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

Percentage Accurate: 79.7% → 86.0%

Time: 18.0s

Alternatives: 15

Speedup: 0.7×

• 38.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.7% 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: 86.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := \frac{t_1 + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{if}\;z \leq -1.46 \cdot 10^{+156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+98}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{+72} \lor \neg \left(z \leq 1.95 \cdot 10^{+159}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(\left(x \cdot 9\right) \cdot y - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))) (t_2 (/ (+ t_1 (* 9.0 (/ y (/ z x)))) c)))
   (if (<= z -1.46e+156)
     t_2
     (if (<= z -5.2e+98)
       (/ (+ t_1 (/ b z)) c)
       (if (or (<= z -9.8e+72) (not (<= z 1.95e+159)))
         t_2
         (/ (+ b (- (* (* x 9.0) y) (* a (* t (* z 4.0))))) (* z 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 t_2 = (t_1 + (9.0 * (y / (z / x)))) / c;
	double tmp;
	if (z <= -1.46e+156) {
		tmp = t_2;
	} else if (z <= -5.2e+98) {
		tmp = (t_1 + (b / z)) / c;
	} else if ((z <= -9.8e+72) || !(z <= 1.95e+159)) {
		tmp = t_2;
	} else {
		tmp = (b + (((x * 9.0) * y) - (a * (t * (z * 4.0))))) / (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    t_2 = (t_1 + (9.0d0 * (y / (z / x)))) / c
    if (z <= (-1.46d+156)) then
        tmp = t_2
    else if (z <= (-5.2d+98)) then
        tmp = (t_1 + (b / z)) / c
    else if ((z <= (-9.8d+72)) .or. (.not. (z <= 1.95d+159))) then
        tmp = t_2
    else
        tmp = (b + (((x * 9.0d0) * y) - (a * (t * (z * 4.0d0))))) / (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 t_1 = t * (a * -4.0);
	double t_2 = (t_1 + (9.0 * (y / (z / x)))) / c;
	double tmp;
	if (z <= -1.46e+156) {
		tmp = t_2;
	} else if (z <= -5.2e+98) {
		tmp = (t_1 + (b / z)) / c;
	} else if ((z <= -9.8e+72) || !(z <= 1.95e+159)) {
		tmp = t_2;
	} else {
		tmp = (b + (((x * 9.0) * y) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = t * (a * -4.0)
	t_2 = (t_1 + (9.0 * (y / (z / x)))) / c
	tmp = 0
	if z <= -1.46e+156:
		tmp = t_2
	elif z <= -5.2e+98:
		tmp = (t_1 + (b / z)) / c
	elif (z <= -9.8e+72) or not (z <= 1.95e+159):
		tmp = t_2
	else:
		tmp = (b + (((x * 9.0) * y) - (a * (t * (z * 4.0))))) / (z * 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))
	t_2 = Float64(Float64(t_1 + Float64(9.0 * Float64(y / Float64(z / x)))) / c)
	tmp = 0.0
	if (z <= -1.46e+156)
		tmp = t_2;
	elseif (z <= -5.2e+98)
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	elseif ((z <= -9.8e+72) || !(z <= 1.95e+159))
		tmp = t_2;
	else
		tmp = Float64(Float64(b + Float64(Float64(Float64(x * 9.0) * y) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * 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);
	t_2 = (t_1 + (9.0 * (y / (z / x)))) / c;
	tmp = 0.0;
	if (z <= -1.46e+156)
		tmp = t_2;
	elseif (z <= -5.2e+98)
		tmp = (t_1 + (b / z)) / c;
	elseif ((z <= -9.8e+72) || ~((z <= 1.95e+159)))
		tmp = t_2;
	else
		tmp = (b + (((x * 9.0) * y) - (a * (t * (z * 4.0))))) / (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_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(9.0 * N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.46e+156], t$95$2, If[LessEqual[z, -5.2e+98], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[Or[LessEqual[z, -9.8e+72], N[Not[LessEqual[z, 1.95e+159]], $MachinePrecision]], t$95$2, 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[(z * c), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.46000000000000007e156 or -5.1999999999999999e98 < z < -9.80000000000000012e72 or 1.95e159 < z

   1. Initial program 49.9%

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

      1. associate-/r* 59.7%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in x around inf 82.4%

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

      1. associate-/l* 93.5%

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

   6. Simplified 93.5%

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

   if -1.46000000000000007e156 < z < -5.1999999999999999e98

   1. Initial program 60.0%

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

      1. associate-/r* 75.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in x around 0 83.2%

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

   if -9.80000000000000012e72 < z < 1.95e159

   1. Initial program 93.2%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{+156}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+98}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{+72} \lor \neg \left(z \leq 1.95 \cdot 10^{+159}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(\left(x \cdot 9\right) \cdot y - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 2: 87.5% accurate, 0.1× speedup

Math

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

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 (<= (* (* x 9.0) y) 1e+233)
   (/ (fma t (* a -4.0) (/ (fma x (* 9.0 y) b) z)) c)
   (* 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 tmp;
	if (((x * 9.0) * y) <= 1e+233) {
		tmp = fma(t, (a * -4.0), (fma(x, (9.0 * y), b) / z)) / c;
	} else {
		tmp = 9.0 * ((y / z) * (x / c));
	}
	return tmp;
}

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(Float64(x * 9.0) * y) <= 1e+233)
		tmp = Float64(fma(t, Float64(a * -4.0), Float64(fma(x, Float64(9.0 * y), b) / z)) / c);
	else
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / 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_] := If[LessEqual[N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision], 1e+233], N[(N[(t * N[(a * -4.0), $MachinePrecision] + N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x 9) y) < 9.99999999999999974e232

   1. Initial program 85.2%

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

      1. associate-/r* 84.0%

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

   3. Simplified 92.9%

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

   if 9.99999999999999974e232 < (*.f64 (*.f64 x 9) y)

   1. Initial program 51.7%

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

      1. associate-/r* 51.8%

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

   3. Simplified 55.5%

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

   4. Taylor expanded in x around inf 51.8%

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

      1. *-commutative 51.8%

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

      2. times-frac 78.8%

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

   6. Simplified 78.8%

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

4. Final simplification 91.3%

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

Alternative 3: 87.0% accurate, 0.2× speedup

Math

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

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 (<= (* (* x 9.0) y) 1e+233)
   (/ (+ (/ (fma x (* 9.0 y) b) z) (* t (* a -4.0))) c)
   (* 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 tmp;
	if (((x * 9.0) * y) <= 1e+233) {
		tmp = ((fma(x, (9.0 * y), b) / z) + (t * (a * -4.0))) / c;
	} else {
		tmp = 9.0 * ((y / z) * (x / c));
	}
	return tmp;
}

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(Float64(x * 9.0) * y) <= 1e+233)
		tmp = Float64(Float64(Float64(fma(x, Float64(9.0 * y), b) / z) + Float64(t * Float64(a * -4.0))) / c);
	else
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / 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_] := If[LessEqual[N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision], 1e+233], 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[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x 9) y) < 9.99999999999999974e232

   1. Initial program 85.2%

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

      1. associate-/r* 84.0%

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

   3. Simplified 92.4%

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

   if 9.99999999999999974e232 < (*.f64 (*.f64 x 9) y)

   1. Initial program 51.7%

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

      1. associate-/r* 51.8%

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

   3. Simplified 55.5%

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

   4. Taylor expanded in x around inf 51.8%

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

      1. *-commutative 51.8%

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

      2. times-frac 78.8%

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

   6. Simplified 78.8%

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

4. Final simplification 90.9%

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

Alternative 4: 84.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := \frac{t_1 + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{if}\;z \leq -1.62 \cdot 10^{+156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{+98}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -6.7 \cdot 10^{+72} \lor \neg \left(z \leq 3.5 \cdot 10^{+158}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: 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))) (t_2 (/ (+ t_1 (* 9.0 (/ y (/ z x)))) c)))
   (if (<= z -1.62e+156)
     t_2
     (if (<= z -2.35e+98)
       (/ (+ t_1 (/ b z)) c)
       (if (or (<= z -6.7e+72) (not (<= z 3.5e+158)))
         t_2
         (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* t a)))) (* z 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 t_2 = (t_1 + (9.0 * (y / (z / x)))) / c;
	double tmp;
	if (z <= -1.62e+156) {
		tmp = t_2;
	} else if (z <= -2.35e+98) {
		tmp = (t_1 + (b / z)) / c;
	} else if ((z <= -6.7e+72) || !(z <= 3.5e+158)) {
		tmp = t_2;
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    t_2 = (t_1 + (9.0d0 * (y / (z / x)))) / c
    if (z <= (-1.62d+156)) then
        tmp = t_2
    else if (z <= (-2.35d+98)) then
        tmp = (t_1 + (b / z)) / c
    else if ((z <= (-6.7d+72)) .or. (.not. (z <= 3.5d+158))) then
        tmp = t_2
    else
        tmp = (b + ((x * (9.0d0 * y)) - ((z * 4.0d0) * (t * a)))) / (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 t_1 = t * (a * -4.0);
	double t_2 = (t_1 + (9.0 * (y / (z / x)))) / c;
	double tmp;
	if (z <= -1.62e+156) {
		tmp = t_2;
	} else if (z <= -2.35e+98) {
		tmp = (t_1 + (b / z)) / c;
	} else if ((z <= -6.7e+72) || !(z <= 3.5e+158)) {
		tmp = t_2;
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = t * (a * -4.0)
	t_2 = (t_1 + (9.0 * (y / (z / x)))) / c
	tmp = 0
	if z <= -1.62e+156:
		tmp = t_2
	elif z <= -2.35e+98:
		tmp = (t_1 + (b / z)) / c
	elif (z <= -6.7e+72) or not (z <= 3.5e+158):
		tmp = t_2
	else:
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * 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))
	t_2 = Float64(Float64(t_1 + Float64(9.0 * Float64(y / Float64(z / x)))) / c)
	tmp = 0.0
	if (z <= -1.62e+156)
		tmp = t_2;
	elseif (z <= -2.35e+98)
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	elseif ((z <= -6.7e+72) || !(z <= 3.5e+158))
		tmp = t_2;
	else
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(t * a)))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (a * -4.0);
	t_2 = (t_1 + (9.0 * (y / (z / x)))) / c;
	tmp = 0.0;
	if (z <= -1.62e+156)
		tmp = t_2;
	elseif (z <= -2.35e+98)
		tmp = (t_1 + (b / z)) / c;
	elseif ((z <= -6.7e+72) || ~((z <= 3.5e+158)))
		tmp = t_2;
	else
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (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_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(9.0 * N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.62e+156], t$95$2, If[LessEqual[z, -2.35e+98], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[Or[LessEqual[z, -6.7e+72], N[Not[LessEqual[z, 3.5e+158]], $MachinePrecision]], t$95$2, N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.62000000000000006e156 or -2.34999999999999985e98 < z < -6.6999999999999998e72 or 3.5000000000000001e158 < z

   1. Initial program 49.9%

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

      1. associate-/r* 59.7%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in x around inf 82.4%

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

      1. associate-/l* 93.5%

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

   6. Simplified 93.5%

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

   if -1.62000000000000006e156 < z < -2.34999999999999985e98

   1. Initial program 60.0%

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

      1. associate-/r* 75.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in x around 0 83.2%

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

   if -6.6999999999999998e72 < z < 3.5000000000000001e158

   1. Initial program 93.2%

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

      1. associate-*l* 93.2%

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

      2. associate-*l* 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%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{+156}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{+98}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -6.7 \cdot 10^{+72} \lor \neg \left(z \leq 3.5 \cdot 10^{+158}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 5: 71.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ t_2 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{-108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.04 \cdot 10^{+201}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 10^{+208}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{z}{x}} + \frac{b}{z}}{c}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (/ (+ (* t (* a -4.0)) (/ b z)) c))
        (t_2 (/ (+ b (* 9.0 (* x y))) (* z c))))
   (if (<= y -8.2e-108)
     t_2
     (if (<= y 7.8e+105)
       t_1
       (if (<= y 1.04e+201)
         t_2
         (if (<= y 1e+208) t_1 (/ (+ (* 9.0 (/ y (/ z x))) (/ b z)) 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)) + (b / z)) / c;
	double t_2 = (b + (9.0 * (x * y))) / (z * c);
	double tmp;
	if (y <= -8.2e-108) {
		tmp = t_2;
	} else if (y <= 7.8e+105) {
		tmp = t_1;
	} else if (y <= 1.04e+201) {
		tmp = t_2;
	} else if (y <= 1e+208) {
		tmp = t_1;
	} else {
		tmp = ((9.0 * (y / (z / x))) + (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((t * (a * (-4.0d0))) + (b / z)) / c
    t_2 = (b + (9.0d0 * (x * y))) / (z * c)
    if (y <= (-8.2d-108)) then
        tmp = t_2
    else if (y <= 7.8d+105) then
        tmp = t_1
    else if (y <= 1.04d+201) then
        tmp = t_2
    else if (y <= 1d+208) then
        tmp = t_1
    else
        tmp = ((9.0d0 * (y / (z / x))) + (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 t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	double t_2 = (b + (9.0 * (x * y))) / (z * c);
	double tmp;
	if (y <= -8.2e-108) {
		tmp = t_2;
	} else if (y <= 7.8e+105) {
		tmp = t_1;
	} else if (y <= 1.04e+201) {
		tmp = t_2;
	} else if (y <= 1e+208) {
		tmp = t_1;
	} else {
		tmp = ((9.0 * (y / (z / x))) + (b / z)) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = ((t * (a * -4.0)) + (b / z)) / c
	t_2 = (b + (9.0 * (x * y))) / (z * c)
	tmp = 0
	if y <= -8.2e-108:
		tmp = t_2
	elif y <= 7.8e+105:
		tmp = t_1
	elif y <= 1.04e+201:
		tmp = t_2
	elif y <= 1e+208:
		tmp = t_1
	else:
		tmp = ((9.0 * (y / (z / x))) + (b / z)) / c
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c)
	t_2 = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c))
	tmp = 0.0
	if (y <= -8.2e-108)
		tmp = t_2;
	elseif (y <= 7.8e+105)
		tmp = t_1;
	elseif (y <= 1.04e+201)
		tmp = t_2;
	elseif (y <= 1e+208)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(y / Float64(z / x))) + 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)
	t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	t_2 = (b + (9.0 * (x * y))) / (z * c);
	tmp = 0.0;
	if (y <= -8.2e-108)
		tmp = t_2;
	elseif (y <= 7.8e+105)
		tmp = t_1;
	elseif (y <= 1.04e+201)
		tmp = t_2;
	elseif (y <= 1e+208)
		tmp = t_1;
	else
		tmp = ((9.0 * (y / (z / x))) + (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_] := Block[{t$95$1 = N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e-108], t$95$2, If[LessEqual[y, 7.8e+105], t$95$1, If[LessEqual[y, 1.04e+201], t$95$2, If[LessEqual[y, 1e+208], t$95$1, N[(N[(N[(9.0 * N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.20000000000000074e-108 or 7.79999999999999957e105 < y < 1.0400000000000001e201

   1. Initial program 78.4%

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

      1. associate-/r* 72.4%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in z around 0 61.3%

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

   if -8.20000000000000074e-108 < y < 7.79999999999999957e105 or 1.0400000000000001e201 < y < 9.9999999999999998e207

   1. Initial program 84.0%

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

      1. associate-/r* 84.0%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in x around 0 83.0%

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

   if 9.9999999999999998e207 < y

   1. Initial program 79.9%

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

      1. associate-/r* 88.5%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in t around 0 79.4%

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

      1. associate-/l* 88.1%

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

   6. Simplified 88.1%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-108}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+105}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 1.04 \cdot 10^{+201}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;y \leq 10^{+208}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{z}{x}} + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 6: 73.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;b \leq -1.7 \cdot 10^{+33} \lor \neg \left(b \leq 2.4 \cdot 10^{-138}\right):\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (or (<= b -1.7e+33) (not (<= b 2.4e-138)))
     (/ (+ t_1 (/ b z)) c)
     (/ (+ t_1 (* 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 ((b <= -1.7e+33) || !(b <= 2.4e-138)) {
		tmp = (t_1 + (b / z)) / c;
	} else {
		tmp = (t_1 + (9.0 * (y / (z / x)))) / c;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    if ((b <= (-1.7d+33)) .or. (.not. (b <= 2.4d-138))) then
        tmp = (t_1 + (b / z)) / c
    else
        tmp = (t_1 + (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 ((b <= -1.7e+33) || !(b <= 2.4e-138)) {
		tmp = (t_1 + (b / z)) / c;
	} else {
		tmp = (t_1 + (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 (b <= -1.7e+33) or not (b <= 2.4e-138):
		tmp = (t_1 + (b / z)) / c
	else:
		tmp = (t_1 + (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 ((b <= -1.7e+33) || !(b <= 2.4e-138))
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(y / Float64(z / x)))) / c);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if ((b <= -1.7e+33) || ~((b <= 2.4e-138)))
		tmp = (t_1 + (b / z)) / c;
	else
		tmp = (t_1 + (9.0 * (y / (z / x)))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -1.7e+33], N[Not[LessEqual[b, 2.4e-138]], $MachinePrecision]], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(t$95$1 + N[(9.0 * N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.7e33 or 2.3999999999999999e-138 < b

   1. Initial program 80.9%

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

      1. associate-/r* 78.7%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in x around 0 74.6%

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

   if -1.7e33 < b < 2.3999999999999999e-138

   1. Initial program 82.3%

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

      1. associate-/r* 82.7%

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

   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 inf 86.4%

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

      1. associate-/l* 89.8%

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

   6. Simplified 89.8%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+33} \lor \neg \left(b \leq 2.4 \cdot 10^{-138}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \end{array} \]

Alternative 7: 47.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+77}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-267}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-124}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \end{array} \]

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 (* 9.0 (* x (/ (/ y c) z)))))
   (if (<= t -1.15e+77)
     (* -4.0 (/ a (/ c t)))
     (if (<= t -5.5e-130)
       t_1
       (if (<= t 3.6e-267)
         (/ 1.0 (* z (/ c b)))
         (if (<= t 8e-155)
           t_1
           (if (<= t 3.4e-124) (/ b (* z c)) (/ (* 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 = 9.0 * (x * ((y / c) / z));
	double tmp;
	if (t <= -1.15e+77) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= -5.5e-130) {
		tmp = t_1;
	} else if (t <= 3.6e-267) {
		tmp = 1.0 / (z * (c / b));
	} else if (t <= 8e-155) {
		tmp = t_1;
	} else if (t <= 3.4e-124) {
		tmp = b / (z * c);
	} 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) :: tmp
    t_1 = 9.0d0 * (x * ((y / c) / z))
    if (t <= (-1.15d+77)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (t <= (-5.5d-130)) then
        tmp = t_1
    else if (t <= 3.6d-267) then
        tmp = 1.0d0 / (z * (c / b))
    else if (t <= 8d-155) then
        tmp = t_1
    else if (t <= 3.4d-124) then
        tmp = b / (z * c)
    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 = 9.0 * (x * ((y / c) / z));
	double tmp;
	if (t <= -1.15e+77) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= -5.5e-130) {
		tmp = t_1;
	} else if (t <= 3.6e-267) {
		tmp = 1.0 / (z * (c / b));
	} else if (t <= 8e-155) {
		tmp = t_1;
	} else if (t <= 3.4e-124) {
		tmp = b / (z * c);
	} 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 = 9.0 * (x * ((y / c) / z))
	tmp = 0
	if t <= -1.15e+77:
		tmp = -4.0 * (a / (c / t))
	elif t <= -5.5e-130:
		tmp = t_1
	elif t <= 3.6e-267:
		tmp = 1.0 / (z * (c / b))
	elif t <= 8e-155:
		tmp = t_1
	elif t <= 3.4e-124:
		tmp = b / (z * c)
	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(9.0 * Float64(x * Float64(Float64(y / c) / z)))
	tmp = 0.0
	if (t <= -1.15e+77)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (t <= -5.5e-130)
		tmp = t_1;
	elseif (t <= 3.6e-267)
		tmp = Float64(1.0 / Float64(z * Float64(c / b)));
	elseif (t <= 8e-155)
		tmp = t_1;
	elseif (t <= 3.4e-124)
		tmp = Float64(b / Float64(z * c));
	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 = 9.0 * (x * ((y / c) / z));
	tmp = 0.0;
	if (t <= -1.15e+77)
		tmp = -4.0 * (a / (c / t));
	elseif (t <= -5.5e-130)
		tmp = t_1;
	elseif (t <= 3.6e-267)
		tmp = 1.0 / (z * (c / b));
	elseif (t <= 8e-155)
		tmp = t_1;
	elseif (t <= 3.4e-124)
		tmp = b / (z * c);
	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[(9.0 * N[(x * N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+77], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.5e-130], t$95$1, If[LessEqual[t, 3.6e-267], N[(1.0 / N[(z * N[(c / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e-155], t$95$1, If[LessEqual[t, 3.4e-124], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.14999999999999997e77

   1. Initial program 66.9%

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

      1. associate-/r* 67.4%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in t around inf 63.7%

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

      1. associate-/l* 70.1%

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

   6. Simplified 70.1%

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

   if -1.14999999999999997e77 < t < -5.50000000000000007e-130 or 3.6000000000000001e-267 < t < 8.00000000000000011e-155

   1. Initial program 88.6%

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

      1. associate-/r* 77.9%

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

   3. Simplified 82.1%

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

      1. clear-num 82.1%

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

      2. inv-pow 82.1%

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

   5. Applied egg-rr 82.1%

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

   6. Taylor expanded in x around inf 50.0%

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

      1. *-commutative 50.0%

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

      2. *-commutative 50.0%

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

      3. associate-*r/ 50.1%

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

      4. *-commutative 50.1%

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

      5. associate-/r* 54.3%

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

   8. Simplified 54.3%

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

   if -5.50000000000000007e-130 < t < 3.6000000000000001e-267

   1. Initial program 80.9%

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

      1. associate-*l* 80.9%

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

      2. associate-*l* 83.7%

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

   3. Simplified 83.7%

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

      1. clear-num 83.5%

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

      2. inv-pow 83.5%

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

      3. associate-+l- 83.5%

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

      4. associate-*r* 83.5%

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

      5. associate-*r* 80.8%

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

      6. associate-+l- 80.8%

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

      7. +-commutative 80.8%

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

      8. associate-*r* 80.8%

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

      9. *-commutative 80.8%

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

      10. *-commutative 80.8%

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

   5. Applied egg-rr 80.8%

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

   6. Taylor expanded in b around inf 55.8%

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

      1. associate-/l* 53.4%

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

   8. Simplified 53.4%

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

      1. unpow-1 53.4%

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

      2. associate-/r/ 55.9%

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

   10. Applied egg-rr 55.9%

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

   if 8.00000000000000011e-155 < t < 3.4000000000000001e-124

   1. Initial program 84.9%

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

      1. associate-/r* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in b around inf 84.9%

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

      1. *-commutative 84.9%

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

   6. Simplified 84.9%

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

   if 3.4000000000000001e-124 < t

   1. Initial program 84.6%

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

      1. associate-/r* 84.3%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in t around inf 38.5%

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

      1. associate-*r* 38.5%

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

      2. *-commutative 38.5%

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

      3. *-commutative 38.5%

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

      4. *-commutative 38.5%

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

   6. Simplified 38.5%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+77}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-130}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-267}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-155}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-124}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \]

Alternative 8: 71.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;y \leq -1 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+102}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+241}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{\frac{y}{\frac{z}{x}}}{c}\\ \end{array} \end{array} \]

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 (/ (+ b (* 9.0 (* x y))) (* z c))))
   (if (<= y -1e-107)
     t_1
     (if (<= y 1.7e+102)
       (/ (+ (* t (* a -4.0)) (/ b z)) c)
       (if (<= y 6.5e+241) t_1 (* 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 = (b + (9.0 * (x * y))) / (z * c);
	double tmp;
	if (y <= -1e-107) {
		tmp = t_1;
	} else if (y <= 1.7e+102) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else if (y <= 6.5e+241) {
		tmp = t_1;
	} else {
		tmp = 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 = (b + (9.0d0 * (x * y))) / (z * c)
    if (y <= (-1d-107)) then
        tmp = t_1
    else if (y <= 1.7d+102) then
        tmp = ((t * (a * (-4.0d0))) + (b / z)) / c
    else if (y <= 6.5d+241) then
        tmp = t_1
    else
        tmp = 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 = (b + (9.0 * (x * y))) / (z * c);
	double tmp;
	if (y <= -1e-107) {
		tmp = t_1;
	} else if (y <= 1.7e+102) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else if (y <= 6.5e+241) {
		tmp = t_1;
	} else {
		tmp = 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 = (b + (9.0 * (x * y))) / (z * c)
	tmp = 0
	if y <= -1e-107:
		tmp = t_1
	elif y <= 1.7e+102:
		tmp = ((t * (a * -4.0)) + (b / z)) / c
	elif y <= 6.5e+241:
		tmp = t_1
	else:
		tmp = 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(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c))
	tmp = 0.0
	if (y <= -1e-107)
		tmp = t_1;
	elseif (y <= 1.7e+102)
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c);
	elseif (y <= 6.5e+241)
		tmp = t_1;
	else
		tmp = Float64(9.0 * Float64(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 = (b + (9.0 * (x * y))) / (z * c);
	tmp = 0.0;
	if (y <= -1e-107)
		tmp = t_1;
	elseif (y <= 1.7e+102)
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	elseif (y <= 6.5e+241)
		tmp = t_1;
	else
		tmp = 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[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e-107], t$95$1, If[LessEqual[y, 1.7e+102], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[y, 6.5e+241], t$95$1, N[(9.0 * N[(N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1e-107 or 1.7e102 < y < 6.4999999999999994e241

   1. Initial program 80.4%

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

      1. associate-/r* 74.9%

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

   3. Simplified 83.7%

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

   4. Taylor expanded in z around 0 63.8%

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

   if -1e-107 < y < 1.7e102

   1. Initial program 83.9%

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

      1. associate-/r* 83.8%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in x around 0 82.9%

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

   if 6.4999999999999994e241 < y

   1. Initial program 73.4%

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

      1. associate-/r* 84.8%

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

   3. Simplified 84.7%

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

   4. Taylor expanded in x around inf 57.6%

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

      1. associate-/l* 61.4%

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

      2. *-commutative 61.4%

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

   6. Simplified 61.4%

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

   7. Taylor expanded in y around 0 57.6%

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

      1. *-commutative 57.6%

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

      2. associate-*l/ 65.1%

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

      3. *-commutative 65.1%

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

      4. associate-/r* 84.0%

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

   9. Simplified 84.0%

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

       1. associate-*r/ 80.3%

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

   11. Applied egg-rr 80.3%

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

       1. associate-*r/ 69.1%

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

       2. *-commutative 69.1%

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

       3. associate-/l* 80.4%

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

   13. Simplified 80.4%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-107}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+102}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+241}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{\frac{y}{\frac{z}{x}}}{c}\\ \end{array} \]

Alternative 9: 69.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+174}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+71}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -2e+174)
   (/ (* t (* a -4.0)) c)
   (if (<= z 1.1e+71)
     (/ (+ b (* 9.0 (* x y))) (* z c))
     (* -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 tmp;
	if (z <= -2e+174) {
		tmp = (t * (a * -4.0)) / c;
	} else if (z <= 1.1e+71) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-2d+174)) then
        tmp = (t * (a * (-4.0d0))) / c
    else if (z <= 1.1d+71) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    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 tmp;
	if (z <= -2e+174) {
		tmp = (t * (a * -4.0)) / c;
	} else if (z <= 1.1e+71) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -2e+174:
		tmp = (t * (a * -4.0)) / c
	elif z <= 1.1e+71:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = -4.0 * (a / (c / t))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -2e+174)
		tmp = Float64(Float64(t * Float64(a * -4.0)) / c);
	elseif (z <= 1.1e+71)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	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)
	tmp = 0.0;
	if (z <= -2e+174)
		tmp = (t * (a * -4.0)) / c;
	elseif (z <= 1.1e+71)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = -4.0 * (a / (c / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -2e+174], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 1.1e+71], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.00000000000000014e174

   1. Initial program 38.3%

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

      1. associate-/r* 47.3%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in t around inf 70.3%

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

      1. associate-*r* 70.3%

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

      2. *-commutative 70.3%

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

      3. *-commutative 70.3%

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

      4. *-commutative 70.3%

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

   6. Simplified 70.3%

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

   if -2.00000000000000014e174 < z < 1.09999999999999997e71

   1. Initial program 90.4%

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

      1. associate-/r* 85.8%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in z around 0 71.2%

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

   if 1.09999999999999997e71 < z

   1. Initial program 66.0%

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

      1. associate-/r* 74.5%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in t around inf 67.4%

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

      1. associate-/l* 64.3%

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

   6. Simplified 64.3%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+174}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+71}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 10: 50.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+21}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-249}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+77}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \end{array} \end{array} \]

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 -5.2e+21)
   (/ b (* z c))
   (if (<= b 1.9e-249)
     (* 9.0 (* (/ y z) (/ x c)))
     (if (<= b 1.02e+77) (/ (* t (* a -4.0)) c) (/ 1.0 (* z (/ c b)))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -5.2e+21) {
		tmp = b / (z * c);
	} else if (b <= 1.9e-249) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (b <= 1.02e+77) {
		tmp = (t * (a * -4.0)) / c;
	} else {
		tmp = 1.0 / (z * (c / b));
	}
	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 <= (-5.2d+21)) then
        tmp = b / (z * c)
    else if (b <= 1.9d-249) then
        tmp = 9.0d0 * ((y / z) * (x / c))
    else if (b <= 1.02d+77) then
        tmp = (t * (a * (-4.0d0))) / c
    else
        tmp = 1.0d0 / (z * (c / b))
    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 <= -5.2e+21) {
		tmp = b / (z * c);
	} else if (b <= 1.9e-249) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (b <= 1.02e+77) {
		tmp = (t * (a * -4.0)) / c;
	} else {
		tmp = 1.0 / (z * (c / b));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -5.2e+21:
		tmp = b / (z * c)
	elif b <= 1.9e-249:
		tmp = 9.0 * ((y / z) * (x / c))
	elif b <= 1.02e+77:
		tmp = (t * (a * -4.0)) / c
	else:
		tmp = 1.0 / (z * (c / b))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -5.2e+21)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= 1.9e-249)
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	elseif (b <= 1.02e+77)
		tmp = Float64(Float64(t * Float64(a * -4.0)) / c);
	else
		tmp = Float64(1.0 / Float64(z * Float64(c / b)));
	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 <= -5.2e+21)
		tmp = b / (z * c);
	elseif (b <= 1.9e-249)
		tmp = 9.0 * ((y / z) * (x / c));
	elseif (b <= 1.02e+77)
		tmp = (t * (a * -4.0)) / c;
	else
		tmp = 1.0 / (z * (c / b));
	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, -5.2e+21], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.9e-249], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.02e+77], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(1.0 / N[(z * N[(c / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.2e21

   1. Initial program 90.3%

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

      1. associate-/r* 84.8%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in b around inf 64.0%

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

      1. *-commutative 64.0%

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

   6. Simplified 64.0%

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

   if -5.2e21 < b < 1.9e-249

   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-/r* 81.3%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in x around inf 48.6%

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

      1. *-commutative 48.6%

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

      2. times-frac 53.8%

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

   6. Simplified 53.8%

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

   if 1.9e-249 < b < 1.02e77

   1. Initial program 80.1%

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

      1. associate-/r* 81.6%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in t around inf 53.4%

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

      1. associate-*r* 53.4%

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

      2. *-commutative 53.4%

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

      3. *-commutative 53.4%

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

      4. *-commutative 53.4%

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

   6. Simplified 53.4%

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

   if 1.02e77 < b

   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-*l* 74.2%

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

      2. associate-*l* 72.4%

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

   3. Simplified 72.4%

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

      1. clear-num 72.4%

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

      2. inv-pow 72.4%

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

      3. associate-+l- 72.4%

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

      4. associate-*r* 72.4%

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

      5. associate-*r* 74.2%

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

      6. associate-+l- 74.2%

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

      7. +-commutative 74.2%

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

      8. associate-*r* 74.2%

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

      9. *-commutative 74.2%

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

      10. *-commutative 74.2%

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

   5. Applied egg-rr 74.2%

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

   6. Taylor expanded in b around inf 57.3%

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

      1. associate-/l* 57.5%

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

   8. Simplified 57.5%

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

      1. unpow-1 57.5%

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

      2. associate-/r/ 59.5%

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

   10. Applied egg-rr 59.5%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+21}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-249}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+77}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \end{array} \]

Alternative 11: 48.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+28} \lor \neg \left(t \leq 1.6 \cdot 10^{-124}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

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 (or (<= t -4.4e+28) (not (<= t 1.6e-124)))
   (* -4.0 (* t (/ a c)))
   (/ 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 ((t <= -4.4e+28) || !(t <= 1.6e-124)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = 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 ((t <= (-4.4d+28)) .or. (.not. (t <= 1.6d-124))) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = 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 ((t <= -4.4e+28) || !(t <= 1.6e-124)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -4.4e+28) or not (t <= 1.6e-124):
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -4.4e+28) || !(t <= 1.6e-124))
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(b / Float64(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 ((t <= -4.4e+28) || ~((t <= 1.6e-124)))
		tmp = -4.0 * (t * (a / c));
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -4.4e+28], N[Not[LessEqual[t, 1.6e-124]], $MachinePrecision]], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.39999999999999973e28 or 1.60000000000000002e-124 < t

   1. Initial program 78.9%

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

      1. associate-/r* 77.2%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in t around inf 46.8%

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

      1. associate-/l* 48.9%

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

      2. associate-/r/ 47.9%

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

   6. Simplified 47.9%

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

   if -4.39999999999999973e28 < t < 1.60000000000000002e-124

   1. Initial program 85.8%

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

      1. associate-/r* 85.8%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in b around inf 45.2%

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

      1. *-commutative 45.2%

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

   6. Simplified 45.2%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+28} \lor \neg \left(t \leq 1.6 \cdot 10^{-124}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 12: 48.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+28} \lor \neg \left(t \leq 1.4 \cdot 10^{-124}\right):\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

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 (or (<= t -1.22e+28) (not (<= t 1.4e-124)))
   (* -4.0 (/ a (/ c t)))
   (/ 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 ((t <= -1.22e+28) || !(t <= 1.4e-124)) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = 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 ((t <= (-1.22d+28)) .or. (.not. (t <= 1.4d-124))) then
        tmp = (-4.0d0) * (a / (c / t))
    else
        tmp = 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 ((t <= -1.22e+28) || !(t <= 1.4e-124)) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -1.22e+28) or not (t <= 1.4e-124):
		tmp = -4.0 * (a / (c / t))
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -1.22e+28) || !(t <= 1.4e-124))
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	else
		tmp = Float64(b / Float64(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 ((t <= -1.22e+28) || ~((t <= 1.4e-124)))
		tmp = -4.0 * (a / (c / t));
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -1.22e+28], N[Not[LessEqual[t, 1.4e-124]], $MachinePrecision]], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2199999999999999e28 or 1.39999999999999999e-124 < t

   1. Initial program 78.9%

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

      1. associate-/r* 77.2%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in t around inf 46.8%

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

      1. associate-/l* 48.9%

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

   6. Simplified 48.9%

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

   if -1.2199999999999999e28 < t < 1.39999999999999999e-124

   1. Initial program 85.8%

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

      1. associate-/r* 85.8%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in b around inf 45.2%

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

      1. *-commutative 45.2%

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

   6. Simplified 45.2%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+28} \lor \neg \left(t \leq 1.4 \cdot 10^{-124}\right):\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 13: 48.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+28} \lor \neg \left(t \leq 2.9 \cdot 10^{-124}\right):\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \end{array} \end{array} \]

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 (or (<= t -1.3e+28) (not (<= t 2.9e-124)))
   (* -4.0 (/ a (/ c t)))
   (* b (/ 1.0 (* 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 ((t <= -1.3e+28) || !(t <= 2.9e-124)) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = b * (1.0 / (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 ((t <= (-1.3d+28)) .or. (.not. (t <= 2.9d-124))) then
        tmp = (-4.0d0) * (a / (c / t))
    else
        tmp = b * (1.0d0 / (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 ((t <= -1.3e+28) || !(t <= 2.9e-124)) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = b * (1.0 / (z * c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -1.3e+28) or not (t <= 2.9e-124):
		tmp = -4.0 * (a / (c / t))
	else:
		tmp = b * (1.0 / (z * c))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -1.3e+28) || !(t <= 2.9e-124))
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	else
		tmp = Float64(b * Float64(1.0 / Float64(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 ((t <= -1.3e+28) || ~((t <= 2.9e-124)))
		tmp = -4.0 * (a / (c / t));
	else
		tmp = b * (1.0 / (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[Or[LessEqual[t, -1.3e+28], N[Not[LessEqual[t, 2.9e-124]], $MachinePrecision]], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3000000000000001e28 or 2.9000000000000002e-124 < t

   1. Initial program 78.9%

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

      1. associate-/r* 77.2%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in t around inf 46.8%

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

      1. associate-/l* 48.9%

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

   6. Simplified 48.9%

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

   if -1.3000000000000001e28 < t < 2.9000000000000002e-124

   1. Initial program 85.8%

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

      1. associate-/r* 85.8%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in b around inf 45.2%

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

      1. *-commutative 45.2%

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

   6. Simplified 45.2%

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

      1. div-inv 45.2%

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

   8. Applied egg-rr 45.2%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+28} \lor \neg \left(t \leq 2.9 \cdot 10^{-124}\right):\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \end{array} \]

Alternative 14: 47.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+27}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-124}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \end{array} \]

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
 (if (<= t -7e+27)
   (* -4.0 (/ a (/ c t)))
   (if (<= t 1.75e-124) (* b (/ 1.0 (* z c))) (/ (* 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 tmp;
	if (t <= -7e+27) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 1.75e-124) {
		tmp = b * (1.0 / (z * c));
	} 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) :: tmp
    if (t <= (-7d+27)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (t <= 1.75d-124) then
        tmp = b * (1.0d0 / (z * c))
    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 tmp;
	if (t <= -7e+27) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 1.75e-124) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = (t * (a * -4.0)) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -7e+27:
		tmp = -4.0 * (a / (c / t))
	elif t <= 1.75e-124:
		tmp = b * (1.0 / (z * c))
	else:
		tmp = (t * (a * -4.0)) / c
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -7e+27)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (t <= 1.75e-124)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	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)
	tmp = 0.0;
	if (t <= -7e+27)
		tmp = -4.0 * (a / (c / t));
	elseif (t <= 1.75e-124)
		tmp = b * (1.0 / (z * c));
	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_] := If[LessEqual[t, -7e+27], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e-124], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.0000000000000004e27

   1. Initial program 71.0%

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

      1. associate-/r* 67.4%

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

   3. Simplified 84.6%

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

   4. Taylor expanded in t around inf 58.3%

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

      1. associate-/l* 64.8%

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

   6. Simplified 64.8%

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

   if -7.0000000000000004e27 < t < 1.7499999999999999e-124

   1. Initial program 85.8%

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

      1. associate-/r* 85.8%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in b around inf 45.2%

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

      1. *-commutative 45.2%

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

   6. Simplified 45.2%

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

      1. div-inv 45.2%

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

   8. Applied egg-rr 45.2%

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

   if 1.7499999999999999e-124 < t

   1. Initial program 84.6%

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

      1. associate-/r* 84.3%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in t around inf 38.5%

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

      1. associate-*r* 38.5%

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

      2. *-commutative 38.5%

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

      3. *-commutative 38.5%

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

      4. *-commutative 38.5%

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

   6. Simplified 38.5%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+27}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-124}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \]

Alternative 15: 36.0% accurate, 3.8× speedup

Math

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

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 (* z c)))

C

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

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b / (z * c)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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-/r* 80.4%

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

3. Simplified 88.8%

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

4. Taylor expanded in b around inf 32.9%

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

   1. *-commutative 32.9%

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

6. Simplified 32.9%

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

7. Final simplification 32.9%

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

Developer target: 80.3% 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 2023200 
(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)))