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

Percentage Accurate: 79.6% → 91.2%

Time: 17.5s

Alternatives: 18

Speedup: 0.2×

• 37.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-66} \lor \neg \left(z \leq 2.9 \cdot 10^{-137}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: 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 -3e-66) (not (<= z 2.9e-137)))
   (/ (fma t (* a -4.0) (/ (fma x (* 9.0 y) b) z)) c)
   (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* 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 <= -3e-66) || !(z <= 2.9e-137)) {
		tmp = fma(t, (a * -4.0), (fma(x, (9.0 * y), b) / z)) / c;
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (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 <= -3e-66) || !(z <= 2.9e-137))
		tmp = Float64(fma(t, Float64(a * -4.0), Float64(fma(x, Float64(9.0 * y), b) / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: 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, -3e-66], N[Not[LessEqual[z, 2.9e-137]], $MachinePrecision]], N[(N[(t * N[(a * -4.0), $MachinePrecision] + N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.0000000000000002e-66 or 2.89999999999999985e-137 < z

   1. Initial program 69.5%

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

      1. associate-/r* 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 93.4%

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

   if -3.0000000000000002e-66 < z < 2.89999999999999985e-137

   1. Initial program 94.8%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-66} \lor \neg \left(z \leq 2.9 \cdot 10^{-137}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 2: 91.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-64} \lor \neg \left(z \leq 2.9 \cdot 10^{-137}\right):\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: 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 -1.6e-64) (not (<= z 2.9e-137)))
   (/ (+ (/ (fma x (* 9.0 y) b) z) (* t (* a -4.0))) c)
   (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(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 <= -1.6e-64) || !(z <= 2.9e-137)) {
		tmp = ((fma(x, (9.0 * y), b) / z) + (t * (a * -4.0))) / c;
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.6e-64) || !(z <= 2.9e-137))
		tmp = Float64(Float64(Float64(fma(x, Float64(9.0 * y), b) / z) + Float64(t * Float64(a * -4.0))) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: 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, -1.6e-64], N[Not[LessEqual[z, 2.9e-137]], $MachinePrecision]], N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.59999999999999988e-64 or 2.89999999999999985e-137 < z

   1. Initial program 69.5%

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

      1. associate-/r* 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 92.8%

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

   if -1.59999999999999988e-64 < z < 2.89999999999999985e-137

   1. Initial program 94.8%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-64} \lor \neg \left(z \leq 2.9 \cdot 10^{-137}\right):\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 3: 88.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ t_2 := \frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-212}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

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 (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c)))
        (t_2 (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* t a)))) (* z c))))
   (if (<= t_1 -5e-212)
     t_2
     (if (<= t_1 0.0)
       (/ (+ (* t (* a -4.0)) (/ b z)) c)
       (if (<= t_1 INFINITY) t_2 (* -4.0 (* t (/ a 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 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	double t_2 = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
	double tmp;
	if (t_1 <= -5e-212) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

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 + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	double t_2 = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
	double tmp;
	if (t_1 <= -5e-212) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = -4.0 * (t * (a / 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 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)
	t_2 = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c)
	tmp = 0
	if t_1 <= -5e-212:
		tmp = t_2
	elif t_1 <= 0.0:
		tmp = ((t * (a * -4.0)) + (b / z)) / c
	elif t_1 <= math.inf:
		tmp = t_2
	else:
		tmp = -4.0 * (t * (a / 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(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
	t_2 = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(t * a)))) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -5e-212)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c);
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / 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 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	t_2 = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
	tmp = 0.0;
	if (t_1 <= -5e-212)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = -4.0 * (t * (a / 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[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-212], t$95$2, If[LessEqual[t$95$1, 0.0], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$2, N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -5.00000000000000043e-212 or 0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 90.6%

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

      1. associate-*l* 90.6%

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

      2. associate-*l* 90.9%

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

   3. Simplified 90.9%

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

   if -5.00000000000000043e-212 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 30.2%

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

      1. associate-/r* 99.8%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 83.4%

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

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

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

      1. associate-/r* 8.2%

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

   3. Simplified 62.5%

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

   4. Taylor expanded in t around inf 62.5%

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

      1. associate-/l* 83.4%

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

      2. associate-/r/ 83.5%

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

   6. Simplified 83.5%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq -5 \cdot 10^{-212}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 4: 75.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;b \leq -3.1 \cdot 10^{-7}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;b \leq 0.106:\\ \;\;\;\;\frac{t_1 + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \end{array} \end{array} \]

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 (<= b -3.1e-7)
     (/ (+ b (* 9.0 (* x y))) (* z c))
     (if (<= b 0.106)
       (/ (+ t_1 (* 9.0 (/ y (/ z x)))) c)
       (/ (+ t_1 (/ 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) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (b <= -3.1e-7) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (b <= 0.106) {
		tmp = (t_1 + (9.0 * (y / (z / x)))) / c;
	} else {
		tmp = (t_1 + (b / 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) :: t_1
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    if (b <= (-3.1d-7)) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else if (b <= 0.106d0) then
        tmp = (t_1 + (9.0d0 * (y / (z / x)))) / c
    else
        tmp = (t_1 + (b / 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 t_1 = t * (a * -4.0);
	double tmp;
	if (b <= -3.1e-7) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (b <= 0.106) {
		tmp = (t_1 + (9.0 * (y / (z / x)))) / c;
	} else {
		tmp = (t_1 + (b / z)) / 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 b <= -3.1e-7:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	elif b <= 0.106:
		tmp = (t_1 + (9.0 * (y / (z / x)))) / c
	else:
		tmp = (t_1 + (b / z)) / 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 (b <= -3.1e-7)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	elseif (b <= 0.106)
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(y / Float64(z / x)))) / c);
	else
		tmp = Float64(Float64(t_1 + Float64(b / 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)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (b <= -3.1e-7)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	elseif (b <= 0.106)
		tmp = (t_1 + (9.0 * (y / (z / x)))) / c;
	else
		tmp = (t_1 + (b / 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_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.1e-7], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.106], N[(N[(t$95$1 + N[(9.0 * N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.1e-7

   1. Initial program 71.7%

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

      1. associate-/r* 70.5%

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

   3. Simplified 81.3%

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

   4. Taylor expanded in z around 0 65.6%

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

   if -3.1e-7 < b < 0.105999999999999997

   1. Initial program 82.9%

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

      1. associate-/r* 83.5%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in x around inf 89.1%

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

      1. associate-/l* 83.8%

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

   6. Simplified 83.8%

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

   if 0.105999999999999997 < b

   1. Initial program 76.0%

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

      1. associate-/r* 87.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in x around 0 85.6%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{-7}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;b \leq 0.106:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 5: 49.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{if}\;x \leq -4800:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.75 \cdot 10^{-175}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;x \leq 10^{-301}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-43}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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)))))
   (if (<= x -4800.0)
     t_1
     (if (<= x -4.75e-175)
       (* -4.0 (* a (/ t c)))
       (if (<= x 1e-301)
         (/ b (* z c))
         (if (<= x 1.7e-43) (* -4.0 (* t (/ a c))) t_1))))))

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 tmp;
	if (x <= -4800.0) {
		tmp = t_1;
	} else if (x <= -4.75e-175) {
		tmp = -4.0 * (a * (t / c));
	} else if (x <= 1e-301) {
		tmp = b / (z * c);
	} else if (x <= 1.7e-43) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = t_1;
	}
	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 / z) * (x / c))
    if (x <= (-4800.0d0)) then
        tmp = t_1
    else if (x <= (-4.75d-175)) then
        tmp = (-4.0d0) * (a * (t / c))
    else if (x <= 1d-301) then
        tmp = b / (z * c)
    else if (x <= 1.7d-43) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = t_1
    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 tmp;
	if (x <= -4800.0) {
		tmp = t_1;
	} else if (x <= -4.75e-175) {
		tmp = -4.0 * (a * (t / c));
	} else if (x <= 1e-301) {
		tmp = b / (z * c);
	} else if (x <= 1.7e-43) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = t_1;
	}
	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))
	tmp = 0
	if x <= -4800.0:
		tmp = t_1
	elif x <= -4.75e-175:
		tmp = -4.0 * (a * (t / c))
	elif x <= 1e-301:
		tmp = b / (z * c)
	elif x <= 1.7e-43:
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = t_1
	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 / z) * Float64(x / c)))
	tmp = 0.0
	if (x <= -4800.0)
		tmp = t_1;
	elseif (x <= -4.75e-175)
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	elseif (x <= 1e-301)
		tmp = Float64(b / Float64(z * c));
	elseif (x <= 1.7e-43)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = t_1;
	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));
	tmp = 0.0;
	if (x <= -4800.0)
		tmp = t_1;
	elseif (x <= -4.75e-175)
		tmp = -4.0 * (a * (t / c));
	elseif (x <= 1e-301)
		tmp = b / (z * c);
	elseif (x <= 1.7e-43)
		tmp = -4.0 * (t * (a / c));
	else
		tmp = t_1;
	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 / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4800.0], t$95$1, If[LessEqual[x, -4.75e-175], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e-301], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e-43], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4800 or 1.7e-43 < x

   1. Initial program 77.6%

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

      1. associate-/r* 78.4%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in x around inf 53.7%

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

      1. *-commutative 53.7%

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

      2. times-frac 54.9%

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

   6. Simplified 54.9%

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

   if -4800 < x < -4.75000000000000026e-175

   1. Initial program 81.9%

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

      1. associate-/r* 87.9%

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

   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 x around inf 61.2%

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

      1. associate-/l* 56.7%

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

   6. Simplified 56.7%

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

      1. clear-num 55.6%

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

      2. inv-pow 55.6%

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

      3. +-commutative 55.6%

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

      4. fma-def 55.6%

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

      5. associate-/r/ 55.3%

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

   8. Applied egg-rr 55.3%

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

      1. unpow-1 55.3%

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

      2. fma-udef 55.3%

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

      3. *-commutative 55.3%

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

      4. *-commutative 55.3%

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

      5. associate-*r* 55.3%

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

      6. associate-*l/ 60.1%

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

      7. +-commutative 60.1%

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

      8. fma-def 60.1%

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

      9. associate-/l* 55.6%

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

      10. associate-*r* 55.6%

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

      11. *-commutative 55.6%

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

      12. *-commutative 55.6%

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

   10. Simplified 55.6%

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

   11. Taylor expanded in y around 0 40.5%

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

       1. associate-*r/ 40.6%

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

   13. Simplified 40.6%

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

   if -4.75000000000000026e-175 < x < 1.00000000000000007e-301

   1. Initial program 88.4%

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

      1. associate-/r* 88.8%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in b around inf 59.4%

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

      1. *-commutative 59.4%

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

   6. Simplified 59.4%

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

   if 1.00000000000000007e-301 < x < 1.7e-43

   1. Initial program 72.1%

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

      1. associate-/r* 81.7%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in t around inf 54.3%

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

      1. associate-/l* 54.2%

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

      2. associate-/r/ 47.8%

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

   6. Simplified 47.8%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4800:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq -4.75 \cdot 10^{-175}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;x \leq 10^{-301}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-43}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \end{array} \]

Alternative 6: 50.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2100:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-176}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-301}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-43}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{c}{\frac{x}{z}}}\\ \end{array} \end{array} \]

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 (<= x -2100.0)
   (* 9.0 (* (/ y z) (/ x c)))
   (if (<= x -6.4e-176)
     (* -4.0 (* a (/ t c)))
     (if (<= x 4.4e-301)
       (/ b (* z c))
       (if (<= x 2e-43) (* -4.0 (* t (/ a c))) (* 9.0 (/ y (/ c (/ x 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 (x <= -2100.0) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (x <= -6.4e-176) {
		tmp = -4.0 * (a * (t / c));
	} else if (x <= 4.4e-301) {
		tmp = b / (z * c);
	} else if (x <= 2e-43) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = 9.0 * (y / (c / (x / 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 (x <= (-2100.0d0)) then
        tmp = 9.0d0 * ((y / z) * (x / c))
    else if (x <= (-6.4d-176)) then
        tmp = (-4.0d0) * (a * (t / c))
    else if (x <= 4.4d-301) then
        tmp = b / (z * c)
    else if (x <= 2d-43) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = 9.0d0 * (y / (c / (x / 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 (x <= -2100.0) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (x <= -6.4e-176) {
		tmp = -4.0 * (a * (t / c));
	} else if (x <= 4.4e-301) {
		tmp = b / (z * c);
	} else if (x <= 2e-43) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = 9.0 * (y / (c / (x / 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 x <= -2100.0:
		tmp = 9.0 * ((y / z) * (x / c))
	elif x <= -6.4e-176:
		tmp = -4.0 * (a * (t / c))
	elif x <= 4.4e-301:
		tmp = b / (z * c)
	elif x <= 2e-43:
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = 9.0 * (y / (c / (x / 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 (x <= -2100.0)
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	elseif (x <= -6.4e-176)
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	elseif (x <= 4.4e-301)
		tmp = Float64(b / Float64(z * c));
	elseif (x <= 2e-43)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(9.0 * Float64(y / Float64(c / Float64(x / 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 (x <= -2100.0)
		tmp = 9.0 * ((y / z) * (x / c));
	elseif (x <= -6.4e-176)
		tmp = -4.0 * (a * (t / c));
	elseif (x <= 4.4e-301)
		tmp = b / (z * c);
	elseif (x <= 2e-43)
		tmp = -4.0 * (t * (a / c));
	else
		tmp = 9.0 * (y / (c / (x / 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[x, -2100.0], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.4e-176], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.4e-301], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e-43], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(y / N[(c / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2100

   1. Initial program 77.5%

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

      1. associate-/r* 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 91.3%

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

   4. Taylor expanded in x around inf 60.2%

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

      1. *-commutative 60.2%

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

      2. times-frac 61.3%

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

   6. Simplified 61.3%

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

   if -2100 < x < -6.39999999999999969e-176

   1. Initial program 81.9%

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

      1. associate-/r* 87.9%

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

   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 x around inf 61.2%

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

      1. associate-/l* 56.7%

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

   6. Simplified 56.7%

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

      1. clear-num 55.6%

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

      2. inv-pow 55.6%

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

      3. +-commutative 55.6%

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

      4. fma-def 55.6%

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

      5. associate-/r/ 55.3%

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

   8. Applied egg-rr 55.3%

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

      1. unpow-1 55.3%

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

      2. fma-udef 55.3%

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

      3. *-commutative 55.3%

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

      4. *-commutative 55.3%

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

      5. associate-*r* 55.3%

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

      6. associate-*l/ 60.1%

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

      7. +-commutative 60.1%

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

      8. fma-def 60.1%

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

      9. associate-/l* 55.6%

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

      10. associate-*r* 55.6%

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

      11. *-commutative 55.6%

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

      12. *-commutative 55.6%

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

   10. Simplified 55.6%

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

   11. Taylor expanded in y around 0 40.5%

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

       1. associate-*r/ 40.6%

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

   13. Simplified 40.6%

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

   if -6.39999999999999969e-176 < x < 4.4e-301

   1. Initial program 88.4%

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

      1. associate-/r* 88.8%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in b around inf 59.4%

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

      1. *-commutative 59.4%

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

   6. Simplified 59.4%

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

   if 4.4e-301 < x < 2.00000000000000015e-43

   1. Initial program 72.1%

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

      1. associate-/r* 81.7%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in t around inf 54.3%

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

      1. associate-/l* 54.2%

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

      2. associate-/r/ 47.8%

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

   6. Simplified 47.8%

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

   if 2.00000000000000015e-43 < x

   1. Initial program 77.6%

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

      1. associate-/r* 76.9%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in x around inf 48.4%

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

      1. associate-/l* 48.5%

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

      2. *-commutative 48.5%

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

   6. Simplified 48.5%

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

   7. Taylor expanded in z around 0 48.5%

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

      1. associate-/l* 46.1%

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

   9. Simplified 46.1%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2100:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-176}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-301}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-43}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{c}{\frac{x}{z}}}\\ \end{array} \]

Alternative 7: 50.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+73}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;x \leq -3.45 \cdot 10^{-175}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-302}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-42}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{c}{\frac{x}{z}}}\\ \end{array} \end{array} \]

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 (<= x -4.4e+73)
   (* 9.0 (/ y (/ (* z c) x)))
   (if (<= x -3.45e-175)
     (* -4.0 (* a (/ t c)))
     (if (<= x 7.2e-302)
       (/ b (* z c))
       (if (<= x 2.3e-42)
         (* -4.0 (* t (/ a c)))
         (* 9.0 (/ y (/ c (/ x 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 (x <= -4.4e+73) {
		tmp = 9.0 * (y / ((z * c) / x));
	} else if (x <= -3.45e-175) {
		tmp = -4.0 * (a * (t / c));
	} else if (x <= 7.2e-302) {
		tmp = b / (z * c);
	} else if (x <= 2.3e-42) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = 9.0 * (y / (c / (x / 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 (x <= (-4.4d+73)) then
        tmp = 9.0d0 * (y / ((z * c) / x))
    else if (x <= (-3.45d-175)) then
        tmp = (-4.0d0) * (a * (t / c))
    else if (x <= 7.2d-302) then
        tmp = b / (z * c)
    else if (x <= 2.3d-42) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = 9.0d0 * (y / (c / (x / 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 (x <= -4.4e+73) {
		tmp = 9.0 * (y / ((z * c) / x));
	} else if (x <= -3.45e-175) {
		tmp = -4.0 * (a * (t / c));
	} else if (x <= 7.2e-302) {
		tmp = b / (z * c);
	} else if (x <= 2.3e-42) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = 9.0 * (y / (c / (x / 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 x <= -4.4e+73:
		tmp = 9.0 * (y / ((z * c) / x))
	elif x <= -3.45e-175:
		tmp = -4.0 * (a * (t / c))
	elif x <= 7.2e-302:
		tmp = b / (z * c)
	elif x <= 2.3e-42:
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = 9.0 * (y / (c / (x / 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 (x <= -4.4e+73)
		tmp = Float64(9.0 * Float64(y / Float64(Float64(z * c) / x)));
	elseif (x <= -3.45e-175)
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	elseif (x <= 7.2e-302)
		tmp = Float64(b / Float64(z * c));
	elseif (x <= 2.3e-42)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(9.0 * Float64(y / Float64(c / Float64(x / 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 (x <= -4.4e+73)
		tmp = 9.0 * (y / ((z * c) / x));
	elseif (x <= -3.45e-175)
		tmp = -4.0 * (a * (t / c));
	elseif (x <= 7.2e-302)
		tmp = b / (z * c);
	elseif (x <= 2.3e-42)
		tmp = -4.0 * (t * (a / c));
	else
		tmp = 9.0 * (y / (c / (x / 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[x, -4.4e+73], N[(9.0 * N[(y / N[(N[(z * c), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.45e-175], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.2e-302], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e-42], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(y / N[(c / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.4e73

   1. Initial program 75.6%

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

      1. associate-/r* 77.4%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in x around inf 61.2%

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

      1. associate-/l* 64.6%

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

      2. *-commutative 64.6%

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

   6. Simplified 64.6%

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

   if -4.4e73 < x < -3.4500000000000003e-175

   1. Initial program 82.8%

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

      1. associate-/r* 89.0%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in x around inf 65.3%

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

      1. associate-/l* 61.9%

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

   6. Simplified 61.9%

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

      1. clear-num 61.1%

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

      2. inv-pow 61.1%

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

      3. +-commutative 61.1%

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

      4. fma-def 61.1%

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

      5. associate-/r/ 60.9%

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

   8. Applied egg-rr 60.9%

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

      1. unpow-1 60.9%

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

      2. fma-udef 60.9%

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

      3. *-commutative 60.9%

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

      4. *-commutative 60.9%

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

      5. associate-*r* 60.9%

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

      6. associate-*l/ 64.6%

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

      7. +-commutative 64.6%

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

      8. fma-def 64.6%

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

      9. associate-/l* 61.1%

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

      10. associate-*r* 61.1%

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

      11. *-commutative 61.1%

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

      12. *-commutative 61.1%

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

   10. Simplified 61.1%

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

   11. Taylor expanded in y around 0 37.0%

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

       1. associate-*r/ 38.8%

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

   13. Simplified 38.8%

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

   if -3.4500000000000003e-175 < x < 7.2000000000000001e-302

   1. Initial program 88.4%

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

      1. associate-/r* 88.8%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in b around inf 59.4%

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

      1. *-commutative 59.4%

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

   6. Simplified 59.4%

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

   if 7.2000000000000001e-302 < x < 2.30000000000000004e-42

   1. Initial program 72.1%

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

      1. associate-/r* 81.7%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in t around inf 54.3%

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

      1. associate-/l* 54.2%

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

      2. associate-/r/ 47.8%

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

   6. Simplified 47.8%

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

   if 2.30000000000000004e-42 < x

   1. Initial program 77.6%

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

      1. associate-/r* 76.9%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in x around inf 48.4%

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

      1. associate-/l* 48.5%

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

      2. *-commutative 48.5%

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

   6. Simplified 48.5%

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

   7. Taylor expanded in z around 0 48.5%

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

      1. associate-/l* 46.1%

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

   9. Simplified 46.1%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+73}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;x \leq -3.45 \cdot 10^{-175}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-302}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-42}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{c}{\frac{x}{z}}}\\ \end{array} \]

Alternative 8: 50.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+74}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{-176}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-303}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-43}:\\ \;\;\;\;\frac{1}{-0.25 \cdot \frac{\frac{c}{a}}{t}}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{c}{\frac{x}{z}}}\\ \end{array} \end{array} \]

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 (<= x -1.55e+74)
   (* 9.0 (/ y (/ (* z c) x)))
   (if (<= x -9.6e-176)
     (* -4.0 (* a (/ t c)))
     (if (<= x 4.4e-303)
       (/ b (* z c))
       (if (<= x 6e-43)
         (/ 1.0 (* -0.25 (/ (/ c a) t)))
         (* 9.0 (/ y (/ c (/ x 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 (x <= -1.55e+74) {
		tmp = 9.0 * (y / ((z * c) / x));
	} else if (x <= -9.6e-176) {
		tmp = -4.0 * (a * (t / c));
	} else if (x <= 4.4e-303) {
		tmp = b / (z * c);
	} else if (x <= 6e-43) {
		tmp = 1.0 / (-0.25 * ((c / a) / t));
	} else {
		tmp = 9.0 * (y / (c / (x / 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 (x <= (-1.55d+74)) then
        tmp = 9.0d0 * (y / ((z * c) / x))
    else if (x <= (-9.6d-176)) then
        tmp = (-4.0d0) * (a * (t / c))
    else if (x <= 4.4d-303) then
        tmp = b / (z * c)
    else if (x <= 6d-43) then
        tmp = 1.0d0 / ((-0.25d0) * ((c / a) / t))
    else
        tmp = 9.0d0 * (y / (c / (x / 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 (x <= -1.55e+74) {
		tmp = 9.0 * (y / ((z * c) / x));
	} else if (x <= -9.6e-176) {
		tmp = -4.0 * (a * (t / c));
	} else if (x <= 4.4e-303) {
		tmp = b / (z * c);
	} else if (x <= 6e-43) {
		tmp = 1.0 / (-0.25 * ((c / a) / t));
	} else {
		tmp = 9.0 * (y / (c / (x / 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 x <= -1.55e+74:
		tmp = 9.0 * (y / ((z * c) / x))
	elif x <= -9.6e-176:
		tmp = -4.0 * (a * (t / c))
	elif x <= 4.4e-303:
		tmp = b / (z * c)
	elif x <= 6e-43:
		tmp = 1.0 / (-0.25 * ((c / a) / t))
	else:
		tmp = 9.0 * (y / (c / (x / 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 (x <= -1.55e+74)
		tmp = Float64(9.0 * Float64(y / Float64(Float64(z * c) / x)));
	elseif (x <= -9.6e-176)
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	elseif (x <= 4.4e-303)
		tmp = Float64(b / Float64(z * c));
	elseif (x <= 6e-43)
		tmp = Float64(1.0 / Float64(-0.25 * Float64(Float64(c / a) / t)));
	else
		tmp = Float64(9.0 * Float64(y / Float64(c / Float64(x / 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 (x <= -1.55e+74)
		tmp = 9.0 * (y / ((z * c) / x));
	elseif (x <= -9.6e-176)
		tmp = -4.0 * (a * (t / c));
	elseif (x <= 4.4e-303)
		tmp = b / (z * c);
	elseif (x <= 6e-43)
		tmp = 1.0 / (-0.25 * ((c / a) / t));
	else
		tmp = 9.0 * (y / (c / (x / 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[x, -1.55e+74], N[(9.0 * N[(y / N[(N[(z * c), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9.6e-176], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.4e-303], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e-43], N[(1.0 / N[(-0.25 * N[(N[(c / a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(y / N[(c / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.55000000000000011e74

   1. Initial program 75.6%

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

      1. associate-/r* 77.4%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in x around inf 61.2%

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

      1. associate-/l* 64.6%

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

      2. *-commutative 64.6%

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

   6. Simplified 64.6%

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

   if -1.55000000000000011e74 < x < -9.60000000000000024e-176

   1. Initial program 82.8%

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

      1. associate-/r* 89.0%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in x around inf 65.3%

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

      1. associate-/l* 61.9%

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

   6. Simplified 61.9%

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

      1. clear-num 61.1%

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

      2. inv-pow 61.1%

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

      3. +-commutative 61.1%

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

      4. fma-def 61.1%

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

      5. associate-/r/ 60.9%

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

   8. Applied egg-rr 60.9%

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

      1. unpow-1 60.9%

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

      2. fma-udef 60.9%

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

      3. *-commutative 60.9%

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

      4. *-commutative 60.9%

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

      5. associate-*r* 60.9%

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

      6. associate-*l/ 64.6%

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

      7. +-commutative 64.6%

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

      8. fma-def 64.6%

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

      9. associate-/l* 61.1%

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

      10. associate-*r* 61.1%

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

      11. *-commutative 61.1%

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

      12. *-commutative 61.1%

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

   10. Simplified 61.1%

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

   11. Taylor expanded in y around 0 37.0%

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

       1. associate-*r/ 38.8%

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

   13. Simplified 38.8%

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

   if -9.60000000000000024e-176 < x < 4.40000000000000028e-303

   1. Initial program 88.4%

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

      1. associate-/r* 88.8%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in b around inf 59.4%

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

      1. *-commutative 59.4%

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

   6. Simplified 59.4%

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

   if 4.40000000000000028e-303 < x < 6.00000000000000007e-43

   1. Initial program 72.1%

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

      1. associate-/r* 81.7%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in x around inf 69.4%

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

      1. associate-/l* 67.1%

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

   6. Simplified 67.1%

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

      1. clear-num 67.2%

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

      2. inv-pow 67.2%

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

      3. +-commutative 67.2%

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

      4. fma-def 67.2%

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

      5. associate-/r/ 62.3%

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

   8. Applied egg-rr 62.3%

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

      1. unpow-1 62.3%

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

      2. fma-udef 62.3%

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

      3. *-commutative 62.3%

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

      4. *-commutative 62.3%

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

      5. associate-*r* 62.3%

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

      6. associate-*l/ 69.5%

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

      7. +-commutative 69.5%

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

      8. fma-def 69.5%

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

      9. associate-/l* 67.2%

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

      10. associate-*r* 67.2%

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

      11. *-commutative 67.2%

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

      12. *-commutative 67.2%

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

   10. Simplified 67.2%

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

   11. Taylor expanded in y around 0 54.4%

       \[\leadsto \frac{1}{\color{blue}{-0.25 \cdot \frac{c}{a \cdot t}}} \]
   12. Step-by-step derivation

       1. associate-/r* 50.2%

          \[\leadsto \frac{1}{-0.25 \cdot \color{blue}{\frac{\frac{c}{a}}{t}}} \]

   13. Simplified 50.2%

       \[\leadsto \frac{1}{\color{blue}{-0.25 \cdot \frac{\frac{c}{a}}{t}}} \]

   if 6.00000000000000007e-43 < x

   1. Initial program 77.6%

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

      1. associate-/r* 76.9%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in x around inf 48.4%

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

      1. associate-/l* 48.5%

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

      2. *-commutative 48.5%

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

   6. Simplified 48.5%

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

   7. Taylor expanded in z around 0 48.5%

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

      1. associate-/l* 46.1%

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

   9. Simplified 46.1%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+74}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{-176}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-303}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-43}:\\ \;\;\;\;\frac{1}{-0.25 \cdot \frac{\frac{c}{a}}{t}}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{c}{\frac{x}{z}}}\\ \end{array} \]

Alternative 9: 50.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-91}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-218}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{b}{c}}}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+23}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{0.1111111111111111}{x} \cdot \frac{z}{\frac{y}{c}}}\\ \end{array} \end{array} \]

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 (<= y -1.85e-91)
   (/ (* 9.0 (/ y (/ z x))) c)
   (if (<= y 8.5e-218)
     (/ 1.0 (/ z (/ b c)))
     (if (<= y 7.2e+23)
       (* -4.0 (/ a (/ c t)))
       (/ 1.0 (* (/ 0.1111111111111111 x) (/ z (/ y 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 (y <= -1.85e-91) {
		tmp = (9.0 * (y / (z / x))) / c;
	} else if (y <= 8.5e-218) {
		tmp = 1.0 / (z / (b / c));
	} else if (y <= 7.2e+23) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = 1.0 / ((0.1111111111111111 / x) * (z / (y / 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 (y <= (-1.85d-91)) then
        tmp = (9.0d0 * (y / (z / x))) / c
    else if (y <= 8.5d-218) then
        tmp = 1.0d0 / (z / (b / c))
    else if (y <= 7.2d+23) then
        tmp = (-4.0d0) * (a / (c / t))
    else
        tmp = 1.0d0 / ((0.1111111111111111d0 / x) * (z / (y / 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 (y <= -1.85e-91) {
		tmp = (9.0 * (y / (z / x))) / c;
	} else if (y <= 8.5e-218) {
		tmp = 1.0 / (z / (b / c));
	} else if (y <= 7.2e+23) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = 1.0 / ((0.1111111111111111 / x) * (z / (y / 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 y <= -1.85e-91:
		tmp = (9.0 * (y / (z / x))) / c
	elif y <= 8.5e-218:
		tmp = 1.0 / (z / (b / c))
	elif y <= 7.2e+23:
		tmp = -4.0 * (a / (c / t))
	else:
		tmp = 1.0 / ((0.1111111111111111 / x) * (z / (y / 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 (y <= -1.85e-91)
		tmp = Float64(Float64(9.0 * Float64(y / Float64(z / x))) / c);
	elseif (y <= 8.5e-218)
		tmp = Float64(1.0 / Float64(z / Float64(b / c)));
	elseif (y <= 7.2e+23)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	else
		tmp = Float64(1.0 / Float64(Float64(0.1111111111111111 / x) * Float64(z / Float64(y / 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 (y <= -1.85e-91)
		tmp = (9.0 * (y / (z / x))) / c;
	elseif (y <= 8.5e-218)
		tmp = 1.0 / (z / (b / c));
	elseif (y <= 7.2e+23)
		tmp = -4.0 * (a / (c / t));
	else
		tmp = 1.0 / ((0.1111111111111111 / x) * (z / (y / 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[y, -1.85e-91], N[(N[(9.0 * N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[y, 8.5e-218], N[(1.0 / N[(z / N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+23], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(0.1111111111111111 / x), $MachinePrecision] * N[(z / N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.8500000000000001e-91

   1. Initial program 78.5%

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

      1. associate-/r* 82.9%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in x around inf 77.7%

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

      1. associate-/l* 79.1%

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

   6. Simplified 79.1%

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

   7. Taylor expanded in y around inf 62.7%

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

      1. associate-/l* 63.1%

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

   9. Simplified 63.1%

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

   if -1.8500000000000001e-91 < y < 8.5000000000000004e-218

   1. Initial program 78.7%

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

      1. associate-/r* 79.1%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in b around inf 53.7%

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

      1. *-commutative 53.7%

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

   6. Simplified 53.7%

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

      1. clear-num 53.6%

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

      2. inv-pow 53.6%

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

   8. Applied egg-rr 53.6%

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

      1. unpow-1 53.6%

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

      2. associate-/l* 56.4%

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

   10. Simplified 56.4%

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

   if 8.5000000000000004e-218 < y < 7.1999999999999997e23

   1. Initial program 77.5%

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

      1. associate-/r* 81.1%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in t around inf 55.3%

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

      1. associate-/l* 53.8%

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

   6. Simplified 53.8%

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

   if 7.1999999999999997e23 < y

   1. Initial program 78.5%

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

      1. associate-/r* 81.9%

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

   3. Simplified 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 x around inf 72.9%

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

      1. associate-/l* 71.4%

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

   6. Simplified 71.4%

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

      1. clear-num 71.4%

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

      2. inv-pow 71.4%

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

      3. +-commutative 71.4%

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

      4. fma-def 73.1%

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

      5. associate-/r/ 68.0%

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

   8. Applied egg-rr 68.0%

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

      1. unpow-1 68.0%

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

      2. fma-udef 66.3%

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

      3. *-commutative 66.3%

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

      4. *-commutative 66.3%

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

      5. associate-*r* 66.3%

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

      6. associate-*l/ 72.9%

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

      7. +-commutative 72.9%

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

      8. fma-def 72.9%

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

      9. associate-/l* 71.4%

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

      10. associate-*r* 71.4%

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

      11. *-commutative 71.4%

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

      12. *-commutative 71.4%

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

   10. Simplified 71.4%

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

   11. Taylor expanded in y around inf 53.9%

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

       1. associate-*r/ 53.9%

          \[\leadsto \frac{1}{\color{blue}{\frac{0.1111111111111111 \cdot \left(c \cdot z\right)}{y \cdot x}}} \]

       2. *-commutative 53.9%

          \[\leadsto \frac{1}{\frac{0.1111111111111111 \cdot \left(c \cdot z\right)}{\color{blue}{x \cdot y}}} \]

       3. times-frac 57.2%

          \[\leadsto \frac{1}{\color{blue}{\frac{0.1111111111111111}{x} \cdot \frac{c \cdot z}{y}}} \]

       4. *-commutative 57.2%

          \[\leadsto \frac{1}{\frac{0.1111111111111111}{x} \cdot \frac{\color{blue}{z \cdot c}}{y}} \]

       5. associate-/l* 62.1%

          \[\leadsto \frac{1}{\frac{0.1111111111111111}{x} \cdot \color{blue}{\frac{z}{\frac{y}{c}}}} \]

   13. Simplified 62.1%

       \[\leadsto \frac{1}{\color{blue}{\frac{0.1111111111111111}{x} \cdot \frac{z}{\frac{y}{c}}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-91}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-218}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{b}{c}}}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+23}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{0.1111111111111111}{x} \cdot \frac{z}{\frac{y}{c}}}\\ \end{array} \]

Alternative 10: 50.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-96}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-217}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{b}{c}}}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+23}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{0.1111111111111111}{x \cdot \frac{\frac{y}{c}}{z}}}\\ \end{array} \end{array} \]

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 (<= y -1e-96)
   (/ (* 9.0 (/ y (/ z x))) c)
   (if (<= y 1.02e-217)
     (/ 1.0 (/ z (/ b c)))
     (if (<= y 2.35e+23)
       (* -4.0 (/ a (/ c t)))
       (/ 1.0 (/ 0.1111111111111111 (* x (/ (/ y 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 (y <= -1e-96) {
		tmp = (9.0 * (y / (z / x))) / c;
	} else if (y <= 1.02e-217) {
		tmp = 1.0 / (z / (b / c));
	} else if (y <= 2.35e+23) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = 1.0 / (0.1111111111111111 / (x * ((y / 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 (y <= (-1d-96)) then
        tmp = (9.0d0 * (y / (z / x))) / c
    else if (y <= 1.02d-217) then
        tmp = 1.0d0 / (z / (b / c))
    else if (y <= 2.35d+23) then
        tmp = (-4.0d0) * (a / (c / t))
    else
        tmp = 1.0d0 / (0.1111111111111111d0 / (x * ((y / 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 (y <= -1e-96) {
		tmp = (9.0 * (y / (z / x))) / c;
	} else if (y <= 1.02e-217) {
		tmp = 1.0 / (z / (b / c));
	} else if (y <= 2.35e+23) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = 1.0 / (0.1111111111111111 / (x * ((y / 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 y <= -1e-96:
		tmp = (9.0 * (y / (z / x))) / c
	elif y <= 1.02e-217:
		tmp = 1.0 / (z / (b / c))
	elif y <= 2.35e+23:
		tmp = -4.0 * (a / (c / t))
	else:
		tmp = 1.0 / (0.1111111111111111 / (x * ((y / 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 (y <= -1e-96)
		tmp = Float64(Float64(9.0 * Float64(y / Float64(z / x))) / c);
	elseif (y <= 1.02e-217)
		tmp = Float64(1.0 / Float64(z / Float64(b / c)));
	elseif (y <= 2.35e+23)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	else
		tmp = Float64(1.0 / Float64(0.1111111111111111 / Float64(x * Float64(Float64(y / 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 (y <= -1e-96)
		tmp = (9.0 * (y / (z / x))) / c;
	elseif (y <= 1.02e-217)
		tmp = 1.0 / (z / (b / c));
	elseif (y <= 2.35e+23)
		tmp = -4.0 * (a / (c / t));
	else
		tmp = 1.0 / (0.1111111111111111 / (x * ((y / 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[LessEqual[y, -1e-96], N[(N[(9.0 * N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[y, 1.02e-217], N[(1.0 / N[(z / N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.35e+23], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(0.1111111111111111 / N[(x * N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.9999999999999991e-97

   1. Initial program 78.5%

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

      1. associate-/r* 82.9%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in x around inf 77.7%

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

      1. associate-/l* 79.1%

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

   6. Simplified 79.1%

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

   7. Taylor expanded in y around inf 62.7%

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

      1. associate-/l* 63.1%

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

   9. Simplified 63.1%

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

   if -9.9999999999999991e-97 < y < 1.02e-217

   1. Initial program 78.7%

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

      1. associate-/r* 79.1%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in b around inf 53.7%

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

      1. *-commutative 53.7%

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

   6. Simplified 53.7%

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

      1. clear-num 53.6%

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

      2. inv-pow 53.6%

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

   8. Applied egg-rr 53.6%

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

      1. unpow-1 53.6%

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

      2. associate-/l* 56.4%

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

   10. Simplified 56.4%

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

   if 1.02e-217 < y < 2.3499999999999999e23

   1. Initial program 77.5%

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

      1. associate-/r* 81.1%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in t around inf 55.3%

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

      1. associate-/l* 53.8%

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

   6. Simplified 53.8%

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

   if 2.3499999999999999e23 < y

   1. Initial program 78.5%

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

      1. associate-/r* 81.9%

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

   3. Simplified 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 x around inf 72.9%

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

      1. associate-/l* 71.4%

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

   6. Simplified 71.4%

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

      1. clear-num 71.4%

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

      2. inv-pow 71.4%

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

      3. +-commutative 71.4%

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

      4. fma-def 73.1%

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

      5. associate-/r/ 68.0%

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

   8. Applied egg-rr 68.0%

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

      1. unpow-1 68.0%

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

      2. fma-udef 66.3%

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

      3. *-commutative 66.3%

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

      4. *-commutative 66.3%

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

      5. associate-*r* 66.3%

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

      6. associate-*l/ 72.9%

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

      7. +-commutative 72.9%

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

      8. fma-def 72.9%

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

      9. associate-/l* 71.4%

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

      10. associate-*r* 71.4%

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

      11. *-commutative 71.4%

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

      12. *-commutative 71.4%

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

   10. Simplified 71.4%

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

   11. Taylor expanded in y around inf 53.9%

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

       1. associate-*r/ 53.9%

          \[\leadsto \frac{1}{\color{blue}{\frac{0.1111111111111111 \cdot \left(c \cdot z\right)}{y \cdot x}}} \]

       2. *-commutative 53.9%

          \[\leadsto \frac{1}{\frac{0.1111111111111111 \cdot \left(c \cdot z\right)}{\color{blue}{x \cdot y}}} \]

       3. times-frac 57.2%

          \[\leadsto \frac{1}{\color{blue}{\frac{0.1111111111111111}{x} \cdot \frac{c \cdot z}{y}}} \]

       4. *-commutative 57.2%

          \[\leadsto \frac{1}{\frac{0.1111111111111111}{x} \cdot \frac{\color{blue}{z \cdot c}}{y}} \]

       5. associate-/l* 62.1%

          \[\leadsto \frac{1}{\frac{0.1111111111111111}{x} \cdot \color{blue}{\frac{z}{\frac{y}{c}}}} \]

   13. Simplified 62.1%

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

       1. *-commutative 62.1%

          \[\leadsto \frac{1}{\color{blue}{\frac{z}{\frac{y}{c}} \cdot \frac{0.1111111111111111}{x}}} \]

       2. clear-num 63.6%

          \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{\frac{y}{c}}{z}}} \cdot \frac{0.1111111111111111}{x}} \]

       3. frac-times 63.8%

          \[\leadsto \frac{1}{\color{blue}{\frac{1 \cdot 0.1111111111111111}{\frac{\frac{y}{c}}{z} \cdot x}}} \]

       4. metadata-eval 63.8%

          \[\leadsto \frac{1}{\frac{\color{blue}{0.1111111111111111}}{\frac{\frac{y}{c}}{z} \cdot x}} \]

   15. Applied egg-rr 63.8%

       \[\leadsto \frac{1}{\color{blue}{\frac{0.1111111111111111}{\frac{\frac{y}{c}}{z} \cdot x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-96}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-217}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{b}{c}}}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+23}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{0.1111111111111111}{x \cdot \frac{\frac{y}{c}}{z}}}\\ \end{array} \]

Alternative 11: 74.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+147} \lor \neg \left(z \leq 106\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: 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 -4.9e+147) (not (<= z 106.0)))
   (/ (+ (* t (* a -4.0)) (/ b z)) 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 <= -4.9e+147) || !(z <= 106.0)) {
		tmp = ((t * (a * -4.0)) + (b / z)) / 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 <= (-4.9d+147)) .or. (.not. (z <= 106.0d0))) then
        tmp = ((t * (a * (-4.0d0))) + (b / z)) / c
    else
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    end if
    code = tmp
end function

Java

assert 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 <= -4.9e+147) || !(z <= 106.0)) {
		tmp = ((t * (a * -4.0)) + (b / z)) / 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 <= -4.9e+147) or not (z <= 106.0):
		tmp = ((t * (a * -4.0)) + (b / z)) / 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 <= -4.9e+147) || !(z <= 106.0))
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	end
	return tmp
end

MATLAB

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 <= -4.9e+147) || ~((z <= 106.0)))
		tmp = ((t * (a * -4.0)) + (b / z)) / 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, -4.9e+147], N[Not[LessEqual[z, 106.0]], $MachinePrecision]], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8999999999999998e147 or 106 < z

   1. Initial program 57.5%

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

      1. associate-/r* 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 92.1%

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

   4. Taylor expanded in x around 0 80.5%

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

   if -4.8999999999999998e147 < z < 106

   1. Initial program 91.9%

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

      1. associate-/r* 87.2%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in z around 0 78.9%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+147} \lor \neg \left(z \leq 106\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 12: 67.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+152}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+146}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

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 -4.1e+152)
   (/ (* -4.0 (* t a)) c)
   (if (<= z 3.8e+146)
     (/ (+ b (* 9.0 (* x y))) (* z c))
     (* -4.0 (* a (/ t 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 <= -4.1e+152) {
		tmp = (-4.0 * (t * a)) / c;
	} else if (z <= 3.8e+146) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = -4.0 * (a * (t / 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 <= (-4.1d+152)) then
        tmp = ((-4.0d0) * (t * a)) / c
    else if (z <= 3.8d+146) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else
        tmp = (-4.0d0) * (a * (t / 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 <= -4.1e+152) {
		tmp = (-4.0 * (t * a)) / c;
	} else if (z <= 3.8e+146) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = -4.0 * (a * (t / 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 <= -4.1e+152:
		tmp = (-4.0 * (t * a)) / c
	elif z <= 3.8e+146:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = -4.0 * (a * (t / 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 <= -4.1e+152)
		tmp = Float64(Float64(-4.0 * Float64(t * a)) / c);
	elseif (z <= 3.8e+146)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(a * Float64(t / 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 <= -4.1e+152)
		tmp = (-4.0 * (t * a)) / c;
	elseif (z <= 3.8e+146)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = -4.0 * (a * (t / 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, -4.1e+152], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 3.8e+146], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0999999999999998e152

   1. Initial program 36.9%

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

      1. associate-/r* 58.7%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in t around inf 65.0%

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

   if -4.0999999999999998e152 < z < 3.79999999999999979e146

   1. Initial program 90.1%

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

      1. associate-/r* 87.8%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in z around 0 74.7%

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

   if 3.79999999999999979e146 < z

   1. Initial program 56.0%

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

      1. associate-/r* 69.0%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in x around inf 72.9%

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

      1. associate-/l* 76.1%

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

   6. Simplified 76.1%

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

      1. clear-num 74.9%

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

      2. inv-pow 74.9%

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

      3. +-commutative 74.9%

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

      4. fma-def 74.9%

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

      5. associate-/r/ 76.0%

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

   8. Applied egg-rr 76.0%

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

      1. unpow-1 76.0%

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

      2. fma-udef 76.0%

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

      3. *-commutative 76.0%

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

      4. *-commutative 76.0%

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

      5. associate-*r* 76.0%

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

      6. associate-*l/ 71.7%

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

      7. +-commutative 71.7%

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

      8. fma-def 71.7%

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

      9. associate-/l* 74.9%

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

      10. associate-*r* 74.9%

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

      11. *-commutative 74.9%

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

      12. *-commutative 74.9%

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

   10. Simplified 74.9%

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

   11. Taylor expanded in y around 0 57.8%

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

       1. associate-*r/ 66.3%

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

   13. Simplified 66.3%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+152}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+146}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 13: 51.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+23} \lor \neg \left(t \leq 1.06 \cdot 10^{-69}\right):\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \end{array} \]

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 (<= t -1.3e+23) (not (<= t 1.06e-69)))
   (* -4.0 (* a (/ t c)))
   (/ (/ 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) {
	double tmp;
	if ((t <= -1.3e+23) || !(t <= 1.06e-69)) {
		tmp = -4.0 * (a * (t / c));
	} else {
		tmp = (b / 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 ((t <= (-1.3d+23)) .or. (.not. (t <= 1.06d-69))) then
        tmp = (-4.0d0) * (a * (t / c))
    else
        tmp = (b / 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 ((t <= -1.3e+23) || !(t <= 1.06e-69)) {
		tmp = -4.0 * (a * (t / c));
	} else {
		tmp = (b / 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 (t <= -1.3e+23) or not (t <= 1.06e-69):
		tmp = -4.0 * (a * (t / c))
	else:
		tmp = (b / 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 ((t <= -1.3e+23) || !(t <= 1.06e-69))
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	else
		tmp = Float64(Float64(b / 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 ((t <= -1.3e+23) || ~((t <= 1.06e-69)))
		tmp = -4.0 * (a * (t / c));
	else
		tmp = (b / 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[t, -1.3e+23], N[Not[LessEqual[t, 1.06e-69]], $MachinePrecision]], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.29999999999999996e23 or 1.05999999999999997e-69 < t

   1. Initial program 72.5%

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

      1. associate-/r* 73.1%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in x around inf 72.7%

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

      1. associate-/l* 71.9%

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

   6. Simplified 71.9%

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

      1. clear-num 71.8%

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

      2. inv-pow 71.8%

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

      3. +-commutative 71.8%

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

      4. fma-def 73.3%

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

      5. associate-/r/ 73.4%

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

   8. Applied egg-rr 73.4%

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

      1. unpow-1 73.4%

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

      2. fma-udef 71.9%

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

      3. *-commutative 71.9%

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

      4. *-commutative 71.9%

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

      5. associate-*r* 71.9%

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

      6. associate-*l/ 72.6%

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

      7. +-commutative 72.6%

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

      8. fma-def 72.6%

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

      9. associate-/l* 71.8%

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

      10. associate-*r* 71.8%

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

      11. *-commutative 71.8%

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

      12. *-commutative 71.8%

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

   10. Simplified 71.8%

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

   11. Taylor expanded in y around 0 55.6%

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

       1. associate-*r/ 59.2%

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

   13. Simplified 59.2%

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

   if -1.29999999999999996e23 < t < 1.05999999999999997e-69

   1. Initial program 84.5%

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

      1. associate-/r* 90.1%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in x around 0 53.8%

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

   5. Taylor expanded in b around inf 41.2%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+23} \lor \neg \left(t \leq 1.06 \cdot 10^{-69}\right):\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 14: 49.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+102}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{-69}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

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 (<= t -1.55e+102)
   (* -4.0 (* t (/ a c)))
   (if (<= t 2.85e-69) (/ (/ b z) c) (* -4.0 (* a (/ t 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 (t <= -1.55e+102) {
		tmp = -4.0 * (t * (a / c));
	} else if (t <= 2.85e-69) {
		tmp = (b / z) / c;
	} else {
		tmp = -4.0 * (a * (t / 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 (t <= (-1.55d+102)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (t <= 2.85d-69) then
        tmp = (b / z) / c
    else
        tmp = (-4.0d0) * (a * (t / 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 (t <= -1.55e+102) {
		tmp = -4.0 * (t * (a / c));
	} else if (t <= 2.85e-69) {
		tmp = (b / z) / c;
	} else {
		tmp = -4.0 * (a * (t / 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 t <= -1.55e+102:
		tmp = -4.0 * (t * (a / c))
	elif t <= 2.85e-69:
		tmp = (b / z) / c
	else:
		tmp = -4.0 * (a * (t / 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 (t <= -1.55e+102)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (t <= 2.85e-69)
		tmp = Float64(Float64(b / z) / c);
	else
		tmp = Float64(-4.0 * Float64(a * Float64(t / 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 (t <= -1.55e+102)
		tmp = -4.0 * (t * (a / c));
	elseif (t <= 2.85e-69)
		tmp = (b / z) / c;
	else
		tmp = -4.0 * (a * (t / 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[t, -1.55e+102], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.85e-69], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.54999999999999993e102

   1. Initial program 70.3%

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

      1. associate-/r* 67.2%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in t around inf 60.8%

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

      1. associate-/l* 60.8%

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

      2. associate-/r/ 62.3%

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

   6. Simplified 62.3%

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

   if -1.54999999999999993e102 < t < 2.85e-69

   1. Initial program 84.3%

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

      1. associate-/r* 90.6%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in x around 0 55.9%

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

   5. Taylor expanded in b around inf 41.4%

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

   if 2.85e-69 < t

   1. Initial program 71.5%

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

      1. associate-/r* 72.1%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in x around inf 71.7%

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

      1. associate-/l* 68.5%

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

   6. Simplified 68.5%

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

      1. clear-num 68.4%

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

      2. inv-pow 68.5%

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

      3. +-commutative 68.5%

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

      4. fma-def 68.5%

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

      5. associate-/r/ 70.0%

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

   8. Applied egg-rr 70.0%

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

      1. unpow-1 70.0%

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

      2. fma-udef 70.0%

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

      3. *-commutative 70.0%

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

      4. *-commutative 70.0%

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

      5. associate-*r* 70.0%

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

      6. associate-*l/ 71.6%

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

      7. +-commutative 71.6%

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

      8. fma-def 71.6%

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

      9. associate-/l* 68.4%

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

      10. associate-*r* 68.4%

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

      11. *-commutative 68.4%

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

      12. *-commutative 68.4%

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

   10. Simplified 68.4%

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

   11. Taylor expanded in y around 0 54.8%

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

       1. associate-*r/ 59.2%

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

   13. Simplified 59.2%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+102}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{-69}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 15: 49.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+102}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-69}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \end{array} \]

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 (<= t -1.55e+102)
   (* -4.0 (* t (/ a c)))
   (if (<= t 2.3e-69) (/ (/ b z) c) (* -4.0 (/ a (/ c t))))))

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 <= -1.55e+102) {
		tmp = -4.0 * (t * (a / c));
	} else if (t <= 2.3e-69) {
		tmp = (b / z) / c;
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	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 <= (-1.55d+102)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (t <= 2.3d-69) then
        tmp = (b / z) / c
    else
        tmp = (-4.0d0) * (a / (c / t))
    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 <= -1.55e+102) {
		tmp = -4.0 * (t * (a / c));
	} else if (t <= 2.3e-69) {
		tmp = (b / z) / c;
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	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 <= -1.55e+102:
		tmp = -4.0 * (t * (a / c))
	elif t <= 2.3e-69:
		tmp = (b / z) / c
	else:
		tmp = -4.0 * (a / (c / t))
	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 <= -1.55e+102)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (t <= 2.3e-69)
		tmp = Float64(Float64(b / z) / c);
	else
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	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 <= -1.55e+102)
		tmp = -4.0 * (t * (a / c));
	elseif (t <= 2.3e-69)
		tmp = (b / z) / c;
	else
		tmp = -4.0 * (a / (c / t));
	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[t, -1.55e+102], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e-69], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.54999999999999993e102

   1. Initial program 70.3%

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

      1. associate-/r* 67.2%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in t around inf 60.8%

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

      1. associate-/l* 60.8%

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

      2. associate-/r/ 62.3%

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

   6. Simplified 62.3%

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

   if -1.54999999999999993e102 < t < 2.3000000000000001e-69

   1. Initial program 84.3%

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

      1. associate-/r* 90.6%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in x around 0 55.9%

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

   5. Taylor expanded in b around inf 41.4%

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

   if 2.3000000000000001e-69 < t

   1. Initial program 71.5%

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

      1. associate-/r* 72.1%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in t around inf 54.8%

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

      1. associate-/l* 59.2%

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

   6. Simplified 59.2%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+102}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-69}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 16: 49.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+102}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq 1.82 \cdot 10^{-68}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{b}{c}}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \end{array} \]

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 (<= t -1.55e+102)
   (* -4.0 (* t (/ a c)))
   (if (<= t 1.82e-68) (/ 1.0 (/ z (/ b c))) (* -4.0 (/ a (/ c t))))))

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 <= -1.55e+102) {
		tmp = -4.0 * (t * (a / c));
	} else if (t <= 1.82e-68) {
		tmp = 1.0 / (z / (b / c));
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	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 <= (-1.55d+102)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (t <= 1.82d-68) then
        tmp = 1.0d0 / (z / (b / c))
    else
        tmp = (-4.0d0) * (a / (c / t))
    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 <= -1.55e+102) {
		tmp = -4.0 * (t * (a / c));
	} else if (t <= 1.82e-68) {
		tmp = 1.0 / (z / (b / c));
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	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 <= -1.55e+102:
		tmp = -4.0 * (t * (a / c))
	elif t <= 1.82e-68:
		tmp = 1.0 / (z / (b / c))
	else:
		tmp = -4.0 * (a / (c / t))
	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 <= -1.55e+102)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (t <= 1.82e-68)
		tmp = Float64(1.0 / Float64(z / Float64(b / c)));
	else
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	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 <= -1.55e+102)
		tmp = -4.0 * (t * (a / c));
	elseif (t <= 1.82e-68)
		tmp = 1.0 / (z / (b / c));
	else
		tmp = -4.0 * (a / (c / t));
	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[t, -1.55e+102], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.82e-68], N[(1.0 / N[(z / N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.54999999999999993e102

   1. Initial program 70.3%

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

      1. associate-/r* 67.2%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in t around inf 60.8%

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

      1. associate-/l* 60.8%

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

      2. associate-/r/ 62.3%

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

   6. Simplified 62.3%

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

   if -1.54999999999999993e102 < t < 1.81999999999999994e-68

   1. Initial program 84.3%

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

      1. associate-/r* 90.6%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in b around inf 37.4%

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

      1. *-commutative 37.4%

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

   6. Simplified 37.4%

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

      1. clear-num 37.4%

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

      2. inv-pow 37.4%

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

   8. Applied egg-rr 37.4%

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

      1. unpow-1 37.4%

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

      2. associate-/l* 42.1%

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

   10. Simplified 42.1%

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

   if 1.81999999999999994e-68 < t

   1. Initial program 71.5%

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

      1. associate-/r* 72.1%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in t around inf 54.8%

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

      1. associate-/l* 59.2%

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

   6. Simplified 59.2%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+102}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq 1.82 \cdot 10^{-68}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{b}{c}}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 17: 34.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq 4.7 \cdot 10^{-116}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \end{array} \]

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 (<= b 4.7e-116) (/ b (* z c)) (/ (/ 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) {
	double tmp;
	if (b <= 4.7e-116) {
		tmp = b / (z * c);
	} else {
		tmp = (b / 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 (b <= 4.7d-116) then
        tmp = b / (z * c)
    else
        tmp = (b / 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 (b <= 4.7e-116) {
		tmp = b / (z * c);
	} else {
		tmp = (b / 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 b <= 4.7e-116:
		tmp = b / (z * c)
	else:
		tmp = (b / 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 (b <= 4.7e-116)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(Float64(b / 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 (b <= 4.7e-116)
		tmp = b / (z * c);
	else
		tmp = (b / 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[LessEqual[b, 4.7e-116], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 4.69999999999999994e-116

   1. Initial program 78.1%

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

      1. associate-/r* 78.0%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in b around inf 24.2%

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

      1. *-commutative 24.2%

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

   6. Simplified 24.2%

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

   if 4.69999999999999994e-116 < b

   1. Initial program 78.8%

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

      1. associate-/r* 87.4%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in x around 0 79.5%

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

   5. Taylor expanded in b around inf 54.7%

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

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 4.7 \cdot 10^{-116}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 18: 35.5% 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 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* 81.3%

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

3. Simplified 90.5%

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

4. Taylor expanded in b around inf 32.0%

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

   1. *-commutative 32.0%

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

6. Simplified 32.0%

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

7. Final simplification 32.0%

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

Developer target: 81.4% 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 2023255 
(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)))