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

Percentage Accurate: 80.1% → 91.6%

Time: 20.2s

Alternatives: 18

Speedup: 1.1×

• 37.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.1% 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, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\\ \mathbf{if}\;z \leq -9 \cdot 10^{-55}:\\ \;\;\;\;\frac{t_1 + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-16}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - 4 \cdot \left(t \cdot \left(z \cdot a\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, t_1\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 (/ (fma x (* 9.0 y) b) z)))
   (if (<= z -9e-55)
     (/ (+ t_1 (* t (* a -4.0))) c)
     (if (<= z 2.4e-16)
       (/ (+ b (- (* x (* 9.0 y)) (* 4.0 (* t (* z a))))) (* z c))
       (/ (fma t (* a -4.0) t_1) c)))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(x, (9.0 * y), b) / z;
	double tmp;
	if (z <= -9e-55) {
		tmp = (t_1 + (t * (a * -4.0))) / c;
	} else if (z <= 2.4e-16) {
		tmp = (b + ((x * (9.0 * y)) - (4.0 * (t * (z * a))))) / (z * c);
	} else {
		tmp = fma(t, (a * -4.0), t_1) / c;
	}
	return tmp;
}

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(x, Float64(9.0 * y), b) / z)
	tmp = 0.0
	if (z <= -9e-55)
		tmp = Float64(Float64(t_1 + Float64(t * Float64(a * -4.0))) / c);
	elseif (z <= 2.4e-16)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(4.0 * Float64(t * Float64(z * a))))) / Float64(z * c));
	else
		tmp = Float64(fma(t, Float64(a * -4.0), t_1) / c);
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -9e-55], N[(N[(t$95$1 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 2.4e-16], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(a * -4.0), $MachinePrecision] + t$95$1), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.99999999999999941e-55

   1. Initial program 62.6%

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

      1. associate-/r* 71.9%

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

   3. Simplified 91.1%

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

   if -8.99999999999999941e-55 < z < 2.40000000000000005e-16

   1. Initial program 91.2%

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

      1. associate-*l* 91.2%

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

      2. associate-*l* 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in z around 0 91.2%

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

      1. associate-*r* 86.3%

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

      2. *-commutative 86.3%

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

      3. associate-*l* 90.5%

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

   6. Simplified 90.5%

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

   if 2.40000000000000005e-16 < z

   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* 69.4%

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

   3. Simplified 90.6%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-55}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-16}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - 4 \cdot \left(t \cdot \left(z \cdot a\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \end{array} \]

Alternative 2: 91.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-55} \lor \neg \left(z \leq 2.2 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - 4 \cdot \left(t \cdot \left(z \cdot a\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 -7.6e-55) (not (<= z 2.2e-16)))
   (/ (+ (/ (fma x (* 9.0 y) b) z) (* t (* a -4.0))) c)
   (/ (+ b (- (* x (* 9.0 y)) (* 4.0 (* t (* z a))))) (* z c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -7.6e-55) || !(z <= 2.2e-16)) {
		tmp = ((fma(x, (9.0 * y), b) / z) + (t * (a * -4.0))) / c;
	} else {
		tmp = (b + ((x * (9.0 * y)) - (4.0 * (t * (z * a))))) / (z * c);
	}
	return tmp;
}

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -7.6e-55) || !(z <= 2.2e-16))
		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(x * Float64(9.0 * y)) - Float64(4.0 * Float64(t * Float64(z * a))))) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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, -7.6e-55], N[Not[LessEqual[z, 2.2e-16]], $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[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5999999999999993e-55 or 2.2e-16 < z

   1. Initial program 62.2%

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

      1. associate-/r* 70.7%

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

   3. Simplified 90.1%

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

   if -7.5999999999999993e-55 < z < 2.2e-16

   1. Initial program 91.2%

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

      1. associate-*l* 91.2%

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

      2. associate-*l* 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in z around 0 91.2%

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

      1. associate-*r* 86.3%

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

      2. *-commutative 86.3%

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

      3. associate-*l* 90.5%

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

   6. Simplified 90.5%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-55} \lor \neg \left(z \leq 2.2 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - 4 \cdot \left(t \cdot \left(z \cdot a\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 3: 49.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := 9 \cdot \frac{y}{\frac{z}{\frac{x}{c}}}\\ t_2 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;t \leq -1 \cdot 10^{+194}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.35 \cdot 10^{+167}:\\ \;\;\;\;\frac{y}{z} \cdot \frac{x \cdot 9}{c}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{+17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-114}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-230}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-42}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 (/ y (/ z (/ x c))))) (t_2 (* -4.0 (/ a (/ c t)))))
   (if (<= t -1e+194)
     t_2
     (if (<= t -3.35e+167)
       (* (/ y z) (/ (* x 9.0) c))
       (if (<= t -4.6e+17)
         t_2
         (if (<= t -2.4e-94)
           t_1
           (if (<= t -8e-114)
             (/ (/ b z) c)
             (if (<= t -1e-128)
               t_1
               (if (<= t 1.45e-230)
                 (* (/ b c) (/ 1.0 z))
                 (if (<= t 4.2e-42)
                   (* 9.0 (* (/ y c) (/ x z)))
                   (* -4.0 (/ t (/ c a)))))))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * (y / (z / (x / c)));
	double t_2 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -1e+194) {
		tmp = t_2;
	} else if (t <= -3.35e+167) {
		tmp = (y / z) * ((x * 9.0) / c);
	} else if (t <= -4.6e+17) {
		tmp = t_2;
	} else if (t <= -2.4e-94) {
		tmp = t_1;
	} else if (t <= -8e-114) {
		tmp = (b / z) / c;
	} else if (t <= -1e-128) {
		tmp = t_1;
	} else if (t <= 1.45e-230) {
		tmp = (b / c) * (1.0 / z);
	} else if (t <= 4.2e-42) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 * (y / (z / (x / c)))
    t_2 = (-4.0d0) * (a / (c / t))
    if (t <= (-1d+194)) then
        tmp = t_2
    else if (t <= (-3.35d+167)) then
        tmp = (y / z) * ((x * 9.0d0) / c)
    else if (t <= (-4.6d+17)) then
        tmp = t_2
    else if (t <= (-2.4d-94)) then
        tmp = t_1
    else if (t <= (-8d-114)) then
        tmp = (b / z) / c
    else if (t <= (-1d-128)) then
        tmp = t_1
    else if (t <= 1.45d-230) then
        tmp = (b / c) * (1.0d0 / z)
    else if (t <= 4.2d-42) then
        tmp = 9.0d0 * ((y / c) * (x / z))
    else
        tmp = (-4.0d0) * (t / (c / a))
    end if
    code = tmp
end function

Java

assert x < y;
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 * (y / (z / (x / c)));
	double t_2 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -1e+194) {
		tmp = t_2;
	} else if (t <= -3.35e+167) {
		tmp = (y / z) * ((x * 9.0) / c);
	} else if (t <= -4.6e+17) {
		tmp = t_2;
	} else if (t <= -2.4e-94) {
		tmp = t_1;
	} else if (t <= -8e-114) {
		tmp = (b / z) / c;
	} else if (t <= -1e-128) {
		tmp = t_1;
	} else if (t <= 1.45e-230) {
		tmp = (b / c) * (1.0 / z);
	} else if (t <= 4.2e-42) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * (y / (z / (x / c)))
	t_2 = -4.0 * (a / (c / t))
	tmp = 0
	if t <= -1e+194:
		tmp = t_2
	elif t <= -3.35e+167:
		tmp = (y / z) * ((x * 9.0) / c)
	elif t <= -4.6e+17:
		tmp = t_2
	elif t <= -2.4e-94:
		tmp = t_1
	elif t <= -8e-114:
		tmp = (b / z) / c
	elif t <= -1e-128:
		tmp = t_1
	elif t <= 1.45e-230:
		tmp = (b / c) * (1.0 / z)
	elif t <= 4.2e-42:
		tmp = 9.0 * ((y / c) * (x / z))
	else:
		tmp = -4.0 * (t / (c / a))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(y / Float64(z / Float64(x / c))))
	t_2 = Float64(-4.0 * Float64(a / Float64(c / t)))
	tmp = 0.0
	if (t <= -1e+194)
		tmp = t_2;
	elseif (t <= -3.35e+167)
		tmp = Float64(Float64(y / z) * Float64(Float64(x * 9.0) / c));
	elseif (t <= -4.6e+17)
		tmp = t_2;
	elseif (t <= -2.4e-94)
		tmp = t_1;
	elseif (t <= -8e-114)
		tmp = Float64(Float64(b / z) / c);
	elseif (t <= -1e-128)
		tmp = t_1;
	elseif (t <= 1.45e-230)
		tmp = Float64(Float64(b / c) * Float64(1.0 / z));
	elseif (t <= 4.2e-42)
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	else
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * (y / (z / (x / c)));
	t_2 = -4.0 * (a / (c / t));
	tmp = 0.0;
	if (t <= -1e+194)
		tmp = t_2;
	elseif (t <= -3.35e+167)
		tmp = (y / z) * ((x * 9.0) / c);
	elseif (t <= -4.6e+17)
		tmp = t_2;
	elseif (t <= -2.4e-94)
		tmp = t_1;
	elseif (t <= -8e-114)
		tmp = (b / z) / c;
	elseif (t <= -1e-128)
		tmp = t_1;
	elseif (t <= 1.45e-230)
		tmp = (b / c) * (1.0 / z);
	elseif (t <= 4.2e-42)
		tmp = 9.0 * ((y / c) * (x / z));
	else
		tmp = -4.0 * (t / (c / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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[(y / N[(z / N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e+194], t$95$2, If[LessEqual[t, -3.35e+167], N[(N[(y / z), $MachinePrecision] * N[(N[(x * 9.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.6e+17], t$95$2, If[LessEqual[t, -2.4e-94], t$95$1, If[LessEqual[t, -8e-114], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, -1e-128], t$95$1, If[LessEqual[t, 1.45e-230], N[(N[(b / c), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e-42], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -9.99999999999999945e193 or -3.34999999999999984e167 < t < -4.6e17

   1. Initial program 73.1%

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

      1. associate-*l* 73.1%

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

      2. associate-*l* 65.6%

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

   3. Simplified 65.6%

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

   4. Taylor expanded in z around inf 36.9%

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

      1. *-commutative 36.9%

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

      2. associate-/l* 47.9%

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

   6. Simplified 47.9%

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

   if -9.99999999999999945e193 < t < -3.34999999999999984e167

   1. Initial program 75.0%

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

      1. associate-*l* 75.0%

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

      2. associate-*l* 77.5%

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

   3. Simplified 77.5%

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

      1. *-un-lft-identity 77.5%

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

      2. times-frac 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around inf 52.5%

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

      1. associate-*r/ 52.5%

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

      2. associate-*r* 52.5%

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

      3. *-commutative 52.5%

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

      4. associate-*r* 52.5%

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

      5. times-frac 75.0%

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

      6. *-commutative 75.0%

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

   8. Simplified 75.0%

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

   if -4.6e17 < t < -2.4e-94 or -8.0000000000000004e-114 < t < -1.00000000000000005e-128

   1. Initial program 76.6%

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

      1. associate-*l* 76.7%

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

      2. associate-*l* 76.6%

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

   3. Simplified 76.6%

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

      1. *-un-lft-identity 76.6%

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

      2. times-frac 72.3%

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

   5. Applied egg-rr 72.3%

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

   6. Taylor expanded in x around inf 50.3%

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

      1. associate-/l* 59.4%

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

      2. *-commutative 59.4%

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

      3. associate-/l* 59.3%

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

   8. Simplified 59.3%

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

   if -2.4e-94 < t < -8.0000000000000004e-114

   1. Initial program 86.4%

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

      1. associate-/r* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 100.0%

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

   5. Taylor expanded in z around 0 86.4%

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

   6. Taylor expanded in y around 0 72.1%

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

   if -1.00000000000000005e-128 < t < 1.45000000000000003e-230

   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. Step-by-step derivation

      1. associate-*l* 83.0%

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

      2. associate-*l* 83.2%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in b around inf 50.5%

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

      1. associate-/r* 52.2%

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

      2. div-inv 52.2%

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

   6. Applied egg-rr 52.2%

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

   if 1.45000000000000003e-230 < t < 4.20000000000000013e-42

   1. Initial program 92.6%

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

      1. associate-/r* 94.9%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in z around 0 95.0%

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

   5. Taylor expanded in y around inf 56.3%

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

      1. times-frac 55.8%

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

   7. Simplified 55.8%

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

   if 4.20000000000000013e-42 < t

   1. Initial program 63.0%

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

      1. associate-*l* 63.0%

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

      2. associate-*l* 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in z around inf 56.9%

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

      1. *-commutative 56.9%

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

      2. *-commutative 56.9%

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

      3. associate-/l* 60.6%

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

   6. Simplified 60.6%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+194}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -3.35 \cdot 10^{+167}:\\ \;\;\;\;\frac{y}{z} \cdot \frac{x \cdot 9}{c}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{+17}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-94}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z}{\frac{x}{c}}}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-114}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-128}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z}{\frac{x}{c}}}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-230}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-42}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 4: 91.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-55} \lor \neg \left(z \leq 2 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - 4 \cdot \left(t \cdot \left(z \cdot a\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 -2e-55) (not (<= z 2e-16)))
   (/ (+ (* t (* a -4.0)) (/ (+ b (* 9.0 (* x y))) z)) c)
   (/ (+ b (- (* x (* 9.0 y)) (* 4.0 (* t (* z a))))) (* z c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2e-55) || !(z <= 2e-16)) {
		tmp = ((t * (a * -4.0)) + ((b + (9.0 * (x * y))) / z)) / c;
	} else {
		tmp = (b + ((x * (9.0 * y)) - (4.0 * (t * (z * a))))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 <= (-2d-55)) .or. (.not. (z <= 2d-16))) then
        tmp = ((t * (a * (-4.0d0))) + ((b + (9.0d0 * (x * y))) / z)) / c
    else
        tmp = (b + ((x * (9.0d0 * y)) - (4.0d0 * (t * (z * a))))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
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 <= -2e-55) || !(z <= 2e-16)) {
		tmp = ((t * (a * -4.0)) + ((b + (9.0 * (x * y))) / z)) / c;
	} else {
		tmp = (b + ((x * (9.0 * y)) - (4.0 * (t * (z * a))))) / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -2e-55) or not (z <= 2e-16):
		tmp = ((t * (a * -4.0)) + ((b + (9.0 * (x * y))) / z)) / c
	else:
		tmp = (b + ((x * (9.0 * y)) - (4.0 * (t * (z * a))))) / (z * c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -2e-55) || !(z <= 2e-16))
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(Float64(b + Float64(9.0 * Float64(x * y))) / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(4.0 * Float64(t * Float64(z * a))))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -2e-55) || ~((z <= 2e-16)))
		tmp = ((t * (a * -4.0)) + ((b + (9.0 * (x * y))) / z)) / c;
	else
		tmp = (b + ((x * (9.0 * y)) - (4.0 * (t * (z * a))))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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, -2e-55], N[Not[LessEqual[z, 2e-16]], $MachinePrecision]], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.99999999999999999e-55 or 2e-16 < z

   1. Initial program 62.2%

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

      1. associate-/r* 70.7%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in z around 0 90.1%

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

   if -1.99999999999999999e-55 < z < 2e-16

   1. Initial program 91.2%

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

      1. associate-*l* 91.2%

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

      2. associate-*l* 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in z around 0 91.2%

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

      1. associate-*r* 86.3%

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

      2. *-commutative 86.3%

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

      3. associate-*l* 90.5%

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

   6. Simplified 90.5%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-55} \lor \neg \left(z \leq 2 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - 4 \cdot \left(t \cdot \left(z \cdot a\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 5: 50.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{-38}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-282}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z}{\frac{x}{c}}}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-220}:\\ \;\;\;\;\frac{1}{c \cdot \frac{z}{b}}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-27}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b}}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{+59}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 (* (/ y c) (/ x z)))))
   (if (<= a -4.2e-38)
     (* -4.0 (* t (/ a c)))
     (if (<= a -5e-282)
       (* 9.0 (/ y (/ z (/ x c))))
       (if (<= a 2.8e-220)
         (/ 1.0 (* c (/ z b)))
         (if (<= a 5.5e-149)
           t_1
           (if (<= a 9e-27)
             (/ 1.0 (/ (* z c) b))
             (if (<= a 3.3e+32)
               t_1
               (if (<= a 2.85e+59)
                 (/ b (* z c))
                 (* -4.0 (/ t (/ c a))))))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((y / c) * (x / z));
	double tmp;
	if (a <= -4.2e-38) {
		tmp = -4.0 * (t * (a / c));
	} else if (a <= -5e-282) {
		tmp = 9.0 * (y / (z / (x / c)));
	} else if (a <= 2.8e-220) {
		tmp = 1.0 / (c * (z / b));
	} else if (a <= 5.5e-149) {
		tmp = t_1;
	} else if (a <= 9e-27) {
		tmp = 1.0 / ((z * c) / b);
	} else if (a <= 3.3e+32) {
		tmp = t_1;
	} else if (a <= 2.85e+59) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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) :: tmp
    t_1 = 9.0d0 * ((y / c) * (x / z))
    if (a <= (-4.2d-38)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (a <= (-5d-282)) then
        tmp = 9.0d0 * (y / (z / (x / c)))
    else if (a <= 2.8d-220) then
        tmp = 1.0d0 / (c * (z / b))
    else if (a <= 5.5d-149) then
        tmp = t_1
    else if (a <= 9d-27) then
        tmp = 1.0d0 / ((z * c) / b)
    else if (a <= 3.3d+32) then
        tmp = t_1
    else if (a <= 2.85d+59) then
        tmp = b / (z * c)
    else
        tmp = (-4.0d0) * (t / (c / a))
    end if
    code = tmp
end function

Java

assert x < y;
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 * ((y / c) * (x / z));
	double tmp;
	if (a <= -4.2e-38) {
		tmp = -4.0 * (t * (a / c));
	} else if (a <= -5e-282) {
		tmp = 9.0 * (y / (z / (x / c)));
	} else if (a <= 2.8e-220) {
		tmp = 1.0 / (c * (z / b));
	} else if (a <= 5.5e-149) {
		tmp = t_1;
	} else if (a <= 9e-27) {
		tmp = 1.0 / ((z * c) / b);
	} else if (a <= 3.3e+32) {
		tmp = t_1;
	} else if (a <= 2.85e+59) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * ((y / c) * (x / z))
	tmp = 0
	if a <= -4.2e-38:
		tmp = -4.0 * (t * (a / c))
	elif a <= -5e-282:
		tmp = 9.0 * (y / (z / (x / c)))
	elif a <= 2.8e-220:
		tmp = 1.0 / (c * (z / b))
	elif a <= 5.5e-149:
		tmp = t_1
	elif a <= 9e-27:
		tmp = 1.0 / ((z * c) / b)
	elif a <= 3.3e+32:
		tmp = t_1
	elif a <= 2.85e+59:
		tmp = b / (z * c)
	else:
		tmp = -4.0 * (t / (c / a))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)))
	tmp = 0.0
	if (a <= -4.2e-38)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (a <= -5e-282)
		tmp = Float64(9.0 * Float64(y / Float64(z / Float64(x / c))));
	elseif (a <= 2.8e-220)
		tmp = Float64(1.0 / Float64(c * Float64(z / b)));
	elseif (a <= 5.5e-149)
		tmp = t_1;
	elseif (a <= 9e-27)
		tmp = Float64(1.0 / Float64(Float64(z * c) / b));
	elseif (a <= 3.3e+32)
		tmp = t_1;
	elseif (a <= 2.85e+59)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * ((y / c) * (x / z));
	tmp = 0.0;
	if (a <= -4.2e-38)
		tmp = -4.0 * (t * (a / c));
	elseif (a <= -5e-282)
		tmp = 9.0 * (y / (z / (x / c)));
	elseif (a <= 2.8e-220)
		tmp = 1.0 / (c * (z / b));
	elseif (a <= 5.5e-149)
		tmp = t_1;
	elseif (a <= 9e-27)
		tmp = 1.0 / ((z * c) / b);
	elseif (a <= 3.3e+32)
		tmp = t_1;
	elseif (a <= 2.85e+59)
		tmp = b / (z * c);
	else
		tmp = -4.0 * (t / (c / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.2e-38], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5e-282], N[(9.0 * N[(y / N[(z / N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e-220], N[(1.0 / N[(c * N[(z / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e-149], t$95$1, If[LessEqual[a, 9e-27], N[(1.0 / N[(N[(z * c), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e+32], t$95$1, If[LessEqual[a, 2.85e+59], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -4.20000000000000026e-38

   1. Initial program 76.2%

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

      1. associate-*l* 76.2%

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

      2. associate-*l* 74.8%

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

   3. Simplified 74.8%

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

      1. *-un-lft-identity 74.8%

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

      2. times-frac 75.0%

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

   5. Applied egg-rr 75.0%

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

   6. Taylor expanded in z around inf 55.0%

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

      1. associate-/l* 59.8%

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

      2. associate-/r/ 63.6%

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

   8. Simplified 63.6%

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

   if -4.20000000000000026e-38 < a < -5.0000000000000001e-282

   1. Initial program 74.8%

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

      1. associate-*l* 74.8%

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

      2. associate-*l* 75.0%

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

   3. Simplified 75.0%

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

      1. *-un-lft-identity 75.0%

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

      2. times-frac 81.0%

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

   5. Applied egg-rr 81.0%

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

   6. Taylor expanded in x around inf 32.6%

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

      1. associate-/l* 39.0%

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

      2. *-commutative 39.0%

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

      3. associate-/l* 41.0%

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

   8. Simplified 41.0%

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

   if -5.0000000000000001e-282 < a < 2.7999999999999999e-220

   1. Initial program 74.1%

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

      1. associate-*l* 74.0%

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

      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%

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

   4. Taylor expanded in b around inf 57.9%

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

      1. clear-num 57.9%

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

      2. inv-pow 57.9%

         \[\leadsto \color{blue}{{\left(\frac{c \cdot z}{b}\right)}^{-1}} \]

      3. *-commutative 57.9%

         \[\leadsto {\left(\frac{\color{blue}{z \cdot c}}{b}\right)}^{-1} \]

   6. Applied egg-rr 57.9%

      \[\leadsto \color{blue}{{\left(\frac{z \cdot c}{b}\right)}^{-1}} \]
   7. Step-by-step derivation

      1. unpow-1 57.9%

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

      2. associate-/l* 70.4%

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

   8. Simplified 70.4%

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{\frac{b}{c}}}} \]
   9. Step-by-step derivation

      1. associate-/r/ 66.0%

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

   10. Applied egg-rr 66.0%

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

   if 2.7999999999999999e-220 < a < 5.50000000000000043e-149 or 9.0000000000000003e-27 < a < 3.3000000000000002e32

   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. Step-by-step derivation

      1. associate-/r* 69.1%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in z around 0 82.5%

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

   5. Taylor expanded in y around inf 56.5%

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

      1. times-frac 65.4%

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

   7. Simplified 65.4%

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

   if 5.50000000000000043e-149 < a < 9.0000000000000003e-27

   1. Initial program 74.1%

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

      1. associate-*l* 74.2%

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

      2. associate-*l* 83.6%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in b around inf 44.0%

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

      1. clear-num 44.0%

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

      2. inv-pow 44.0%

         \[\leadsto \color{blue}{{\left(\frac{c \cdot z}{b}\right)}^{-1}} \]

      3. *-commutative 44.0%

         \[\leadsto {\left(\frac{\color{blue}{z \cdot c}}{b}\right)}^{-1} \]

   6. Applied egg-rr 44.0%

      \[\leadsto \color{blue}{{\left(\frac{z \cdot c}{b}\right)}^{-1}} \]
   7. Step-by-step derivation

      1. unpow-1 44.0%

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

   8. Simplified 44.0%

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

   if 3.3000000000000002e32 < a < 2.8500000000000001e59

   1. Initial program 100.0%

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

      1. associate-*l* 100.0%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in b around inf 37.0%

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

   if 2.8500000000000001e59 < a

   1. Initial program 74.0%

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

      1. associate-*l* 74.0%

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

      2. associate-*l* 65.0%

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

   3. Simplified 65.0%

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

   4. Taylor expanded in z around inf 44.2%

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

      1. *-commutative 44.2%

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

      2. *-commutative 44.2%

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

      3. associate-/l* 57.1%

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

   6. Simplified 57.1%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-38}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-282}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z}{\frac{x}{c}}}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-220}:\\ \;\;\;\;\frac{1}{c \cdot \frac{z}{b}}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-149}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-27}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b}}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+32}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{+59}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 6: 76.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+14} \lor \neg \left(z \leq 5.6 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 -7.2e+14) (not (<= z 5.6e-26)))
   (/ (+ (* t (* a -4.0)) (* 9.0 (/ y (/ z x)))) c)
   (/ (+ b (* 9.0 (* x y))) (* z c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -7.2e+14) || !(z <= 5.6e-26)) {
		tmp = ((t * (a * -4.0)) + (9.0 * (y / (z / x)))) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 <= (-7.2d+14)) .or. (.not. (z <= 5.6d-26))) then
        tmp = ((t * (a * (-4.0d0))) + (9.0d0 * (y / (z / x)))) / c
    else
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
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 <= -7.2e+14) || !(z <= 5.6e-26)) {
		tmp = ((t * (a * -4.0)) + (9.0 * (y / (z / x)))) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -7.2e+14) or not (z <= 5.6e-26):
		tmp = ((t * (a * -4.0)) + (9.0 * (y / (z / x)))) / c
	else:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -7.2e+14) || !(z <= 5.6e-26))
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(9.0 * Float64(y / Float64(z / x)))) / c);
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -7.2e+14) || ~((z <= 5.6e-26)))
		tmp = ((t * (a * -4.0)) + (9.0 * (y / (z / x)))) / c;
	else
		tmp = (b + (9.0 * (x * y))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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, -7.2e+14], N[Not[LessEqual[z, 5.6e-26]], $MachinePrecision]], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $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 z < -7.2e14 or 5.6000000000000002e-26 < z

   1. Initial program 58.2%

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

      1. associate-/r* 67.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in x around inf 73.8%

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

      1. associate-/l* 77.6%

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

   6. Simplified 77.6%

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

   if -7.2e14 < z < 5.6000000000000002e-26

   1. Initial program 91.5%

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

      1. associate-*l* 91.5%

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

      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 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 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+14} \lor \neg \left(z \leq 5.6 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 7: 76.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+14}:\\ \;\;\;\;\left(t_1 + 9 \cdot \left(x \cdot \frac{y}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-24}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 (* t (* a -4.0))))
   (if (<= z -7.8e+14)
     (* (+ t_1 (* 9.0 (* x (/ y z)))) (/ 1.0 c))
     (if (<= z 1.15e-24)
       (/ (+ b (* 9.0 (* x y))) (* z c))
       (/ (+ t_1 (* 9.0 (/ y (/ z x)))) c)))))

C

assert(x < y);
assert(t < a);
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 <= -7.8e+14) {
		tmp = (t_1 + (9.0 * (x * (y / z)))) * (1.0 / c);
	} else if (z <= 1.15e-24) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = (t_1 + (9.0 * (y / (z / x)))) / c;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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) :: tmp
    t_1 = t * (a * (-4.0d0))
    if (z <= (-7.8d+14)) then
        tmp = (t_1 + (9.0d0 * (x * (y / z)))) * (1.0d0 / c)
    else if (z <= 1.15d-24) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else
        tmp = (t_1 + (9.0d0 * (y / (z / x)))) / c
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
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 <= -7.8e+14) {
		tmp = (t_1 + (9.0 * (x * (y / z)))) * (1.0 / c);
	} else if (z <= 1.15e-24) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = (t_1 + (9.0 * (y / (z / x)))) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = t * (a * -4.0)
	tmp = 0
	if z <= -7.8e+14:
		tmp = (t_1 + (9.0 * (x * (y / z)))) * (1.0 / c)
	elif z <= 1.15e-24:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = (t_1 + (9.0 * (y / (z / x)))) / c
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (z <= -7.8e+14)
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(x * Float64(y / z)))) * Float64(1.0 / c));
	elseif (z <= 1.15e-24)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	else
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(y / Float64(z / x)))) / c);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (z <= -7.8e+14)
		tmp = (t_1 + (9.0 * (x * (y / z)))) * (1.0 / c);
	elseif (z <= 1.15e-24)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = (t_1 + (9.0 * (y / (z / x)))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e+14], N[(N[(t$95$1 + N[(9.0 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e-24], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 + N[(9.0 * N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.8e14

   1. Initial program 53.6%

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

      1. associate-/r* 65.9%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in x around inf 78.0%

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

      1. div-inv 78.0%

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

      2. fma-def 78.0%

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

      3. associate-/l* 79.6%

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

   6. Applied egg-rr 79.6%

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

      1. fma-udef 79.6%

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

      2. associate-/r/ 78.1%

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

   8. Applied egg-rr 78.1%

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

   if -7.8e14 < z < 1.1500000000000001e-24

   1. Initial program 91.5%

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

      1. associate-*l* 91.5%

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

      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 x around inf 77.9%

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

   if 1.1500000000000001e-24 < z

   1. Initial program 62.1%

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

      1. associate-/r* 69.4%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in x around inf 70.1%

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

      1. associate-/l* 75.8%

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

   6. Simplified 75.8%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+14}:\\ \;\;\;\;\left(t \cdot \left(a \cdot -4\right) + 9 \cdot \left(x \cdot \frac{y}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-24}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \end{array} \]

Alternative 8: 47.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{-176}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-144}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 (* (/ y c) (/ x z)))))
   (if (<= z -1.3e-176)
     (* (* a -4.0) (/ t c))
     (if (<= z 3.6e-296)
       t_1
       (if (<= z 1.35e-144)
         (/ b (* z c))
         (if (<= z 3.6e-9) t_1 (/ (* t (* a -4.0)) c)))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((y / c) * (x / z));
	double tmp;
	if (z <= -1.3e-176) {
		tmp = (a * -4.0) * (t / c);
	} else if (z <= 3.6e-296) {
		tmp = t_1;
	} else if (z <= 1.35e-144) {
		tmp = b / (z * c);
	} else if (z <= 3.6e-9) {
		tmp = t_1;
	} else {
		tmp = (t * (a * -4.0)) / c;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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) :: tmp
    t_1 = 9.0d0 * ((y / c) * (x / z))
    if (z <= (-1.3d-176)) then
        tmp = (a * (-4.0d0)) * (t / c)
    else if (z <= 3.6d-296) then
        tmp = t_1
    else if (z <= 1.35d-144) then
        tmp = b / (z * c)
    else if (z <= 3.6d-9) then
        tmp = t_1
    else
        tmp = (t * (a * (-4.0d0))) / c
    end if
    code = tmp
end function

Java

assert x < y;
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 * ((y / c) * (x / z));
	double tmp;
	if (z <= -1.3e-176) {
		tmp = (a * -4.0) * (t / c);
	} else if (z <= 3.6e-296) {
		tmp = t_1;
	} else if (z <= 1.35e-144) {
		tmp = b / (z * c);
	} else if (z <= 3.6e-9) {
		tmp = t_1;
	} else {
		tmp = (t * (a * -4.0)) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * ((y / c) * (x / z))
	tmp = 0
	if z <= -1.3e-176:
		tmp = (a * -4.0) * (t / c)
	elif z <= 3.6e-296:
		tmp = t_1
	elif z <= 1.35e-144:
		tmp = b / (z * c)
	elif z <= 3.6e-9:
		tmp = t_1
	else:
		tmp = (t * (a * -4.0)) / c
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)))
	tmp = 0.0
	if (z <= -1.3e-176)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	elseif (z <= 3.6e-296)
		tmp = t_1;
	elseif (z <= 1.35e-144)
		tmp = Float64(b / Float64(z * c));
	elseif (z <= 3.6e-9)
		tmp = t_1;
	else
		tmp = Float64(Float64(t * Float64(a * -4.0)) / c);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * ((y / c) * (x / z));
	tmp = 0.0;
	if (z <= -1.3e-176)
		tmp = (a * -4.0) * (t / c);
	elseif (z <= 3.6e-296)
		tmp = t_1;
	elseif (z <= 1.35e-144)
		tmp = b / (z * c);
	elseif (z <= 3.6e-9)
		tmp = t_1;
	else
		tmp = (t * (a * -4.0)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e-176], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-296], t$95$1, If[LessEqual[z, 1.35e-144], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-9], t$95$1, N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.29999999999999996e-176

   1. Initial program 65.3%

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

      1. associate-/r* 70.9%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in z around 0 87.4%

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

   5. Taylor expanded in z around inf 49.3%

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

      1. associate-*r/ 49.3%

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

      2. associate-*r* 49.3%

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

      3. *-commutative 49.3%

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

      4. associate-*r/ 55.4%

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

      5. *-commutative 55.4%

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

   7. Simplified 55.4%

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

   if -1.29999999999999996e-176 < z < 3.5999999999999998e-296 or 1.34999999999999988e-144 < z < 3.6e-9

   1. Initial program 92.6%

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

      1. associate-/r* 85.0%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in z around 0 80.4%

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

   5. Taylor expanded in y around inf 61.2%

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

      1. times-frac 57.6%

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

   7. Simplified 57.6%

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

   if 3.5999999999999998e-296 < z < 1.34999999999999988e-144

   1. Initial program 95.4%

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

      1. associate-*l* 95.3%

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

      2. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in b around inf 71.4%

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

   if 3.6e-9 < z

   1. Initial program 60.6%

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

      1. associate-/r* 68.4%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in z around inf 48.5%

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

      1. associate-*r* 48.5%

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

      2. *-commutative 48.5%

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

      3. *-commutative 48.5%

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

   6. Simplified 48.5%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-176}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-296}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-144}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-9}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \]

Alternative 9: 49.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-103}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-296}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-145}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-7}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 -5.4e-103)
   (* -4.0 (* t (/ a c)))
   (if (<= z 8.4e-296)
     (* 9.0 (/ (* x y) (* z c)))
     (if (<= z 9.6e-145)
       (/ b (* z c))
       (if (<= z 2.9e-7)
         (* 9.0 (* (/ y c) (/ x z)))
         (/ (* t (* a -4.0)) c))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -5.4e-103) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= 8.4e-296) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (z <= 9.6e-145) {
		tmp = b / (z * c);
	} else if (z <= 2.9e-7) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else {
		tmp = (t * (a * -4.0)) / c;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 <= (-5.4d-103)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (z <= 8.4d-296) then
        tmp = 9.0d0 * ((x * y) / (z * c))
    else if (z <= 9.6d-145) then
        tmp = b / (z * c)
    else if (z <= 2.9d-7) then
        tmp = 9.0d0 * ((y / c) * (x / z))
    else
        tmp = (t * (a * (-4.0d0))) / c
    end if
    code = tmp
end function

Java

assert x < y;
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 <= -5.4e-103) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= 8.4e-296) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (z <= 9.6e-145) {
		tmp = b / (z * c);
	} else if (z <= 2.9e-7) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else {
		tmp = (t * (a * -4.0)) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -5.4e-103:
		tmp = -4.0 * (t * (a / c))
	elif z <= 8.4e-296:
		tmp = 9.0 * ((x * y) / (z * c))
	elif z <= 9.6e-145:
		tmp = b / (z * c)
	elif z <= 2.9e-7:
		tmp = 9.0 * ((y / c) * (x / z))
	else:
		tmp = (t * (a * -4.0)) / c
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -5.4e-103)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (z <= 8.4e-296)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)));
	elseif (z <= 9.6e-145)
		tmp = Float64(b / Float64(z * c));
	elseif (z <= 2.9e-7)
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	else
		tmp = Float64(Float64(t * Float64(a * -4.0)) / c);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -5.4e-103)
		tmp = -4.0 * (t * (a / c));
	elseif (z <= 8.4e-296)
		tmp = 9.0 * ((x * y) / (z * c));
	elseif (z <= 9.6e-145)
		tmp = b / (z * c);
	elseif (z <= 2.9e-7)
		tmp = 9.0 * ((y / c) * (x / z));
	else
		tmp = (t * (a * -4.0)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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, -5.4e-103], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.4e-296], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e-145], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e-7], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.40000000000000019e-103

   1. Initial program 63.5%

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

      1. associate-*l* 63.5%

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

      2. associate-*l* 66.0%

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

   3. Simplified 66.0%

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

      1. *-un-lft-identity 66.0%

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

      2. times-frac 68.7%

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

   5. Applied egg-rr 68.7%

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

   6. Taylor expanded in z around inf 52.6%

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

      1. associate-/l* 57.1%

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

      2. associate-/r/ 57.0%

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

   8. Simplified 57.0%

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

   if -5.40000000000000019e-103 < z < 8.3999999999999997e-296

   1. Initial program 93.3%

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

      1. associate-*l* 93.4%

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

      2. associate-*l* 82.0%

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

   3. Simplified 82.0%

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

   4. Taylor expanded in x around inf 64.0%

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

   if 8.3999999999999997e-296 < z < 9.60000000000000061e-145

   1. Initial program 95.4%

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

      1. associate-*l* 95.3%

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

      2. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in b around inf 71.4%

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

   if 9.60000000000000061e-145 < z < 2.8999999999999998e-7

   1. Initial program 88.0%

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

      1. associate-/r* 88.0%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in z around 0 85.0%

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

   5. Taylor expanded in y around inf 51.3%

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

      1. times-frac 54.2%

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

   7. Simplified 54.2%

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

   if 2.8999999999999998e-7 < z

   1. Initial program 60.6%

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

      1. associate-/r* 68.4%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in z around inf 48.5%

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

      1. associate-*r* 48.5%

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

      2. *-commutative 48.5%

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

      3. *-commutative 48.5%

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

   6. Simplified 48.5%

      \[\leadsto \frac{\color{blue}{t \cdot \left(a \cdot -4\right)}}{c} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-103}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-296}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-145}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-7}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \]

Alternative 10: 69.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00355:\\ \;\;\;\;\frac{x \cdot y}{c} \cdot \frac{9}{z}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-20}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+191}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \frac{x}{\frac{c}{y}}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 (<= y -0.00355)
   (* (/ (* x y) c) (/ 9.0 z))
   (if (<= y 1.02e-20)
     (/ (+ (* t (* a -4.0)) (/ b z)) c)
     (if (<= y 9e+191)
       (/ (+ b (* 9.0 (* x y))) (* z c))
       (/ (* 9.0 (/ x (/ c y))) z)))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -0.00355) {
		tmp = ((x * y) / c) * (9.0 / z);
	} else if (y <= 1.02e-20) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else if (y <= 9e+191) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = (9.0 * (x / (c / y))) / z;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 (y <= (-0.00355d0)) then
        tmp = ((x * y) / c) * (9.0d0 / z)
    else if (y <= 1.02d-20) then
        tmp = ((t * (a * (-4.0d0))) + (b / z)) / c
    else if (y <= 9d+191) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else
        tmp = (9.0d0 * (x / (c / y))) / z
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -0.00355) {
		tmp = ((x * y) / c) * (9.0 / z);
	} else if (y <= 1.02e-20) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else if (y <= 9e+191) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = (9.0 * (x / (c / y))) / z;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -0.00355:
		tmp = ((x * y) / c) * (9.0 / z)
	elif y <= 1.02e-20:
		tmp = ((t * (a * -4.0)) + (b / z)) / c
	elif y <= 9e+191:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = (9.0 * (x / (c / y))) / z
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -0.00355)
		tmp = Float64(Float64(Float64(x * y) / c) * Float64(9.0 / z));
	elseif (y <= 1.02e-20)
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c);
	elseif (y <= 9e+191)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	else
		tmp = Float64(Float64(9.0 * Float64(x / Float64(c / y))) / z);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -0.00355)
		tmp = ((x * y) / c) * (9.0 / z);
	elseif (y <= 1.02e-20)
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	elseif (y <= 9e+191)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = (9.0 * (x / (c / y))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -0.00355], N[(N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.02e-20], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[y, 9e+191], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(9.0 * N[(x / N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -0.0035500000000000002

   1. Initial program 65.4%

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

      1. associate-/r* 72.3%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in z around 0 87.5%

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

   5. Taylor expanded in y around inf 40.5%

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

      1. associate-*r/ 40.5%

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

      2. *-commutative 40.5%

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

      3. times-frac 44.5%

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

   7. Simplified 44.5%

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

   if -0.0035500000000000002 < y < 1.02000000000000001e-20

   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* 80.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in x around 0 71.5%

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

      1. associate-*r* 71.5%

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

      2. *-commutative 71.5%

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

      3. *-commutative 71.5%

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

   6. Simplified 71.5%

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

   if 1.02000000000000001e-20 < y < 9.0000000000000005e191

   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-*l* 82.9%

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

      2. associate-*l* 83.1%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in x around inf 73.7%

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

   if 9.0000000000000005e191 < y

   1. Initial program 75.3%

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

      1. associate-*l* 75.3%

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

      2. associate-*l* 70.3%

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

   3. Simplified 70.3%

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

   4. Taylor expanded in x around inf 61.1%

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

      1. associate-/r* 65.9%

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

      2. associate-*r/ 65.9%

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

      3. *-commutative 65.9%

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

      4. associate-/l* 70.6%

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

   6. Simplified 70.6%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00355:\\ \;\;\;\;\frac{x \cdot y}{c} \cdot \frac{9}{z}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-20}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+191}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \frac{x}{\frac{c}{y}}}{z}\\ \end{array} \]

Alternative 11: 70.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := b + 9 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{-68}:\\ \;\;\;\;\frac{\frac{t_1}{z}}{c}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-25}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+192}:\\ \;\;\;\;\frac{t_1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \frac{x}{\frac{c}{y}}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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)))))
   (if (<= y -3.9e-68)
     (/ (/ t_1 z) c)
     (if (<= y 3.3e-25)
       (/ (+ (* t (* a -4.0)) (/ b z)) c)
       (if (<= y 1.22e+192) (/ t_1 (* z c)) (/ (* 9.0 (/ x (/ c y))) z))))))

C

assert(x < y);
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));
	double tmp;
	if (y <= -3.9e-68) {
		tmp = (t_1 / z) / c;
	} else if (y <= 3.3e-25) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else if (y <= 1.22e+192) {
		tmp = t_1 / (z * c);
	} else {
		tmp = (9.0 * (x / (c / y))) / z;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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) :: tmp
    t_1 = b + (9.0d0 * (x * y))
    if (y <= (-3.9d-68)) then
        tmp = (t_1 / z) / c
    else if (y <= 3.3d-25) then
        tmp = ((t * (a * (-4.0d0))) + (b / z)) / c
    else if (y <= 1.22d+192) then
        tmp = t_1 / (z * c)
    else
        tmp = (9.0d0 * (x / (c / y))) / z
    end if
    code = tmp
end function

Java

assert x < y;
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));
	double tmp;
	if (y <= -3.9e-68) {
		tmp = (t_1 / z) / c;
	} else if (y <= 3.3e-25) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else if (y <= 1.22e+192) {
		tmp = t_1 / (z * c);
	} else {
		tmp = (9.0 * (x / (c / y))) / z;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = b + (9.0 * (x * y))
	tmp = 0
	if y <= -3.9e-68:
		tmp = (t_1 / z) / c
	elif y <= 3.3e-25:
		tmp = ((t * (a * -4.0)) + (b / z)) / c
	elif y <= 1.22e+192:
		tmp = t_1 / (z * c)
	else:
		tmp = (9.0 * (x / (c / y))) / z
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(b + Float64(9.0 * Float64(x * y)))
	tmp = 0.0
	if (y <= -3.9e-68)
		tmp = Float64(Float64(t_1 / z) / c);
	elseif (y <= 3.3e-25)
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c);
	elseif (y <= 1.22e+192)
		tmp = Float64(t_1 / Float64(z * c));
	else
		tmp = Float64(Float64(9.0 * Float64(x / Float64(c / y))) / z);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b + (9.0 * (x * y));
	tmp = 0.0;
	if (y <= -3.9e-68)
		tmp = (t_1 / z) / c;
	elseif (y <= 3.3e-25)
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	elseif (y <= 1.22e+192)
		tmp = t_1 / (z * c);
	else
		tmp = (9.0 * (x / (c / y))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.9e-68], N[(N[(t$95$1 / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[y, 3.3e-25], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[y, 1.22e+192], N[(t$95$1 / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(9.0 * N[(x / N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.90000000000000032e-68

   1. Initial program 68.0%

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

      1. associate-/r* 74.0%

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

   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 0 88.0%

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

   5. Taylor expanded in z around 0 66.2%

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

   if -3.90000000000000032e-68 < y < 3.2999999999999998e-25

   1. Initial program 77.7%

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

      1. associate-/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 88.2%

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

   4. Taylor expanded in x around 0 71.1%

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

      1. associate-*r* 71.1%

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

      2. *-commutative 71.1%

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

      3. *-commutative 71.1%

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

   6. Simplified 71.1%

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

   if 3.2999999999999998e-25 < y < 1.2200000000000001e192

   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-*l* 82.9%

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

      2. associate-*l* 83.1%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in x around inf 73.7%

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

   if 1.2200000000000001e192 < y

   1. Initial program 75.3%

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

      1. associate-*l* 75.3%

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

      2. associate-*l* 70.3%

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

   3. Simplified 70.3%

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

   4. Taylor expanded in x around inf 61.1%

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

      1. associate-/r* 65.9%

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

      2. associate-*r/ 65.9%

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

      3. *-commutative 65.9%

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

      4. associate-/l* 70.6%

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

   6. Simplified 70.6%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-68}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-25}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+192}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \frac{x}{\frac{c}{y}}}{z}\\ \end{array} \]

Alternative 12: 85.8% accurate, 1.1× speedup

Math

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a 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 (* 9.0 (* x y))) z)) c))

C

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

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 = ((t * (a * (-4.0d0))) + ((b + (9.0d0 * (x * y))) / z)) / c
end function

Java

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

Python

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

Julia

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

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = ((t * (a * -4.0)) + ((b + (9.0 * (x * y))) / z)) / c;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a 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[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]

Derivation

1. Initial program 75.3%

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

   1. associate-/r* 76.2%

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

3. Simplified 85.9%

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

4. Taylor expanded in z around 0 85.9%

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

5. Final simplification 85.9%

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

Alternative 13: 67.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-38}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{+95}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 (<= a -2.7e-38)
   (* -4.0 (* t (/ a c)))
   (if (<= a 1.06e+95)
     (/ (+ b (* 9.0 (* x y))) (* z c))
     (* -4.0 (/ t (/ c a))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -2.7e-38) {
		tmp = -4.0 * (t * (a / c));
	} else if (a <= 1.06e+95) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 <= (-2.7d-38)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (a <= 1.06d+95) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else
        tmp = (-4.0d0) * (t / (c / a))
    end if
    code = tmp
end function

Java

assert x < y;
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 <= -2.7e-38) {
		tmp = -4.0 * (t * (a / c));
	} else if (a <= 1.06e+95) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -2.7e-38:
		tmp = -4.0 * (t * (a / c))
	elif a <= 1.06e+95:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = -4.0 * (t / (c / a))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -2.7e-38)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (a <= 1.06e+95)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -2.7e-38)
		tmp = -4.0 * (t * (a / c));
	elseif (a <= 1.06e+95)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = -4.0 * (t / (c / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -2.7e-38], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.06e+95], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.70000000000000005e-38

   1. Initial program 76.2%

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

      1. associate-*l* 76.2%

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

      2. associate-*l* 74.8%

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

   3. Simplified 74.8%

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

      1. *-un-lft-identity 74.8%

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

      2. times-frac 75.0%

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

   5. Applied egg-rr 75.0%

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

   6. Taylor expanded in z around inf 55.0%

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

      1. associate-/l* 59.8%

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

      2. associate-/r/ 63.6%

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

   8. Simplified 63.6%

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

   if -2.70000000000000005e-38 < a < 1.06000000000000001e95

   1. Initial program 76.3%

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

      1. associate-*l* 76.4%

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

      2. associate-*l* 80.9%

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

   3. Simplified 80.9%

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

   4. Taylor expanded in x around inf 71.9%

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

   if 1.06000000000000001e95 < a

   1. Initial program 71.3%

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

      1. associate-*l* 71.2%

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

      2. associate-*l* 61.3%

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

   3. Simplified 61.3%

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

   4. Taylor expanded in z around inf 44.4%

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

      1. *-commutative 44.4%

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

      2. *-commutative 44.4%

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

      3. associate-/l* 58.7%

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

   6. Simplified 58.7%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-38}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{+95}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 14: 49.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-11} \lor \neg \left(t \leq 8.2 \cdot 10^{-128}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 (<= t -8e-11) (not (<= t 8.2e-128)))
   (* -4.0 (* t (/ a c)))
   (/ (/ b c) z)))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -8e-11) || !(t <= 8.2e-128)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 ((t <= (-8d-11)) .or. (.not. (t <= 8.2d-128))) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -8e-11) || !(t <= 8.2e-128)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -8e-11) or not (t <= 8.2e-128):
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = (b / c) / z
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -8e-11) || !(t <= 8.2e-128))
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -8e-11) || ~((t <= 8.2e-128)))
		tmp = -4.0 * (t * (a / c));
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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[t, -8e-11], N[Not[LessEqual[t, 8.2e-128]], $MachinePrecision]], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.99999999999999952e-11 or 8.1999999999999999e-128 < t

   1. Initial program 69.3%

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

      1. associate-*l* 69.3%

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

      2. associate-*l* 69.5%

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

   3. Simplified 69.5%

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

      1. *-un-lft-identity 69.5%

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

      2. times-frac 71.5%

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

   5. Applied egg-rr 71.5%

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

   6. Taylor expanded in z around inf 47.8%

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

      1. associate-/l* 53.5%

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

      2. associate-/r/ 52.4%

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

   8. Simplified 52.4%

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

   if -7.99999999999999952e-11 < t < 8.1999999999999999e-128

   1. Initial program 85.2%

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

      1. associate-*l* 85.2%

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

      2. associate-*l* 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in b around inf 47.6%

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

      1. associate-/r* 48.4%

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

   6. Simplified 48.4%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-11} \lor \neg \left(t \leq 8.2 \cdot 10^{-128}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 15: 50.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{-194}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-25}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-4}{\frac{c}{a}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 (<= a -2.55e-194)
   (* (* a -4.0) (/ t c))
   (if (<= a 3.5e-25) (/ (/ b c) z) (* t (/ -4.0 (/ c a))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -2.55e-194) {
		tmp = (a * -4.0) * (t / c);
	} else if (a <= 3.5e-25) {
		tmp = (b / c) / z;
	} else {
		tmp = t * (-4.0 / (c / a));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 <= (-2.55d-194)) then
        tmp = (a * (-4.0d0)) * (t / c)
    else if (a <= 3.5d-25) then
        tmp = (b / c) / z
    else
        tmp = t * ((-4.0d0) / (c / a))
    end if
    code = tmp
end function

Java

assert x < y;
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 <= -2.55e-194) {
		tmp = (a * -4.0) * (t / c);
	} else if (a <= 3.5e-25) {
		tmp = (b / c) / z;
	} else {
		tmp = t * (-4.0 / (c / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -2.55e-194:
		tmp = (a * -4.0) * (t / c)
	elif a <= 3.5e-25:
		tmp = (b / c) / z
	else:
		tmp = t * (-4.0 / (c / a))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -2.55e-194)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	elseif (a <= 3.5e-25)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(t * Float64(-4.0 / Float64(c / a)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -2.55e-194)
		tmp = (a * -4.0) * (t / c);
	elseif (a <= 3.5e-25)
		tmp = (b / c) / z;
	else
		tmp = t * (-4.0 / (c / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -2.55e-194], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e-25], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(t * N[(-4.0 / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.5499999999999999e-194

   1. Initial program 73.4%

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

      1. associate-/r* 77.8%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in z around 0 86.6%

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

   5. Taylor expanded in z around inf 45.5%

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

      1. associate-*r/ 45.5%

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

      2. associate-*r* 45.5%

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

      3. *-commutative 45.5%

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

      4. associate-*r/ 48.9%

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

      5. *-commutative 48.9%

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

   7. Simplified 48.9%

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

   if -2.5499999999999999e-194 < a < 3.5000000000000002e-25

   1. Initial program 77.9%

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

      1. associate-*l* 78.0%

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

      2. associate-*l* 85.4%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in b around inf 48.8%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   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 3.5000000000000002e-25 < a

   1. Initial program 75.4%

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

      1. associate-/r* 74.1%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in x around inf 66.0%

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

      1. div-inv 66.0%

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

      2. fma-def 66.0%

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

      3. associate-/l* 64.4%

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

   6. Applied egg-rr 64.4%

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

   7. Taylor expanded in y around 0 40.6%

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

      1. *-commutative 40.6%

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

      2. associate-/l* 50.6%

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

      3. associate-*r/ 50.6%

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

      4. *-commutative 50.6%

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

      5. associate-*r/ 50.4%

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

   9. Simplified 50.4%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{-194}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-25}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-4}{\frac{c}{a}}\\ \end{array} \]

Alternative 16: 50.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{-194}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-25}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 (<= a -2.55e-194)
   (* (* a -4.0) (/ t c))
   (if (<= a 5.2e-25) (/ (/ b c) z) (* -4.0 (/ t (/ c a))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -2.55e-194) {
		tmp = (a * -4.0) * (t / c);
	} else if (a <= 5.2e-25) {
		tmp = (b / c) / z;
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 <= (-2.55d-194)) then
        tmp = (a * (-4.0d0)) * (t / c)
    else if (a <= 5.2d-25) then
        tmp = (b / c) / z
    else
        tmp = (-4.0d0) * (t / (c / a))
    end if
    code = tmp
end function

Java

assert x < y;
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 <= -2.55e-194) {
		tmp = (a * -4.0) * (t / c);
	} else if (a <= 5.2e-25) {
		tmp = (b / c) / z;
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -2.55e-194:
		tmp = (a * -4.0) * (t / c)
	elif a <= 5.2e-25:
		tmp = (b / c) / z
	else:
		tmp = -4.0 * (t / (c / a))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -2.55e-194)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	elseif (a <= 5.2e-25)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -2.55e-194)
		tmp = (a * -4.0) * (t / c);
	elseif (a <= 5.2e-25)
		tmp = (b / c) / z;
	else
		tmp = -4.0 * (t / (c / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -2.55e-194], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e-25], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.5499999999999999e-194

   1. Initial program 73.4%

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

      1. associate-/r* 77.8%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in z around 0 86.6%

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

   5. Taylor expanded in z around inf 45.5%

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

      1. associate-*r/ 45.5%

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

      2. associate-*r* 45.5%

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

      3. *-commutative 45.5%

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

      4. associate-*r/ 48.9%

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

      5. *-commutative 48.9%

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

   7. Simplified 48.9%

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

   if -2.5499999999999999e-194 < a < 5.2e-25

   1. Initial program 77.9%

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

      1. associate-*l* 78.0%

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

      2. associate-*l* 85.4%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in b around inf 48.8%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   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 5.2e-25 < a

   1. Initial program 75.4%

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

      1. associate-*l* 75.4%

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

      2. associate-*l* 68.4%

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

   3. Simplified 68.4%

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

   4. Taylor expanded in z around inf 40.6%

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

      1. *-commutative 40.6%

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

      2. *-commutative 40.6%

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

      3. associate-/l* 50.6%

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

   6. Simplified 50.6%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{-194}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-25}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 17: 35.1% accurate, 3.8× speedup

Math

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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(x < y);
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: x and y should be sorted in increasing order before calling this function.
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 x < y;
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

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

Julia

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

MATLAB

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

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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 75.3%

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

   1. associate-*l* 75.4%

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

   2. associate-*l* 75.5%

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

3. Simplified 75.5%

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

4. Taylor expanded in b around inf 32.9%

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

5. Final simplification 32.9%

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

Alternative 18: 34.5% accurate, 3.8× speedup

Math

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 c) z))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 75.3%

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

   1. associate-*l* 75.4%

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

   2. associate-*l* 75.5%

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

3. Simplified 75.5%

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

4. Taylor expanded in b around inf 32.9%

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

   1. associate-/r* 34.6%

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

6. Simplified 34.6%

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

7. Final simplification 34.6%

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

Developer target: 80.2% 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 2023181 
(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)))