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

Percentage Accurate: 79.3% → 91.6%

Time: 13.3s

Alternatives: 12

Speedup: 0.9×

• 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: 79.3% 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, 0.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+60} \lor \neg \left(z \leq 1.5 \cdot 10^{-39}\right):\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -4e+60) (not (<= z 1.5e-39)))
   (/ (+ (/ (fma x (* 9.0 y) b) z) (* t (* a -4.0))) c)
   (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -4e+60) || !(z <= 1.5e-39)) {
		tmp = ((fma(x, (9.0 * y), b) / z) + (t * (a * -4.0))) / c;
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -4e+60) || !(z <= 1.5e-39))
		tmp = Float64(Float64(Float64(fma(x, Float64(9.0 * y), b) / z) + Float64(t * Float64(a * -4.0))) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -4e+60], N[Not[LessEqual[z, 1.5e-39]], $MachinePrecision]], N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9999999999999998e60 or 1.50000000000000014e-39 < z

   1. Initial program 73.5%

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

      1. associate-/r* 78.8%

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

   3. Simplified 94.2%

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

   if -3.9999999999999998e60 < z < 1.50000000000000014e-39

   1. Initial program 93.4%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+60} \lor \neg \left(z \leq 1.5 \cdot 10^{-39}\right):\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 2: 83.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+116}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+89}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -2.3e+116)
   (/ (+ (* t (* a -4.0)) (/ b z)) c)
   (if (<= z 1.15e+89)
     (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))
     (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* t a)))) (* z c)))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -2.3e+116) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else if (z <= 1.15e+89) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: t and a 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 <= (-2.3d+116)) then
        tmp = ((t * (a * (-4.0d0))) + (b / z)) / c
    else if (z <= 1.15d+89) then
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (z * c)
    else
        tmp = (b + ((x * (9.0d0 * y)) - ((z * 4.0d0) * (t * a)))) / (z * c)
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -2.3e+116) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else if (z <= 1.15e+89) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -2.3e+116:
		tmp = ((t * (a * -4.0)) + (b / z)) / c
	elif z <= 1.15e+89:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)
	else:
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c)
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -2.3e+116)
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c);
	elseif (z <= 1.15e+89)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(t * a)))) / Float64(z * c));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -2.3e+116)
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	elseif (z <= 1.15e+89)
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	else
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -2.3e+116], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 1.15e+89], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.29999999999999995e116

   1. Initial program 59.8%

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

      1. associate-/r* 67.0%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in x around 0 84.0%

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

      1. associate-*r* 84.1%

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

      2. *-commutative 84.1%

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

      3. *-commutative 84.1%

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

   6. Simplified 84.1%

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

   if -2.29999999999999995e116 < z < 1.1499999999999999e89

   1. Initial program 91.4%

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

   if 1.1499999999999999e89 < z

   1. Initial program 81.8%

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

      1. associate-*l* 81.9%

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

      2. associate-*l* 87.1%

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

   3. Simplified 87.1%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+116}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+89}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 3: 49.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := 9 \cdot \frac{x \cdot y}{z \cdot c}\\ t_2 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{-39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-225}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-172}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{+158}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{+186}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (/ (* x y) (* z c)))) (t_2 (* -4.0 (* t (/ a c)))))
   (if (<= a -3.4e-39)
     t_2
     (if (<= a 3.9e-225)
       t_1
       (if (<= a 9.8e-172)
         (/ (/ b c) z)
         (if (<= a 2.9e+56)
           t_1
           (if (<= a 5.1e+158)
             (* -4.0 (/ t (/ c a)))
             (if (<= a 2.45e+186) t_1 t_2))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((x * y) / (z * c));
	double t_2 = -4.0 * (t * (a / c));
	double tmp;
	if (a <= -3.4e-39) {
		tmp = t_2;
	} else if (a <= 3.9e-225) {
		tmp = t_1;
	} else if (a <= 9.8e-172) {
		tmp = (b / c) / z;
	} else if (a <= 2.9e+56) {
		tmp = t_1;
	} else if (a <= 5.1e+158) {
		tmp = -4.0 * (t / (c / a));
	} else if (a <= 2.45e+186) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: t and a 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 = 9.0d0 * ((x * y) / (z * c))
    t_2 = (-4.0d0) * (t * (a / c))
    if (a <= (-3.4d-39)) then
        tmp = t_2
    else if (a <= 3.9d-225) then
        tmp = t_1
    else if (a <= 9.8d-172) then
        tmp = (b / c) / z
    else if (a <= 2.9d+56) then
        tmp = t_1
    else if (a <= 5.1d+158) then
        tmp = (-4.0d0) * (t / (c / a))
    else if (a <= 2.45d+186) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((x * y) / (z * c));
	double t_2 = -4.0 * (t * (a / c));
	double tmp;
	if (a <= -3.4e-39) {
		tmp = t_2;
	} else if (a <= 3.9e-225) {
		tmp = t_1;
	} else if (a <= 9.8e-172) {
		tmp = (b / c) / z;
	} else if (a <= 2.9e+56) {
		tmp = t_1;
	} else if (a <= 5.1e+158) {
		tmp = -4.0 * (t / (c / a));
	} else if (a <= 2.45e+186) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * ((x * y) / (z * c))
	t_2 = -4.0 * (t * (a / c))
	tmp = 0
	if a <= -3.4e-39:
		tmp = t_2
	elif a <= 3.9e-225:
		tmp = t_1
	elif a <= 9.8e-172:
		tmp = (b / c) / z
	elif a <= 2.9e+56:
		tmp = t_1
	elif a <= 5.1e+158:
		tmp = -4.0 * (t / (c / a))
	elif a <= 2.45e+186:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)))
	t_2 = Float64(-4.0 * Float64(t * Float64(a / c)))
	tmp = 0.0
	if (a <= -3.4e-39)
		tmp = t_2;
	elseif (a <= 3.9e-225)
		tmp = t_1;
	elseif (a <= 9.8e-172)
		tmp = Float64(Float64(b / c) / z);
	elseif (a <= 2.9e+56)
		tmp = t_1;
	elseif (a <= 5.1e+158)
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	elseif (a <= 2.45e+186)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * ((x * y) / (z * c));
	t_2 = -4.0 * (t * (a / c));
	tmp = 0.0;
	if (a <= -3.4e-39)
		tmp = t_2;
	elseif (a <= 3.9e-225)
		tmp = t_1;
	elseif (a <= 9.8e-172)
		tmp = (b / c) / z;
	elseif (a <= 2.9e+56)
		tmp = t_1;
	elseif (a <= 5.1e+158)
		tmp = -4.0 * (t / (c / a));
	elseif (a <= 2.45e+186)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a 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[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e-39], t$95$2, If[LessEqual[a, 3.9e-225], t$95$1, If[LessEqual[a, 9.8e-172], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 2.9e+56], t$95$1, If[LessEqual[a, 5.1e+158], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.45e+186], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.3999999999999999e-39 or 2.44999999999999986e186 < a

   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. Step-by-step derivation

      1. associate-*l* 83.6%

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

      2. associate-*l* 81.7%

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

   3. Simplified 81.7%

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

   4. Taylor expanded in z around inf 51.2%

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

      1. *-commutative 51.2%

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

      2. associate-/l* 50.9%

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

      3. associate-/r/ 50.8%

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

   6. Simplified 50.8%

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

   if -3.3999999999999999e-39 < a < 3.9e-225 or 9.8000000000000001e-172 < a < 2.90000000000000007e56 or 5.09999999999999987e158 < a < 2.44999999999999986e186

   1. Initial program 83.4%

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

      1. associate-*l* 83.4%

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

      2. associate-*l* 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in x around inf 49.6%

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

   if 3.9e-225 < a < 9.8000000000000001e-172

   1. Initial program 79.9%

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

      1. associate-*l* 79.9%

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

      2. associate-*l* 86.8%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in b around inf 44.6%

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

      1. associate-/r* 50.9%

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

   6. Simplified 50.9%

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

   if 2.90000000000000007e56 < a < 5.09999999999999987e158

   1. Initial program 90.2%

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

      1. associate-/r* 85.5%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in z around inf 75.8%

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

      1. associate-*r* 75.8%

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

      2. *-commutative 75.8%

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

      3. *-commutative 75.8%

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

   6. Simplified 75.8%

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

   7. Taylor expanded in t around 0 75.8%

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

      1. *-commutative 75.8%

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

      2. associate-/l* 66.5%

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

   9. Simplified 66.5%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-39}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-225}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-172}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+56}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{+158}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{+186}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 4: 49.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := 9 \cdot \frac{x \cdot y}{z \cdot c}\\ t_2 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;a \leq -4.1 \cdot 10^{-39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-174}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+158}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{+186}:\\ \;\;\;\;\frac{9}{\frac{c}{x \cdot \frac{y}{z}}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (/ (* x y) (* z c)))) (t_2 (* -4.0 (* t (/ a c)))))
   (if (<= a -4.1e-39)
     t_2
     (if (<= a 1.05e-224)
       t_1
       (if (<= a 2.1e-174)
         (/ (/ b c) z)
         (if (<= a 1.7e+56)
           t_1
           (if (<= a 5.2e+158)
             (* -4.0 (/ t (/ c a)))
             (if (<= a 2.45e+186) (/ 9.0 (/ c (* x (/ y z)))) t_2))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((x * y) / (z * c));
	double t_2 = -4.0 * (t * (a / c));
	double tmp;
	if (a <= -4.1e-39) {
		tmp = t_2;
	} else if (a <= 1.05e-224) {
		tmp = t_1;
	} else if (a <= 2.1e-174) {
		tmp = (b / c) / z;
	} else if (a <= 1.7e+56) {
		tmp = t_1;
	} else if (a <= 5.2e+158) {
		tmp = -4.0 * (t / (c / a));
	} else if (a <= 2.45e+186) {
		tmp = 9.0 / (c / (x * (y / z)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: t and a 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 = 9.0d0 * ((x * y) / (z * c))
    t_2 = (-4.0d0) * (t * (a / c))
    if (a <= (-4.1d-39)) then
        tmp = t_2
    else if (a <= 1.05d-224) then
        tmp = t_1
    else if (a <= 2.1d-174) then
        tmp = (b / c) / z
    else if (a <= 1.7d+56) then
        tmp = t_1
    else if (a <= 5.2d+158) then
        tmp = (-4.0d0) * (t / (c / a))
    else if (a <= 2.45d+186) then
        tmp = 9.0d0 / (c / (x * (y / z)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((x * y) / (z * c));
	double t_2 = -4.0 * (t * (a / c));
	double tmp;
	if (a <= -4.1e-39) {
		tmp = t_2;
	} else if (a <= 1.05e-224) {
		tmp = t_1;
	} else if (a <= 2.1e-174) {
		tmp = (b / c) / z;
	} else if (a <= 1.7e+56) {
		tmp = t_1;
	} else if (a <= 5.2e+158) {
		tmp = -4.0 * (t / (c / a));
	} else if (a <= 2.45e+186) {
		tmp = 9.0 / (c / (x * (y / z)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * ((x * y) / (z * c))
	t_2 = -4.0 * (t * (a / c))
	tmp = 0
	if a <= -4.1e-39:
		tmp = t_2
	elif a <= 1.05e-224:
		tmp = t_1
	elif a <= 2.1e-174:
		tmp = (b / c) / z
	elif a <= 1.7e+56:
		tmp = t_1
	elif a <= 5.2e+158:
		tmp = -4.0 * (t / (c / a))
	elif a <= 2.45e+186:
		tmp = 9.0 / (c / (x * (y / z)))
	else:
		tmp = t_2
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)))
	t_2 = Float64(-4.0 * Float64(t * Float64(a / c)))
	tmp = 0.0
	if (a <= -4.1e-39)
		tmp = t_2;
	elseif (a <= 1.05e-224)
		tmp = t_1;
	elseif (a <= 2.1e-174)
		tmp = Float64(Float64(b / c) / z);
	elseif (a <= 1.7e+56)
		tmp = t_1;
	elseif (a <= 5.2e+158)
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	elseif (a <= 2.45e+186)
		tmp = Float64(9.0 / Float64(c / Float64(x * Float64(y / z))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * ((x * y) / (z * c));
	t_2 = -4.0 * (t * (a / c));
	tmp = 0.0;
	if (a <= -4.1e-39)
		tmp = t_2;
	elseif (a <= 1.05e-224)
		tmp = t_1;
	elseif (a <= 2.1e-174)
		tmp = (b / c) / z;
	elseif (a <= 1.7e+56)
		tmp = t_1;
	elseif (a <= 5.2e+158)
		tmp = -4.0 * (t / (c / a));
	elseif (a <= 2.45e+186)
		tmp = 9.0 / (c / (x * (y / z)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a 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[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.1e-39], t$95$2, If[LessEqual[a, 1.05e-224], t$95$1, If[LessEqual[a, 2.1e-174], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 1.7e+56], t$95$1, If[LessEqual[a, 5.2e+158], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.45e+186], N[(9.0 / N[(c / N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.1e-39 or 2.44999999999999986e186 < a

   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. Step-by-step derivation

      1. associate-*l* 83.6%

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

      2. associate-*l* 81.7%

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

   3. Simplified 81.7%

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

   4. Taylor expanded in z around inf 51.2%

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

      1. *-commutative 51.2%

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

      2. associate-/l* 50.9%

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

      3. associate-/r/ 50.8%

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

   6. Simplified 50.8%

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

   if -4.1e-39 < a < 1.05000000000000003e-224 or 2.1000000000000001e-174 < a < 1.7e56

   1. Initial program 84.3%

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

      1. associate-*l* 84.3%

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

      2. associate-*l* 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in x around inf 50.7%

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

   if 1.05000000000000003e-224 < a < 2.1000000000000001e-174

   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-*l* 78.3%

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

      2. associate-*l* 85.8%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in b around inf 47.9%

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

      1. associate-/r* 54.6%

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

   6. Simplified 54.6%

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

   if 1.7e56 < a < 5.2e158

   1. Initial program 90.2%

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

      1. associate-/r* 85.5%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in z around inf 75.8%

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

      1. associate-*r* 75.8%

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

      2. *-commutative 75.8%

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

      3. *-commutative 75.8%

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

   6. Simplified 75.8%

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

   7. Taylor expanded in t around 0 75.8%

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

      1. *-commutative 75.8%

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

      2. associate-/l* 66.5%

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

   9. Simplified 66.5%

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

   if 5.2e158 < a < 2.44999999999999986e186

   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* 68.1%

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

   3. Simplified 51.4%

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

   4. Taylor expanded in x around inf 51.6%

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

   5. Taylor expanded in y around inf 35.1%

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

      1. *-un-lft-identity 35.1%

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

      2. associate-/l* 34.9%

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

      3. associate-/l* 35.1%

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

      4. associate-/r/ 35.1%

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

   7. Applied egg-rr 35.1%

      \[\leadsto \color{blue}{1 \cdot \frac{9}{\frac{c}{\frac{y}{z} \cdot x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{-39}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-224}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-174}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+56}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+158}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{+186}:\\ \;\;\;\;\frac{9}{\frac{c}{x \cdot \frac{y}{z}}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 5: 82.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+112}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -5e+112)
   (/ (+ (* t (* a -4.0)) (/ b z)) c)
   (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* t a)))) (* z c))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -5e+112) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: t and a 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 <= (-5d+112)) then
        tmp = ((t * (a * (-4.0d0))) + (b / z)) / c
    else
        tmp = (b + ((x * (9.0d0 * y)) - ((z * 4.0d0) * (t * a)))) / (z * c)
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -5e+112) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -5e+112:
		tmp = ((t * (a * -4.0)) + (b / z)) / c
	else:
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c)
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -5e+112)
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(t * a)))) / Float64(z * c));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -5e+112)
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	else
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -5e+112], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5e112

   1. Initial program 59.8%

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

      1. associate-/r* 67.0%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in x around 0 84.0%

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

      1. associate-*r* 84.1%

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

      2. *-commutative 84.1%

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

      3. *-commutative 84.1%

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

   6. Simplified 84.1%

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

   if -5e112 < z

   1. Initial program 89.6%

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

      1. associate-*l* 89.6%

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

      2. associate-*l* 88.7%

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

   3. Simplified 88.7%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+112}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 6: 70.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.08 \cdot 10^{-41} \lor \neg \left(a \leq 1.72 \cdot 10^{+59} \lor \neg \left(a \leq 3.2 \cdot 10^{+148}\right) \land a \leq 2.45 \cdot 10^{+186}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -1.08e-41)
         (not
          (or (<= a 1.72e+59) (and (not (<= a 3.2e+148)) (<= a 2.45e+186)))))
   (/ (+ (* t (* a -4.0)) (/ b z)) c)
   (/ (+ b (* 9.0 (* x y))) (* z c))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -1.08e-41) || !((a <= 1.72e+59) || (!(a <= 3.2e+148) && (a <= 2.45e+186)))) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a <= (-1.08d-41)) .or. (.not. (a <= 1.72d+59) .or. (.not. (a <= 3.2d+148)) .and. (a <= 2.45d+186))) then
        tmp = ((t * (a * (-4.0d0))) + (b / z)) / c
    else
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -1.08e-41) || !((a <= 1.72e+59) || (!(a <= 3.2e+148) && (a <= 2.45e+186)))) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -1.08e-41) or not ((a <= 1.72e+59) or (not (a <= 3.2e+148) and (a <= 2.45e+186))):
		tmp = ((t * (a * -4.0)) + (b / z)) / c
	else:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -1.08e-41) || !((a <= 1.72e+59) || (!(a <= 3.2e+148) && (a <= 2.45e+186))))
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -1.08e-41) || ~(((a <= 1.72e+59) || (~((a <= 3.2e+148)) && (a <= 2.45e+186)))))
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	else
		tmp = (b + (9.0 * (x * y))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -1.08e-41], N[Not[Or[LessEqual[a, 1.72e+59], And[N[Not[LessEqual[a, 3.2e+148]], $MachinePrecision], LessEqual[a, 2.45e+186]]]], $MachinePrecision]], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.08e-41 or 1.71999999999999996e59 < a < 3.1999999999999999e148 or 2.44999999999999986e186 < a

   1. Initial program 84.5%

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

      1. associate-/r* 81.2%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in x around 0 75.0%

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

      1. associate-*r* 75.0%

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

      2. *-commutative 75.0%

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

      3. *-commutative 75.0%

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

   6. Simplified 75.0%

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

   if -1.08e-41 < a < 1.71999999999999996e59 or 3.1999999999999999e148 < a < 2.44999999999999986e186

   1. Initial program 83.3%

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

      1. associate-*l* 83.3%

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

      2. associate-*l* 87.7%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in x around inf 77.9%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.08 \cdot 10^{-41} \lor \neg \left(a \leq 1.72 \cdot 10^{+59} \lor \neg \left(a \leq 3.2 \cdot 10^{+148}\right) \land a \leq 2.45 \cdot 10^{+186}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 7: 66.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ t_2 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;a \leq -5.8 \cdot 10^{-39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+145}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+186}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: t and a 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 (* x y))) (* z c))) (t_2 (* -4.0 (* t (/ a c)))))
   (if (<= a -5.8e-39)
     t_2
     (if (<= a 1.55e+58)
       t_1
       (if (<= a 4e+145)
         (/ (* t (* a -4.0)) c)
         (if (<= a 5.8e+186) t_1 t_2))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (9.0 * (x * y))) / (z * c);
	double t_2 = -4.0 * (t * (a / c));
	double tmp;
	if (a <= -5.8e-39) {
		tmp = t_2;
	} else if (a <= 1.55e+58) {
		tmp = t_1;
	} else if (a <= 4e+145) {
		tmp = (t * (a * -4.0)) / c;
	} else if (a <= 5.8e+186) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: t and a 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 * (x * y))) / (z * c)
    t_2 = (-4.0d0) * (t * (a / c))
    if (a <= (-5.8d-39)) then
        tmp = t_2
    else if (a <= 1.55d+58) then
        tmp = t_1
    else if (a <= 4d+145) then
        tmp = (t * (a * (-4.0d0))) / c
    else if (a <= 5.8d+186) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (9.0 * (x * y))) / (z * c);
	double t_2 = -4.0 * (t * (a / c));
	double tmp;
	if (a <= -5.8e-39) {
		tmp = t_2;
	} else if (a <= 1.55e+58) {
		tmp = t_1;
	} else if (a <= 4e+145) {
		tmp = (t * (a * -4.0)) / c;
	} else if (a <= 5.8e+186) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (b + (9.0 * (x * y))) / (z * c)
	t_2 = -4.0 * (t * (a / c))
	tmp = 0
	if a <= -5.8e-39:
		tmp = t_2
	elif a <= 1.55e+58:
		tmp = t_1
	elif a <= 4e+145:
		tmp = (t * (a * -4.0)) / c
	elif a <= 5.8e+186:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c))
	t_2 = Float64(-4.0 * Float64(t * Float64(a / c)))
	tmp = 0.0
	if (a <= -5.8e-39)
		tmp = t_2;
	elseif (a <= 1.55e+58)
		tmp = t_1;
	elseif (a <= 4e+145)
		tmp = Float64(Float64(t * Float64(a * -4.0)) / c);
	elseif (a <= 5.8e+186)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + (9.0 * (x * y))) / (z * c);
	t_2 = -4.0 * (t * (a / c));
	tmp = 0.0;
	if (a <= -5.8e-39)
		tmp = t_2;
	elseif (a <= 1.55e+58)
		tmp = t_1;
	elseif (a <= 4e+145)
		tmp = (t * (a * -4.0)) / c;
	elseif (a <= 5.8e+186)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.8e-39], t$95$2, If[LessEqual[a, 1.55e+58], t$95$1, If[LessEqual[a, 4e+145], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[a, 5.8e+186], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.79999999999999975e-39 or 5.8e186 < a

   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. Step-by-step derivation

      1. associate-*l* 83.6%

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

      2. associate-*l* 81.7%

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

   3. Simplified 81.7%

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

   4. Taylor expanded in z around inf 51.2%

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

      1. *-commutative 51.2%

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

      2. associate-/l* 50.9%

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

      3. associate-/r/ 50.8%

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

   6. Simplified 50.8%

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

   if -5.79999999999999975e-39 < a < 1.55e58 or 4e145 < a < 5.8e186

   1. Initial program 83.3%

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

      1. associate-*l* 83.3%

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

      2. associate-*l* 87.7%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in x around inf 77.9%

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

   if 1.55e58 < a < 4e145

   1. Initial program 89.1%

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

      1. associate-/r* 89.3%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 78.3%

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

      1. associate-*r* 78.3%

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

      2. *-commutative 78.3%

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

      3. *-commutative 78.3%

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

   6. Simplified 78.3%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-39}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+58}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+145}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+186}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 8: 73.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+42} \lor \neg \left(b \leq 7.5 \cdot 10^{-75}\right):\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -2.6e+42) (not (<= b 7.5e-75)))
   (/ (+ b (* 9.0 (* x y))) (* z c))
   (/ (+ (* t (* a -4.0)) (* 9.0 (/ (* x y) z))) c)))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -2.6e+42) || !(b <= 7.5e-75)) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = ((t * (a * -4.0)) + (9.0 * ((x * y) / z))) / c;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-2.6d+42)) .or. (.not. (b <= 7.5d-75))) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else
        tmp = ((t * (a * (-4.0d0))) + (9.0d0 * ((x * y) / z))) / c
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -2.6e+42) || !(b <= 7.5e-75)) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = ((t * (a * -4.0)) + (9.0 * ((x * y) / z))) / c;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -2.6e+42) or not (b <= 7.5e-75):
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = ((t * (a * -4.0)) + (9.0 * ((x * y) / z))) / c
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -2.6e+42) || !(b <= 7.5e-75))
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -2.6e+42) || ~((b <= 7.5e-75)))
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = ((t * (a * -4.0)) + (9.0 * ((x * y) / z))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -2.6e+42], N[Not[LessEqual[b, 7.5e-75]], $MachinePrecision]], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.5999999999999999e42 or 7.50000000000000017e-75 < b

   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-*l* 87.2%

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

      2. associate-*l* 89.4%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in x around inf 81.4%

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

   if -2.5999999999999999e42 < b < 7.50000000000000017e-75

   1. Initial program 80.4%

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

      1. associate-/r* 80.3%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in x around inf 82.1%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+42} \lor \neg \left(b \leq 7.5 \cdot 10^{-75}\right):\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \end{array} \]

Alternative 9: 49.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+40} \lor \neg \left(b \leq 2.5 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -3.1e+40) (not (<= b 2.5e-62)))
   (/ (/ b c) z)
   (* -4.0 (/ t (/ c a)))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -3.1e+40) || !(b <= 2.5e-62)) {
		tmp = (b / c) / z;
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-3.1d+40)) .or. (.not. (b <= 2.5d-62))) then
        tmp = (b / c) / z
    else
        tmp = (-4.0d0) * (t / (c / a))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -3.1e+40) || !(b <= 2.5e-62)) {
		tmp = (b / c) / z;
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -3.1e+40) or not (b <= 2.5e-62):
		tmp = (b / c) / z
	else:
		tmp = -4.0 * (t / (c / a))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -3.1e+40) || !(b <= 2.5e-62))
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -3.1e+40) || ~((b <= 2.5e-62)))
		tmp = (b / c) / z;
	else
		tmp = -4.0 * (t / (c / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -3.1e+40], N[Not[LessEqual[b, 2.5e-62]], $MachinePrecision]], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.0999999999999998e40 or 2.5000000000000001e-62 < b

   1. Initial program 87.7%

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

      1. associate-*l* 87.7%

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

      2. associate-*l* 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in b around inf 55.1%

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

      1. associate-/r* 56.5%

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

   6. Simplified 56.5%

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

   if -3.0999999999999998e40 < b < 2.5000000000000001e-62

   1. Initial program 80.1%

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

      1. associate-/r* 80.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in z around inf 52.2%

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

      1. associate-*r* 52.2%

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

      2. *-commutative 52.2%

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

      3. *-commutative 52.2%

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

   6. Simplified 52.2%

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

   7. Taylor expanded in t around 0 52.1%

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

      1. *-commutative 52.1%

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

      2. associate-/l* 48.8%

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

   9. Simplified 48.8%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+40} \lor \neg \left(b \leq 2.5 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 10: 49.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+41} \lor \neg \left(b \leq 3 \cdot 10^{-53}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -5.2e+41) (not (<= b 3e-53)))
   (/ (/ b c) z)
   (/ (* t (* a -4.0)) c)))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -5.2e+41) || !(b <= 3e-53)) {
		tmp = (b / c) / z;
	} else {
		tmp = (t * (a * -4.0)) / c;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-5.2d+41)) .or. (.not. (b <= 3d-53))) then
        tmp = (b / c) / z
    else
        tmp = (t * (a * (-4.0d0))) / c
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -5.2e+41) || !(b <= 3e-53)) {
		tmp = (b / c) / z;
	} else {
		tmp = (t * (a * -4.0)) / c;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -5.2e+41) or not (b <= 3e-53):
		tmp = (b / c) / z
	else:
		tmp = (t * (a * -4.0)) / c
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -5.2e+41) || !(b <= 3e-53))
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(Float64(t * Float64(a * -4.0)) / c);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -5.2e+41) || ~((b <= 3e-53)))
		tmp = (b / c) / z;
	else
		tmp = (t * (a * -4.0)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -5.2e+41], N[Not[LessEqual[b, 3e-53]], $MachinePrecision]], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.2000000000000001e41 or 3.0000000000000002e-53 < b

   1. Initial program 87.7%

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

      1. associate-*l* 87.7%

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

      2. associate-*l* 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in b around inf 55.1%

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

      1. associate-/r* 56.5%

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

   6. Simplified 56.5%

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

   if -5.2000000000000001e41 < b < 3.0000000000000002e-53

   1. Initial program 80.1%

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

      1. associate-/r* 80.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in z around inf 52.2%

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

      1. associate-*r* 52.2%

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

      2. *-commutative 52.2%

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

      3. *-commutative 52.2%

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

   6. Simplified 52.2%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+41} \lor \neg \left(b \leq 3 \cdot 10^{-53}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \]

Alternative 11: 34.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-180}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= x -3.8e-180) (/ b (* z c)) (/ (/ b c) z)))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -3.8e-180) {
		tmp = b / (z * c);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: t and a 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 (x <= (-3.8d-180)) then
        tmp = b / (z * c)
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -3.8e-180) {
		tmp = b / (z * c);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if x <= -3.8e-180:
		tmp = b / (z * c)
	else:
		tmp = (b / c) / z
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (x <= -3.8e-180)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (x <= -3.8e-180)
		tmp = b / (z * c);
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[x, -3.8e-180], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.79999999999999999e-180

   1. Initial program 83.8%

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

      1. associate-*l* 83.8%

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

      2. associate-*l* 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in b around inf 30.8%

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

   if -3.79999999999999999e-180 < x

   1. Initial program 83.8%

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

      1. associate-*l* 83.8%

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

      2. associate-*l* 84.5%

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

   3. Simplified 84.5%

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

   4. Taylor expanded in b around inf 37.1%

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

      1. associate-/r* 37.6%

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

   6. Simplified 37.6%

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

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-180}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 12: 35.2% accurate, 3.8× speedup

Math

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

FPCore

NOTE: t and a 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(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Fortran

NOTE: t and a 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 t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: t and a 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 83.8%

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

   1. associate-*l* 83.8%

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

   2. associate-*l* 85.6%

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

3. Simplified 85.6%

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

4. Taylor expanded in b around inf 34.5%

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

5. Final simplification 34.5%

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

Developer target: 80.5% accurate, 0.2× 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 2023257 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :herbie-target
  (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -1.100156740804105e-171) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 0.0) (/ (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9.0 (/ y c)) (/ x z)) (/ b (* c z))) (* 4.0 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (- (+ (* 9.0 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4.0 (/ (* a t) c))))))))

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