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

Percentage Accurate: 79.4% → 88.3%

Time: 17.0s

Alternatives: 16

Speedup: 0.8×

• Unsound rule application detected in e-graph. Results may not be sound.

• 36.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+233}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{c}{x}}}{z}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+247}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (if (<= t_1 -4e+233)
     (/ (* 9.0 (/ y (/ c x))) z)
     (if (<= t_1 5e+247)
       (/ (+ (/ (fma x (* 9.0 y) b) z) (* t (* a -4.0))) c)
       (* (/ x z) (/ (* 9.0 y) c))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if (t_1 <= -4e+233) {
		tmp = (9.0 * (y / (c / x))) / z;
	} else if (t_1 <= 5e+247) {
		tmp = ((fma(x, (9.0 * y), b) / z) + (t * (a * -4.0))) / c;
	} else {
		tmp = (x / z) * ((9.0 * y) / c);
	}
	return tmp;
}

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_1 <= -4e+233)
		tmp = Float64(Float64(9.0 * Float64(y / Float64(c / x))) / z);
	elseif (t_1 <= 5e+247)
		tmp = Float64(Float64(Float64(fma(x, Float64(9.0 * y), b) / z) + Float64(t * Float64(a * -4.0))) / c);
	else
		tmp = Float64(Float64(x / z) * Float64(Float64(9.0 * y) / c));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+233], N[(N[(9.0 * N[(y / N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 5e+247], 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[(x / z), $MachinePrecision] * N[(N[(9.0 * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x 9) y) < -3.99999999999999989e233

   1. Initial program 61.2%

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

      1. associate-*l* 64.1%

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

      2. associate-*l* 66.8%

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

   3. Simplified 66.8%

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

   4. Taylor expanded in x around inf 63.4%

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

      1. *-commutative 63.4%

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

      2. associate-/r* 63.7%

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

      3. associate-*l/ 63.7%

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

      4. associate-/l* 81.7%

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

   6. Simplified 81.7%

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

   if -3.99999999999999989e233 < (*.f64 (*.f64 x 9) y) < 5.00000000000000023e247

   1. Initial program 82.4%

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

      1. associate-/r* 82.2%

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

   3. Simplified 91.4%

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

   if 5.00000000000000023e247 < (*.f64 (*.f64 x 9) y)

   1. Initial program 61.5%

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

      1. associate-*l* 61.5%

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

      2. associate-*l* 61.3%

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

   3. Simplified 61.3%

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

   4. Taylor expanded in x around inf 69.3%

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

      1. associate-*r/ 69.3%

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

      2. associate-*r* 69.3%

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

      3. times-frac 96.0%

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

      4. *-commutative 96.0%

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

   6. Simplified 96.0%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 9\right) \cdot y \leq -4 \cdot 10^{+233}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{c}{x}}}{z}\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \leq 5 \cdot 10^{+247}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \end{array} \]

Alternative 2: 86.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(\left(x \cdot 9\right) \cdot y - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-238}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-209}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - 4 \cdot \left(t \cdot \left(z \cdot a\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (- (* (* x 9.0) y) (* a (* t (* z 4.0))))) (* c z))))
   (if (<= t_1 -1e-238)
     t_1
     (if (<= t_1 2e-209)
       (/ (+ (* t (* a -4.0)) (* 9.0 (/ (* x y) z))) c)
       (if (<= t_1 INFINITY)
         (/ (+ b (- (* x (* 9.0 y)) (* 4.0 (* t (* z a))))) (* c z))
         (* (* a -4.0) (/ t c)))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (((x * 9.0) * y) - (a * (t * (z * 4.0))))) / (c * z);
	double tmp;
	if (t_1 <= -1e-238) {
		tmp = t_1;
	} else if (t_1 <= 2e-209) {
		tmp = ((t * (a * -4.0)) + (9.0 * ((x * y) / z))) / c;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (b + ((x * (9.0 * y)) - (4.0 * (t * (z * a))))) / (c * z);
	} else {
		tmp = (a * -4.0) * (t / c);
	}
	return tmp;
}

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (((x * 9.0) * y) - (a * (t * (z * 4.0))))) / (c * z);
	double tmp;
	if (t_1 <= -1e-238) {
		tmp = t_1;
	} else if (t_1 <= 2e-209) {
		tmp = ((t * (a * -4.0)) + (9.0 * ((x * y) / z))) / c;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (b + ((x * (9.0 * y)) - (4.0 * (t * (z * a))))) / (c * z);
	} else {
		tmp = (a * -4.0) * (t / c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = (b + (((x * 9.0) * y) - (a * (t * (z * 4.0))))) / (c * z)
	tmp = 0
	if t_1 <= -1e-238:
		tmp = t_1
	elif t_1 <= 2e-209:
		tmp = ((t * (a * -4.0)) + (9.0 * ((x * y) / z))) / c
	elif t_1 <= math.inf:
		tmp = (b + ((x * (9.0 * y)) - (4.0 * (t * (z * a))))) / (c * z)
	else:
		tmp = (a * -4.0) * (t / c)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(Float64(Float64(x * 9.0) * y) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c * z))
	tmp = 0.0
	if (t_1 <= -1e-238)
		tmp = t_1;
	elseif (t_1 <= 2e-209)
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(4.0 * Float64(t * Float64(z * a))))) / Float64(c * z));
	else
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + (((x * 9.0) * y) - (a * (t * (z * 4.0))))) / (c * z);
	tmp = 0.0;
	if (t_1 <= -1e-238)
		tmp = t_1;
	elseif (t_1 <= 2e-209)
		tmp = ((t * (a * -4.0)) + (9.0 * ((x * y) / z))) / c;
	elseif (t_1 <= Inf)
		tmp = (b + ((x * (9.0 * y)) - (4.0 * (t * (z * a))))) / (c * z);
	else
		tmp = (a * -4.0) * (t / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y 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[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-238], t$95$1, If[LessEqual[t$95$1, 2e-209], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -9.9999999999999999e-239

   1. Initial program 87.8%

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

   if -9.9999999999999999e-239 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 2.0000000000000001e-209

   1. Initial program 45.2%

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

      1. associate-/r* 99.4%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 80.4%

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

   if 2.0000000000000001e-209 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 87.5%

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

      1. associate-*l* 88.5%

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

      2. associate-*l* 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in z around 0 88.5%

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

      1. associate-*r* 88.5%

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

      2. *-commutative 88.5%

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

      3. associate-*l* 85.7%

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

   6. Simplified 85.7%

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

   if +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* 7.8%

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

   3. Simplified 51.8%

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

      1. div-inv 51.8%

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

      2. +-commutative 51.8%

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

      3. fma-def 51.8%

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

   5. Applied egg-rr 51.8%

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

   6. Taylor expanded in t around inf 51.6%

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

      1. associate-*r/ 51.6%

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

      2. associate-*r* 51.6%

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

      3. *-commutative 51.6%

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

      4. *-commutative 51.6%

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

      5. associate-*l/ 77.7%

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

      6. *-commutative 77.7%

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

      7. *-commutative 77.7%

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

   8. Simplified 77.7%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(\left(x \cdot 9\right) \cdot y - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq -1 \cdot 10^{-238}:\\ \;\;\;\;\frac{b + \left(\left(x \cdot 9\right) \cdot y - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{elif}\;\frac{b + \left(\left(x \cdot 9\right) \cdot y - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq 2 \cdot 10^{-209}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;\frac{b + \left(\left(x \cdot 9\right) \cdot y - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq \infty:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - 4 \cdot \left(t \cdot \left(z \cdot a\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \end{array} \]

Alternative 3: 86.1% accurate, 0.3× speedup

Math

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (- (* (* x 9.0) y) (* a (* t (* z 4.0))))) (* c z))))
   (if (<= t_1 -1e-81)
     t_1
     (if (<= t_1 INFINITY)
       (* (/ 1.0 z) (/ (+ b (- (* x (* 9.0 y)) (* z (* 4.0 (* t a))))) c))
       (* (* a -4.0) (/ t c))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (((x * 9.0) * y) - (a * (t * (z * 4.0))))) / (c * z);
	double tmp;
	if (t_1 <= -1e-81) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (1.0 / z) * ((b + ((x * (9.0 * y)) - (z * (4.0 * (t * a))))) / c);
	} else {
		tmp = (a * -4.0) * (t / c);
	}
	return tmp;
}

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (((x * 9.0) * y) - (a * (t * (z * 4.0))))) / (c * z);
	double tmp;
	if (t_1 <= -1e-81) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (1.0 / z) * ((b + ((x * (9.0 * y)) - (z * (4.0 * (t * a))))) / c);
	} else {
		tmp = (a * -4.0) * (t / c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = (b + (((x * 9.0) * y) - (a * (t * (z * 4.0))))) / (c * z)
	tmp = 0
	if t_1 <= -1e-81:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = (1.0 / z) * ((b + ((x * (9.0 * y)) - (z * (4.0 * (t * a))))) / c)
	else:
		tmp = (a * -4.0) * (t / c)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(Float64(Float64(x * 9.0) * y) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c * z))
	tmp = 0.0
	if (t_1 <= -1e-81)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(1.0 / z) * Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(z * Float64(4.0 * Float64(t * a))))) / c));
	else
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + (((x * 9.0) * y) - (a * (t * (z * 4.0))))) / (c * z);
	tmp = 0.0;
	if (t_1 <= -1e-81)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = (1.0 / z) * ((b + ((x * (9.0 * y)) - (z * (4.0 * (t * a))))) / c);
	else
		tmp = (a * -4.0) * (t / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y 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[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-81], t$95$1, If[LessEqual[t$95$1, Infinity], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(z * N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $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)) < -9.9999999999999996e-82

   1. Initial program 87.2%

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

   if -9.9999999999999996e-82 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 82.6%

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

      1. associate-*l* 83.3%

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

      2. associate-*l* 83.4%

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

   3. Simplified 83.4%

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

      1. *-un-lft-identity 83.4%

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

      2. times-frac 90.4%

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

      3. associate-*r* 89.6%

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

      4. associate-*r* 88.8%

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

      5. associate-*r* 89.6%

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

      6. associate-*r* 90.4%

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

      7. associate-*l* 90.4%

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

   5. Applied egg-rr 90.4%

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

   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* 7.8%

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

   3. Simplified 51.8%

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

      1. div-inv 51.8%

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

      2. +-commutative 51.8%

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

      3. fma-def 51.8%

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

   5. Applied egg-rr 51.8%

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

   6. Taylor expanded in t around inf 51.6%

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

      1. associate-*r/ 51.6%

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

      2. associate-*r* 51.6%

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

      3. *-commutative 51.6%

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

      4. *-commutative 51.6%

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

      5. associate-*l/ 77.7%

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

      6. *-commutative 77.7%

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

      7. *-commutative 77.7%

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

   8. Simplified 77.7%

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

4. Final simplification 87.9%

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

Alternative 4: 47.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := \left(x \cdot \frac{y}{z}\right) \cdot \frac{9}{c}\\ t_2 := 9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+200}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1360:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-45}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-173}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-281}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-185}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-23}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x (/ y z)) (/ 9.0 c))) (t_2 (* 9.0 (/ (* x y) (* c z)))))
   (if (<= z -1.05e+200)
     (* (* a -4.0) (/ t c))
     (if (<= z -5.2e+117)
       t_1
       (if (<= z -1360.0)
         (* -4.0 (* t (/ a c)))
         (if (<= z -2e-45)
           (* b (/ 1.0 (* c z)))
           (if (<= z -3.3e-173)
             t_2
             (if (<= z 2.25e-281)
               (/ (/ b c) z)
               (if (<= z 1.85e-185)
                 t_2
                 (if (<= z 1.22e-23)
                   (/ b (* c z))
                   (if (<= z 9.2e+101) t_1 (/ (* t (* a -4.0)) c))))))))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * (y / z)) * (9.0 / c);
	double t_2 = 9.0 * ((x * y) / (c * z));
	double tmp;
	if (z <= -1.05e+200) {
		tmp = (a * -4.0) * (t / c);
	} else if (z <= -5.2e+117) {
		tmp = t_1;
	} else if (z <= -1360.0) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= -2e-45) {
		tmp = b * (1.0 / (c * z));
	} else if (z <= -3.3e-173) {
		tmp = t_2;
	} else if (z <= 2.25e-281) {
		tmp = (b / c) / z;
	} else if (z <= 1.85e-185) {
		tmp = t_2;
	} else if (z <= 1.22e-23) {
		tmp = b / (c * z);
	} else if (z <= 9.2e+101) {
		tmp = t_1;
	} else {
		tmp = (t * (a * -4.0)) / c;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * (y / z)) * (9.0d0 / c)
    t_2 = 9.0d0 * ((x * y) / (c * z))
    if (z <= (-1.05d+200)) then
        tmp = (a * (-4.0d0)) * (t / c)
    else if (z <= (-5.2d+117)) then
        tmp = t_1
    else if (z <= (-1360.0d0)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (z <= (-2d-45)) then
        tmp = b * (1.0d0 / (c * z))
    else if (z <= (-3.3d-173)) then
        tmp = t_2
    else if (z <= 2.25d-281) then
        tmp = (b / c) / z
    else if (z <= 1.85d-185) then
        tmp = t_2
    else if (z <= 1.22d-23) then
        tmp = b / (c * z)
    else if (z <= 9.2d+101) then
        tmp = t_1
    else
        tmp = (t * (a * (-4.0d0))) / c
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * (y / z)) * (9.0 / c);
	double t_2 = 9.0 * ((x * y) / (c * z));
	double tmp;
	if (z <= -1.05e+200) {
		tmp = (a * -4.0) * (t / c);
	} else if (z <= -5.2e+117) {
		tmp = t_1;
	} else if (z <= -1360.0) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= -2e-45) {
		tmp = b * (1.0 / (c * z));
	} else if (z <= -3.3e-173) {
		tmp = t_2;
	} else if (z <= 2.25e-281) {
		tmp = (b / c) / z;
	} else if (z <= 1.85e-185) {
		tmp = t_2;
	} else if (z <= 1.22e-23) {
		tmp = b / (c * z);
	} else if (z <= 9.2e+101) {
		tmp = t_1;
	} else {
		tmp = (t * (a * -4.0)) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = (x * (y / z)) * (9.0 / c)
	t_2 = 9.0 * ((x * y) / (c * z))
	tmp = 0
	if z <= -1.05e+200:
		tmp = (a * -4.0) * (t / c)
	elif z <= -5.2e+117:
		tmp = t_1
	elif z <= -1360.0:
		tmp = -4.0 * (t * (a / c))
	elif z <= -2e-45:
		tmp = b * (1.0 / (c * z))
	elif z <= -3.3e-173:
		tmp = t_2
	elif z <= 2.25e-281:
		tmp = (b / c) / z
	elif z <= 1.85e-185:
		tmp = t_2
	elif z <= 1.22e-23:
		tmp = b / (c * z)
	elif z <= 9.2e+101:
		tmp = t_1
	else:
		tmp = (t * (a * -4.0)) / c
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * Float64(y / z)) * Float64(9.0 / c))
	t_2 = Float64(9.0 * Float64(Float64(x * y) / Float64(c * z)))
	tmp = 0.0
	if (z <= -1.05e+200)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	elseif (z <= -5.2e+117)
		tmp = t_1;
	elseif (z <= -1360.0)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (z <= -2e-45)
		tmp = Float64(b * Float64(1.0 / Float64(c * z)));
	elseif (z <= -3.3e-173)
		tmp = t_2;
	elseif (z <= 2.25e-281)
		tmp = Float64(Float64(b / c) / z);
	elseif (z <= 1.85e-185)
		tmp = t_2;
	elseif (z <= 1.22e-23)
		tmp = Float64(b / Float64(c * z));
	elseif (z <= 9.2e+101)
		tmp = t_1;
	else
		tmp = Float64(Float64(t * Float64(a * -4.0)) / c);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * (y / z)) * (9.0 / c);
	t_2 = 9.0 * ((x * y) / (c * z));
	tmp = 0.0;
	if (z <= -1.05e+200)
		tmp = (a * -4.0) * (t / c);
	elseif (z <= -5.2e+117)
		tmp = t_1;
	elseif (z <= -1360.0)
		tmp = -4.0 * (t * (a / c));
	elseif (z <= -2e-45)
		tmp = b * (1.0 / (c * z));
	elseif (z <= -3.3e-173)
		tmp = t_2;
	elseif (z <= 2.25e-281)
		tmp = (b / c) / z;
	elseif (z <= 1.85e-185)
		tmp = t_2;
	elseif (z <= 1.22e-23)
		tmp = b / (c * z);
	elseif (z <= 9.2e+101)
		tmp = t_1;
	else
		tmp = (t * (a * -4.0)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] * N[(9.0 / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e+200], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.2e+117], t$95$1, If[LessEqual[z, -1360.0], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e-45], N[(b * N[(1.0 / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.3e-173], t$95$2, If[LessEqual[z, 2.25e-281], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.85e-185], t$95$2, If[LessEqual[z, 1.22e-23], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e+101], t$95$1, N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if z < -1.04999999999999999e200

   1. Initial program 36.3%

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

      1. associate-/r* 48.5%

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

   3. Simplified 82.8%

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

      1. div-inv 82.7%

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

      2. +-commutative 82.7%

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

      3. fma-def 82.7%

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

   5. Applied egg-rr 82.7%

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

   6. Taylor expanded in t around inf 71.9%

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

      1. associate-*r/ 71.9%

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

      2. associate-*r* 71.9%

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

      3. *-commutative 71.9%

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

      4. *-commutative 71.9%

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

      5. associate-*l/ 75.5%

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

      6. *-commutative 75.5%

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

      7. *-commutative 75.5%

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

   8. Simplified 75.5%

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

   if -1.04999999999999999e200 < z < -5.1999999999999999e117 or 1.22000000000000007e-23 < z < 9.2000000000000005e101

   1. Initial program 69.0%

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

      1. associate-/r* 74.1%

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

   3. Simplified 76.6%

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

      1. div-inv 76.5%

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

      2. +-commutative 76.5%

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

      3. fma-def 76.5%

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

   5. Applied egg-rr 76.5%

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

   6. Taylor expanded in x around inf 40.9%

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

      1. associate-*r/ 40.8%

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

      2. *-commutative 40.8%

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

      3. *-commutative 40.8%

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

      4. *-commutative 40.8%

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

      5. times-frac 45.7%

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

      6. *-commutative 45.7%

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

      7. associate-/l* 55.0%

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

      8. associate-/r/ 57.3%

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

   8. Simplified 57.3%

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

   if -5.1999999999999999e117 < z < -1360

   1. Initial program 81.5%

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

      1. associate-*l* 81.5%

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

      2. associate-*l* 81.6%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in z around inf 46.7%

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

      1. *-commutative 46.7%

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

      2. associate-/l* 50.0%

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

      3. associate-/r/ 46.8%

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

   6. Simplified 46.8%

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

   if -1360 < z < -1.99999999999999997e-45

   1. Initial program 99.8%

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

      1. associate-*l* 99.8%

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

      2. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in b around inf 65.6%

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

      1. div-inv 65.7%

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

      2. *-commutative 65.7%

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

   6. Applied egg-rr 65.7%

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

   if -1.99999999999999997e-45 < z < -3.3000000000000003e-173 or 2.24999999999999997e-281 < z < 1.85e-185

   1. Initial program 98.3%

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

      1. associate-*l* 98.3%

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

      2. associate-*l* 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in x around inf 66.7%

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

   if -3.3000000000000003e-173 < z < 2.24999999999999997e-281

   1. Initial program 93.4%

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

      1. associate-*l* 93.4%

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

      2. associate-*l* 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in b around inf 64.4%

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

      1. associate-/r* 67.6%

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

   6. Simplified 67.6%

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

   if 1.85e-185 < z < 1.22000000000000007e-23

   1. Initial program 99.2%

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

      1. associate-*l* 99.2%

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

      2. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in b around inf 60.1%

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

   if 9.2000000000000005e101 < z

   1. Initial program 58.9%

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

      1. associate-/r* 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 89.3%

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

   4. Taylor expanded in z around inf 60.8%

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

      1. associate-*r* 60.8%

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

      2. *-commutative 60.8%

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

      3. *-commutative 60.8%

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

   6. Simplified 60.8%

      \[\leadsto \frac{\color{blue}{t \cdot \left(a \cdot -4\right)}}{c} \]
3. Recombined 8 regimes into one program.

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+200}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+117}:\\ \;\;\;\;\left(x \cdot \frac{y}{z}\right) \cdot \frac{9}{c}\\ \mathbf{elif}\;z \leq -1360:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-45}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-173}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-281}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-185}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-23}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+101}:\\ \;\;\;\;\left(x \cdot \frac{y}{z}\right) \cdot \frac{9}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \]

Alternative 5: 46.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := 9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+193}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+112}:\\ \;\;\;\;\left(x \cdot \frac{y}{z}\right) \cdot \frac{9}{c}\\ \mathbf{elif}\;z \leq -3.5:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-45}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-281}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-122}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+144}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(a \cdot -4\right)\right) \cdot \frac{1}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (/ (* x y) (* c z)))))
   (if (<= z -2.5e+193)
     (* (* a -4.0) (/ t c))
     (if (<= z -2.9e+112)
       (* (* x (/ y z)) (/ 9.0 c))
       (if (<= z -3.5)
         (* -4.0 (* t (/ a c)))
         (if (<= z -2.6e-45)
           (* b (/ 1.0 (* c z)))
           (if (<= z -1e-172)
             t_1
             (if (<= z 1.22e-281)
               (/ (/ b c) z)
               (if (<= z 1.05e-175)
                 t_1
                 (if (<= z 6.4e-122)
                   (/ b (* c z))
                   (if (<= z 4.6e+144)
                     (* (/ x z) (/ (* 9.0 y) c))
                     (* (* t (* a -4.0)) (/ 1.0 c)))))))))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((x * y) / (c * z));
	double tmp;
	if (z <= -2.5e+193) {
		tmp = (a * -4.0) * (t / c);
	} else if (z <= -2.9e+112) {
		tmp = (x * (y / z)) * (9.0 / c);
	} else if (z <= -3.5) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= -2.6e-45) {
		tmp = b * (1.0 / (c * z));
	} else if (z <= -1e-172) {
		tmp = t_1;
	} else if (z <= 1.22e-281) {
		tmp = (b / c) / z;
	} else if (z <= 1.05e-175) {
		tmp = t_1;
	} else if (z <= 6.4e-122) {
		tmp = b / (c * z);
	} else if (z <= 4.6e+144) {
		tmp = (x / z) * ((9.0 * y) / c);
	} else {
		tmp = (t * (a * -4.0)) * (1.0 / c);
	}
	return tmp;
}

Fortran

NOTE: x and y 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 * ((x * y) / (c * z))
    if (z <= (-2.5d+193)) then
        tmp = (a * (-4.0d0)) * (t / c)
    else if (z <= (-2.9d+112)) then
        tmp = (x * (y / z)) * (9.0d0 / c)
    else if (z <= (-3.5d0)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (z <= (-2.6d-45)) then
        tmp = b * (1.0d0 / (c * z))
    else if (z <= (-1d-172)) then
        tmp = t_1
    else if (z <= 1.22d-281) then
        tmp = (b / c) / z
    else if (z <= 1.05d-175) then
        tmp = t_1
    else if (z <= 6.4d-122) then
        tmp = b / (c * z)
    else if (z <= 4.6d+144) then
        tmp = (x / z) * ((9.0d0 * y) / c)
    else
        tmp = (t * (a * (-4.0d0))) * (1.0d0 / c)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((x * y) / (c * z));
	double tmp;
	if (z <= -2.5e+193) {
		tmp = (a * -4.0) * (t / c);
	} else if (z <= -2.9e+112) {
		tmp = (x * (y / z)) * (9.0 / c);
	} else if (z <= -3.5) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= -2.6e-45) {
		tmp = b * (1.0 / (c * z));
	} else if (z <= -1e-172) {
		tmp = t_1;
	} else if (z <= 1.22e-281) {
		tmp = (b / c) / z;
	} else if (z <= 1.05e-175) {
		tmp = t_1;
	} else if (z <= 6.4e-122) {
		tmp = b / (c * z);
	} else if (z <= 4.6e+144) {
		tmp = (x / z) * ((9.0 * y) / c);
	} else {
		tmp = (t * (a * -4.0)) * (1.0 / c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * ((x * y) / (c * z))
	tmp = 0
	if z <= -2.5e+193:
		tmp = (a * -4.0) * (t / c)
	elif z <= -2.9e+112:
		tmp = (x * (y / z)) * (9.0 / c)
	elif z <= -3.5:
		tmp = -4.0 * (t * (a / c))
	elif z <= -2.6e-45:
		tmp = b * (1.0 / (c * z))
	elif z <= -1e-172:
		tmp = t_1
	elif z <= 1.22e-281:
		tmp = (b / c) / z
	elif z <= 1.05e-175:
		tmp = t_1
	elif z <= 6.4e-122:
		tmp = b / (c * z)
	elif z <= 4.6e+144:
		tmp = (x / z) * ((9.0 * y) / c)
	else:
		tmp = (t * (a * -4.0)) * (1.0 / c)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(Float64(x * y) / Float64(c * z)))
	tmp = 0.0
	if (z <= -2.5e+193)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	elseif (z <= -2.9e+112)
		tmp = Float64(Float64(x * Float64(y / z)) * Float64(9.0 / c));
	elseif (z <= -3.5)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (z <= -2.6e-45)
		tmp = Float64(b * Float64(1.0 / Float64(c * z)));
	elseif (z <= -1e-172)
		tmp = t_1;
	elseif (z <= 1.22e-281)
		tmp = Float64(Float64(b / c) / z);
	elseif (z <= 1.05e-175)
		tmp = t_1;
	elseif (z <= 6.4e-122)
		tmp = Float64(b / Float64(c * z));
	elseif (z <= 4.6e+144)
		tmp = Float64(Float64(x / z) * Float64(Float64(9.0 * y) / c));
	else
		tmp = Float64(Float64(t * Float64(a * -4.0)) * Float64(1.0 / c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * ((x * y) / (c * z));
	tmp = 0.0;
	if (z <= -2.5e+193)
		tmp = (a * -4.0) * (t / c);
	elseif (z <= -2.9e+112)
		tmp = (x * (y / z)) * (9.0 / c);
	elseif (z <= -3.5)
		tmp = -4.0 * (t * (a / c));
	elseif (z <= -2.6e-45)
		tmp = b * (1.0 / (c * z));
	elseif (z <= -1e-172)
		tmp = t_1;
	elseif (z <= 1.22e-281)
		tmp = (b / c) / z;
	elseif (z <= 1.05e-175)
		tmp = t_1;
	elseif (z <= 6.4e-122)
		tmp = b / (c * z);
	elseif (z <= 4.6e+144)
		tmp = (x / z) * ((9.0 * y) / c);
	else
		tmp = (t * (a * -4.0)) * (1.0 / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+193], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.9e+112], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] * N[(9.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.5], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e-45], N[(b * N[(1.0 / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1e-172], t$95$1, If[LessEqual[z, 1.22e-281], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.05e-175], t$95$1, If[LessEqual[z, 6.4e-122], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+144], N[(N[(x / z), $MachinePrecision] * N[(N[(9.0 * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if z < -2.49999999999999986e193

   1. Initial program 36.3%

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

      1. associate-/r* 48.5%

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

   3. Simplified 82.8%

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

      1. div-inv 82.7%

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

      2. +-commutative 82.7%

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

      3. fma-def 82.7%

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

   5. Applied egg-rr 82.7%

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

   6. Taylor expanded in t around inf 71.9%

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

      1. associate-*r/ 71.9%

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

      2. associate-*r* 71.9%

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

      3. *-commutative 71.9%

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

      4. *-commutative 71.9%

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

      5. associate-*l/ 75.5%

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

      6. *-commutative 75.5%

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

      7. *-commutative 75.5%

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

   8. Simplified 75.5%

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

   if -2.49999999999999986e193 < z < -2.9000000000000002e112

   1. Initial program 67.1%

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

      1. associate-/r* 73.7%

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

   3. Simplified 80.5%

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

      1. div-inv 80.5%

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

      2. +-commutative 80.5%

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

      3. fma-def 80.5%

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

   5. Applied egg-rr 80.5%

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

   6. Taylor expanded in x around inf 41.6%

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

      1. associate-*r/ 41.4%

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

      2. *-commutative 41.4%

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

      3. *-commutative 41.4%

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

      4. *-commutative 41.4%

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

      5. times-frac 48.1%

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

      6. *-commutative 48.1%

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

      7. associate-/l* 54.5%

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

      8. associate-/r/ 60.8%

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

   8. Simplified 60.8%

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

   if -2.9000000000000002e112 < z < -3.5

   1. Initial program 81.5%

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

      1. associate-*l* 81.5%

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

      2. associate-*l* 81.6%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in z around inf 46.7%

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

      1. *-commutative 46.7%

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

      2. associate-/l* 50.0%

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

      3. associate-/r/ 46.8%

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

   6. Simplified 46.8%

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

   if -3.5 < z < -2.59999999999999987e-45

   1. Initial program 99.8%

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

      1. associate-*l* 99.8%

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

      2. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in b around inf 65.6%

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

      1. div-inv 65.7%

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

      2. *-commutative 65.7%

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

   6. Applied egg-rr 65.7%

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

   if -2.59999999999999987e-45 < z < -1e-172 or 1.21999999999999996e-281 < z < 1.05e-175

   1. Initial program 98.3%

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

      1. associate-*l* 98.3%

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

      2. associate-*l* 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in x around inf 66.7%

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

   if -1e-172 < z < 1.21999999999999996e-281

   1. Initial program 93.4%

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

      1. associate-*l* 93.4%

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

      2. associate-*l* 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in b around inf 64.4%

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

      1. associate-/r* 67.6%

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

   6. Simplified 67.6%

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

   if 1.05e-175 < z < 6.4000000000000004e-122

   1. Initial program 100.0%

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

      1. associate-*l* 100.0%

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

      2. associate-*l* 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in b around inf 88.9%

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

   if 6.4000000000000004e-122 < z < 4.6000000000000003e144

   1. Initial program 78.3%

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

      1. associate-*l* 78.4%

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

      2. associate-*l* 81.9%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in x around inf 38.5%

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

      1. associate-*r/ 38.5%

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

      2. associate-*r* 38.5%

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

      3. times-frac 50.0%

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

      4. *-commutative 50.0%

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

   6. Simplified 50.0%

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

   if 4.6000000000000003e144 < z

   1. Initial program 57.3%

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

      1. associate-/r* 68.0%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in z around inf 70.2%

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

      1. associate-*r* 70.2%

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

      2. *-commutative 70.2%

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

      3. *-commutative 70.2%

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

   6. Simplified 70.2%

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

      1. div-inv 70.2%

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

   8. Applied egg-rr 70.2%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+193}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+112}:\\ \;\;\;\;\left(x \cdot \frac{y}{z}\right) \cdot \frac{9}{c}\\ \mathbf{elif}\;z \leq -3.5:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-45}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-172}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-281}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-175}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-122}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+144}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(a \cdot -4\right)\right) \cdot \frac{1}{c}\\ \end{array} \]

Alternative 6: 46.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot \left(9 \cdot y\right)}{c \cdot z}\\ \mathbf{if}\;z \leq -2.65 \cdot 10^{+193}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+116}:\\ \;\;\;\;\left(x \cdot \frac{y}{z}\right) \cdot \frac{9}{c}\\ \mathbf{elif}\;z \leq -3.1:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-45}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-279}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-122}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(a \cdot -4\right)\right) \cdot \frac{1}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* x (* 9.0 y)) (* c z))))
   (if (<= z -2.65e+193)
     (* (* a -4.0) (/ t c))
     (if (<= z -4.2e+116)
       (* (* x (/ y z)) (/ 9.0 c))
       (if (<= z -3.1)
         (* -4.0 (* t (/ a c)))
         (if (<= z -2.35e-45)
           (* b (/ 1.0 (* c z)))
           (if (<= z -5.3e-173)
             t_1
             (if (<= z 1.15e-279)
               (/ (/ b c) z)
               (if (<= z 2.2e-171)
                 t_1
                 (if (<= z 2.9e-122)
                   (/ b (* c z))
                   (if (<= z 1.6e+145)
                     (* (/ x z) (/ (* 9.0 y) c))
                     (* (* t (* a -4.0)) (/ 1.0 c)))))))))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * (9.0 * y)) / (c * z);
	double tmp;
	if (z <= -2.65e+193) {
		tmp = (a * -4.0) * (t / c);
	} else if (z <= -4.2e+116) {
		tmp = (x * (y / z)) * (9.0 / c);
	} else if (z <= -3.1) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= -2.35e-45) {
		tmp = b * (1.0 / (c * z));
	} else if (z <= -5.3e-173) {
		tmp = t_1;
	} else if (z <= 1.15e-279) {
		tmp = (b / c) / z;
	} else if (z <= 2.2e-171) {
		tmp = t_1;
	} else if (z <= 2.9e-122) {
		tmp = b / (c * z);
	} else if (z <= 1.6e+145) {
		tmp = (x / z) * ((9.0 * y) / c);
	} else {
		tmp = (t * (a * -4.0)) * (1.0 / c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (9.0d0 * y)) / (c * z)
    if (z <= (-2.65d+193)) then
        tmp = (a * (-4.0d0)) * (t / c)
    else if (z <= (-4.2d+116)) then
        tmp = (x * (y / z)) * (9.0d0 / c)
    else if (z <= (-3.1d0)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (z <= (-2.35d-45)) then
        tmp = b * (1.0d0 / (c * z))
    else if (z <= (-5.3d-173)) then
        tmp = t_1
    else if (z <= 1.15d-279) then
        tmp = (b / c) / z
    else if (z <= 2.2d-171) then
        tmp = t_1
    else if (z <= 2.9d-122) then
        tmp = b / (c * z)
    else if (z <= 1.6d+145) then
        tmp = (x / z) * ((9.0d0 * y) / c)
    else
        tmp = (t * (a * (-4.0d0))) * (1.0d0 / c)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * (9.0 * y)) / (c * z);
	double tmp;
	if (z <= -2.65e+193) {
		tmp = (a * -4.0) * (t / c);
	} else if (z <= -4.2e+116) {
		tmp = (x * (y / z)) * (9.0 / c);
	} else if (z <= -3.1) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= -2.35e-45) {
		tmp = b * (1.0 / (c * z));
	} else if (z <= -5.3e-173) {
		tmp = t_1;
	} else if (z <= 1.15e-279) {
		tmp = (b / c) / z;
	} else if (z <= 2.2e-171) {
		tmp = t_1;
	} else if (z <= 2.9e-122) {
		tmp = b / (c * z);
	} else if (z <= 1.6e+145) {
		tmp = (x / z) * ((9.0 * y) / c);
	} else {
		tmp = (t * (a * -4.0)) * (1.0 / c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = (x * (9.0 * y)) / (c * z)
	tmp = 0
	if z <= -2.65e+193:
		tmp = (a * -4.0) * (t / c)
	elif z <= -4.2e+116:
		tmp = (x * (y / z)) * (9.0 / c)
	elif z <= -3.1:
		tmp = -4.0 * (t * (a / c))
	elif z <= -2.35e-45:
		tmp = b * (1.0 / (c * z))
	elif z <= -5.3e-173:
		tmp = t_1
	elif z <= 1.15e-279:
		tmp = (b / c) / z
	elif z <= 2.2e-171:
		tmp = t_1
	elif z <= 2.9e-122:
		tmp = b / (c * z)
	elif z <= 1.6e+145:
		tmp = (x / z) * ((9.0 * y) / c)
	else:
		tmp = (t * (a * -4.0)) * (1.0 / c)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * Float64(9.0 * y)) / Float64(c * z))
	tmp = 0.0
	if (z <= -2.65e+193)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	elseif (z <= -4.2e+116)
		tmp = Float64(Float64(x * Float64(y / z)) * Float64(9.0 / c));
	elseif (z <= -3.1)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (z <= -2.35e-45)
		tmp = Float64(b * Float64(1.0 / Float64(c * z)));
	elseif (z <= -5.3e-173)
		tmp = t_1;
	elseif (z <= 1.15e-279)
		tmp = Float64(Float64(b / c) / z);
	elseif (z <= 2.2e-171)
		tmp = t_1;
	elseif (z <= 2.9e-122)
		tmp = Float64(b / Float64(c * z));
	elseif (z <= 1.6e+145)
		tmp = Float64(Float64(x / z) * Float64(Float64(9.0 * y) / c));
	else
		tmp = Float64(Float64(t * Float64(a * -4.0)) * Float64(1.0 / c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * (9.0 * y)) / (c * z);
	tmp = 0.0;
	if (z <= -2.65e+193)
		tmp = (a * -4.0) * (t / c);
	elseif (z <= -4.2e+116)
		tmp = (x * (y / z)) * (9.0 / c);
	elseif (z <= -3.1)
		tmp = -4.0 * (t * (a / c));
	elseif (z <= -2.35e-45)
		tmp = b * (1.0 / (c * z));
	elseif (z <= -5.3e-173)
		tmp = t_1;
	elseif (z <= 1.15e-279)
		tmp = (b / c) / z;
	elseif (z <= 2.2e-171)
		tmp = t_1;
	elseif (z <= 2.9e-122)
		tmp = b / (c * z);
	elseif (z <= 1.6e+145)
		tmp = (x / z) * ((9.0 * y) / c);
	else
		tmp = (t * (a * -4.0)) * (1.0 / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.65e+193], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.2e+116], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] * N[(9.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.1], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.35e-45], N[(b * N[(1.0 / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.3e-173], t$95$1, If[LessEqual[z, 1.15e-279], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 2.2e-171], t$95$1, If[LessEqual[z, 2.9e-122], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+145], N[(N[(x / z), $MachinePrecision] * N[(N[(9.0 * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if z < -2.6499999999999999e193

   1. Initial program 36.3%

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

      1. associate-/r* 48.5%

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

   3. Simplified 82.8%

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

      1. div-inv 82.7%

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

      2. +-commutative 82.7%

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

      3. fma-def 82.7%

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

   5. Applied egg-rr 82.7%

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

   6. Taylor expanded in t around inf 71.9%

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

      1. associate-*r/ 71.9%

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

      2. associate-*r* 71.9%

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

      3. *-commutative 71.9%

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

      4. *-commutative 71.9%

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

      5. associate-*l/ 75.5%

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

      6. *-commutative 75.5%

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

      7. *-commutative 75.5%

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

   8. Simplified 75.5%

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

   if -2.6499999999999999e193 < z < -4.2000000000000002e116

   1. Initial program 67.1%

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

      1. associate-/r* 73.7%

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

   3. Simplified 80.5%

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

      1. div-inv 80.5%

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

      2. +-commutative 80.5%

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

      3. fma-def 80.5%

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

   5. Applied egg-rr 80.5%

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

   6. Taylor expanded in x around inf 41.6%

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

      1. associate-*r/ 41.4%

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

      2. *-commutative 41.4%

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

      3. *-commutative 41.4%

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

      4. *-commutative 41.4%

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

      5. times-frac 48.1%

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

      6. *-commutative 48.1%

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

      7. associate-/l* 54.5%

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

      8. associate-/r/ 60.8%

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

   8. Simplified 60.8%

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

   if -4.2000000000000002e116 < z < -3.10000000000000009

   1. Initial program 81.5%

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

      1. associate-*l* 81.5%

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

      2. associate-*l* 81.6%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in z around inf 46.7%

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

      1. *-commutative 46.7%

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

      2. associate-/l* 50.0%

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

      3. associate-/r/ 46.8%

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

   6. Simplified 46.8%

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

   if -3.10000000000000009 < z < -2.3499999999999999e-45

   1. Initial program 99.8%

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

      1. associate-*l* 99.8%

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

      2. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in b around inf 65.6%

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

      1. div-inv 65.7%

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

      2. *-commutative 65.7%

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

   6. Applied egg-rr 65.7%

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

   if -2.3499999999999999e-45 < z < -5.29999999999999964e-173 or 1.14999999999999998e-279 < z < 2.2000000000000001e-171

   1. Initial program 98.3%

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

      1. associate-*l* 98.3%

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

      2. associate-*l* 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in x around inf 66.7%

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

      1. associate-*r/ 66.7%

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

      2. associate-*r* 66.8%

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

      3. times-frac 53.0%

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

      4. *-commutative 53.0%

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

   6. Simplified 53.0%

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

      1. frac-times 66.8%

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

   8. Applied egg-rr 66.8%

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

   if -5.29999999999999964e-173 < z < 1.14999999999999998e-279

   1. Initial program 93.4%

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

      1. associate-*l* 93.4%

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

      2. associate-*l* 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in b around inf 64.4%

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

      1. associate-/r* 67.6%

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

   6. Simplified 67.6%

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

   if 2.2000000000000001e-171 < z < 2.9000000000000002e-122

   1. Initial program 100.0%

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

      1. associate-*l* 100.0%

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

      2. associate-*l* 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in b around inf 88.9%

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

   if 2.9000000000000002e-122 < z < 1.60000000000000004e145

   1. Initial program 78.3%

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

      1. associate-*l* 78.4%

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

      2. associate-*l* 81.9%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in x around inf 38.5%

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

      1. associate-*r/ 38.5%

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

      2. associate-*r* 38.5%

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

      3. times-frac 50.0%

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

      4. *-commutative 50.0%

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

   6. Simplified 50.0%

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

   if 1.60000000000000004e145 < z

   1. Initial program 57.3%

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

      1. associate-/r* 68.0%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in z around inf 70.2%

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

      1. associate-*r* 70.2%

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

      2. *-commutative 70.2%

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

      3. *-commutative 70.2%

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

   6. Simplified 70.2%

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

      1. div-inv 70.2%

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

   8. Applied egg-rr 70.2%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+193}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+116}:\\ \;\;\;\;\left(x \cdot \frac{y}{z}\right) \cdot \frac{9}{c}\\ \mathbf{elif}\;z \leq -3.1:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-45}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-173}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-279}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-171}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-122}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(a \cdot -4\right)\right) \cdot \frac{1}{c}\\ \end{array} \]

Alternative 7: 46.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+200}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+117}:\\ \;\;\;\;\left(9 \cdot \frac{y}{\frac{z}{x}}\right) \cdot \frac{1}{c}\\ \mathbf{elif}\;z \leq -225:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-45}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-172}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{c}{x}}}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-281}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-183}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-127}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(a \cdot -4\right)\right) \cdot \frac{1}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1e+200)
   (* (* a -4.0) (/ t c))
   (if (<= z -1.55e+117)
     (* (* 9.0 (/ y (/ z x))) (/ 1.0 c))
     (if (<= z -225.0)
       (* -4.0 (* t (/ a c)))
       (if (<= z -2.6e-45)
         (* b (/ 1.0 (* c z)))
         (if (<= z -3e-172)
           (/ (* 9.0 (/ y (/ c x))) z)
           (if (<= z 2.1e-281)
             (/ (/ b c) z)
             (if (<= z 9.5e-183)
               (/ (* x (* 9.0 y)) (* c z))
               (if (<= z 2.5e-127)
                 (/ b (* c z))
                 (if (<= z 3.7e+143)
                   (* (/ x z) (/ (* 9.0 y) c))
                   (* (* t (* a -4.0)) (/ 1.0 c))))))))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1e+200) {
		tmp = (a * -4.0) * (t / c);
	} else if (z <= -1.55e+117) {
		tmp = (9.0 * (y / (z / x))) * (1.0 / c);
	} else if (z <= -225.0) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= -2.6e-45) {
		tmp = b * (1.0 / (c * z));
	} else if (z <= -3e-172) {
		tmp = (9.0 * (y / (c / x))) / z;
	} else if (z <= 2.1e-281) {
		tmp = (b / c) / z;
	} else if (z <= 9.5e-183) {
		tmp = (x * (9.0 * y)) / (c * z);
	} else if (z <= 2.5e-127) {
		tmp = b / (c * z);
	} else if (z <= 3.7e+143) {
		tmp = (x / z) * ((9.0 * y) / c);
	} else {
		tmp = (t * (a * -4.0)) * (1.0 / c);
	}
	return tmp;
}

Fortran

NOTE: x and y 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 <= (-1d+200)) then
        tmp = (a * (-4.0d0)) * (t / c)
    else if (z <= (-1.55d+117)) then
        tmp = (9.0d0 * (y / (z / x))) * (1.0d0 / c)
    else if (z <= (-225.0d0)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (z <= (-2.6d-45)) then
        tmp = b * (1.0d0 / (c * z))
    else if (z <= (-3d-172)) then
        tmp = (9.0d0 * (y / (c / x))) / z
    else if (z <= 2.1d-281) then
        tmp = (b / c) / z
    else if (z <= 9.5d-183) then
        tmp = (x * (9.0d0 * y)) / (c * z)
    else if (z <= 2.5d-127) then
        tmp = b / (c * z)
    else if (z <= 3.7d+143) then
        tmp = (x / z) * ((9.0d0 * y) / c)
    else
        tmp = (t * (a * (-4.0d0))) * (1.0d0 / c)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1e+200) {
		tmp = (a * -4.0) * (t / c);
	} else if (z <= -1.55e+117) {
		tmp = (9.0 * (y / (z / x))) * (1.0 / c);
	} else if (z <= -225.0) {
		tmp = -4.0 * (t * (a / c));
	} else if (z <= -2.6e-45) {
		tmp = b * (1.0 / (c * z));
	} else if (z <= -3e-172) {
		tmp = (9.0 * (y / (c / x))) / z;
	} else if (z <= 2.1e-281) {
		tmp = (b / c) / z;
	} else if (z <= 9.5e-183) {
		tmp = (x * (9.0 * y)) / (c * z);
	} else if (z <= 2.5e-127) {
		tmp = b / (c * z);
	} else if (z <= 3.7e+143) {
		tmp = (x / z) * ((9.0 * y) / c);
	} else {
		tmp = (t * (a * -4.0)) * (1.0 / c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -1e+200:
		tmp = (a * -4.0) * (t / c)
	elif z <= -1.55e+117:
		tmp = (9.0 * (y / (z / x))) * (1.0 / c)
	elif z <= -225.0:
		tmp = -4.0 * (t * (a / c))
	elif z <= -2.6e-45:
		tmp = b * (1.0 / (c * z))
	elif z <= -3e-172:
		tmp = (9.0 * (y / (c / x))) / z
	elif z <= 2.1e-281:
		tmp = (b / c) / z
	elif z <= 9.5e-183:
		tmp = (x * (9.0 * y)) / (c * z)
	elif z <= 2.5e-127:
		tmp = b / (c * z)
	elif z <= 3.7e+143:
		tmp = (x / z) * ((9.0 * y) / c)
	else:
		tmp = (t * (a * -4.0)) * (1.0 / c)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1e+200)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	elseif (z <= -1.55e+117)
		tmp = Float64(Float64(9.0 * Float64(y / Float64(z / x))) * Float64(1.0 / c));
	elseif (z <= -225.0)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (z <= -2.6e-45)
		tmp = Float64(b * Float64(1.0 / Float64(c * z)));
	elseif (z <= -3e-172)
		tmp = Float64(Float64(9.0 * Float64(y / Float64(c / x))) / z);
	elseif (z <= 2.1e-281)
		tmp = Float64(Float64(b / c) / z);
	elseif (z <= 9.5e-183)
		tmp = Float64(Float64(x * Float64(9.0 * y)) / Float64(c * z));
	elseif (z <= 2.5e-127)
		tmp = Float64(b / Float64(c * z));
	elseif (z <= 3.7e+143)
		tmp = Float64(Float64(x / z) * Float64(Float64(9.0 * y) / c));
	else
		tmp = Float64(Float64(t * Float64(a * -4.0)) * Float64(1.0 / c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -1e+200)
		tmp = (a * -4.0) * (t / c);
	elseif (z <= -1.55e+117)
		tmp = (9.0 * (y / (z / x))) * (1.0 / c);
	elseif (z <= -225.0)
		tmp = -4.0 * (t * (a / c));
	elseif (z <= -2.6e-45)
		tmp = b * (1.0 / (c * z));
	elseif (z <= -3e-172)
		tmp = (9.0 * (y / (c / x))) / z;
	elseif (z <= 2.1e-281)
		tmp = (b / c) / z;
	elseif (z <= 9.5e-183)
		tmp = (x * (9.0 * y)) / (c * z);
	elseif (z <= 2.5e-127)
		tmp = b / (c * z);
	elseif (z <= 3.7e+143)
		tmp = (x / z) * ((9.0 * y) / c);
	else
		tmp = (t * (a * -4.0)) * (1.0 / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1e+200], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.55e+117], N[(N[(9.0 * N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -225.0], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e-45], N[(b * N[(1.0 / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3e-172], N[(N[(9.0 * N[(y / N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 2.1e-281], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 9.5e-183], N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-127], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e+143], N[(N[(x / z), $MachinePrecision] * N[(N[(9.0 * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if z < -9.9999999999999997e199

   1. Initial program 36.3%

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

      1. associate-/r* 48.5%

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

   3. Simplified 82.8%

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

      1. div-inv 82.7%

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

      2. +-commutative 82.7%

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

      3. fma-def 82.7%

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

   5. Applied egg-rr 82.7%

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

   6. Taylor expanded in t around inf 71.9%

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

      1. associate-*r/ 71.9%

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

      2. associate-*r* 71.9%

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

      3. *-commutative 71.9%

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

      4. *-commutative 71.9%

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

      5. associate-*l/ 75.5%

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

      6. *-commutative 75.5%

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

      7. *-commutative 75.5%

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

   8. Simplified 75.5%

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

   if -9.9999999999999997e199 < z < -1.54999999999999988e117

   1. Initial program 67.1%

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

      1. associate-/r* 73.7%

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

   3. Simplified 80.5%

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

      1. div-inv 80.5%

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

      2. +-commutative 80.5%

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

      3. fma-def 80.5%

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

   5. Applied egg-rr 80.5%

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

   6. Taylor expanded in x around inf 48.1%

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

      1. associate-/l* 54.5%

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

   8. Simplified 54.5%

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

   if -1.54999999999999988e117 < z < -225

   1. Initial program 81.5%

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

      1. associate-*l* 81.5%

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

      2. associate-*l* 81.6%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in z around inf 46.7%

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

      1. *-commutative 46.7%

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

      2. associate-/l* 50.0%

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

      3. associate-/r/ 46.8%

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

   6. Simplified 46.8%

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

   if -225 < z < -2.59999999999999987e-45

   1. Initial program 99.8%

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

      1. associate-*l* 99.8%

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

      2. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in b around inf 65.6%

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

      1. div-inv 65.7%

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

      2. *-commutative 65.7%

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

   6. Applied egg-rr 65.7%

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

   if -2.59999999999999987e-45 < z < -2.99999999999999984e-172

   1. Initial program 99.7%

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

      1. associate-*l* 99.7%

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

      2. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 64.2%

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

      1. *-commutative 64.2%

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

      2. associate-/r* 64.3%

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

      3. associate-*l/ 64.4%

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

      4. associate-/l* 64.4%

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

   6. Simplified 64.4%

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

   if -2.99999999999999984e-172 < z < 2.0999999999999999e-281

   1. Initial program 93.4%

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

      1. associate-*l* 93.4%

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

      2. associate-*l* 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in b around inf 64.4%

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

      1. associate-/r* 67.6%

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

   6. Simplified 67.6%

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

   if 2.0999999999999999e-281 < z < 9.5000000000000008e-183

   1. Initial program 95.0%

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

      1. associate-*l* 95.0%

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

      2. associate-*l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in x around inf 72.6%

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

      1. associate-*r/ 72.6%

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

      2. associate-*r* 72.7%

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

      3. times-frac 41.8%

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

      4. *-commutative 41.8%

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

   6. Simplified 41.8%

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

      1. frac-times 72.7%

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

   8. Applied egg-rr 72.7%

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

   if 9.5000000000000008e-183 < z < 2.4999999999999999e-127

   1. Initial program 100.0%

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

      1. associate-*l* 100.0%

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

      2. associate-*l* 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in b around inf 88.9%

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

   if 2.4999999999999999e-127 < z < 3.7000000000000002e143

   1. Initial program 78.3%

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

      1. associate-*l* 78.4%

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

      2. associate-*l* 81.9%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in x around inf 38.5%

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

      1. associate-*r/ 38.5%

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

      2. associate-*r* 38.5%

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

      3. times-frac 50.0%

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

      4. *-commutative 50.0%

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

   6. Simplified 50.0%

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

   if 3.7000000000000002e143 < z

   1. Initial program 57.3%

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

      1. associate-/r* 68.0%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in z around inf 70.2%

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

      1. associate-*r* 70.2%

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

      2. *-commutative 70.2%

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

      3. *-commutative 70.2%

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

   6. Simplified 70.2%

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

      1. div-inv 70.2%

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

   8. Applied egg-rr 70.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(a \cdot -4\right)\right) \cdot \frac{1}{c}} \]
3. Recombined 10 regimes into one program.

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+200}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+117}:\\ \;\;\;\;\left(9 \cdot \frac{y}{\frac{z}{x}}\right) \cdot \frac{1}{c}\\ \mathbf{elif}\;z \leq -225:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-45}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-172}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{c}{x}}}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-281}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-183}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-127}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(a \cdot -4\right)\right) \cdot \frac{1}{c}\\ \end{array} \]

Alternative 8: 48.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{+29}:\\ \;\;\;\;\frac{x \cdot \frac{9}{\frac{c}{y}}}{z}\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-218}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-286}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-253}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{-89}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \frac{y}{z}\right) \cdot \frac{9}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ b c) z)))
   (if (<= x -1.05e+29)
     (/ (* x (/ 9.0 (/ c y))) z)
     (if (<= x -1e-164)
       t_1
       (if (<= x -1.15e-218)
         (* -4.0 (* t (/ a c)))
         (if (<= x -3.9e-286)
           (/ (/ b z) c)
           (if (<= x 5.3e-253)
             (* -4.0 (/ a (/ c t)))
             (if (<= x 2.6e-122)
               t_1
               (if (<= x 1.06e-89)
                 (* (* a -4.0) (/ t c))
                 (* (* x (/ y z)) (/ 9.0 c)))))))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double tmp;
	if (x <= -1.05e+29) {
		tmp = (x * (9.0 / (c / y))) / z;
	} else if (x <= -1e-164) {
		tmp = t_1;
	} else if (x <= -1.15e-218) {
		tmp = -4.0 * (t * (a / c));
	} else if (x <= -3.9e-286) {
		tmp = (b / z) / c;
	} else if (x <= 5.3e-253) {
		tmp = -4.0 * (a / (c / t));
	} else if (x <= 2.6e-122) {
		tmp = t_1;
	} else if (x <= 1.06e-89) {
		tmp = (a * -4.0) * (t / c);
	} else {
		tmp = (x * (y / z)) * (9.0 / c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b / c) / z
    if (x <= (-1.05d+29)) then
        tmp = (x * (9.0d0 / (c / y))) / z
    else if (x <= (-1d-164)) then
        tmp = t_1
    else if (x <= (-1.15d-218)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (x <= (-3.9d-286)) then
        tmp = (b / z) / c
    else if (x <= 5.3d-253) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (x <= 2.6d-122) then
        tmp = t_1
    else if (x <= 1.06d-89) then
        tmp = (a * (-4.0d0)) * (t / c)
    else
        tmp = (x * (y / z)) * (9.0d0 / c)
    end if
    code = tmp
end function

Java

assert x < y;
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 tmp;
	if (x <= -1.05e+29) {
		tmp = (x * (9.0 / (c / y))) / z;
	} else if (x <= -1e-164) {
		tmp = t_1;
	} else if (x <= -1.15e-218) {
		tmp = -4.0 * (t * (a / c));
	} else if (x <= -3.9e-286) {
		tmp = (b / z) / c;
	} else if (x <= 5.3e-253) {
		tmp = -4.0 * (a / (c / t));
	} else if (x <= 2.6e-122) {
		tmp = t_1;
	} else if (x <= 1.06e-89) {
		tmp = (a * -4.0) * (t / c);
	} else {
		tmp = (x * (y / z)) * (9.0 / c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = (b / c) / z
	tmp = 0
	if x <= -1.05e+29:
		tmp = (x * (9.0 / (c / y))) / z
	elif x <= -1e-164:
		tmp = t_1
	elif x <= -1.15e-218:
		tmp = -4.0 * (t * (a / c))
	elif x <= -3.9e-286:
		tmp = (b / z) / c
	elif x <= 5.3e-253:
		tmp = -4.0 * (a / (c / t))
	elif x <= 2.6e-122:
		tmp = t_1
	elif x <= 1.06e-89:
		tmp = (a * -4.0) * (t / c)
	else:
		tmp = (x * (y / z)) * (9.0 / c)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (x <= -1.05e+29)
		tmp = Float64(Float64(x * Float64(9.0 / Float64(c / y))) / z);
	elseif (x <= -1e-164)
		tmp = t_1;
	elseif (x <= -1.15e-218)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (x <= -3.9e-286)
		tmp = Float64(Float64(b / z) / c);
	elseif (x <= 5.3e-253)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (x <= 2.6e-122)
		tmp = t_1;
	elseif (x <= 1.06e-89)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	else
		tmp = Float64(Float64(x * Float64(y / z)) * Float64(9.0 / c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b / c) / z;
	tmp = 0.0;
	if (x <= -1.05e+29)
		tmp = (x * (9.0 / (c / y))) / z;
	elseif (x <= -1e-164)
		tmp = t_1;
	elseif (x <= -1.15e-218)
		tmp = -4.0 * (t * (a / c));
	elseif (x <= -3.9e-286)
		tmp = (b / z) / c;
	elseif (x <= 5.3e-253)
		tmp = -4.0 * (a / (c / t));
	elseif (x <= 2.6e-122)
		tmp = t_1;
	elseif (x <= 1.06e-89)
		tmp = (a * -4.0) * (t / c);
	else
		tmp = (x * (y / z)) * (9.0 / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y 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 / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[x, -1.05e+29], N[(N[(x * N[(9.0 / N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, -1e-164], t$95$1, If[LessEqual[x, -1.15e-218], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.9e-286], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[x, 5.3e-253], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e-122], t$95$1, If[LessEqual[x, 1.06e-89], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] * N[(9.0 / c), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -1.0500000000000001e29

   1. Initial program 67.6%

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

      1. associate-*l* 67.6%

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

      2. associate-*l* 67.6%

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

   3. Simplified 67.6%

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

   4. Taylor expanded in x around inf 41.6%

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

      1. associate-*r/ 41.6%

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

      2. associate-*r* 41.6%

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

      3. times-frac 55.7%

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

      4. *-commutative 55.7%

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

   6. Simplified 55.7%

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

      1. associate-*l/ 57.5%

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

      2. associate-/l* 57.5%

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

   8. Applied egg-rr 57.5%

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

   if -1.0500000000000001e29 < x < -9.99999999999999962e-165 or 5.3000000000000002e-253 < x < 2.59999999999999975e-122

   1. Initial program 89.3%

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

      1. associate-*l* 89.3%

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

      2. associate-*l* 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in b around inf 50.8%

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

      1. associate-/r* 52.2%

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

   6. Simplified 52.2%

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

   if -9.99999999999999962e-165 < x < -1.14999999999999997e-218

   1. Initial program 89.1%

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

      1. associate-*l* 89.3%

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

      2. associate-*l* 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in z around inf 37.9%

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

      1. *-commutative 37.9%

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

      2. associate-/l* 38.1%

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

      3. associate-/r/ 37.9%

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

   6. Simplified 37.9%

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

   if -1.14999999999999997e-218 < x < -3.89999999999999995e-286

   1. Initial program 55.4%

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

      1. associate-/r* 73.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in x around 0 91.0%

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

      1. associate-*r* 91.0%

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

      2. *-commutative 91.0%

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

      3. *-commutative 91.0%

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

   6. Simplified 91.0%

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

   7. Taylor expanded in b around inf 38.0%

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

   if -3.89999999999999995e-286 < x < 5.3000000000000002e-253

   1. Initial program 80.3%

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

      1. associate-*l* 80.3%

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

      2. associate-*l* 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in z around inf 41.5%

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

      1. *-commutative 41.5%

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

      2. associate-/l* 38.1%

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

   6. Simplified 38.1%

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

   if 2.59999999999999975e-122 < x < 1.0600000000000001e-89

   1. Initial program 67.0%

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

      1. associate-/r* 67.6%

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

   3. Simplified 83.9%

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

      1. div-inv 83.9%

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

      2. +-commutative 83.9%

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

      3. fma-def 83.9%

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

   5. Applied egg-rr 83.9%

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

   6. Taylor expanded in t around inf 36.6%

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

      1. associate-*r/ 36.6%

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

      2. associate-*r* 36.6%

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

      3. *-commutative 36.6%

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

      4. *-commutative 36.6%

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

      5. associate-*l/ 52.7%

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

      6. *-commutative 52.7%

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

      7. *-commutative 52.7%

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

   8. Simplified 52.7%

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

   if 1.0600000000000001e-89 < x

   1. Initial program 76.7%

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

      1. associate-/r* 73.6%

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

   3. Simplified 83.2%

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

      1. div-inv 83.1%

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

      2. +-commutative 83.1%

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

      3. fma-def 83.1%

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

   5. Applied egg-rr 83.1%

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

   6. Taylor expanded in x around inf 49.9%

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

      1. associate-*r/ 49.9%

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

      2. *-commutative 49.9%

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

      3. *-commutative 49.9%

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

      4. *-commutative 49.9%

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

      5. times-frac 47.7%

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

      6. *-commutative 47.7%

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

      7. associate-/l* 54.7%

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

      8. associate-/r/ 54.8%

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

   8. Simplified 54.8%

      \[\leadsto \color{blue}{\left(\frac{y}{z} \cdot x\right) \cdot \frac{9}{c}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+29}:\\ \;\;\;\;\frac{x \cdot \frac{9}{\frac{c}{y}}}{z}\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-164}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-218}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-286}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-253}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-122}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{-89}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \frac{y}{z}\right) \cdot \frac{9}{c}\\ \end{array} \]

Alternative 9: 49.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{+28}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{c}{x}}}{z}\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-219}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-285}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq 10^{-249}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-90}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \frac{y}{z}\right) \cdot \frac{9}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ b c) z)))
   (if (<= x -2.7e+28)
     (/ (* 9.0 (/ y (/ c x))) z)
     (if (<= x -1.1e-164)
       t_1
       (if (<= x -4.8e-219)
         (* -4.0 (* t (/ a c)))
         (if (<= x -4.5e-285)
           (/ (/ b z) c)
           (if (<= x 1e-249)
             (* -4.0 (/ a (/ c t)))
             (if (<= x 2.5e-122)
               t_1
               (if (<= x 1.9e-90)
                 (* (* a -4.0) (/ t c))
                 (* (* x (/ y z)) (/ 9.0 c)))))))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double tmp;
	if (x <= -2.7e+28) {
		tmp = (9.0 * (y / (c / x))) / z;
	} else if (x <= -1.1e-164) {
		tmp = t_1;
	} else if (x <= -4.8e-219) {
		tmp = -4.0 * (t * (a / c));
	} else if (x <= -4.5e-285) {
		tmp = (b / z) / c;
	} else if (x <= 1e-249) {
		tmp = -4.0 * (a / (c / t));
	} else if (x <= 2.5e-122) {
		tmp = t_1;
	} else if (x <= 1.9e-90) {
		tmp = (a * -4.0) * (t / c);
	} else {
		tmp = (x * (y / z)) * (9.0 / c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b / c) / z
    if (x <= (-2.7d+28)) then
        tmp = (9.0d0 * (y / (c / x))) / z
    else if (x <= (-1.1d-164)) then
        tmp = t_1
    else if (x <= (-4.8d-219)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (x <= (-4.5d-285)) then
        tmp = (b / z) / c
    else if (x <= 1d-249) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (x <= 2.5d-122) then
        tmp = t_1
    else if (x <= 1.9d-90) then
        tmp = (a * (-4.0d0)) * (t / c)
    else
        tmp = (x * (y / z)) * (9.0d0 / c)
    end if
    code = tmp
end function

Java

assert x < y;
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 tmp;
	if (x <= -2.7e+28) {
		tmp = (9.0 * (y / (c / x))) / z;
	} else if (x <= -1.1e-164) {
		tmp = t_1;
	} else if (x <= -4.8e-219) {
		tmp = -4.0 * (t * (a / c));
	} else if (x <= -4.5e-285) {
		tmp = (b / z) / c;
	} else if (x <= 1e-249) {
		tmp = -4.0 * (a / (c / t));
	} else if (x <= 2.5e-122) {
		tmp = t_1;
	} else if (x <= 1.9e-90) {
		tmp = (a * -4.0) * (t / c);
	} else {
		tmp = (x * (y / z)) * (9.0 / c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = (b / c) / z
	tmp = 0
	if x <= -2.7e+28:
		tmp = (9.0 * (y / (c / x))) / z
	elif x <= -1.1e-164:
		tmp = t_1
	elif x <= -4.8e-219:
		tmp = -4.0 * (t * (a / c))
	elif x <= -4.5e-285:
		tmp = (b / z) / c
	elif x <= 1e-249:
		tmp = -4.0 * (a / (c / t))
	elif x <= 2.5e-122:
		tmp = t_1
	elif x <= 1.9e-90:
		tmp = (a * -4.0) * (t / c)
	else:
		tmp = (x * (y / z)) * (9.0 / c)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (x <= -2.7e+28)
		tmp = Float64(Float64(9.0 * Float64(y / Float64(c / x))) / z);
	elseif (x <= -1.1e-164)
		tmp = t_1;
	elseif (x <= -4.8e-219)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (x <= -4.5e-285)
		tmp = Float64(Float64(b / z) / c);
	elseif (x <= 1e-249)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (x <= 2.5e-122)
		tmp = t_1;
	elseif (x <= 1.9e-90)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	else
		tmp = Float64(Float64(x * Float64(y / z)) * Float64(9.0 / c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b / c) / z;
	tmp = 0.0;
	if (x <= -2.7e+28)
		tmp = (9.0 * (y / (c / x))) / z;
	elseif (x <= -1.1e-164)
		tmp = t_1;
	elseif (x <= -4.8e-219)
		tmp = -4.0 * (t * (a / c));
	elseif (x <= -4.5e-285)
		tmp = (b / z) / c;
	elseif (x <= 1e-249)
		tmp = -4.0 * (a / (c / t));
	elseif (x <= 2.5e-122)
		tmp = t_1;
	elseif (x <= 1.9e-90)
		tmp = (a * -4.0) * (t / c);
	else
		tmp = (x * (y / z)) * (9.0 / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y 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 / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[x, -2.7e+28], N[(N[(9.0 * N[(y / N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, -1.1e-164], t$95$1, If[LessEqual[x, -4.8e-219], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.5e-285], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[x, 1e-249], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e-122], t$95$1, If[LessEqual[x, 1.9e-90], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] * N[(9.0 / c), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -2.7000000000000002e28

   1. Initial program 67.6%

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

      1. associate-*l* 67.6%

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

      2. associate-*l* 67.6%

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

   3. Simplified 67.6%

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

   4. Taylor expanded in x around inf 41.6%

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

      1. *-commutative 41.6%

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

      2. associate-/r* 46.1%

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

      3. associate-*l/ 46.2%

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

      4. associate-/l* 57.4%

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

   6. Simplified 57.4%

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

   if -2.7000000000000002e28 < x < -1.09999999999999994e-164 or 1.00000000000000005e-249 < x < 2.4999999999999999e-122

   1. Initial program 89.3%

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

      1. associate-*l* 89.3%

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

      2. associate-*l* 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in b around inf 50.8%

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

      1. associate-/r* 52.2%

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

   6. Simplified 52.2%

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

   if -1.09999999999999994e-164 < x < -4.80000000000000028e-219

   1. Initial program 89.1%

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

      1. associate-*l* 89.3%

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

      2. associate-*l* 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in z around inf 37.9%

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

      1. *-commutative 37.9%

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

      2. associate-/l* 38.1%

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

      3. associate-/r/ 37.9%

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

   6. Simplified 37.9%

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

   if -4.80000000000000028e-219 < x < -4.5000000000000002e-285

   1. Initial program 55.4%

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

      1. associate-/r* 73.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in x around 0 91.0%

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

      1. associate-*r* 91.0%

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

      2. *-commutative 91.0%

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

      3. *-commutative 91.0%

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

   6. Simplified 91.0%

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

   7. Taylor expanded in b around inf 38.0%

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

   if -4.5000000000000002e-285 < x < 1.00000000000000005e-249

   1. Initial program 80.3%

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

      1. associate-*l* 80.3%

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

      2. associate-*l* 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in z around inf 41.5%

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

      1. *-commutative 41.5%

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

      2. associate-/l* 38.1%

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

   6. Simplified 38.1%

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

   if 2.4999999999999999e-122 < x < 1.9e-90

   1. Initial program 67.0%

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

      1. associate-/r* 67.6%

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

   3. Simplified 83.9%

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

      1. div-inv 83.9%

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

      2. +-commutative 83.9%

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

      3. fma-def 83.9%

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

   5. Applied egg-rr 83.9%

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

   6. Taylor expanded in t around inf 36.6%

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

      1. associate-*r/ 36.6%

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

      2. associate-*r* 36.6%

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

      3. *-commutative 36.6%

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

      4. *-commutative 36.6%

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

      5. associate-*l/ 52.7%

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

      6. *-commutative 52.7%

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

      7. *-commutative 52.7%

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

   8. Simplified 52.7%

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

   if 1.9e-90 < x

   1. Initial program 76.7%

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

      1. associate-/r* 73.6%

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

   3. Simplified 83.2%

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

      1. div-inv 83.1%

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

      2. +-commutative 83.1%

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

      3. fma-def 83.1%

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

   5. Applied egg-rr 83.1%

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

   6. Taylor expanded in x around inf 49.9%

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

      1. associate-*r/ 49.9%

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

      2. *-commutative 49.9%

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

      3. *-commutative 49.9%

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

      4. *-commutative 49.9%

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

      5. times-frac 47.7%

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

      6. *-commutative 47.7%

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

      7. associate-/l* 54.7%

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

      8. associate-/r/ 54.8%

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

   8. Simplified 54.8%

      \[\leadsto \color{blue}{\left(\frac{y}{z} \cdot x\right) \cdot \frac{9}{c}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+28}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{c}{x}}}{z}\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-164}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-219}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-285}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq 10^{-249}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-122}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-90}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \frac{y}{z}\right) \cdot \frac{9}{c}\\ \end{array} \]

Alternative 10: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+202}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+143}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - 4 \cdot \left(t \cdot \left(z \cdot a\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -7.6e+202)
   (* (* a -4.0) (/ t c))
   (if (<= z 5.2e+143)
     (/ (+ b (- (* x (* 9.0 y)) (* 4.0 (* t (* z a))))) (* c z))
     (/ (+ (* t (* a -4.0)) (/ b z)) c))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -7.6e+202) {
		tmp = (a * -4.0) * (t / c);
	} else if (z <= 5.2e+143) {
		tmp = (b + ((x * (9.0 * y)) - (4.0 * (t * (z * a))))) / (c * z);
	} else {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-7.6d+202)) then
        tmp = (a * (-4.0d0)) * (t / c)
    else if (z <= 5.2d+143) then
        tmp = (b + ((x * (9.0d0 * y)) - (4.0d0 * (t * (z * a))))) / (c * z)
    else
        tmp = ((t * (a * (-4.0d0))) + (b / z)) / c
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -7.6e+202) {
		tmp = (a * -4.0) * (t / c);
	} else if (z <= 5.2e+143) {
		tmp = (b + ((x * (9.0 * y)) - (4.0 * (t * (z * a))))) / (c * z);
	} else {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -7.6e+202:
		tmp = (a * -4.0) * (t / c)
	elif z <= 5.2e+143:
		tmp = (b + ((x * (9.0 * y)) - (4.0 * (t * (z * a))))) / (c * z)
	else:
		tmp = ((t * (a * -4.0)) + (b / z)) / c
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -7.6e+202)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	elseif (z <= 5.2e+143)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(4.0 * Float64(t * Float64(z * a))))) / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -7.6e+202)
		tmp = (a * -4.0) * (t / c);
	elseif (z <= 5.2e+143)
		tmp = (b + ((x * (9.0 * y)) - (4.0 * (t * (z * a))))) / (c * z);
	else
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -7.6e+202], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+143], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.6000000000000001e202

   1. Initial program 36.3%

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

      1. associate-/r* 48.5%

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

   3. Simplified 82.8%

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

      1. div-inv 82.7%

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

      2. +-commutative 82.7%

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

      3. fma-def 82.7%

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

   5. Applied egg-rr 82.7%

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

   6. Taylor expanded in t around inf 71.9%

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

      1. associate-*r/ 71.9%

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

      2. associate-*r* 71.9%

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

      3. *-commutative 71.9%

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

      4. *-commutative 71.9%

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

      5. associate-*l/ 75.5%

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

      6. *-commutative 75.5%

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

      7. *-commutative 75.5%

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

   8. Simplified 75.5%

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

   if -7.6000000000000001e202 < z < 5.1999999999999998e143

   1. Initial program 87.3%

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

      1. associate-*l* 87.3%

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

      2. associate-*l* 86.8%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in z around 0 87.3%

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

      1. associate-*r* 86.8%

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

      2. *-commutative 86.8%

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

      3. associate-*l* 87.8%

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

   6. Simplified 87.8%

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

   if 5.1999999999999998e143 < z

   1. Initial program 57.3%

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

      1. associate-/r* 68.0%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in x around 0 81.9%

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

      1. associate-*r* 81.9%

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

      2. *-commutative 81.9%

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

      3. *-commutative 81.9%

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

   6. Simplified 81.9%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+202}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+143}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - 4 \cdot \left(t \cdot \left(z \cdot a\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 11: 64.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{if}\;a \leq -205:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+146}:\\ \;\;\;\;\left(t \cdot \left(a \cdot -4\right)\right) \cdot \frac{1}{c}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{+162}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (* 9.0 (* x y))) (* c z))))
   (if (<= a -205.0)
     (* (* a -4.0) (/ t c))
     (if (<= a 7e+92)
       t_1
       (if (<= a 3.5e+146)
         (* (* t (* a -4.0)) (/ 1.0 c))
         (if (<= a 5.4e+162) t_1 (* -4.0 (/ a (/ c t)))))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (9.0 * (x * y))) / (c * z);
	double tmp;
	if (a <= -205.0) {
		tmp = (a * -4.0) * (t / c);
	} else if (a <= 7e+92) {
		tmp = t_1;
	} else if (a <= 3.5e+146) {
		tmp = (t * (a * -4.0)) * (1.0 / c);
	} else if (a <= 5.4e+162) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b + (9.0d0 * (x * y))) / (c * z)
    if (a <= (-205.0d0)) then
        tmp = (a * (-4.0d0)) * (t / c)
    else if (a <= 7d+92) then
        tmp = t_1
    else if (a <= 3.5d+146) then
        tmp = (t * (a * (-4.0d0))) * (1.0d0 / c)
    else if (a <= 5.4d+162) then
        tmp = t_1
    else
        tmp = (-4.0d0) * (a / (c / t))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (9.0 * (x * y))) / (c * z);
	double tmp;
	if (a <= -205.0) {
		tmp = (a * -4.0) * (t / c);
	} else if (a <= 7e+92) {
		tmp = t_1;
	} else if (a <= 3.5e+146) {
		tmp = (t * (a * -4.0)) * (1.0 / c);
	} else if (a <= 5.4e+162) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = (b + (9.0 * (x * y))) / (c * z)
	tmp = 0
	if a <= -205.0:
		tmp = (a * -4.0) * (t / c)
	elif a <= 7e+92:
		tmp = t_1
	elif a <= 3.5e+146:
		tmp = (t * (a * -4.0)) * (1.0 / c)
	elif a <= 5.4e+162:
		tmp = t_1
	else:
		tmp = -4.0 * (a / (c / t))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c * z))
	tmp = 0.0
	if (a <= -205.0)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	elseif (a <= 7e+92)
		tmp = t_1;
	elseif (a <= 3.5e+146)
		tmp = Float64(Float64(t * Float64(a * -4.0)) * Float64(1.0 / c));
	elseif (a <= 5.4e+162)
		tmp = t_1;
	else
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + (9.0 * (x * y))) / (c * z);
	tmp = 0.0;
	if (a <= -205.0)
		tmp = (a * -4.0) * (t / c);
	elseif (a <= 7e+92)
		tmp = t_1;
	elseif (a <= 3.5e+146)
		tmp = (t * (a * -4.0)) * (1.0 / c);
	elseif (a <= 5.4e+162)
		tmp = t_1;
	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.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -205.0], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e+92], t$95$1, If[LessEqual[a, 3.5e+146], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.4e+162], t$95$1, N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -205

   1. Initial program 74.2%

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

      1. associate-/r* 71.7%

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

   3. Simplified 79.1%

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

      1. div-inv 79.0%

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

      2. +-commutative 79.0%

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

      3. fma-def 79.1%

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

   5. Applied egg-rr 79.1%

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

   6. Taylor expanded in t around inf 43.1%

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

      1. associate-*r/ 43.1%

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

      2. associate-*r* 43.1%

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

      3. *-commutative 43.1%

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

      4. *-commutative 43.1%

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

      5. associate-*l/ 48.9%

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

      6. *-commutative 48.9%

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

      7. *-commutative 48.9%

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

   8. Simplified 48.9%

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

   if -205 < a < 6.99999999999999972e92 or 3.5000000000000001e146 < a < 5.4000000000000003e162

   1. Initial program 80.7%

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

      1. associate-*l* 81.3%

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

      2. associate-*l* 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in x around inf 71.0%

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

   if 6.99999999999999972e92 < a < 3.5000000000000001e146

   1. Initial program 79.2%

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

      1. associate-/r* 68.8%

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

   3. Simplified 78.2%

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

   4. Taylor expanded in z around inf 46.3%

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

      1. associate-*r* 46.3%

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

      2. *-commutative 46.3%

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

      3. *-commutative 46.3%

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

   6. Simplified 46.3%

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

      1. div-inv 46.5%

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

   8. Applied egg-rr 46.5%

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

   if 5.4000000000000003e162 < a

   1. Initial program 68.4%

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

      1. associate-*l* 68.4%

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

      2. associate-*l* 65.4%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in z around inf 77.4%

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

      1. *-commutative 77.4%

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

      2. associate-/l* 74.6%

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

   6. Simplified 74.6%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -205:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+92}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+146}:\\ \;\;\;\;\left(t \cdot \left(a \cdot -4\right)\right) \cdot \frac{1}{c}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{+162}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 12: 49.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := 9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{if}\;b \leq -6.4 \cdot 10^{+49}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-264}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+69}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (/ (* x y) (* c z)))))
   (if (<= b -6.4e+49)
     (/ (/ b z) c)
     (if (<= b -3.2e-194)
       t_1
       (if (<= b -2.3e-264)
         (* -4.0 (/ a (/ c t)))
         (if (<= b -2.4e-293)
           t_1
           (if (<= b 3e+69) (* (* a -4.0) (/ t c)) (/ b (* c z)))))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((x * y) / (c * z));
	double tmp;
	if (b <= -6.4e+49) {
		tmp = (b / z) / c;
	} else if (b <= -3.2e-194) {
		tmp = t_1;
	} else if (b <= -2.3e-264) {
		tmp = -4.0 * (a / (c / t));
	} else if (b <= -2.4e-293) {
		tmp = t_1;
	} else if (b <= 3e+69) {
		tmp = (a * -4.0) * (t / c);
	} else {
		tmp = b / (c * z);
	}
	return tmp;
}

Fortran

NOTE: x and y 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 * ((x * y) / (c * z))
    if (b <= (-6.4d+49)) then
        tmp = (b / z) / c
    else if (b <= (-3.2d-194)) then
        tmp = t_1
    else if (b <= (-2.3d-264)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (b <= (-2.4d-293)) then
        tmp = t_1
    else if (b <= 3d+69) then
        tmp = (a * (-4.0d0)) * (t / c)
    else
        tmp = b / (c * z)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((x * y) / (c * z));
	double tmp;
	if (b <= -6.4e+49) {
		tmp = (b / z) / c;
	} else if (b <= -3.2e-194) {
		tmp = t_1;
	} else if (b <= -2.3e-264) {
		tmp = -4.0 * (a / (c / t));
	} else if (b <= -2.4e-293) {
		tmp = t_1;
	} else if (b <= 3e+69) {
		tmp = (a * -4.0) * (t / c);
	} else {
		tmp = b / (c * z);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * ((x * y) / (c * z))
	tmp = 0
	if b <= -6.4e+49:
		tmp = (b / z) / c
	elif b <= -3.2e-194:
		tmp = t_1
	elif b <= -2.3e-264:
		tmp = -4.0 * (a / (c / t))
	elif b <= -2.4e-293:
		tmp = t_1
	elif b <= 3e+69:
		tmp = (a * -4.0) * (t / c)
	else:
		tmp = b / (c * z)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(Float64(x * y) / Float64(c * z)))
	tmp = 0.0
	if (b <= -6.4e+49)
		tmp = Float64(Float64(b / z) / c);
	elseif (b <= -3.2e-194)
		tmp = t_1;
	elseif (b <= -2.3e-264)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (b <= -2.4e-293)
		tmp = t_1;
	elseif (b <= 3e+69)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	else
		tmp = Float64(b / Float64(c * z));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * ((x * y) / (c * z));
	tmp = 0.0;
	if (b <= -6.4e+49)
		tmp = (b / z) / c;
	elseif (b <= -3.2e-194)
		tmp = t_1;
	elseif (b <= -2.3e-264)
		tmp = -4.0 * (a / (c / t));
	elseif (b <= -2.4e-293)
		tmp = t_1;
	elseif (b <= 3e+69)
		tmp = (a * -4.0) * (t / c);
	else
		tmp = b / (c * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.4e+49], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[b, -3.2e-194], t$95$1, If[LessEqual[b, -2.3e-264], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.4e-293], t$95$1, If[LessEqual[b, 3e+69], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -6.40000000000000028e49

   1. Initial program 80.0%

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

      1. associate-/r* 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 90.5%

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

   4. Taylor expanded in x around 0 76.3%

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

      1. associate-*r* 76.3%

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

      2. *-commutative 76.3%

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

      3. *-commutative 76.3%

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

   6. Simplified 76.3%

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

   7. Taylor expanded in b around inf 55.1%

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

   if -6.40000000000000028e49 < b < -3.2000000000000003e-194 or -2.30000000000000012e-264 < b < -2.3999999999999999e-293

   1. Initial program 81.8%

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

      1. associate-*l* 81.8%

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

      2. associate-*l* 81.7%

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

   3. Simplified 81.7%

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

   4. Taylor expanded in x around inf 55.7%

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

   if -3.2000000000000003e-194 < b < -2.30000000000000012e-264

   1. Initial program 73.3%

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

      1. associate-*l* 73.3%

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

      2. associate-*l* 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in z around inf 67.3%

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

      1. *-commutative 67.3%

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

      2. associate-/l* 67.4%

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

   6. Simplified 67.4%

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

   if -2.3999999999999999e-293 < b < 2.99999999999999983e69

   1. Initial program 74.9%

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

      1. associate-/r* 77.3%

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

   3. Simplified 89.7%

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

      1. div-inv 89.7%

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

      2. +-commutative 89.7%

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

      3. fma-def 89.7%

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

   5. Applied egg-rr 89.7%

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

   6. Taylor expanded in t around inf 50.8%

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

      1. associate-*r/ 50.8%

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

      2. associate-*r* 50.8%

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

      3. *-commutative 50.8%

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

      4. *-commutative 50.8%

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

      5. associate-*l/ 48.5%

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

      6. *-commutative 48.5%

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

      7. *-commutative 48.5%

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

   8. Simplified 48.5%

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

   if 2.99999999999999983e69 < b

   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-*l* 75.6%

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

      2. associate-*l* 79.3%

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

   3. Simplified 79.3%

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

   4. Taylor expanded in b around inf 59.6%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{+49}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-194}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-264}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-293}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+69}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]

Alternative 13: 72.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+37}:\\ \;\;\;\;\frac{t_1 + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-90}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= x -2.5e+37)
     (/ (+ t_1 (* 9.0 (/ (* x y) z))) c)
     (if (<= x 4.5e-90)
       (/ (+ t_1 (/ b z)) c)
       (/ (+ (/ b z) (* 9.0 (/ y (/ z x)))) c)))))

C

assert(x < y);
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 (x <= -2.5e+37) {
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	} else if (x <= 4.5e-90) {
		tmp = (t_1 + (b / z)) / c;
	} else {
		tmp = ((b / z) + (9.0 * (y / (z / x)))) / c;
	}
	return tmp;
}

Fortran

NOTE: x and y 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 (x <= (-2.5d+37)) then
        tmp = (t_1 + (9.0d0 * ((x * y) / z))) / c
    else if (x <= 4.5d-90) then
        tmp = (t_1 + (b / z)) / c
    else
        tmp = ((b / z) + (9.0d0 * (y / (z / x)))) / c
    end if
    code = tmp
end function

Java

assert x < y;
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 (x <= -2.5e+37) {
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	} else if (x <= 4.5e-90) {
		tmp = (t_1 + (b / z)) / c;
	} else {
		tmp = ((b / z) + (9.0 * (y / (z / x)))) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = t * (a * -4.0)
	tmp = 0
	if x <= -2.5e+37:
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c
	elif x <= 4.5e-90:
		tmp = (t_1 + (b / z)) / c
	else:
		tmp = ((b / z) + (9.0 * (y / (z / x)))) / c
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (x <= -2.5e+37)
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	elseif (x <= 4.5e-90)
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(Float64(b / z) + Float64(9.0 * Float64(y / Float64(z / x)))) / c);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (x <= -2.5e+37)
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	elseif (x <= 4.5e-90)
		tmp = (t_1 + (b / z)) / c;
	else
		tmp = ((b / z) + (9.0 * (y / (z / x)))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5e+37], N[(N[(t$95$1 + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[x, 4.5e-90], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(b / z), $MachinePrecision] + N[(9.0 * N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.49999999999999994e37

   1. Initial program 65.9%

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

      1. associate-/r* 72.5%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in x around inf 67.6%

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

   if -2.49999999999999994e37 < x < 4.50000000000000009e-90

   1. Initial program 83.4%

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

      1. associate-/r* 80.6%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in x around 0 81.4%

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

      1. associate-*r* 81.4%

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

      2. *-commutative 81.4%

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

      3. *-commutative 81.4%

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

   6. Simplified 81.4%

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

   if 4.50000000000000009e-90 < x

   1. Initial program 76.7%

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

      1. associate-/r* 73.6%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in t around 0 64.5%

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

      1. associate-/l* 70.3%

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

   6. Simplified 70.3%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+37}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-90}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \end{array} \]

Alternative 14: 66.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -200:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+67}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -200.0)
   (* (* a -4.0) (/ t c))
   (if (<= a 2.7e+67)
     (/ (+ b (* 9.0 (* x y))) (* c z))
     (/ (+ (* t (* a -4.0)) (/ b z)) c))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -200.0) {
		tmp = (a * -4.0) * (t / c);
	} else if (a <= 2.7e+67) {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	} else {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (a <= (-200.0d0)) then
        tmp = (a * (-4.0d0)) * (t / c)
    else if (a <= 2.7d+67) then
        tmp = (b + (9.0d0 * (x * y))) / (c * z)
    else
        tmp = ((t * (a * (-4.0d0))) + (b / z)) / c
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -200.0) {
		tmp = (a * -4.0) * (t / c);
	} else if (a <= 2.7e+67) {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	} else {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -200.0:
		tmp = (a * -4.0) * (t / c)
	elif a <= 2.7e+67:
		tmp = (b + (9.0 * (x * y))) / (c * z)
	else:
		tmp = ((t * (a * -4.0)) + (b / z)) / c
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -200.0)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	elseif (a <= 2.7e+67)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -200.0)
		tmp = (a * -4.0) * (t / c);
	elseif (a <= 2.7e+67)
		tmp = (b + (9.0 * (x * y))) / (c * z);
	else
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -200.0], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e+67], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -200

   1. Initial program 74.2%

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

      1. associate-/r* 71.7%

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

   3. Simplified 79.1%

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

      1. div-inv 79.0%

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

      2. +-commutative 79.0%

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

      3. fma-def 79.1%

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

   5. Applied egg-rr 79.1%

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

   6. Taylor expanded in t around inf 43.1%

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

      1. associate-*r/ 43.1%

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

      2. associate-*r* 43.1%

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

      3. *-commutative 43.1%

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

      4. *-commutative 43.1%

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

      5. associate-*l/ 48.9%

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

      6. *-commutative 48.9%

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

      7. *-commutative 48.9%

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

   8. Simplified 48.9%

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

   if -200 < a < 2.6999999999999999e67

   1. Initial program 82.9%

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

      1. associate-*l* 83.0%

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

      2. associate-*l* 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in x around inf 74.3%

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

   if 2.6999999999999999e67 < a

   1. Initial program 67.6%

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

      1. associate-/r* 64.5%

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

   3. Simplified 78.5%

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

   4. Taylor expanded in x around 0 74.6%

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

      1. associate-*r* 74.6%

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

      2. *-commutative 74.6%

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

      3. *-commutative 74.6%

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

   6. Simplified 74.6%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -200:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+67}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 15: 49.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -4.3 \cdot 10^{+38}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+68}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -4.3e+38)
   (/ (/ b z) c)
   (if (<= b 4e+68) (* (* a -4.0) (/ t c)) (/ b (* c z)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -4.3e+38) {
		tmp = (b / z) / c;
	} else if (b <= 4e+68) {
		tmp = (a * -4.0) * (t / c);
	} else {
		tmp = b / (c * z);
	}
	return tmp;
}

Fortran

NOTE: x and y 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 <= (-4.3d+38)) then
        tmp = (b / z) / c
    else if (b <= 4d+68) then
        tmp = (a * (-4.0d0)) * (t / c)
    else
        tmp = b / (c * z)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -4.3e+38) {
		tmp = (b / z) / c;
	} else if (b <= 4e+68) {
		tmp = (a * -4.0) * (t / c);
	} else {
		tmp = b / (c * z);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -4.3e+38:
		tmp = (b / z) / c
	elif b <= 4e+68:
		tmp = (a * -4.0) * (t / c)
	else:
		tmp = b / (c * z)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -4.3e+38)
		tmp = Float64(Float64(b / z) / c);
	elseif (b <= 4e+68)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	else
		tmp = Float64(b / Float64(c * z));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -4.3e+38)
		tmp = (b / z) / c;
	elseif (b <= 4e+68)
		tmp = (a * -4.0) * (t / c);
	else
		tmp = b / (c * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -4.3e+38], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[b, 4e+68], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.2999999999999997e38

   1. Initial program 79.7%

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

      1. associate-/r* 81.2%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in x around 0 74.7%

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

      1. associate-*r* 74.7%

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

      2. *-commutative 74.7%

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

      3. *-commutative 74.7%

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

   6. Simplified 74.7%

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

   7. Taylor expanded in b around inf 54.8%

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

   if -4.2999999999999997e38 < b < 3.99999999999999981e68

   1. Initial program 77.1%

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

      1. associate-/r* 76.4%

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

   3. Simplified 84.2%

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

      1. div-inv 84.2%

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

      2. +-commutative 84.2%

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

      3. fma-def 84.9%

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

   5. Applied egg-rr 84.9%

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

   6. Taylor expanded in t around inf 45.5%

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

      1. associate-*r/ 45.5%

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

      2. associate-*r* 45.5%

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

      3. *-commutative 45.5%

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

      4. *-commutative 45.5%

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

      5. associate-*l/ 44.9%

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

      6. *-commutative 44.9%

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

      7. *-commutative 44.9%

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

   8. Simplified 44.9%

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

   if 3.99999999999999981e68 < b

   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-*l* 75.6%

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

      2. associate-*l* 79.3%

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

   3. Simplified 79.3%

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

   4. Taylor expanded in b around inf 59.6%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.3 \cdot 10^{+38}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+68}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]

Alternative 16: 35.5% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b / (c * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]

Derivation

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-*l* 77.9%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. associate-*l* 79.0%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 79.0%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

4. Taylor expanded in b around inf 35.6%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

5. Final simplification 35.6%

   \[\leadsto \frac{b}{c \cdot z} \]

Developer target: 80.1% 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 2023176 
(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)))