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

Percentage Accurate: 79.9% → 90.7%

Time: 15.1s

Alternatives: 20

Speedup: 0.8×

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

• 37.8% 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: 79.9% 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: 90.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+98}:\\ \;\;\;\;\left(\frac{b}{z} + \mathsf{fma}\left(9, \frac{y}{\frac{z}{x}}, t_1\right)\right) \cdot \frac{1}{c}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+182}:\\ \;\;\;\;\frac{b - \left(a \cdot \left(t \cdot \left(z \cdot 4\right)\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{c} \cdot \left(\frac{b}{z} + \left(t_1 + 9 \cdot \left(x \cdot \frac{y}{z}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (* a t))))
   (if (<= z -1.4e+98)
     (* (+ (/ b z) (fma 9.0 (/ y (/ z x)) t_1)) (/ 1.0 c))
     (if (<= z 1.22e+182)
       (/ (- b (- (* a (* t (* z 4.0))) (* y (* 9.0 x)))) (* z c))
       (* (/ 1.0 c) (+ (/ b z) (+ t_1 (* 9.0 (* x (/ y z))))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a * t);
	double tmp;
	if (z <= -1.4e+98) {
		tmp = ((b / z) + fma(9.0, (y / (z / x)), t_1)) * (1.0 / c);
	} else if (z <= 1.22e+182) {
		tmp = (b - ((a * (t * (z * 4.0))) - (y * (9.0 * x)))) / (z * c);
	} else {
		tmp = (1.0 / c) * ((b / z) + (t_1 + (9.0 * (x * (y / z)))));
	}
	return tmp;
}

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(a * t))
	tmp = 0.0
	if (z <= -1.4e+98)
		tmp = Float64(Float64(Float64(b / z) + fma(9.0, Float64(y / Float64(z / x)), t_1)) * Float64(1.0 / c));
	elseif (z <= 1.22e+182)
		tmp = Float64(Float64(b - Float64(Float64(a * Float64(t * Float64(z * 4.0))) - Float64(y * Float64(9.0 * x)))) / Float64(z * c));
	else
		tmp = Float64(Float64(1.0 / c) * Float64(Float64(b / z) + Float64(t_1 + Float64(9.0 * Float64(x * Float64(y / z))))));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+98], N[(N[(N[(b / z), $MachinePrecision] + N[(9.0 * N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.22e+182], N[(N[(b - N[(N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / c), $MachinePrecision] * N[(N[(b / z), $MachinePrecision] + N[(t$95$1 + N[(9.0 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4e98

   1. Initial program 54.9%

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

      1. associate-/r* 75.8%

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

      2. div-inv 75.8%

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

      3. associate-*l* 75.8%

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

      4. associate-*l* 87.8%

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

   3. Applied egg-rr 87.8%

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

   4. Taylor expanded in x around 0 90.9%

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

      1. cancel-sign-sub-inv 90.9%

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

      2. metadata-eval 90.9%

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

      3. associate-+r+ 90.9%

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

      4. fma-def 90.9%

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

      5. associate-/l* 93.8%

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

   6. Simplified 93.8%

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

   if -1.4e98 < z < 1.22e182

   1. Initial program 95.5%

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

   if 1.22e182 < z

   1. Initial program 49.1%

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

      1. associate-/r* 65.5%

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

      2. div-inv 65.5%

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

      3. associate-*l* 65.5%

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

      4. associate-*l* 68.6%

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

   3. Applied egg-rr 68.6%

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

   4. Taylor expanded in x around 0 84.1%

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

      1. cancel-sign-sub-inv 84.1%

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

      2. metadata-eval 84.1%

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

      3. associate-+r+ 84.1%

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

      4. fma-def 84.1%

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

      5. associate-/l* 96.5%

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

   6. Simplified 96.5%

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

      1. fma-udef 96.5%

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

      2. associate-/r/ 93.4%

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

   8. Applied egg-rr 93.4%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+98}:\\ \;\;\;\;\left(\frac{b}{z} + \mathsf{fma}\left(9, \frac{y}{\frac{z}{x}}, -4 \cdot \left(a \cdot t\right)\right)\right) \cdot \frac{1}{c}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+182}:\\ \;\;\;\;\frac{b - \left(a \cdot \left(t \cdot \left(z \cdot 4\right)\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{c} \cdot \left(\frac{b}{z} + \left(-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(x \cdot \frac{y}{z}\right)\right)\right)\\ \end{array} \]

Alternative 2: 90.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+98} \lor \neg \left(z \leq 1.22 \cdot 10^{+182}\right):\\ \;\;\;\;\frac{1}{c} \cdot \left(\frac{b}{z} + \left(-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(x \cdot \frac{y}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \left(a \cdot \left(t \cdot \left(z \cdot 4\right)\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.4e+98) (not (<= z 1.22e+182)))
   (* (/ 1.0 c) (+ (/ b z) (+ (* -4.0 (* a t)) (* 9.0 (* x (/ y z))))))
   (/ (- b (- (* a (* t (* z 4.0))) (* y (* 9.0 x)))) (* z c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.4e+98) || !(z <= 1.22e+182)) {
		tmp = (1.0 / c) * ((b / z) + ((-4.0 * (a * t)) + (9.0 * (x * (y / z)))));
	} else {
		tmp = (b - ((a * (t * (z * 4.0))) - (y * (9.0 * x)))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-1.4d+98)) .or. (.not. (z <= 1.22d+182))) then
        tmp = (1.0d0 / c) * ((b / z) + (((-4.0d0) * (a * t)) + (9.0d0 * (x * (y / z)))))
    else
        tmp = (b - ((a * (t * (z * 4.0d0))) - (y * (9.0d0 * x)))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.4e+98) || !(z <= 1.22e+182)) {
		tmp = (1.0 / c) * ((b / z) + ((-4.0 * (a * t)) + (9.0 * (x * (y / z)))));
	} else {
		tmp = (b - ((a * (t * (z * 4.0))) - (y * (9.0 * x)))) / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -1.4e+98) or not (z <= 1.22e+182):
		tmp = (1.0 / c) * ((b / z) + ((-4.0 * (a * t)) + (9.0 * (x * (y / z)))))
	else:
		tmp = (b - ((a * (t * (z * 4.0))) - (y * (9.0 * x)))) / (z * c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.4e+98) || !(z <= 1.22e+182))
		tmp = Float64(Float64(1.0 / c) * Float64(Float64(b / z) + Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(x * Float64(y / z))))));
	else
		tmp = Float64(Float64(b - Float64(Float64(a * Float64(t * Float64(z * 4.0))) - Float64(y * Float64(9.0 * x)))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -1.4e+98) || ~((z <= 1.22e+182)))
		tmp = (1.0 / c) * ((b / z) + ((-4.0 * (a * t)) + (9.0 * (x * (y / z)))));
	else
		tmp = (b - ((a * (t * (z * 4.0))) - (y * (9.0 * x)))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.4e+98], N[Not[LessEqual[z, 1.22e+182]], $MachinePrecision]], N[(N[(1.0 / c), $MachinePrecision] * N[(N[(b / z), $MachinePrecision] + N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b - N[(N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e98 or 1.22e182 < z

   1. Initial program 52.0%

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

      1. associate-/r* 70.8%

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

      2. div-inv 70.7%

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

      3. associate-*l* 70.7%

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

      4. associate-*l* 78.4%

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

   3. Applied egg-rr 78.4%

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

   4. Taylor expanded in x around 0 87.6%

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

      1. cancel-sign-sub-inv 87.6%

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

      2. metadata-eval 87.6%

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

      3. associate-+r+ 87.6%

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

      4. fma-def 87.6%

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

      5. associate-/l* 95.1%

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

   6. Simplified 95.1%

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

      1. fma-udef 95.1%

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

      2. associate-/r/ 93.6%

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

   8. Applied egg-rr 93.6%

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

   if -1.4e98 < z < 1.22e182

   1. Initial program 95.5%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+98} \lor \neg \left(z \leq 1.22 \cdot 10^{+182}\right):\\ \;\;\;\;\frac{1}{c} \cdot \left(\frac{b}{z} + \left(-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(x \cdot \frac{y}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \left(a \cdot \left(t \cdot \left(z \cdot 4\right)\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 3: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+99} \lor \neg \left(z \leq 1.22 \cdot 10^{+182}\right):\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \left(a \cdot \left(t \cdot \left(z \cdot 4\right)\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.35e+99) (not (<= z 1.22e+182)))
   (/ (+ (/ b z) (* -4.0 (* a t))) c)
   (/ (- b (- (* a (* t (* z 4.0))) (* y (* 9.0 x)))) (* z c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.35e+99) || !(z <= 1.22e+182)) {
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	} else {
		tmp = (b - ((a * (t * (z * 4.0))) - (y * (9.0 * x)))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-1.35d+99)) .or. (.not. (z <= 1.22d+182))) then
        tmp = ((b / z) + ((-4.0d0) * (a * t))) / c
    else
        tmp = (b - ((a * (t * (z * 4.0d0))) - (y * (9.0d0 * x)))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.35e+99) || !(z <= 1.22e+182)) {
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	} else {
		tmp = (b - ((a * (t * (z * 4.0))) - (y * (9.0 * x)))) / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -1.35e+99) or not (z <= 1.22e+182):
		tmp = ((b / z) + (-4.0 * (a * t))) / c
	else:
		tmp = (b - ((a * (t * (z * 4.0))) - (y * (9.0 * x)))) / (z * c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.35e+99) || !(z <= 1.22e+182))
		tmp = Float64(Float64(Float64(b / z) + Float64(-4.0 * Float64(a * t))) / c);
	else
		tmp = Float64(Float64(b - Float64(Float64(a * Float64(t * Float64(z * 4.0))) - Float64(y * Float64(9.0 * x)))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -1.35e+99) || ~((z <= 1.22e+182)))
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	else
		tmp = (b - ((a * (t * (z * 4.0))) - (y * (9.0 * x)))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.35e+99], N[Not[LessEqual[z, 1.22e+182]], $MachinePrecision]], N[(N[(N[(b / z), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b - N[(N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.34999999999999994e99 or 1.22e182 < z

   1. Initial program 52.0%

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

      1. associate-/r* 70.8%

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

      2. div-inv 70.7%

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

      3. associate-*l* 70.7%

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

      4. associate-*l* 78.4%

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

   3. Applied egg-rr 78.4%

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

   4. Taylor expanded in x around 0 87.6%

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

      1. cancel-sign-sub-inv 87.6%

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

      2. metadata-eval 87.6%

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

      3. associate-+r+ 87.6%

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

      4. fma-def 87.6%

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

      5. associate-/l* 95.1%

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

   6. Simplified 95.1%

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

   7. Taylor expanded in y around 0 82.7%

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

   if -1.34999999999999994e99 < z < 1.22e182

   1. Initial program 95.5%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+99} \lor \neg \left(z \leq 1.22 \cdot 10^{+182}\right):\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \left(a \cdot \left(t \cdot \left(z \cdot 4\right)\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 4: 49.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{+198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{+149}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{-143}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-205}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \frac{y}{\frac{c}{\frac{9}{z}}}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (/ a (/ c t)))))
   (if (<= t -1.2e+198)
     t_1
     (if (<= t -4.7e+149)
       (* 9.0 (/ (* y x) (* z c)))
       (if (<= t -1.3e+60)
         t_1
         (if (<= t -1.08e-143)
           (* 9.0 (/ y (/ (* z c) x)))
           (if (<= t 2.6e-205)
             (/ 1.0 (/ c (/ b z)))
             (if (<= t 2.5e-98)
               (* x (/ y (/ c (/ 9.0 z))))
               (if (<= t 2.7e-18) (/ (/ b z) c) (* -4.0 (* t (/ a c))))))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -1.2e+198) {
		tmp = t_1;
	} else if (t <= -4.7e+149) {
		tmp = 9.0 * ((y * x) / (z * c));
	} else if (t <= -1.3e+60) {
		tmp = t_1;
	} else if (t <= -1.08e-143) {
		tmp = 9.0 * (y / ((z * c) / x));
	} else if (t <= 2.6e-205) {
		tmp = 1.0 / (c / (b / z));
	} else if (t <= 2.5e-98) {
		tmp = x * (y / (c / (9.0 / z)));
	} else if (t <= 2.7e-18) {
		tmp = (b / z) / c;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (a / (c / t))
    if (t <= (-1.2d+198)) then
        tmp = t_1
    else if (t <= (-4.7d+149)) then
        tmp = 9.0d0 * ((y * x) / (z * c))
    else if (t <= (-1.3d+60)) then
        tmp = t_1
    else if (t <= (-1.08d-143)) then
        tmp = 9.0d0 * (y / ((z * c) / x))
    else if (t <= 2.6d-205) then
        tmp = 1.0d0 / (c / (b / z))
    else if (t <= 2.5d-98) then
        tmp = x * (y / (c / (9.0d0 / z)))
    else if (t <= 2.7d-18) then
        tmp = (b / z) / c
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -1.2e+198) {
		tmp = t_1;
	} else if (t <= -4.7e+149) {
		tmp = 9.0 * ((y * x) / (z * c));
	} else if (t <= -1.3e+60) {
		tmp = t_1;
	} else if (t <= -1.08e-143) {
		tmp = 9.0 * (y / ((z * c) / x));
	} else if (t <= 2.6e-205) {
		tmp = 1.0 / (c / (b / z));
	} else if (t <= 2.5e-98) {
		tmp = x * (y / (c / (9.0 / z)));
	} else if (t <= 2.7e-18) {
		tmp = (b / z) / c;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a / (c / t))
	tmp = 0
	if t <= -1.2e+198:
		tmp = t_1
	elif t <= -4.7e+149:
		tmp = 9.0 * ((y * x) / (z * c))
	elif t <= -1.3e+60:
		tmp = t_1
	elif t <= -1.08e-143:
		tmp = 9.0 * (y / ((z * c) / x))
	elif t <= 2.6e-205:
		tmp = 1.0 / (c / (b / z))
	elif t <= 2.5e-98:
		tmp = x * (y / (c / (9.0 / z)))
	elif t <= 2.7e-18:
		tmp = (b / z) / c
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(a / Float64(c / t)))
	tmp = 0.0
	if (t <= -1.2e+198)
		tmp = t_1;
	elseif (t <= -4.7e+149)
		tmp = Float64(9.0 * Float64(Float64(y * x) / Float64(z * c)));
	elseif (t <= -1.3e+60)
		tmp = t_1;
	elseif (t <= -1.08e-143)
		tmp = Float64(9.0 * Float64(y / Float64(Float64(z * c) / x)));
	elseif (t <= 2.6e-205)
		tmp = Float64(1.0 / Float64(c / Float64(b / z)));
	elseif (t <= 2.5e-98)
		tmp = Float64(x * Float64(y / Float64(c / Float64(9.0 / z))));
	elseif (t <= 2.7e-18)
		tmp = Float64(Float64(b / z) / c);
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (a / (c / t));
	tmp = 0.0;
	if (t <= -1.2e+198)
		tmp = t_1;
	elseif (t <= -4.7e+149)
		tmp = 9.0 * ((y * x) / (z * c));
	elseif (t <= -1.3e+60)
		tmp = t_1;
	elseif (t <= -1.08e-143)
		tmp = 9.0 * (y / ((z * c) / x));
	elseif (t <= 2.6e-205)
		tmp = 1.0 / (c / (b / z));
	elseif (t <= 2.5e-98)
		tmp = x * (y / (c / (9.0 / z)));
	elseif (t <= 2.7e-18)
		tmp = (b / z) / c;
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.2e+198], t$95$1, If[LessEqual[t, -4.7e+149], N[(9.0 * N[(N[(y * x), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.3e+60], t$95$1, If[LessEqual[t, -1.08e-143], N[(9.0 * N[(y / N[(N[(z * c), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e-205], N[(1.0 / N[(c / N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e-98], N[(x * N[(y / N[(c / N[(9.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e-18], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -1.2000000000000001e198 or -4.7000000000000004e149 < t < -1.30000000000000004e60

   1. Initial program 81.6%

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

      1. associate-/r* 79.6%

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

      2. div-inv 79.5%

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

      3. associate-*l* 79.4%

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

      4. associate-*l* 86.5%

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

   3. Applied egg-rr 86.5%

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

   4. Taylor expanded in z around inf 65.8%

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

      1. associate-/l* 76.7%

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

   6. Simplified 76.7%

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

   if -1.2000000000000001e198 < t < -4.7000000000000004e149

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 51.9%

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

   if -1.30000000000000004e60 < t < -1.0799999999999999e-143

   1. Initial program 90.0%

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

      1. associate-/r* 87.7%

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

      2. div-inv 87.8%

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

      3. associate-*l* 87.8%

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

      4. associate-*l* 87.7%

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

   3. Applied egg-rr 87.7%

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

   4. Taylor expanded in x around 0 85.1%

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

      1. cancel-sign-sub-inv 85.1%

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

      2. metadata-eval 85.1%

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

      3. associate-+r+ 85.1%

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

      4. fma-def 85.1%

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

      5. associate-/l* 87.5%

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

   6. Simplified 87.5%

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

   7. Taylor expanded in y around inf 59.9%

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

      1. associate-/l* 60.5%

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

      2. *-commutative 60.5%

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

   9. Simplified 60.5%

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

   if -1.0799999999999999e-143 < t < 2.5999999999999998e-205

   1. Initial program 89.5%

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

      1. associate-/r* 96.4%

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

      2. div-inv 96.2%

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

      3. associate-*l* 96.2%

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

      4. associate-*l* 96.3%

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

   3. Applied egg-rr 96.3%

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

   4. Taylor expanded in b around inf 52.8%

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

      1. div-inv 52.8%

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

      2. clear-num 52.8%

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

   6. Applied egg-rr 52.8%

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

   if 2.5999999999999998e-205 < t < 2.50000000000000009e-98

   1. Initial program 86.8%

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

      1. associate-/r* 90.1%

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

      2. div-inv 90.0%

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

      3. associate-*l* 89.9%

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

      4. associate-*l* 90.0%

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

   3. Applied egg-rr 90.0%

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

   4. Taylor expanded in x around 0 90.0%

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

      1. cancel-sign-sub-inv 90.0%

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

      2. metadata-eval 90.0%

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

      3. associate-+r+ 90.0%

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

      4. fma-def 90.0%

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

      5. associate-/l* 90.1%

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

   6. Simplified 90.1%

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

      1. fma-udef 90.1%

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

      2. associate-/r/ 90.0%

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

   8. Applied egg-rr 90.0%

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

   9. Taylor expanded in y around inf 45.3%

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

       1. associate-/l* 43.5%

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

       2. associate-*l/ 43.5%

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

       3. associate-*r/ 43.5%

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

       4. associate-/l/ 46.6%

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

       5. associate-*r/ 46.6%

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

       6. associate-/r/ 51.8%

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

       7. *-commutative 51.8%

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

       8. associate-*r/ 52.0%

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

       9. associate-*l/ 51.7%

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

       10. *-commutative 51.7%

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

       11. associate-/l* 48.5%

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

   11. Simplified 48.5%

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

   if 2.50000000000000009e-98 < t < 2.69999999999999989e-18

   1. Initial program 87.9%

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

      1. associate-/r* 92.1%

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

      2. div-inv 92.0%

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

      3. associate-*l* 92.1%

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

      4. associate-*l* 92.0%

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

   3. Applied egg-rr 92.0%

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

   4. Taylor expanded in x around 0 92.0%

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

      1. cancel-sign-sub-inv 92.0%

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

      2. metadata-eval 92.0%

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

      3. associate-+r+ 92.0%

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

      4. fma-def 92.0%

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

      5. associate-/l* 96.2%

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

   6. Simplified 96.2%

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

   7. Taylor expanded in b around inf 61.9%

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

      1. *-commutative 61.9%

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

      2. associate-/r* 57.8%

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

   9. Simplified 57.8%

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

   if 2.69999999999999989e-18 < t

   1. Initial program 75.8%

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

   2. Taylor expanded in z around inf 52.4%

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

      1. *-commutative 52.4%

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

      2. associate-/l* 57.0%

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

      3. associate-/r/ 53.9%

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

   4. Simplified 53.9%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+198}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{+149}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+60}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{-143}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-205}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \frac{y}{\frac{c}{\frac{9}{z}}}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 5: 49.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{+198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{+149}:\\ \;\;\;\;\frac{9}{z} \cdot \frac{y}{\frac{c}{x}}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-144}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-205}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-97}:\\ \;\;\;\;x \cdot \frac{y}{\frac{c}{\frac{9}{z}}}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (/ a (/ c t)))))
   (if (<= t -1.2e+198)
     t_1
     (if (<= t -4.7e+149)
       (* (/ 9.0 z) (/ y (/ c x)))
       (if (<= t -8e+64)
         t_1
         (if (<= t -9.8e-144)
           (* 9.0 (/ y (/ (* z c) x)))
           (if (<= t 6.2e-205)
             (/ 1.0 (/ c (/ b z)))
             (if (<= t 1.15e-97)
               (* x (/ y (/ c (/ 9.0 z))))
               (if (<= t 1.65e-18)
                 (/ (/ b z) c)
                 (* -4.0 (* t (/ a c))))))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -1.2e+198) {
		tmp = t_1;
	} else if (t <= -4.7e+149) {
		tmp = (9.0 / z) * (y / (c / x));
	} else if (t <= -8e+64) {
		tmp = t_1;
	} else if (t <= -9.8e-144) {
		tmp = 9.0 * (y / ((z * c) / x));
	} else if (t <= 6.2e-205) {
		tmp = 1.0 / (c / (b / z));
	} else if (t <= 1.15e-97) {
		tmp = x * (y / (c / (9.0 / z)));
	} else if (t <= 1.65e-18) {
		tmp = (b / z) / c;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (a / (c / t))
    if (t <= (-1.2d+198)) then
        tmp = t_1
    else if (t <= (-4.7d+149)) then
        tmp = (9.0d0 / z) * (y / (c / x))
    else if (t <= (-8d+64)) then
        tmp = t_1
    else if (t <= (-9.8d-144)) then
        tmp = 9.0d0 * (y / ((z * c) / x))
    else if (t <= 6.2d-205) then
        tmp = 1.0d0 / (c / (b / z))
    else if (t <= 1.15d-97) then
        tmp = x * (y / (c / (9.0d0 / z)))
    else if (t <= 1.65d-18) then
        tmp = (b / z) / c
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -1.2e+198) {
		tmp = t_1;
	} else if (t <= -4.7e+149) {
		tmp = (9.0 / z) * (y / (c / x));
	} else if (t <= -8e+64) {
		tmp = t_1;
	} else if (t <= -9.8e-144) {
		tmp = 9.0 * (y / ((z * c) / x));
	} else if (t <= 6.2e-205) {
		tmp = 1.0 / (c / (b / z));
	} else if (t <= 1.15e-97) {
		tmp = x * (y / (c / (9.0 / z)));
	} else if (t <= 1.65e-18) {
		tmp = (b / z) / c;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a / (c / t))
	tmp = 0
	if t <= -1.2e+198:
		tmp = t_1
	elif t <= -4.7e+149:
		tmp = (9.0 / z) * (y / (c / x))
	elif t <= -8e+64:
		tmp = t_1
	elif t <= -9.8e-144:
		tmp = 9.0 * (y / ((z * c) / x))
	elif t <= 6.2e-205:
		tmp = 1.0 / (c / (b / z))
	elif t <= 1.15e-97:
		tmp = x * (y / (c / (9.0 / z)))
	elif t <= 1.65e-18:
		tmp = (b / z) / c
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(a / Float64(c / t)))
	tmp = 0.0
	if (t <= -1.2e+198)
		tmp = t_1;
	elseif (t <= -4.7e+149)
		tmp = Float64(Float64(9.0 / z) * Float64(y / Float64(c / x)));
	elseif (t <= -8e+64)
		tmp = t_1;
	elseif (t <= -9.8e-144)
		tmp = Float64(9.0 * Float64(y / Float64(Float64(z * c) / x)));
	elseif (t <= 6.2e-205)
		tmp = Float64(1.0 / Float64(c / Float64(b / z)));
	elseif (t <= 1.15e-97)
		tmp = Float64(x * Float64(y / Float64(c / Float64(9.0 / z))));
	elseif (t <= 1.65e-18)
		tmp = Float64(Float64(b / z) / c);
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (a / (c / t));
	tmp = 0.0;
	if (t <= -1.2e+198)
		tmp = t_1;
	elseif (t <= -4.7e+149)
		tmp = (9.0 / z) * (y / (c / x));
	elseif (t <= -8e+64)
		tmp = t_1;
	elseif (t <= -9.8e-144)
		tmp = 9.0 * (y / ((z * c) / x));
	elseif (t <= 6.2e-205)
		tmp = 1.0 / (c / (b / z));
	elseif (t <= 1.15e-97)
		tmp = x * (y / (c / (9.0 / z)));
	elseif (t <= 1.65e-18)
		tmp = (b / z) / c;
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.2e+198], t$95$1, If[LessEqual[t, -4.7e+149], N[(N[(9.0 / z), $MachinePrecision] * N[(y / N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8e+64], t$95$1, If[LessEqual[t, -9.8e-144], N[(9.0 * N[(y / N[(N[(z * c), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e-205], N[(1.0 / N[(c / N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e-97], N[(x * N[(y / N[(c / N[(9.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.65e-18], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -1.2000000000000001e198 or -4.7000000000000004e149 < t < -8.00000000000000017e64

   1. Initial program 81.6%

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

      1. associate-/r* 79.6%

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

      2. div-inv 79.5%

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

      3. associate-*l* 79.4%

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

      4. associate-*l* 86.5%

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

   3. Applied egg-rr 86.5%

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

   4. Taylor expanded in z around inf 65.8%

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

      1. associate-/l* 76.7%

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

   6. Simplified 76.7%

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

   if -1.2000000000000001e198 < t < -4.7000000000000004e149

   1. Initial program 100.0%

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

      1. associate-/r* 100.0%

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

      2. div-inv 99.7%

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

      3. associate-*l* 99.7%

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

      4. associate-*l* 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in x around inf 51.9%

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

      1. associate-/r* 51.9%

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

      2. associate-*r/ 51.9%

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

      3. associate-*l/ 51.9%

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

      4. associate-/l* 51.9%

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

   6. Simplified 51.9%

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

   if -8.00000000000000017e64 < t < -9.8000000000000002e-144

   1. Initial program 90.0%

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

      1. associate-/r* 87.7%

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

      2. div-inv 87.8%

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

      3. associate-*l* 87.8%

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

      4. associate-*l* 87.7%

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

   3. Applied egg-rr 87.7%

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

   4. Taylor expanded in x around 0 85.1%

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

      1. cancel-sign-sub-inv 85.1%

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

      2. metadata-eval 85.1%

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

      3. associate-+r+ 85.1%

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

      4. fma-def 85.1%

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

      5. associate-/l* 87.5%

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

   6. Simplified 87.5%

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

   7. Taylor expanded in y around inf 59.9%

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

      1. associate-/l* 60.5%

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

      2. *-commutative 60.5%

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

   9. Simplified 60.5%

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

   if -9.8000000000000002e-144 < t < 6.19999999999999965e-205

   1. Initial program 89.5%

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

      1. associate-/r* 96.4%

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

      2. div-inv 96.2%

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

      3. associate-*l* 96.2%

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

      4. associate-*l* 96.3%

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

   3. Applied egg-rr 96.3%

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

   4. Taylor expanded in b around inf 52.8%

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

      1. div-inv 52.8%

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

      2. clear-num 52.8%

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

   6. Applied egg-rr 52.8%

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

   if 6.19999999999999965e-205 < t < 1.14999999999999997e-97

   1. Initial program 86.8%

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

      1. associate-/r* 90.1%

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

      2. div-inv 90.0%

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

      3. associate-*l* 89.9%

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

      4. associate-*l* 90.0%

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

   3. Applied egg-rr 90.0%

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

   4. Taylor expanded in x around 0 90.0%

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

      1. cancel-sign-sub-inv 90.0%

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

      2. metadata-eval 90.0%

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

      3. associate-+r+ 90.0%

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

      4. fma-def 90.0%

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

      5. associate-/l* 90.1%

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

   6. Simplified 90.1%

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

      1. fma-udef 90.1%

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

      2. associate-/r/ 90.0%

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

   8. Applied egg-rr 90.0%

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

   9. Taylor expanded in y around inf 45.3%

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

       1. associate-/l* 43.5%

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

       2. associate-*l/ 43.5%

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

       3. associate-*r/ 43.5%

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

       4. associate-/l/ 46.6%

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

       5. associate-*r/ 46.6%

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

       6. associate-/r/ 51.8%

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

       7. *-commutative 51.8%

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

       8. associate-*r/ 52.0%

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

       9. associate-*l/ 51.7%

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

       10. *-commutative 51.7%

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

       11. associate-/l* 48.5%

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

   11. Simplified 48.5%

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

   if 1.14999999999999997e-97 < t < 1.6500000000000001e-18

   1. Initial program 87.9%

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

      1. associate-/r* 92.1%

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

      2. div-inv 92.0%

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

      3. associate-*l* 92.1%

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

      4. associate-*l* 92.0%

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

   3. Applied egg-rr 92.0%

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

   4. Taylor expanded in x around 0 92.0%

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

      1. cancel-sign-sub-inv 92.0%

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

      2. metadata-eval 92.0%

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

      3. associate-+r+ 92.0%

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

      4. fma-def 92.0%

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

      5. associate-/l* 96.2%

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

   6. Simplified 96.2%

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

   7. Taylor expanded in b around inf 61.9%

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

      1. *-commutative 61.9%

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

      2. associate-/r* 57.8%

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

   9. Simplified 57.8%

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

   if 1.6500000000000001e-18 < t

   1. Initial program 75.8%

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

   2. Taylor expanded in z around inf 52.4%

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

      1. *-commutative 52.4%

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

      2. associate-/l* 57.0%

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

      3. associate-/r/ 53.9%

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

   4. Simplified 53.9%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+198}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{+149}:\\ \;\;\;\;\frac{9}{z} \cdot \frac{y}{\frac{c}{x}}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+64}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-144}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-205}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-97}:\\ \;\;\;\;x \cdot \frac{y}{\frac{c}{\frac{9}{z}}}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 6: 69.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{+148}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot x\right) - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{b - y \cdot \left(x \cdot -9\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (/ b z) (* -4.0 (* a t))) c)))
   (if (<= t -2.3e+198)
     t_1
     (if (<= t -6.6e+148)
       (/ (- (* 9.0 (* y x)) (* 4.0 (* a (* z t)))) (* z c))
       (if (<= t -9e+58)
         t_1
         (if (<= t 3.3e-18)
           (/ (/ (- b (* y (* x -9.0))) z) c)
           (* -4.0 (* t (/ a c)))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((b / z) + (-4.0 * (a * t))) / c;
	double tmp;
	if (t <= -2.3e+198) {
		tmp = t_1;
	} else if (t <= -6.6e+148) {
		tmp = ((9.0 * (y * x)) - (4.0 * (a * (z * t)))) / (z * c);
	} else if (t <= -9e+58) {
		tmp = t_1;
	} else if (t <= 3.3e-18) {
		tmp = ((b - (y * (x * -9.0))) / z) / c;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((b / z) + ((-4.0d0) * (a * t))) / c
    if (t <= (-2.3d+198)) then
        tmp = t_1
    else if (t <= (-6.6d+148)) then
        tmp = ((9.0d0 * (y * x)) - (4.0d0 * (a * (z * t)))) / (z * c)
    else if (t <= (-9d+58)) then
        tmp = t_1
    else if (t <= 3.3d-18) then
        tmp = ((b - (y * (x * (-9.0d0)))) / z) / c
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((b / z) + (-4.0 * (a * t))) / c;
	double tmp;
	if (t <= -2.3e+198) {
		tmp = t_1;
	} else if (t <= -6.6e+148) {
		tmp = ((9.0 * (y * x)) - (4.0 * (a * (z * t)))) / (z * c);
	} else if (t <= -9e+58) {
		tmp = t_1;
	} else if (t <= 3.3e-18) {
		tmp = ((b - (y * (x * -9.0))) / z) / c;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = ((b / z) + (-4.0 * (a * t))) / c
	tmp = 0
	if t <= -2.3e+198:
		tmp = t_1
	elif t <= -6.6e+148:
		tmp = ((9.0 * (y * x)) - (4.0 * (a * (z * t)))) / (z * c)
	elif t <= -9e+58:
		tmp = t_1
	elif t <= 3.3e-18:
		tmp = ((b - (y * (x * -9.0))) / z) / c
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(b / z) + Float64(-4.0 * Float64(a * t))) / c)
	tmp = 0.0
	if (t <= -2.3e+198)
		tmp = t_1;
	elseif (t <= -6.6e+148)
		tmp = Float64(Float64(Float64(9.0 * Float64(y * x)) - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(z * c));
	elseif (t <= -9e+58)
		tmp = t_1;
	elseif (t <= 3.3e-18)
		tmp = Float64(Float64(Float64(b - Float64(y * Float64(x * -9.0))) / z) / c);
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((b / z) + (-4.0 * (a * t))) / c;
	tmp = 0.0;
	if (t <= -2.3e+198)
		tmp = t_1;
	elseif (t <= -6.6e+148)
		tmp = ((9.0 * (y * x)) - (4.0 * (a * (z * t)))) / (z * c);
	elseif (t <= -9e+58)
		tmp = t_1;
	elseif (t <= 3.3e-18)
		tmp = ((b - (y * (x * -9.0))) / z) / c;
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(b / z), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[t, -2.3e+198], t$95$1, If[LessEqual[t, -6.6e+148], N[(N[(N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9e+58], t$95$1, If[LessEqual[t, 3.3e-18], N[(N[(N[(b - N[(y * N[(x * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.3000000000000001e198 or -6.60000000000000021e148 < t < -8.9999999999999996e58

   1. Initial program 81.2%

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

      1. associate-/r* 79.1%

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

      2. div-inv 79.0%

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

      3. associate-*l* 79.0%

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

      4. associate-*l* 86.2%

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

   3. Applied egg-rr 86.2%

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

   4. Taylor expanded in x around 0 86.1%

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

      1. cancel-sign-sub-inv 86.1%

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

      2. metadata-eval 86.1%

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

      3. associate-+r+ 86.1%

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

      4. fma-def 86.1%

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

      5. associate-/l* 83.7%

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

   6. Simplified 83.7%

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

   7. Taylor expanded in y around 0 86.3%

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

   if -2.3000000000000001e198 < t < -6.60000000000000021e148

   1. Initial program 100.0%

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

   2. Taylor expanded in b around 0 97.4%

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

   if -8.9999999999999996e58 < t < 3.3000000000000002e-18

   1. Initial program 88.9%

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

      1. associate-/r* 92.2%

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

      2. div-inv 92.1%

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

      3. associate-*l* 92.1%

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

      4. associate-*l* 92.1%

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

   3. Applied egg-rr 92.1%

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

   4. Taylor expanded in x around 0 90.7%

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

      1. cancel-sign-sub-inv 90.7%

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

      2. metadata-eval 90.7%

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

      3. associate-+r+ 90.7%

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

      4. fma-def 90.7%

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

      5. associate-/l* 92.6%

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

   6. Simplified 92.6%

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

   7. Taylor expanded in a around 0 78.8%

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

   8. Taylor expanded in z around -inf 80.2%

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

      1. associate-*r/ 80.2%

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

      2. mul-1-neg 80.2%

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

      3. neg-mul-1 80.2%

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

      4. unsub-neg 80.2%

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

      5. associate-*r* 80.3%

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

      6. *-commutative 80.3%

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

      7. associate-*l* 80.3%

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

   10. Simplified 80.3%

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

   if 3.3000000000000002e-18 < t

   1. Initial program 75.8%

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

   2. Taylor expanded in z around inf 52.4%

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

      1. *-commutative 52.4%

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

      2. associate-/l* 57.0%

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

      3. associate-/r/ 53.9%

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

   4. Simplified 53.9%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+198}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{+148}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot x\right) - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+58}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{b - y \cdot \left(x \cdot -9\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 7: 70.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ t_2 := \frac{\frac{b}{z} + t_1}{c}\\ \mathbf{if}\;t \leq -1.95 \cdot 10^{+198}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{+148}:\\ \;\;\;\;\frac{t_1 + 9 \cdot \frac{y \cdot x}{z}}{c}\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{b - y \cdot \left(x \cdot -9\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (* a t))) (t_2 (/ (+ (/ b z) t_1) c)))
   (if (<= t -1.95e+198)
     t_2
     (if (<= t -6.8e+148)
       (/ (+ t_1 (* 9.0 (/ (* y x) z))) c)
       (if (<= t -1.45e+62)
         t_2
         (if (<= t 3.8e-18)
           (/ (/ (- b (* y (* x -9.0))) z) c)
           (* -4.0 (* t (/ a c)))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a * t);
	double t_2 = ((b / z) + t_1) / c;
	double tmp;
	if (t <= -1.95e+198) {
		tmp = t_2;
	} else if (t <= -6.8e+148) {
		tmp = (t_1 + (9.0 * ((y * x) / z))) / c;
	} else if (t <= -1.45e+62) {
		tmp = t_2;
	} else if (t <= 3.8e-18) {
		tmp = ((b - (y * (x * -9.0))) / z) / c;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-4.0d0) * (a * t)
    t_2 = ((b / z) + t_1) / c
    if (t <= (-1.95d+198)) then
        tmp = t_2
    else if (t <= (-6.8d+148)) then
        tmp = (t_1 + (9.0d0 * ((y * x) / z))) / c
    else if (t <= (-1.45d+62)) then
        tmp = t_2
    else if (t <= 3.8d-18) then
        tmp = ((b - (y * (x * (-9.0d0)))) / z) / c
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a * t);
	double t_2 = ((b / z) + t_1) / c;
	double tmp;
	if (t <= -1.95e+198) {
		tmp = t_2;
	} else if (t <= -6.8e+148) {
		tmp = (t_1 + (9.0 * ((y * x) / z))) / c;
	} else if (t <= -1.45e+62) {
		tmp = t_2;
	} else if (t <= 3.8e-18) {
		tmp = ((b - (y * (x * -9.0))) / z) / c;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a * t)
	t_2 = ((b / z) + t_1) / c
	tmp = 0
	if t <= -1.95e+198:
		tmp = t_2
	elif t <= -6.8e+148:
		tmp = (t_1 + (9.0 * ((y * x) / z))) / c
	elif t <= -1.45e+62:
		tmp = t_2
	elif t <= 3.8e-18:
		tmp = ((b - (y * (x * -9.0))) / z) / c
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(a * t))
	t_2 = Float64(Float64(Float64(b / z) + t_1) / c)
	tmp = 0.0
	if (t <= -1.95e+198)
		tmp = t_2;
	elseif (t <= -6.8e+148)
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(Float64(y * x) / z))) / c);
	elseif (t <= -1.45e+62)
		tmp = t_2;
	elseif (t <= 3.8e-18)
		tmp = Float64(Float64(Float64(b - Float64(y * Float64(x * -9.0))) / z) / c);
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (a * t);
	t_2 = ((b / z) + t_1) / c;
	tmp = 0.0;
	if (t <= -1.95e+198)
		tmp = t_2;
	elseif (t <= -6.8e+148)
		tmp = (t_1 + (9.0 * ((y * x) / z))) / c;
	elseif (t <= -1.45e+62)
		tmp = t_2;
	elseif (t <= 3.8e-18)
		tmp = ((b - (y * (x * -9.0))) / z) / c;
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b / z), $MachinePrecision] + t$95$1), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[t, -1.95e+198], t$95$2, If[LessEqual[t, -6.8e+148], N[(N[(t$95$1 + N[(9.0 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, -1.45e+62], t$95$2, If[LessEqual[t, 3.8e-18], N[(N[(N[(b - N[(y * N[(x * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.95e198 or -6.8000000000000006e148 < t < -1.44999999999999992e62

   1. Initial program 81.2%

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

      1. associate-/r* 79.1%

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

      2. div-inv 79.0%

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

      3. associate-*l* 79.0%

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

      4. associate-*l* 86.2%

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

   3. Applied egg-rr 86.2%

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

   4. Taylor expanded in x around 0 86.1%

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

      1. cancel-sign-sub-inv 86.1%

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

      2. metadata-eval 86.1%

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

      3. associate-+r+ 86.1%

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

      4. fma-def 86.1%

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

      5. associate-/l* 83.7%

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

   6. Simplified 83.7%

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

   7. Taylor expanded in y around 0 86.3%

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

   if -1.95e198 < t < -6.8000000000000006e148

   1. Initial program 100.0%

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

      1. associate-/r* 100.0%

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

      2. div-inv 99.6%

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

      3. associate-*l* 99.6%

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

      4. associate-*l* 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in x around 0 85.3%

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

      1. cancel-sign-sub-inv 85.3%

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

      2. metadata-eval 85.3%

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

      3. associate-+r+ 85.3%

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

      4. fma-def 85.3%

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

      5. associate-/l* 85.3%

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

   6. Simplified 85.3%

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

   7. Taylor expanded in b around 0 97.4%

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

   if -1.44999999999999992e62 < t < 3.7999999999999998e-18

   1. Initial program 88.9%

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

      1. associate-/r* 92.2%

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

      2. div-inv 92.1%

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

      3. associate-*l* 92.1%

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

      4. associate-*l* 92.1%

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

   3. Applied egg-rr 92.1%

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

   4. Taylor expanded in x around 0 90.7%

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

      1. cancel-sign-sub-inv 90.7%

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

      2. metadata-eval 90.7%

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

      3. associate-+r+ 90.7%

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

      4. fma-def 90.7%

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

      5. associate-/l* 92.6%

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

   6. Simplified 92.6%

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

   7. Taylor expanded in a around 0 78.8%

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

   8. Taylor expanded in z around -inf 80.2%

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

      1. associate-*r/ 80.2%

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

      2. mul-1-neg 80.2%

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

      3. neg-mul-1 80.2%

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

      4. unsub-neg 80.2%

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

      5. associate-*r* 80.3%

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

      6. *-commutative 80.3%

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

      7. associate-*l* 80.3%

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

   10. Simplified 80.3%

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

   if 3.7999999999999998e-18 < t

   1. Initial program 75.8%

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

   2. Taylor expanded in z around inf 52.4%

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

      1. *-commutative 52.4%

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

      2. associate-/l* 57.0%

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

      3. associate-/r/ 53.9%

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

   4. Simplified 53.9%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+198}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{+148}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{y \cdot x}{z}}{c}\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{+62}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{b - y \cdot \left(x \cdot -9\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 8: 48.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ t_2 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{+198}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.9 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-18}:\\ \;\;\;\;\frac{1}{c \cdot \frac{z}{b}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (* (/ y c) (/ x z)))) (t_2 (* -4.0 (/ a (/ c t)))))
   (if (<= t -1.2e+198)
     t_2
     (if (<= t -4.2e+149)
       t_1
       (if (<= t -4.1e+64)
         t_2
         (if (<= t -5.9e-176)
           t_1
           (if (<= t 2.1e-18)
             (/ 1.0 (* c (/ z b)))
             (* -4.0 (* t (/ a c))))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((y / c) * (x / z));
	double t_2 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -1.2e+198) {
		tmp = t_2;
	} else if (t <= -4.2e+149) {
		tmp = t_1;
	} else if (t <= -4.1e+64) {
		tmp = t_2;
	} else if (t <= -5.9e-176) {
		tmp = t_1;
	} else if (t <= 2.1e-18) {
		tmp = 1.0 / (c * (z / b));
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 9.0d0 * ((y / c) * (x / z))
    t_2 = (-4.0d0) * (a / (c / t))
    if (t <= (-1.2d+198)) then
        tmp = t_2
    else if (t <= (-4.2d+149)) then
        tmp = t_1
    else if (t <= (-4.1d+64)) then
        tmp = t_2
    else if (t <= (-5.9d-176)) then
        tmp = t_1
    else if (t <= 2.1d-18) then
        tmp = 1.0d0 / (c * (z / b))
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((y / c) * (x / z));
	double t_2 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -1.2e+198) {
		tmp = t_2;
	} else if (t <= -4.2e+149) {
		tmp = t_1;
	} else if (t <= -4.1e+64) {
		tmp = t_2;
	} else if (t <= -5.9e-176) {
		tmp = t_1;
	} else if (t <= 2.1e-18) {
		tmp = 1.0 / (c * (z / b));
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * ((y / c) * (x / z))
	t_2 = -4.0 * (a / (c / t))
	tmp = 0
	if t <= -1.2e+198:
		tmp = t_2
	elif t <= -4.2e+149:
		tmp = t_1
	elif t <= -4.1e+64:
		tmp = t_2
	elif t <= -5.9e-176:
		tmp = t_1
	elif t <= 2.1e-18:
		tmp = 1.0 / (c * (z / b))
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)))
	t_2 = Float64(-4.0 * Float64(a / Float64(c / t)))
	tmp = 0.0
	if (t <= -1.2e+198)
		tmp = t_2;
	elseif (t <= -4.2e+149)
		tmp = t_1;
	elseif (t <= -4.1e+64)
		tmp = t_2;
	elseif (t <= -5.9e-176)
		tmp = t_1;
	elseif (t <= 2.1e-18)
		tmp = Float64(1.0 / Float64(c * Float64(z / b)));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * ((y / c) * (x / z));
	t_2 = -4.0 * (a / (c / t));
	tmp = 0.0;
	if (t <= -1.2e+198)
		tmp = t_2;
	elseif (t <= -4.2e+149)
		tmp = t_1;
	elseif (t <= -4.1e+64)
		tmp = t_2;
	elseif (t <= -5.9e-176)
		tmp = t_1;
	elseif (t <= 2.1e-18)
		tmp = 1.0 / (c * (z / b));
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.2e+198], t$95$2, If[LessEqual[t, -4.2e+149], t$95$1, If[LessEqual[t, -4.1e+64], t$95$2, If[LessEqual[t, -5.9e-176], t$95$1, If[LessEqual[t, 2.1e-18], N[(1.0 / N[(c * N[(z / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.2000000000000001e198 or -4.2000000000000003e149 < t < -4.09999999999999978e64

   1. Initial program 81.6%

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

      1. associate-/r* 79.6%

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

      2. div-inv 79.5%

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

      3. associate-*l* 79.4%

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

      4. associate-*l* 86.5%

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

   3. Applied egg-rr 86.5%

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

   4. Taylor expanded in z around inf 65.8%

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

      1. associate-/l* 76.7%

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

   6. Simplified 76.7%

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

   if -1.2000000000000001e198 < t < -4.2000000000000003e149 or -4.09999999999999978e64 < t < -5.8999999999999997e-176

   1. Initial program 92.4%

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

   2. Taylor expanded in x around inf 60.0%

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

      1. times-frac 58.4%

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

   4. Simplified 58.4%

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

   if -5.8999999999999997e-176 < t < 2.1e-18

   1. Initial program 87.8%

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

      1. associate-/r* 93.4%

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

      2. div-inv 93.3%

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

      3. associate-*l* 93.3%

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

      4. associate-*l* 93.3%

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

   3. Applied egg-rr 93.3%

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

   4. Taylor expanded in b around inf 48.4%

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

      1. clear-num 48.3%

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

      2. frac-times 49.0%

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

      3. metadata-eval 49.0%

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

   6. Applied egg-rr 49.0%

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

   if 2.1e-18 < t

   1. Initial program 75.8%

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

   2. Taylor expanded in z around inf 52.4%

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

      1. *-commutative 52.4%

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

      2. associate-/l* 57.0%

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

      3. associate-/r/ 53.9%

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

   4. Simplified 53.9%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+198}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{+149}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{+64}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -5.9 \cdot 10^{-176}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-18}:\\ \;\;\;\;\frac{1}{c \cdot \frac{z}{b}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 9: 48.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{+149}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-143}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-18}:\\ \;\;\;\;\frac{1}{c \cdot \frac{z}{b}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (/ a (/ c t)))))
   (if (<= t -1.5e+198)
     t_1
     (if (<= t -4.7e+149)
       (* 9.0 (* (/ y c) (/ x z)))
       (if (<= t -7.8e+70)
         t_1
         (if (<= t -1.15e-143)
           (* 9.0 (/ y (/ (* z c) x)))
           (if (<= t 2.9e-18)
             (/ 1.0 (* c (/ z b)))
             (* -4.0 (* t (/ a c))))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -1.5e+198) {
		tmp = t_1;
	} else if (t <= -4.7e+149) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if (t <= -7.8e+70) {
		tmp = t_1;
	} else if (t <= -1.15e-143) {
		tmp = 9.0 * (y / ((z * c) / x));
	} else if (t <= 2.9e-18) {
		tmp = 1.0 / (c * (z / b));
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (a / (c / t))
    if (t <= (-1.5d+198)) then
        tmp = t_1
    else if (t <= (-4.7d+149)) then
        tmp = 9.0d0 * ((y / c) * (x / z))
    else if (t <= (-7.8d+70)) then
        tmp = t_1
    else if (t <= (-1.15d-143)) then
        tmp = 9.0d0 * (y / ((z * c) / x))
    else if (t <= 2.9d-18) then
        tmp = 1.0d0 / (c * (z / b))
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -1.5e+198) {
		tmp = t_1;
	} else if (t <= -4.7e+149) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if (t <= -7.8e+70) {
		tmp = t_1;
	} else if (t <= -1.15e-143) {
		tmp = 9.0 * (y / ((z * c) / x));
	} else if (t <= 2.9e-18) {
		tmp = 1.0 / (c * (z / b));
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a / (c / t))
	tmp = 0
	if t <= -1.5e+198:
		tmp = t_1
	elif t <= -4.7e+149:
		tmp = 9.0 * ((y / c) * (x / z))
	elif t <= -7.8e+70:
		tmp = t_1
	elif t <= -1.15e-143:
		tmp = 9.0 * (y / ((z * c) / x))
	elif t <= 2.9e-18:
		tmp = 1.0 / (c * (z / b))
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(a / Float64(c / t)))
	tmp = 0.0
	if (t <= -1.5e+198)
		tmp = t_1;
	elseif (t <= -4.7e+149)
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	elseif (t <= -7.8e+70)
		tmp = t_1;
	elseif (t <= -1.15e-143)
		tmp = Float64(9.0 * Float64(y / Float64(Float64(z * c) / x)));
	elseif (t <= 2.9e-18)
		tmp = Float64(1.0 / Float64(c * Float64(z / b)));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (a / (c / t));
	tmp = 0.0;
	if (t <= -1.5e+198)
		tmp = t_1;
	elseif (t <= -4.7e+149)
		tmp = 9.0 * ((y / c) * (x / z));
	elseif (t <= -7.8e+70)
		tmp = t_1;
	elseif (t <= -1.15e-143)
		tmp = 9.0 * (y / ((z * c) / x));
	elseif (t <= 2.9e-18)
		tmp = 1.0 / (c * (z / b));
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.5e+198], t$95$1, If[LessEqual[t, -4.7e+149], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.8e+70], t$95$1, If[LessEqual[t, -1.15e-143], N[(9.0 * N[(y / N[(N[(z * c), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e-18], N[(1.0 / N[(c * N[(z / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.50000000000000009e198 or -4.7000000000000004e149 < t < -7.79999999999999949e70

   1. Initial program 81.6%

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

      1. associate-/r* 79.6%

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

      2. div-inv 79.5%

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

      3. associate-*l* 79.4%

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

      4. associate-*l* 86.5%

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

   3. Applied egg-rr 86.5%

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

   4. Taylor expanded in z around inf 65.8%

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

      1. associate-/l* 76.7%

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

   6. Simplified 76.7%

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

   if -1.50000000000000009e198 < t < -4.7000000000000004e149

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 51.9%

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

      1. times-frac 51.9%

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

   4. Simplified 51.9%

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

   if -7.79999999999999949e70 < t < -1.15000000000000006e-143

   1. Initial program 90.0%

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

      1. associate-/r* 87.7%

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

      2. div-inv 87.8%

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

      3. associate-*l* 87.8%

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

      4. associate-*l* 87.7%

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

   3. Applied egg-rr 87.7%

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

   4. Taylor expanded in x around 0 85.1%

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

      1. cancel-sign-sub-inv 85.1%

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

      2. metadata-eval 85.1%

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

      3. associate-+r+ 85.1%

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

      4. fma-def 85.1%

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

      5. associate-/l* 87.5%

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

   6. Simplified 87.5%

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

   7. Taylor expanded in y around inf 59.9%

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

      1. associate-/l* 60.5%

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

      2. *-commutative 60.5%

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

   9. Simplified 60.5%

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

   if -1.15000000000000006e-143 < t < 2.9e-18

   1. Initial program 88.4%

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

      1. associate-/r* 93.8%

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

      2. div-inv 93.7%

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

      3. associate-*l* 93.7%

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

      4. associate-*l* 93.7%

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

   3. Applied egg-rr 93.7%

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

   4. Taylor expanded in b around inf 49.0%

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

      1. clear-num 48.9%

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

      2. frac-times 49.6%

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

      3. metadata-eval 49.6%

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

   6. Applied egg-rr 49.6%

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

   if 2.9e-18 < t

   1. Initial program 75.8%

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

   2. Taylor expanded in z around inf 52.4%

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

      1. *-commutative 52.4%

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

      2. associate-/l* 57.0%

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

      3. associate-/r/ 53.9%

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

   4. Simplified 53.9%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+198}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{+149}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{+70}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-143}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-18}:\\ \;\;\;\;\frac{1}{c \cdot \frac{z}{b}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 10: 48.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{+198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{+149}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-143}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-19}:\\ \;\;\;\;\frac{1}{c \cdot \frac{z}{b}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (/ a (/ c t)))))
   (if (<= t -1.2e+198)
     t_1
     (if (<= t -4.4e+149)
       (* 9.0 (/ (* y x) (* z c)))
       (if (<= t -2.9e+60)
         t_1
         (if (<= t -1.02e-143)
           (* 9.0 (/ y (/ (* z c) x)))
           (if (<= t 7e-19) (/ 1.0 (* c (/ z b))) (* -4.0 (* t (/ a c))))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -1.2e+198) {
		tmp = t_1;
	} else if (t <= -4.4e+149) {
		tmp = 9.0 * ((y * x) / (z * c));
	} else if (t <= -2.9e+60) {
		tmp = t_1;
	} else if (t <= -1.02e-143) {
		tmp = 9.0 * (y / ((z * c) / x));
	} else if (t <= 7e-19) {
		tmp = 1.0 / (c * (z / b));
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (a / (c / t))
    if (t <= (-1.2d+198)) then
        tmp = t_1
    else if (t <= (-4.4d+149)) then
        tmp = 9.0d0 * ((y * x) / (z * c))
    else if (t <= (-2.9d+60)) then
        tmp = t_1
    else if (t <= (-1.02d-143)) then
        tmp = 9.0d0 * (y / ((z * c) / x))
    else if (t <= 7d-19) then
        tmp = 1.0d0 / (c * (z / b))
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -1.2e+198) {
		tmp = t_1;
	} else if (t <= -4.4e+149) {
		tmp = 9.0 * ((y * x) / (z * c));
	} else if (t <= -2.9e+60) {
		tmp = t_1;
	} else if (t <= -1.02e-143) {
		tmp = 9.0 * (y / ((z * c) / x));
	} else if (t <= 7e-19) {
		tmp = 1.0 / (c * (z / b));
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a / (c / t))
	tmp = 0
	if t <= -1.2e+198:
		tmp = t_1
	elif t <= -4.4e+149:
		tmp = 9.0 * ((y * x) / (z * c))
	elif t <= -2.9e+60:
		tmp = t_1
	elif t <= -1.02e-143:
		tmp = 9.0 * (y / ((z * c) / x))
	elif t <= 7e-19:
		tmp = 1.0 / (c * (z / b))
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(a / Float64(c / t)))
	tmp = 0.0
	if (t <= -1.2e+198)
		tmp = t_1;
	elseif (t <= -4.4e+149)
		tmp = Float64(9.0 * Float64(Float64(y * x) / Float64(z * c)));
	elseif (t <= -2.9e+60)
		tmp = t_1;
	elseif (t <= -1.02e-143)
		tmp = Float64(9.0 * Float64(y / Float64(Float64(z * c) / x)));
	elseif (t <= 7e-19)
		tmp = Float64(1.0 / Float64(c * Float64(z / b)));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (a / (c / t));
	tmp = 0.0;
	if (t <= -1.2e+198)
		tmp = t_1;
	elseif (t <= -4.4e+149)
		tmp = 9.0 * ((y * x) / (z * c));
	elseif (t <= -2.9e+60)
		tmp = t_1;
	elseif (t <= -1.02e-143)
		tmp = 9.0 * (y / ((z * c) / x));
	elseif (t <= 7e-19)
		tmp = 1.0 / (c * (z / b));
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.2e+198], t$95$1, If[LessEqual[t, -4.4e+149], N[(9.0 * N[(N[(y * x), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.9e+60], t$95$1, If[LessEqual[t, -1.02e-143], N[(9.0 * N[(y / N[(N[(z * c), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-19], N[(1.0 / N[(c * N[(z / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.2000000000000001e198 or -4.4e149 < t < -2.9e60

   1. Initial program 81.6%

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

      1. associate-/r* 79.6%

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

      2. div-inv 79.5%

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

      3. associate-*l* 79.4%

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

      4. associate-*l* 86.5%

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

   3. Applied egg-rr 86.5%

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

   4. Taylor expanded in z around inf 65.8%

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

      1. associate-/l* 76.7%

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

   6. Simplified 76.7%

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

   if -1.2000000000000001e198 < t < -4.4e149

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 51.9%

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

   if -2.9e60 < t < -1.02e-143

   1. Initial program 90.0%

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

      1. associate-/r* 87.7%

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

      2. div-inv 87.8%

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

      3. associate-*l* 87.8%

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

      4. associate-*l* 87.7%

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

   3. Applied egg-rr 87.7%

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

   4. Taylor expanded in x around 0 85.1%

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

      1. cancel-sign-sub-inv 85.1%

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

      2. metadata-eval 85.1%

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

      3. associate-+r+ 85.1%

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

      4. fma-def 85.1%

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

      5. associate-/l* 87.5%

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

   6. Simplified 87.5%

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

   7. Taylor expanded in y around inf 59.9%

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

      1. associate-/l* 60.5%

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

      2. *-commutative 60.5%

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

   9. Simplified 60.5%

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

   if -1.02e-143 < t < 7.00000000000000031e-19

   1. Initial program 88.4%

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

      1. associate-/r* 93.8%

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

      2. div-inv 93.7%

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

      3. associate-*l* 93.7%

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

      4. associate-*l* 93.7%

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

   3. Applied egg-rr 93.7%

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

   4. Taylor expanded in b around inf 49.0%

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

      1. clear-num 48.9%

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

      2. frac-times 49.6%

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

      3. metadata-eval 49.6%

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

   6. Applied egg-rr 49.6%

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

   if 7.00000000000000031e-19 < t

   1. Initial program 75.8%

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

   2. Taylor expanded in z around inf 52.4%

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

      1. *-commutative 52.4%

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

      2. associate-/l* 57.0%

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

      3. associate-/r/ 53.9%

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

   4. Simplified 53.9%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+198}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{+149}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{+60}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-143}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-19}:\\ \;\;\;\;\frac{1}{c \cdot \frac{z}{b}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 11: 49.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+147} \lor \neg \left(t \leq -1.5 \cdot 10^{+125} \lor \neg \left(t \leq -1.16 \cdot 10^{+14}\right) \land t \leq 1.05 \cdot 10^{-18}\right):\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -2.1e+147)
         (not
          (or (<= t -1.5e+125) (and (not (<= t -1.16e+14)) (<= t 1.05e-18)))))
   (* -4.0 (/ a (/ c t)))
   (/ (/ b z) c)))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -2.1e+147) || !((t <= -1.5e+125) || (!(t <= -1.16e+14) && (t <= 1.05e-18)))) {
		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.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-2.1d+147)) .or. (.not. (t <= (-1.5d+125)) .or. (.not. (t <= (-1.16d+14))) .and. (t <= 1.05d-18))) then
        tmp = (-4.0d0) * (a / (c / t))
    else
        tmp = (b / z) / c
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -2.1e+147) || !((t <= -1.5e+125) || (!(t <= -1.16e+14) && (t <= 1.05e-18)))) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = (b / z) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -2.1e+147) or not ((t <= -1.5e+125) or (not (t <= -1.16e+14) and (t <= 1.05e-18))):
		tmp = -4.0 * (a / (c / t))
	else:
		tmp = (b / z) / c
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -2.1e+147) || !((t <= -1.5e+125) || (!(t <= -1.16e+14) && (t <= 1.05e-18))))
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	else
		tmp = Float64(Float64(b / z) / c);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -2.1e+147) || ~(((t <= -1.5e+125) || (~((t <= -1.16e+14)) && (t <= 1.05e-18)))))
		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.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -2.1e+147], N[Not[Or[LessEqual[t, -1.5e+125], And[N[Not[LessEqual[t, -1.16e+14]], $MachinePrecision], LessEqual[t, 1.05e-18]]]], $MachinePrecision]], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.10000000000000006e147 or -1.50000000000000008e125 < t < -1.16e14 or 1.05e-18 < t

   1. Initial program 81.3%

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

      1. associate-/r* 81.6%

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

      2. div-inv 81.5%

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

      3. associate-*l* 81.5%

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

      4. associate-*l* 85.7%

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

   3. Applied egg-rr 85.7%

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

   4. Taylor expanded in z around inf 57.8%

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

      1. associate-/l* 62.8%

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

   6. Simplified 62.8%

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

   if -2.10000000000000006e147 < t < -1.50000000000000008e125 or -1.16e14 < t < 1.05e-18

   1. Initial program 87.7%

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

      1. associate-/r* 91.1%

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

      2. div-inv 91.1%

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

      3. associate-*l* 91.0%

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

      4. associate-*l* 91.8%

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

   3. Applied egg-rr 91.8%

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

   4. Taylor expanded in x around 0 89.6%

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

      1. cancel-sign-sub-inv 89.6%

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

      2. metadata-eval 89.6%

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

      3. associate-+r+ 89.6%

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

      4. fma-def 89.6%

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

      5. associate-/l* 92.3%

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

   6. Simplified 92.3%

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

   7. Taylor expanded in b around inf 44.0%

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

      1. *-commutative 44.0%

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

      2. associate-/r* 48.6%

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

   9. Simplified 48.6%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+147} \lor \neg \left(t \leq -1.5 \cdot 10^{+125} \lor \neg \left(t \leq -1.16 \cdot 10^{+14}\right) \land t \leq 1.05 \cdot 10^{-18}\right):\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 12: 48.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{z}}{c}\\ t_2 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{+147}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -195000000000:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ b z) c)) (t_2 (* -4.0 (* t (/ a c)))))
   (if (<= t -2e+147)
     t_2
     (if (<= t -1.5e+125)
       t_1
       (if (<= t -195000000000.0)
         (* -4.0 (/ a (/ c t)))
         (if (<= t 2.2e-18) t_1 t_2))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / z) / c;
	double t_2 = -4.0 * (t * (a / c));
	double tmp;
	if (t <= -2e+147) {
		tmp = t_2;
	} else if (t <= -1.5e+125) {
		tmp = t_1;
	} else if (t <= -195000000000.0) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 2.2e-18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b / z) / c
    t_2 = (-4.0d0) * (t * (a / c))
    if (t <= (-2d+147)) then
        tmp = t_2
    else if (t <= (-1.5d+125)) then
        tmp = t_1
    else if (t <= (-195000000000.0d0)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (t <= 2.2d-18) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / z) / c;
	double t_2 = -4.0 * (t * (a / c));
	double tmp;
	if (t <= -2e+147) {
		tmp = t_2;
	} else if (t <= -1.5e+125) {
		tmp = t_1;
	} else if (t <= -195000000000.0) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 2.2e-18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (b / z) / c
	t_2 = -4.0 * (t * (a / c))
	tmp = 0
	if t <= -2e+147:
		tmp = t_2
	elif t <= -1.5e+125:
		tmp = t_1
	elif t <= -195000000000.0:
		tmp = -4.0 * (a / (c / t))
	elif t <= 2.2e-18:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b / z) / c)
	t_2 = Float64(-4.0 * Float64(t * Float64(a / c)))
	tmp = 0.0
	if (t <= -2e+147)
		tmp = t_2;
	elseif (t <= -1.5e+125)
		tmp = t_1;
	elseif (t <= -195000000000.0)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (t <= 2.2e-18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b / z) / c;
	t_2 = -4.0 * (t * (a / c));
	tmp = 0.0;
	if (t <= -2e+147)
		tmp = t_2;
	elseif (t <= -1.5e+125)
		tmp = t_1;
	elseif (t <= -195000000000.0)
		tmp = -4.0 * (a / (c / t));
	elseif (t <= 2.2e-18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e+147], t$95$2, If[LessEqual[t, -1.5e+125], t$95$1, If[LessEqual[t, -195000000000.0], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e-18], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2e147 or 2.1999999999999998e-18 < t

   1. Initial program 79.3%

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

   2. Taylor expanded in z around inf 56.7%

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

      1. *-commutative 56.7%

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

      2. associate-/l* 61.7%

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

      3. associate-/r/ 60.5%

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

   4. Simplified 60.5%

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

   if -2e147 < t < -1.50000000000000008e125 or -1.95e11 < t < 2.1999999999999998e-18

   1. Initial program 87.7%

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

      1. associate-/r* 91.1%

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

      2. div-inv 91.1%

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

      3. associate-*l* 91.0%

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

      4. associate-*l* 91.8%

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

   3. Applied egg-rr 91.8%

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

   4. Taylor expanded in x around 0 89.6%

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

      1. cancel-sign-sub-inv 89.6%

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

      2. metadata-eval 89.6%

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

      3. associate-+r+ 89.6%

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

      4. fma-def 89.6%

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

      5. associate-/l* 92.3%

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

   6. Simplified 92.3%

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

   7. Taylor expanded in b around inf 44.0%

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

      1. *-commutative 44.0%

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

      2. associate-/r* 48.6%

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

   9. Simplified 48.6%

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

   if -1.50000000000000008e125 < t < -1.95e11

   1. Initial program 90.6%

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

      1. associate-/r* 90.6%

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

      2. div-inv 90.5%

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

      3. associate-*l* 90.5%

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

      4. associate-*l* 95.1%

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

   3. Applied egg-rr 95.1%

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

   4. Taylor expanded in z around inf 63.0%

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

      1. associate-/l* 67.4%

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

   6. Simplified 67.4%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+147}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+125}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq -195000000000:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 13: 48.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{+147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+126}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;t \leq -70000000000:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t (/ a c)))))
   (if (<= t -2e+147)
     t_1
     (if (<= t -1.15e+126)
       (* (/ b z) (/ 1.0 c))
       (if (<= t -70000000000.0)
         (* -4.0 (/ a (/ c t)))
         (if (<= t 2.7e-18) (/ (/ b z) c) t_1))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double tmp;
	if (t <= -2e+147) {
		tmp = t_1;
	} else if (t <= -1.15e+126) {
		tmp = (b / z) * (1.0 / c);
	} else if (t <= -70000000000.0) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 2.7e-18) {
		tmp = (b / z) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (t * (a / c))
    if (t <= (-2d+147)) then
        tmp = t_1
    else if (t <= (-1.15d+126)) then
        tmp = (b / z) * (1.0d0 / c)
    else if (t <= (-70000000000.0d0)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (t <= 2.7d-18) then
        tmp = (b / z) / c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double tmp;
	if (t <= -2e+147) {
		tmp = t_1;
	} else if (t <= -1.15e+126) {
		tmp = (b / z) * (1.0 / c);
	} else if (t <= -70000000000.0) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 2.7e-18) {
		tmp = (b / z) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (t * (a / c))
	tmp = 0
	if t <= -2e+147:
		tmp = t_1
	elif t <= -1.15e+126:
		tmp = (b / z) * (1.0 / c)
	elif t <= -70000000000.0:
		tmp = -4.0 * (a / (c / t))
	elif t <= 2.7e-18:
		tmp = (b / z) / c
	else:
		tmp = t_1
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(t * Float64(a / c)))
	tmp = 0.0
	if (t <= -2e+147)
		tmp = t_1;
	elseif (t <= -1.15e+126)
		tmp = Float64(Float64(b / z) * Float64(1.0 / c));
	elseif (t <= -70000000000.0)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (t <= 2.7e-18)
		tmp = Float64(Float64(b / z) / c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (t * (a / c));
	tmp = 0.0;
	if (t <= -2e+147)
		tmp = t_1;
	elseif (t <= -1.15e+126)
		tmp = (b / z) * (1.0 / c);
	elseif (t <= -70000000000.0)
		tmp = -4.0 * (a / (c / t));
	elseif (t <= 2.7e-18)
		tmp = (b / z) / c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e+147], t$95$1, If[LessEqual[t, -1.15e+126], N[(N[(b / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -70000000000.0], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e-18], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2e147 or 2.69999999999999989e-18 < t

   1. Initial program 79.3%

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

   2. Taylor expanded in z around inf 56.7%

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

      1. *-commutative 56.7%

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

      2. associate-/l* 61.7%

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

      3. associate-/r/ 60.5%

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

   4. Simplified 60.5%

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

   if -2e147 < t < -1.15e126

   1. Initial program 75.0%

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

      1. associate-/r* 74.6%

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

      2. div-inv 74.6%

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

      3. associate-*l* 74.6%

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

      4. associate-*l* 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in b around inf 74.6%

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

   if -1.15e126 < t < -7e10

   1. Initial program 90.6%

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

      1. associate-/r* 90.6%

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

      2. div-inv 90.5%

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

      3. associate-*l* 90.5%

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

      4. associate-*l* 95.1%

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

   3. Applied egg-rr 95.1%

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

   4. Taylor expanded in z around inf 63.0%

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

      1. associate-/l* 67.4%

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

   6. Simplified 67.4%

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

   if -7e10 < t < 2.69999999999999989e-18

   1. Initial program 88.1%

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

      1. associate-/r* 91.6%

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

      2. div-inv 91.5%

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

      3. associate-*l* 91.5%

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

      4. associate-*l* 91.5%

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

   3. Applied egg-rr 91.5%

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

   4. Taylor expanded in x around 0 90.0%

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

      1. cancel-sign-sub-inv 90.0%

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

      2. metadata-eval 90.0%

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

      3. associate-+r+ 90.0%

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

      4. fma-def 90.0%

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

      5. associate-/l* 92.8%

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

   6. Simplified 92.8%

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

   7. Taylor expanded in b around inf 43.1%

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

      1. *-commutative 43.1%

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

      2. associate-/r* 47.8%

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

   9. Simplified 47.8%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+147}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+126}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;t \leq -70000000000:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 14: 48.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{1}{c \cdot \frac{z}{b}}\\ t_2 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+147}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{+14}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ 1.0 (* c (/ z b)))) (t_2 (* -4.0 (* t (/ a c)))))
   (if (<= t -4.2e+147)
     t_2
     (if (<= t -1.15e+126)
       t_1
       (if (<= t -2.8e+14)
         (* -4.0 (/ a (/ c t)))
         (if (<= t 3.15e-18) t_1 t_2))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 1.0 / (c * (z / b));
	double t_2 = -4.0 * (t * (a / c));
	double tmp;
	if (t <= -4.2e+147) {
		tmp = t_2;
	} else if (t <= -1.15e+126) {
		tmp = t_1;
	} else if (t <= -2.8e+14) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 3.15e-18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 1.0d0 / (c * (z / b))
    t_2 = (-4.0d0) * (t * (a / c))
    if (t <= (-4.2d+147)) then
        tmp = t_2
    else if (t <= (-1.15d+126)) then
        tmp = t_1
    else if (t <= (-2.8d+14)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (t <= 3.15d-18) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 1.0 / (c * (z / b));
	double t_2 = -4.0 * (t * (a / c));
	double tmp;
	if (t <= -4.2e+147) {
		tmp = t_2;
	} else if (t <= -1.15e+126) {
		tmp = t_1;
	} else if (t <= -2.8e+14) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 3.15e-18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = 1.0 / (c * (z / b))
	t_2 = -4.0 * (t * (a / c))
	tmp = 0
	if t <= -4.2e+147:
		tmp = t_2
	elif t <= -1.15e+126:
		tmp = t_1
	elif t <= -2.8e+14:
		tmp = -4.0 * (a / (c / t))
	elif t <= 3.15e-18:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(1.0 / Float64(c * Float64(z / b)))
	t_2 = Float64(-4.0 * Float64(t * Float64(a / c)))
	tmp = 0.0
	if (t <= -4.2e+147)
		tmp = t_2;
	elseif (t <= -1.15e+126)
		tmp = t_1;
	elseif (t <= -2.8e+14)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (t <= 3.15e-18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 1.0 / (c * (z / b));
	t_2 = -4.0 * (t * (a / c));
	tmp = 0.0;
	if (t <= -4.2e+147)
		tmp = t_2;
	elseif (t <= -1.15e+126)
		tmp = t_1;
	elseif (t <= -2.8e+14)
		tmp = -4.0 * (a / (c / t));
	elseif (t <= 3.15e-18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(1.0 / N[(c * N[(z / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e+147], t$95$2, If[LessEqual[t, -1.15e+126], t$95$1, If[LessEqual[t, -2.8e+14], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.15e-18], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.20000000000000012e147 or 3.1500000000000002e-18 < t

   1. Initial program 79.3%

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

   2. Taylor expanded in z around inf 56.7%

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

      1. *-commutative 56.7%

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

      2. associate-/l* 61.7%

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

      3. associate-/r/ 60.5%

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

   4. Simplified 60.5%

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

   if -4.20000000000000012e147 < t < -1.15e126 or -2.8e14 < t < 3.1500000000000002e-18

   1. Initial program 87.7%

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

      1. associate-/r* 91.1%

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

      2. div-inv 91.1%

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

      3. associate-*l* 91.0%

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

      4. associate-*l* 91.8%

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

   3. Applied egg-rr 91.8%

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

   4. Taylor expanded in b around inf 48.6%

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

      1. clear-num 48.5%

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

      2. frac-times 49.0%

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

      3. metadata-eval 49.0%

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

   6. Applied egg-rr 49.0%

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

   if -1.15e126 < t < -2.8e14

   1. Initial program 90.6%

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

      1. associate-/r* 90.6%

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

      2. div-inv 90.5%

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

      3. associate-*l* 90.5%

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

      4. associate-*l* 95.1%

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

   3. Applied egg-rr 95.1%

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

   4. Taylor expanded in z around inf 63.0%

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

      1. associate-/l* 67.4%

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

   6. Simplified 67.4%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+147}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+126}:\\ \;\;\;\;\frac{1}{c \cdot \frac{z}{b}}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{+14}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{-18}:\\ \;\;\;\;\frac{1}{c \cdot \frac{z}{b}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 15: 70.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -4.9 \cdot 10^{-93} \lor \neg \left(a \leq 8 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -4.9e-93) (not (<= a 8e+52)))
   (/ (+ (/ b z) (* -4.0 (* a t))) c)
   (/ (+ b (* x (* 9.0 y))) (* z c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -4.9e-93) || !(a <= 8e+52)) {
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	} else {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a <= (-4.9d-93)) .or. (.not. (a <= 8d+52))) then
        tmp = ((b / z) + ((-4.0d0) * (a * t))) / c
    else
        tmp = (b + (x * (9.0d0 * y))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -4.9e-93) || !(a <= 8e+52)) {
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	} else {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -4.9e-93) or not (a <= 8e+52):
		tmp = ((b / z) + (-4.0 * (a * t))) / c
	else:
		tmp = (b + (x * (9.0 * y))) / (z * c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -4.9e-93) || !(a <= 8e+52))
		tmp = Float64(Float64(Float64(b / z) + Float64(-4.0 * Float64(a * t))) / c);
	else
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -4.9e-93) || ~((a <= 8e+52)))
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	else
		tmp = (b + (x * (9.0 * y))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -4.9e-93], N[Not[LessEqual[a, 8e+52]], $MachinePrecision]], N[(N[(N[(b / z), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.89999999999999965e-93 or 7.9999999999999999e52 < a

   1. Initial program 86.8%

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

      1. associate-/r* 87.7%

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

      2. div-inv 87.7%

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

      3. associate-*l* 87.7%

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

      4. associate-*l* 87.7%

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

   3. Applied egg-rr 87.7%

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

   4. Taylor expanded in x around 0 86.0%

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

      1. cancel-sign-sub-inv 86.0%

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

      2. metadata-eval 86.0%

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

      3. associate-+r+ 86.0%

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

      4. fma-def 86.0%

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

      5. associate-/l* 87.5%

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

   6. Simplified 87.5%

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

   7. Taylor expanded in y around 0 75.0%

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

   if -4.89999999999999965e-93 < a < 7.9999999999999999e52

   1. Initial program 82.7%

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

   2. Taylor expanded in x around inf 78.1%

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

      1. associate-*r* 78.1%

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

      2. *-commutative 78.1%

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

   4. Simplified 78.1%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.9 \cdot 10^{-93} \lor \neg \left(a \leq 8 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 16: 70.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-93} \lor \neg \left(a \leq 6.9 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b - y \cdot \left(x \cdot -9\right)}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -1.6e-93) (not (<= a 6.9e+56)))
   (/ (+ (/ b z) (* -4.0 (* a t))) c)
   (/ (/ (- b (* y (* x -9.0))) z) c)))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -1.6e-93) || !(a <= 6.9e+56)) {
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	} else {
		tmp = ((b - (y * (x * -9.0))) / z) / c;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a <= (-1.6d-93)) .or. (.not. (a <= 6.9d+56))) then
        tmp = ((b / z) + ((-4.0d0) * (a * t))) / c
    else
        tmp = ((b - (y * (x * (-9.0d0)))) / z) / c
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -1.6e-93) || !(a <= 6.9e+56)) {
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	} else {
		tmp = ((b - (y * (x * -9.0))) / z) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -1.6e-93) or not (a <= 6.9e+56):
		tmp = ((b / z) + (-4.0 * (a * t))) / c
	else:
		tmp = ((b - (y * (x * -9.0))) / z) / c
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -1.6e-93) || !(a <= 6.9e+56))
		tmp = Float64(Float64(Float64(b / z) + Float64(-4.0 * Float64(a * t))) / c);
	else
		tmp = Float64(Float64(Float64(b - Float64(y * Float64(x * -9.0))) / z) / c);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -1.6e-93) || ~((a <= 6.9e+56)))
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	else
		tmp = ((b - (y * (x * -9.0))) / z) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -1.6e-93], N[Not[LessEqual[a, 6.9e+56]], $MachinePrecision]], N[(N[(N[(b / z), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(b - N[(y * N[(x * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.5999999999999999e-93 or 6.9e56 < a

   1. Initial program 86.8%

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

      1. associate-/r* 87.7%

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

      2. div-inv 87.7%

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

      3. associate-*l* 87.7%

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

      4. associate-*l* 87.7%

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

   3. Applied egg-rr 87.7%

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

   4. Taylor expanded in x around 0 86.0%

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

      1. cancel-sign-sub-inv 86.0%

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

      2. metadata-eval 86.0%

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

      3. associate-+r+ 86.0%

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

      4. fma-def 86.0%

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

      5. associate-/l* 87.5%

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

   6. Simplified 87.5%

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

   7. Taylor expanded in y around 0 75.0%

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

   if -1.5999999999999999e-93 < a < 6.9e56

   1. Initial program 82.7%

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

      1. associate-/r* 85.8%

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

      2. div-inv 85.8%

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

      3. associate-*l* 85.8%

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

      4. associate-*l* 90.6%

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

   3. Applied egg-rr 90.6%

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

   4. Taylor expanded in x around 0 92.1%

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

      1. cancel-sign-sub-inv 92.1%

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

      2. metadata-eval 92.1%

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

      3. associate-+r+ 92.1%

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

      4. fma-def 92.1%

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

      5. associate-/l* 92.2%

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

   6. Simplified 92.2%

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

   7. Taylor expanded in a around 0 79.5%

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

   8. Taylor expanded in z around -inf 80.4%

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

      1. associate-*r/ 80.4%

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

      2. mul-1-neg 80.4%

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

      3. neg-mul-1 80.4%

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

      4. unsub-neg 80.4%

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

      5. associate-*r* 80.4%

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

      6. *-commutative 80.4%

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

      7. associate-*l* 80.4%

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

   10. Simplified 80.4%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-93} \lor \neg \left(a \leq 6.9 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b - y \cdot \left(x \cdot -9\right)}{z}}{c}\\ \end{array} \]

Alternative 17: 66.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+198}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-18}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -3.5e+198)
   (* -4.0 (/ a (/ c t)))
   (if (<= t 3.8e-18)
     (/ (+ b (* 9.0 (* y x))) (* z c))
     (* -4.0 (* t (/ a c))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -3.5e+198) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 3.8e-18) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-3.5d+198)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (t <= 3.8d-18) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c)
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -3.5e+198) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 3.8e-18) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -3.5e+198:
		tmp = -4.0 * (a / (c / t))
	elif t <= 3.8e-18:
		tmp = (b + (9.0 * (y * x))) / (z * c)
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -3.5e+198)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (t <= 3.8e-18)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -3.5e+198)
		tmp = -4.0 * (a / (c / t));
	elseif (t <= 3.8e-18)
		tmp = (b + (9.0 * (y * x))) / (z * c);
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -3.5e+198], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e-18], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.50000000000000013e198

   1. Initial program 81.0%

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

      1. associate-/r* 77.5%

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

      2. div-inv 77.6%

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

      3. associate-*l* 77.6%

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

      4. associate-*l* 81.5%

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

   3. Applied egg-rr 81.5%

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

   4. Taylor expanded in z around inf 61.8%

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

      1. associate-/l* 76.4%

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

   6. Simplified 76.4%

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

   if -3.50000000000000013e198 < t < 3.7999999999999998e-18

   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. Taylor expanded in x around inf 73.2%

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

   if 3.7999999999999998e-18 < t

   1. Initial program 75.8%

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

   2. Taylor expanded in z around inf 52.4%

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

      1. *-commutative 52.4%

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

      2. associate-/l* 57.0%

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

      3. associate-/r/ 53.9%

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

   4. Simplified 53.9%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+198}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-18}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 18: 66.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+198}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-18}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.2e+198)
   (* -4.0 (/ a (/ c t)))
   (if (<= t 3.8e-18)
     (/ (+ b (* x (* 9.0 y))) (* z c))
     (* -4.0 (* t (/ a c))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.2e+198) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 3.8e-18) {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-1.2d+198)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (t <= 3.8d-18) then
        tmp = (b + (x * (9.0d0 * y))) / (z * c)
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.2e+198) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 3.8e-18) {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -1.2e+198:
		tmp = -4.0 * (a / (c / t))
	elif t <= 3.8e-18:
		tmp = (b + (x * (9.0 * y))) / (z * c)
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.2e+198)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (t <= 3.8e-18)
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -1.2e+198)
		tmp = -4.0 * (a / (c / t));
	elseif (t <= 3.8e-18)
		tmp = (b + (x * (9.0 * y))) / (z * c);
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -1.2e+198], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e-18], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2000000000000001e198

   1. Initial program 81.0%

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

      1. associate-/r* 77.5%

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

      2. div-inv 77.6%

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

      3. associate-*l* 77.6%

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

      4. associate-*l* 81.5%

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

   3. Applied egg-rr 81.5%

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

   4. Taylor expanded in z around inf 61.8%

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

      1. associate-/l* 76.4%

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

   6. Simplified 76.4%

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

   if -1.2000000000000001e198 < t < 3.7999999999999998e-18

   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. Taylor expanded in x around inf 73.2%

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

      1. associate-*r* 73.2%

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

      2. *-commutative 73.2%

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

   4. Simplified 73.2%

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

   if 3.7999999999999998e-18 < t

   1. Initial program 75.8%

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

   2. Taylor expanded in z around inf 52.4%

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

      1. *-commutative 52.4%

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

      2. associate-/l* 57.0%

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

      3. associate-/r/ 53.9%

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

   4. Simplified 53.9%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+198}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-18}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 19: 35.2% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.8%

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

2. Taylor expanded in b around inf 37.7%

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

   1. *-commutative 37.7%

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

4. Simplified 37.7%

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

5. Final simplification 37.7%

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

Alternative 20: 33.4% accurate, 3.8× speedup

Math

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ (/ b z) c))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.8%

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

   1. associate-/r* 86.8%

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

   2. div-inv 86.8%

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

   3. associate-*l* 86.8%

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

   4. associate-*l* 89.0%

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

3. Applied egg-rr 89.0%

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

4. Taylor expanded in x around 0 88.9%

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

   1. cancel-sign-sub-inv 88.9%

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

   2. metadata-eval 88.9%

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

   3. associate-+r+ 88.9%

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

   4. fma-def 88.9%

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

   5. associate-/l* 89.7%

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

6. Simplified 89.7%

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

7. Taylor expanded in b around inf 37.7%

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

   1. *-commutative 37.7%

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

   2. associate-/r* 39.5%

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

9. Simplified 39.5%

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

10. Final simplification 39.5%

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

Developer target: 80.0% 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 2023187 
(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)))