}{c} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\frac{\left(9 \cdot y\right) \cdot x}{z}}{c} \]

      4. *-commutative N/A

         \[\leadsto \frac{\frac{x \cdot \left(9 \cdot y\right)}{z}}{c} \]

      5. associate-/l/ N/A

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right)}{\color{blue}{c \cdot z}} \]

      6. *-commutative N/A

         \[\leadsto \frac{\left(9 \cdot y\right) \cdot x}{\color{blue}{c} \cdot z} \]

      7. times-frac N/A

         \[\leadsto \frac{9 \cdot y}{c} \cdot \color{blue}{\frac{x}{z}} \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{9 \cdot y}{c}\right), \color{blue}{\left(\frac{x}{z}\right)}\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(9 \cdot y\right), c\right), \left(\frac{\color{blue}{x}}{z}\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, y\right), c\right), \left(\frac{x}{z}\right)\right) \]

      11. /-lowering-/.f64 63.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, y\right), c\right), \mathsf{/.f64}\left(x, \color{blue}{z}\right)\right) \]

   9. Applied egg-rr 63.9%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{c} \cdot \frac{x}{z}} \]

   if -5.59999999999999959e-69 < y < 2.79999999999999997e190

   1. Initial program 82.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 90.6%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{b}{z}\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 75.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 75.6%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}} + t \cdot \left(a \cdot -4\right)}{c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-69}:\\ \;\;\;\;\frac{y \cdot 9}{c} \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+190}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 9}{c} \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(t \cdot -4\right) \cdot \frac{a}{c}\\ \mathbf{if}\;z \leq -5 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 540:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* t -4.0) (/ a c))))
   (if (<= z -5e-18) t_1 (if (<= z 540.0) (* b (/ (/ 1.0 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 = (t * -4.0) * (a / c);
	double tmp;
	if (z <= -5e-18) {
		tmp = t_1;
	} else if (z <= 540.0) {
		tmp = b * ((1.0 / 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 = (t * (-4.0d0)) * (a / c)
    if (z <= (-5d-18)) then
        tmp = t_1
    else if (z <= 540.0d0) then
        tmp = b * ((1.0d0 / 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 = (t * -4.0) * (a / c);
	double tmp;
	if (z <= -5e-18) {
		tmp = t_1;
	} else if (z <= 540.0) {
		tmp = b * ((1.0 / 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 = (t * -4.0) * (a / c)
	tmp = 0
	if z <= -5e-18:
		tmp = t_1
	elif z <= 540.0:
		tmp = b * ((1.0 / 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(t * -4.0) * Float64(a / c))
	tmp = 0.0
	if (z <= -5e-18)
		tmp = t_1;
	elseif (z <= 540.0)
		tmp = Float64(b * Float64(Float64(1.0 / 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 (z <= -5e-18)
		tmp = t_1;
	elseif (z <= 540.0)
		tmp = b * ((1.0 / 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[(t * -4.0), $MachinePrecision] * N[(a / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e-18], t$95$1, If[LessEqual[z, 540.0], N[(b * N[(N[(1.0 / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.00000000000000036e-18 or 540 < z

   1. Initial program 65.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right)}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot t\right)\right), \color{blue}{c}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot t\right) \cdot -4\right), c\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(t \cdot -4\right)\right), c\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(-4 \cdot t\right)\right), c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(-4 \cdot t\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(t \cdot -4\right)\right), c\right) \]

      8. *-lowering-*.f64 54.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, -4\right)\right), c\right) \]

   5. Simplified 54.1%

      \[\leadsto \color{blue}{\frac{a \cdot \left(t \cdot -4\right)}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(t \cdot -4\right) \cdot a}{c} \]

      2. associate-/l* N/A

         \[\leadsto \left(t \cdot -4\right) \cdot \color{blue}{\frac{a}{c}} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t \cdot -4\right), \color{blue}{\left(\frac{a}{c}\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, -4\right), \left(\frac{\color{blue}{a}}{c}\right)\right) \]

      5. /-lowering-/.f64 57.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, -4\right), \mathsf{/.f64}\left(a, \color{blue}{c}\right)\right) \]

   7. Applied egg-rr 57.9%

      \[\leadsto \color{blue}{\left(t \cdot -4\right) \cdot \frac{a}{c}} \]

   if -5.00000000000000036e-18 < z < 540

   1. Initial program 95.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. 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 55.2%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 55.2%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   6. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{z \cdot c}{b}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{z \cdot c} \cdot \color{blue}{b} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{z \cdot c}\right), \color{blue}{b}\right) \]

      4. associate-/r* N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{z}}{c}\right), b\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{z}\right), c\right), b\right) \]

      6. /-lowering-/.f64 55.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, z\right), c\right), b\right) \]

   7. Applied egg-rr 55.9%

      \[\leadsto \color{blue}{\frac{\frac{1}{z}}{c} \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-18}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c}\\ \mathbf{elif}\;z \leq 540:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(t \cdot -4\right) \cdot \frac{a}{c}\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 54:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* t -4.0) (/ a c))))
   (if (<= z -5.4e-18) t_1 (if (<= z 54.0) (/ b (* z c)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (t * -4.0) * (a / c);
	double tmp;
	if (z <= -5.4e-18) {
		tmp = t_1;
	} else if (z <= 54.0) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * (-4.0d0)) * (a / c)
    if (z <= (-5.4d-18)) then
        tmp = t_1
    else if (z <= 54.0d0) then
        tmp = b / (z * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (t * -4.0) * (a / c);
	double tmp;
	if (z <= -5.4e-18) {
		tmp = t_1;
	} else if (z <= 54.0) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (t * -4.0) * (a / c)
	tmp = 0
	if z <= -5.4e-18:
		tmp = t_1
	elif z <= 54.0:
		tmp = b / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(t * -4.0) * Float64(a / c))
	tmp = 0.0
	if (z <= -5.4e-18)
		tmp = t_1;
	elseif (z <= 54.0)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (t * -4.0) * (a / c);
	tmp = 0.0;
	if (z <= -5.4e-18)
		tmp = t_1;
	elseif (z <= 54.0)
		tmp = b / (z * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(t * -4.0), $MachinePrecision] * N[(a / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4e-18], t$95$1, If[LessEqual[z, 54.0], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.39999999999999977e-18 or 54 < z

   1. Initial program 65.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right)}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot t\right)\right), \color{blue}{c}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot t\right) \cdot -4\right), c\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(t \cdot -4\right)\right), c\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(-4 \cdot t\right)\right), c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(-4 \cdot t\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(t \cdot -4\right)\right), c\right) \]

      8. *-lowering-*.f64 54.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, -4\right)\right), c\right) \]

   5. Simplified 54.1%

      \[\leadsto \color{blue}{\frac{a \cdot \left(t \cdot -4\right)}{c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(t \cdot -4\right) \cdot a}{c} \]

      2. associate-/l* N/A

         \[\leadsto \left(t \cdot -4\right) \cdot \color{blue}{\frac{a}{c}} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t \cdot -4\right), \color{blue}{\left(\frac{a}{c}\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, -4\right), \left(\frac{\color{blue}{a}}{c}\right)\right) \]

      5. /-lowering-/.f64 57.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, -4\right), \mathsf{/.f64}\left(a, \color{blue}{c}\right)\right) \]

   7. Applied egg-rr 57.9%

      \[\leadsto \color{blue}{\left(t \cdot -4\right) \cdot \frac{a}{c}} \]

   if -5.39999999999999977e-18 < z < 54

   1. Initial program 95.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. 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 55.2%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 55.2%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 49.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-18}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-62}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -3.9e-18)
   (* -4.0 (/ (* t a) c))
   (if (<= z 3e-62) (/ b (* z c)) (* a (* -4.0 (/ t c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.9e-18) {
		tmp = -4.0 * ((t * a) / c);
	} else if (z <= 3e-62) {
		tmp = b / (z * c);
	} else {
		tmp = a * (-4.0 * (t / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-3.9d-18)) then
        tmp = (-4.0d0) * ((t * a) / c)
    else if (z <= 3d-62) then
        tmp = b / (z * c)
    else
        tmp = a * ((-4.0d0) * (t / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.9e-18) {
		tmp = -4.0 * ((t * a) / c);
	} else if (z <= 3e-62) {
		tmp = b / (z * c);
	} else {
		tmp = a * (-4.0 * (t / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -3.9e-18:
		tmp = -4.0 * ((t * a) / c)
	elif z <= 3e-62:
		tmp = b / (z * c)
	else:
		tmp = a * (-4.0 * (t / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -3.9e-18)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c));
	elseif (z <= 3e-62)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(a * Float64(-4.0 * Float64(t / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -3.9e-18)
		tmp = -4.0 * ((t * a) / c);
	elseif (z <= 3e-62)
		tmp = b / (z * c);
	else
		tmp = a * (-4.0 * (t / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -3.9e-18], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-62], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.90000000000000005e-18

   1. Initial program 64.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 87.1%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{c}{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{c}{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \color{blue}{\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)\right)}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z}\right), \color{blue}{\left(t \cdot \left(a \cdot -4\right)\right)}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \left(9 \cdot y\right) + b\right), z\right), \left(\color{blue}{t} \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(x \cdot 9\right) \cdot y + b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(x \cdot 9\right) \cdot y\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \mathsf{*.f64}\left(t, \color{blue}{\left(a \cdot -4\right)}\right)\right)\right)\right) \]

      13. *-lowering-*.f64 87.0%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, \color{blue}{-4}\right)\right)\right)\right)\right) \]

   6. Applied egg-rr 87.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{c}{\frac{9 \cdot \left(x \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}}} \]

   7. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(\frac{a \cdot t}{c}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\left(a \cdot t\right), \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 46.3%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right)\right) \]

   9. Simplified 46.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

   if -3.90000000000000005e-18 < z < 3.0000000000000001e-62

   1. Initial program 95.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 57.5%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 57.5%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if 3.0000000000000001e-62 < z

   1. Initial program 72.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right)}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot \left(a \cdot t\right)\right), \color{blue}{c}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot t\right) \cdot -4\right), c\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(t \cdot -4\right)\right), c\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(-4 \cdot t\right)\right), c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(-4 \cdot t\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(t \cdot -4\right)\right), c\right) \]

      8. *-lowering-*.f64 56.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, -4\right)\right), c\right) \]

   5. Simplified 56.9%

      \[\leadsto \color{blue}{\frac{a \cdot \left(t \cdot -4\right)}{c}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto a \cdot \color{blue}{\frac{t \cdot -4}{c}} \]

      2. *-commutative N/A

         \[\leadsto \frac{t \cdot -4}{c} \cdot \color{blue}{a} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t \cdot -4}{c}\right), \color{blue}{a}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{-4 \cdot t}{c}\right), a\right) \]

      5. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-4 \cdot \frac{t}{c}\right), a\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-4, \left(\frac{t}{c}\right)\right), a\right) \]

      7. /-lowering-/.f64 58.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(t, c\right)\right), a\right) \]

   7. Applied egg-rr 58.1%

      \[\leadsto \color{blue}{\left(-4 \cdot \frac{t}{c}\right) \cdot a} \]
3. Recombined 3 regimes into one program.

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-18}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-62}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{t \cdot a}{c}\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6400:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (/ (* t a) c))))
   (if (<= z -6.5e-18) t_1 (if (<= z 6400.0) (/ b (* z c)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * ((t * a) / c);
	double tmp;
	if (z <= -6.5e-18) {
		tmp = t_1;
	} else if (z <= 6400.0) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * ((t * a) / c)
    if (z <= (-6.5d-18)) then
        tmp = t_1
    else if (z <= 6400.0d0) then
        tmp = b / (z * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * ((t * a) / c);
	double tmp;
	if (z <= -6.5e-18) {
		tmp = t_1;
	} else if (z <= 6400.0) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * ((t * a) / c)
	tmp = 0
	if z <= -6.5e-18:
		tmp = t_1
	elif z <= 6400.0:
		tmp = b / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(Float64(t * a) / c))
	tmp = 0.0
	if (z <= -6.5e-18)
		tmp = t_1;
	elseif (z <= 6400.0)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * ((t * a) / c);
	tmp = 0.0;
	if (z <= -6.5e-18)
		tmp = t_1;
	elseif (z <= 6400.0)
		tmp = b / (z * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e-18], t$95$1, If[LessEqual[z, 6400.0], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.50000000000000008e-18 or 6400 < z

   1. Initial program 65.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 89.6%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{c}{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{c}{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \color{blue}{\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)\right)}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z}\right), \color{blue}{\left(t \cdot \left(a \cdot -4\right)\right)}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \left(9 \cdot y\right) + b\right), z\right), \left(\color{blue}{t} \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(x \cdot 9\right) \cdot y + b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(x \cdot 9\right) \cdot y\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \mathsf{*.f64}\left(t, \color{blue}{\left(a \cdot -4\right)}\right)\right)\right)\right) \]

      13. *-lowering-*.f64 89.5%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, \color{blue}{-4}\right)\right)\right)\right)\right) \]

   6. Applied egg-rr 89.5%

      \[\leadsto \color{blue}{\frac{1}{\frac{c}{\frac{9 \cdot \left(x \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}}} \]

   7. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(\frac{a \cdot t}{c}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\left(a \cdot t\right), \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 54.1%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), c\right)\right) \]

   9. Simplified 54.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

   if -6.50000000000000008e-18 < z < 6400

   1. Initial program 95.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. 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 55.2%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 55.2%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-18}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;z \leq 6400:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 86.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{t \cdot \left(a \cdot -4\right) + \frac{b + x \cdot \left(y \cdot 9\right)}{z}}{c} \end{array} \]

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
 (/ (+ (* t (* a -4.0)) (/ (+ b (* x (* y 9.0))) z)) c))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((t * (a * -4.0)) + ((b + (x * (y * 9.0))) / 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 = ((t * (a * (-4.0d0))) + ((b + (x * (y * 9.0d0))) / 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 ((t * (a * -4.0)) + ((b + (x * (y * 9.0))) / 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 ((t * (a * -4.0)) + ((b + (x * (y * 9.0))) / 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(Float64(Float64(t * Float64(a * -4.0)) + Float64(Float64(b + Float64(x * Float64(y * 9.0))) / 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 = ((t * (a * -4.0)) + ((b + (x * (y * 9.0))) / 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[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(b + N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]

Derivation

1. Initial program 81.3%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-/r* N/A

      \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

   2. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

3. Simplified 87.9%

   \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
4. Add Preprocessing

5. Final simplification 87.9%

   \[\leadsto \frac{t \cdot \left(a \cdot -4\right) + \frac{b + x \cdot \left(y \cdot 9\right)}{z}}{c} \]
6. Add Preprocessing

Alternative 18: 35.7% accurate, 3.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{z \cdot c} \end{array} \]

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 81.3%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
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 39.4%

      \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

5. Simplified 39.4%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
6. Add Preprocessing

Developer Target 1: 80.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t\_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t\_4}{z \cdot c}\\ t_6 := \frac{\left(t\_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 0:\\ \;\;\;\;\frac{\frac{t\_4}{z}}{c}\\ \mathbf{elif}\;t\_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t\_1\right) - t\_2\\ \mathbf{elif}\;t\_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024160 
(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)))