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

Percentage Accurate: 79.3% → 90.5%

Time: 22.5s

Alternatives: 16

Speedup: 0.8×

• 37.1% 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: 79.3% 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: 90.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+28} \lor \neg \left(z \leq 2.3 \cdot 10^{-178}\right):\\ \;\;\;\;\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(z \cdot \left(-4 \cdot a\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

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 -2.5e+28) (not (<= z 2.3e-178)))
   (* (+ (* -4.0 (* a t)) (+ (* 9.0 (/ (* x y) z)) (/ b z))) (/ 1.0 c))
   (/ (+ b (fma x (* 9.0 y) (* t (* z (* -4.0 a))))) (* z c))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2.5e+28) || !(z <= 2.3e-178)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) * (1.0 / c);
	} else {
		tmp = (b + fma(x, (9.0 * y), (t * (z * (-4.0 * a))))) / (z * c);
	}
	return tmp;
}

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -2.5e+28) || !(z <= 2.3e-178))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z))) * Float64(1.0 / c));
	else
		tmp = Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(t * Float64(z * Float64(-4.0 * a))))) / Float64(z * c));
	end
	return tmp
end

Wolfram

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, -2.5e+28], N[Not[LessEqual[z, 2.3e-178]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(t * N[(z * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.49999999999999979e28 or 2.29999999999999994e-178 < z

   1. Initial program 66.1%

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

      1. associate-+l- 66.1%

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

      2. div-sub 62.5%

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

      3. *-commutative 62.5%

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

      4. associate-*r* 61.0%

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

      5. *-commutative 61.0%

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

      6. div-sub 64.7%

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

      7. associate-+l- 64.7%

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

   3. Simplified 68.3%

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

   5. Applied egg-rr 79.6%

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

   6. Taylor expanded in x around 0 90.0%

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

   if -2.49999999999999979e28 < z < 2.29999999999999994e-178

   1. Initial program 99.0%

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

      1. associate-+l- 99.0%

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

      2. div-sub 83.9%

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

      3. *-commutative 83.9%

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

      4. associate-*r* 83.9%

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

      5. *-commutative 83.9%

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

      6. div-sub 98.2%

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

      7. associate-+l- 98.2%

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

   3. Simplified 98.3%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+28} \lor \neg \left(z \leq 2.3 \cdot 10^{-178}\right):\\ \;\;\;\;\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(z \cdot \left(-4 \cdot a\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 2: 90.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+22} \lor \neg \left(z \leq 2.3 \cdot 10^{-178}\right):\\ \;\;\;\;\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

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 -4e+22) (not (<= z 2.3e-178)))
   (* (+ (* -4.0 (* a t)) (+ (* 9.0 (/ (* x y) z)) (/ b z))) (/ 1.0 c))
   (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -4e+22) || !(z <= 2.3e-178)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) * (1.0 / c);
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Fortran

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 <= (-4d+22)) .or. (.not. (z <= 2.3d-178))) then
        tmp = (((-4.0d0) * (a * t)) + ((9.0d0 * ((x * y) / z)) + (b / z))) * (1.0d0 / c)
    else
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (z * c)
    end if
    code = tmp
end function

Java

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 <= -4e+22) || !(z <= 2.3e-178)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) * (1.0 / c);
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -4e+22) or not (z <= 2.3e-178):
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) * (1.0 / c)
	else:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -4e+22) || !(z <= 2.3e-178))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z))) * Float64(1.0 / c));
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -4e+22) || ~((z <= 2.3e-178)))
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) * (1.0 / c);
	else
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

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, -4e+22], N[Not[LessEqual[z, 2.3e-178]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4e22 or 2.29999999999999994e-178 < z

   1. Initial program 66.6%

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

      1. associate-+l- 66.6%

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

      2. div-sub 63.0%

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

      3. *-commutative 63.0%

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

      4. associate-*r* 60.9%

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

      5. *-commutative 60.9%

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

      6. div-sub 64.5%

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

      7. associate-+l- 64.5%

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

   3. Simplified 68.7%

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

   5. Applied egg-rr 79.9%

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

   6. Taylor expanded in x around 0 90.1%

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

   if -4e22 < z < 2.29999999999999994e-178

   1. Initial program 99.0%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+22} \lor \neg \left(z \leq 2.3 \cdot 10^{-178}\right):\\ \;\;\;\;\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 3: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+166} \lor \neg \left(z \leq 2.7 \cdot 10^{+100}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

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+166) (not (<= z 2.7e+100)))
   (/ (+ (* -4.0 (* a t)) (/ b z)) c)
   (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* a t)))) (* z c))))

C

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+166) || !(z <= 2.7e+100)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (z * c);
	}
	return tmp;
}

Fortran

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+166)) .or. (.not. (z <= 2.7d+100))) then
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    else
        tmp = (b + ((x * (9.0d0 * y)) - ((z * 4.0d0) * (a * t)))) / (z * c)
    end if
    code = tmp
end function

Java

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+166) || !(z <= 2.7e+100)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (z * c);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -1.35e+166) or not (z <= 2.7e+100):
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	else:
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (z * c)
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.35e+166) || !(z <= 2.7e+100))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(a * t)))) / Float64(z * c));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -1.35e+166) || ~((z <= 2.7e+100)))
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	else
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

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+166], N[Not[LessEqual[z, 2.7e+100]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35000000000000006e166 or 2.69999999999999998e100 < z

   1. Initial program 53.8%

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

      1. associate-+l- 53.8%

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

      2. div-sub 52.3%

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

      3. *-commutative 52.3%

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

      4. associate-*r* 49.5%

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

      5. *-commutative 49.5%

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

      6. div-sub 50.9%

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

      7. associate-+l- 50.9%

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

   3. Simplified 55.1%

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

   5. Applied egg-rr 75.5%

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

   6. Taylor expanded in x around 0 94.2%

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

   7. Taylor expanded in x around 0 82.4%

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

   if -1.35000000000000006e166 < z < 2.69999999999999998e100

   1. Initial program 92.0%

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

      1. associate-+l- 92.0%

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

      2. div-sub 80.1%

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

      3. *-commutative 80.1%

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

      4. associate-*r* 80.2%

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

      5. *-commutative 80.2%

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

      6. div-sub 91.6%

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

      7. associate-+l- 91.6%

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

   3. Simplified 91.1%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+166} \lor \neg \left(z \leq 2.7 \cdot 10^{+100}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 4: 85.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+132} \lor \neg \left(z \leq 9 \cdot 10^{+105}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

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 -2.75e+132) (not (<= z 9e+105)))
   (/ (+ (* -4.0 (* a t)) (/ b z)) c)
   (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2.75e+132) || !(z <= 9e+105)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Fortran

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 <= (-2.75d+132)) .or. (.not. (z <= 9d+105))) then
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    else
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (z * c)
    end if
    code = tmp
end function

Java

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 <= -2.75e+132) || !(z <= 9e+105)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -2.75e+132) or not (z <= 9e+105):
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	else:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -2.75e+132) || !(z <= 9e+105))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -2.75e+132) || ~((z <= 9e+105)))
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	else
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

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, -2.75e+132], N[Not[LessEqual[z, 9e+105]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.75e132 or 9.0000000000000002e105 < z

   1. Initial program 57.7%

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

      1. associate-+l- 57.7%

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

      2. div-sub 56.5%

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

      3. *-commutative 56.5%

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

      4. associate-*r* 54.0%

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

      5. *-commutative 54.0%

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

      6. div-sub 55.2%

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

      7. associate-+l- 55.2%

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

   3. Simplified 60.1%

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

   5. Applied egg-rr 78.2%

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

   6. Taylor expanded in x around 0 94.8%

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

   7. Taylor expanded in x around 0 81.9%

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

   if -2.75e132 < z < 9.0000000000000002e105

   1. Initial program 92.2%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+132} \lor \neg \left(z \leq 9 \cdot 10^{+105}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 5: 50.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -540000000000:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-216}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-260}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;b \leq 4.25 \cdot 10^{-306}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-200}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+46}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -540000000000.0)
   (/ (/ 1.0 z) (/ c b))
   (if (<= b -2.8e-216)
     (* -4.0 (* t (/ a c)))
     (if (<= b -1.45e-260)
       (* 9.0 (* (/ y z) (/ x c)))
       (if (<= b 4.25e-306)
         (* -4.0 (/ t (/ c a)))
         (if (<= b 1.5e-200)
           (* 9.0 (/ (* x y) (* z c)))
           (if (<= b 7.2e+46) (* -4.0 (/ a (/ c t))) (/ (/ b c) z))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -540000000000.0) {
		tmp = (1.0 / z) / (c / b);
	} else if (b <= -2.8e-216) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= -1.45e-260) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (b <= 4.25e-306) {
		tmp = -4.0 * (t / (c / a));
	} else if (b <= 1.5e-200) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (b <= 7.2e+46) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-540000000000.0d0)) then
        tmp = (1.0d0 / z) / (c / b)
    else if (b <= (-2.8d-216)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (b <= (-1.45d-260)) then
        tmp = 9.0d0 * ((y / z) * (x / c))
    else if (b <= 4.25d-306) then
        tmp = (-4.0d0) * (t / (c / a))
    else if (b <= 1.5d-200) then
        tmp = 9.0d0 * ((x * y) / (z * c))
    else if (b <= 7.2d+46) then
        tmp = (-4.0d0) * (a / (c / t))
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -540000000000.0) {
		tmp = (1.0 / z) / (c / b);
	} else if (b <= -2.8e-216) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= -1.45e-260) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (b <= 4.25e-306) {
		tmp = -4.0 * (t / (c / a));
	} else if (b <= 1.5e-200) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (b <= 7.2e+46) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -540000000000.0:
		tmp = (1.0 / z) / (c / b)
	elif b <= -2.8e-216:
		tmp = -4.0 * (t * (a / c))
	elif b <= -1.45e-260:
		tmp = 9.0 * ((y / z) * (x / c))
	elif b <= 4.25e-306:
		tmp = -4.0 * (t / (c / a))
	elif b <= 1.5e-200:
		tmp = 9.0 * ((x * y) / (z * c))
	elif b <= 7.2e+46:
		tmp = -4.0 * (a / (c / t))
	else:
		tmp = (b / c) / z
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -540000000000.0)
		tmp = Float64(Float64(1.0 / z) / Float64(c / b));
	elseif (b <= -2.8e-216)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (b <= -1.45e-260)
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	elseif (b <= 4.25e-306)
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	elseif (b <= 1.5e-200)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)));
	elseif (b <= 7.2e+46)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -540000000000.0)
		tmp = (1.0 / z) / (c / b);
	elseif (b <= -2.8e-216)
		tmp = -4.0 * (t * (a / c));
	elseif (b <= -1.45e-260)
		tmp = 9.0 * ((y / z) * (x / c));
	elseif (b <= 4.25e-306)
		tmp = -4.0 * (t / (c / a));
	elseif (b <= 1.5e-200)
		tmp = 9.0 * ((x * y) / (z * c));
	elseif (b <= 7.2e+46)
		tmp = -4.0 * (a / (c / t));
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -540000000000.0], N[(N[(1.0 / z), $MachinePrecision] / N[(c / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.8e-216], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.45e-260], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.25e-306], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.5e-200], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.2e+46], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -5.4e11

   1. Initial program 82.8%

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

      1. associate-+l- 82.8%

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

      2. div-sub 74.6%

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

      3. *-commutative 74.6%

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

      4. associate-*r* 77.8%

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

      5. *-commutative 77.8%

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

      6. div-sub 86.0%

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

      7. associate-+l- 86.0%

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

   3. Simplified 84.5%

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

   4. Taylor expanded in b around inf 67.6%

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

      1. *-commutative 67.6%

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

   6. Simplified 67.6%

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

      1. frac-2neg 67.6%

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

      2. neg-mul-1 67.6%

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

      3. metadata-eval 67.6%

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

      4. distribute-rgt-neg-in 67.6%

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

      5. times-frac 70.3%

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

      6. metadata-eval 70.3%

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

   8. Applied egg-rr 70.3%

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

      1. associate-*l/ 70.4%

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

      2. associate-*r/ 70.4%

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

      3. neg-mul-1 70.4%

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

   10. Simplified 70.4%

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

       1. clear-num 69.2%

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

       2. frac-2neg 69.2%

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

       3. div-inv 69.2%

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

       4. metadata-eval 69.2%

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

       5. clear-num 69.1%

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

       6. associate-/l/ 67.5%

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

       7. clear-num 67.6%

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

       8. div-inv 67.6%

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

       9. associate-*r* 69.1%

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

       10. div-inv 69.1%

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

       11. frac-2neg 69.1%

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

   12. Applied egg-rr 69.1%

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

       1. associate-*r/ 69.1%

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

       2. metadata-eval 69.1%

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

       3. neg-mul-1 69.1%

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

       4. associate-/r* 69.1%

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

       5. metadata-eval 69.1%

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

       6. associate-/r* 70.4%

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

   14. Simplified 70.4%

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

   if -5.4e11 < b < -2.8e-216

   1. Initial program 88.6%

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

      1. associate-+l- 88.6%

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

      2. div-sub 79.5%

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

      3. *-commutative 79.5%

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

      4. associate-*r* 75.2%

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

      5. *-commutative 75.2%

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

      6. div-sub 82.0%

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

      7. associate-+l- 82.0%

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

   3. Simplified 84.6%

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

   4. Taylor expanded in z around inf 64.7%

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

      1. associate-/l* 66.6%

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

      2. associate-/r/ 62.5%

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

   6. Applied egg-rr 62.5%

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

   if -2.8e-216 < b < -1.45e-260

   1. Initial program 78.0%

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

      1. associate-+l- 78.0%

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

      2. div-sub 47.3%

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

      3. *-commutative 47.3%

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

      4. associate-*r* 47.3%

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

      5. *-commutative 47.3%

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

      6. div-sub 78.0%

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

      7. associate-+l- 78.0%

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

   3. Simplified 78.0%

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

   4. Taylor expanded in x around inf 50.2%

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

      1. times-frac 57.3%

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

   6. Simplified 57.3%

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

   if -1.45e-260 < b < 4.2500000000000001e-306

   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-+l- 81.2%

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

      2. div-sub 81.2%

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

      3. *-commutative 81.2%

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

      4. associate-*r* 81.2%

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

      5. *-commutative 81.2%

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

      6. div-sub 81.2%

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

      7. associate-+l- 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in z around inf 80.0%

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

      1. *-commutative 80.0%

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

      2. *-commutative 80.0%

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

      3. associate-/l* 80.0%

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

   6. Simplified 80.0%

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

   if 4.2500000000000001e-306 < b < 1.49999999999999997e-200

   1. Initial program 92.1%

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

      1. associate-+l- 92.1%

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

      2. div-sub 92.1%

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

      3. *-commutative 92.1%

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

      4. associate-*r* 92.1%

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

      5. *-commutative 92.1%

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

      6. div-sub 92.1%

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

      7. associate-+l- 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in x around inf 84.8%

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

   if 1.49999999999999997e-200 < b < 7.1999999999999997e46

   1. Initial program 81.9%

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

      1. associate-+l- 81.9%

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

      2. div-sub 68.3%

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

      3. *-commutative 68.3%

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

      4. associate-*r* 66.1%

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

      5. *-commutative 66.1%

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

      6. div-sub 79.8%

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

      7. associate-+l- 79.8%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in z around inf 48.6%

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

      1. *-commutative 48.6%

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

      2. associate-/l* 52.9%

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

   6. Simplified 52.9%

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

   if 7.1999999999999997e46 < b

   1. Initial program 71.0%

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

      1. associate-+l- 71.0%

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

      2. div-sub 64.7%

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

      3. *-commutative 64.7%

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

      4. associate-*r* 63.0%

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

      5. *-commutative 63.0%

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

      6. div-sub 69.4%

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

      7. associate-+l- 69.4%

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

   3. Simplified 71.1%

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

   4. Taylor expanded in b around inf 51.2%

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

      1. *-commutative 51.2%

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

   6. Simplified 51.2%

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

      1. frac-2neg 51.2%

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

      2. neg-mul-1 51.2%

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

      3. metadata-eval 51.2%

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

      4. distribute-rgt-neg-in 51.2%

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

      5. times-frac 64.2%

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

      6. metadata-eval 64.2%

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

   8. Applied egg-rr 64.2%

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

      1. associate-*l/ 64.2%

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

      2. associate-*r/ 64.2%

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

      3. neg-mul-1 64.2%

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

   10. Simplified 64.2%

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

       1. div-inv 64.2%

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

       2. frac-2neg 64.2%

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

       3. frac-times 51.2%

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

       4. remove-double-neg 51.2%

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

       5. remove-double-neg 51.2%

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

       6. times-frac 64.2%

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

       7. associate-*l/ 59.5%

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

       8. *-rgt-identity 59.5%

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

       9. *-commutative 59.5%

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

       10. times-frac 51.2%

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

       11. remove-double-neg 51.2%

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

       12. metadata-eval 51.2%

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

       13. metadata-eval 51.2%

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

       14. frac-2neg 51.2%

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

       15. div-inv 51.2%

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

       16. metadata-eval 51.2%

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

       17. metadata-eval 51.2%

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

       18. metadata-eval 51.2%

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

       19. *-commutative 51.2%

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

       20. metadata-eval 51.2%

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

       21. neg-mul-1 51.2%

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

       22. remove-double-neg 51.2%

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

   12. Applied egg-rr 51.2%

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

       1. *-commutative 51.2%

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

       2. associate-/l/ 51.1%

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

       3. un-div-inv 51.2%

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

       4. associate-/r* 64.2%

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

   14. Applied egg-rr 64.2%

       \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -540000000000:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-216}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-260}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;b \leq 4.25 \cdot 10^{-306}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-200}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+46}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 6: 50.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -42000000000:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-217}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-260}:\\ \;\;\;\;\frac{x}{c} \cdot \frac{9 \cdot y}{z}\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{-302}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-196}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{+46}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -42000000000.0)
   (/ (/ 1.0 z) (/ c b))
   (if (<= b -6.5e-217)
     (* -4.0 (* t (/ a c)))
     (if (<= b -1.4e-260)
       (* (/ x c) (/ (* 9.0 y) z))
       (if (<= b 4.3e-302)
         (* -4.0 (/ t (/ c a)))
         (if (<= b 4.1e-196)
           (* 9.0 (/ (* x y) (* z c)))
           (if (<= b 2.65e+46) (* -4.0 (/ a (/ c t))) (/ (/ b c) z))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -42000000000.0) {
		tmp = (1.0 / z) / (c / b);
	} else if (b <= -6.5e-217) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= -1.4e-260) {
		tmp = (x / c) * ((9.0 * y) / z);
	} else if (b <= 4.3e-302) {
		tmp = -4.0 * (t / (c / a));
	} else if (b <= 4.1e-196) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (b <= 2.65e+46) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-42000000000.0d0)) then
        tmp = (1.0d0 / z) / (c / b)
    else if (b <= (-6.5d-217)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (b <= (-1.4d-260)) then
        tmp = (x / c) * ((9.0d0 * y) / z)
    else if (b <= 4.3d-302) then
        tmp = (-4.0d0) * (t / (c / a))
    else if (b <= 4.1d-196) then
        tmp = 9.0d0 * ((x * y) / (z * c))
    else if (b <= 2.65d+46) then
        tmp = (-4.0d0) * (a / (c / t))
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -42000000000.0) {
		tmp = (1.0 / z) / (c / b);
	} else if (b <= -6.5e-217) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= -1.4e-260) {
		tmp = (x / c) * ((9.0 * y) / z);
	} else if (b <= 4.3e-302) {
		tmp = -4.0 * (t / (c / a));
	} else if (b <= 4.1e-196) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (b <= 2.65e+46) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -42000000000.0:
		tmp = (1.0 / z) / (c / b)
	elif b <= -6.5e-217:
		tmp = -4.0 * (t * (a / c))
	elif b <= -1.4e-260:
		tmp = (x / c) * ((9.0 * y) / z)
	elif b <= 4.3e-302:
		tmp = -4.0 * (t / (c / a))
	elif b <= 4.1e-196:
		tmp = 9.0 * ((x * y) / (z * c))
	elif b <= 2.65e+46:
		tmp = -4.0 * (a / (c / t))
	else:
		tmp = (b / c) / z
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -42000000000.0)
		tmp = Float64(Float64(1.0 / z) / Float64(c / b));
	elseif (b <= -6.5e-217)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (b <= -1.4e-260)
		tmp = Float64(Float64(x / c) * Float64(Float64(9.0 * y) / z));
	elseif (b <= 4.3e-302)
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	elseif (b <= 4.1e-196)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)));
	elseif (b <= 2.65e+46)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -42000000000.0)
		tmp = (1.0 / z) / (c / b);
	elseif (b <= -6.5e-217)
		tmp = -4.0 * (t * (a / c));
	elseif (b <= -1.4e-260)
		tmp = (x / c) * ((9.0 * y) / z);
	elseif (b <= 4.3e-302)
		tmp = -4.0 * (t / (c / a));
	elseif (b <= 4.1e-196)
		tmp = 9.0 * ((x * y) / (z * c));
	elseif (b <= 2.65e+46)
		tmp = -4.0 * (a / (c / t));
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -42000000000.0], N[(N[(1.0 / z), $MachinePrecision] / N[(c / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.5e-217], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.4e-260], N[(N[(x / c), $MachinePrecision] * N[(N[(9.0 * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.3e-302], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.1e-196], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.65e+46], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -4.2e10

   1. Initial program 82.8%

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

      1. associate-+l- 82.8%

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

      2. div-sub 74.6%

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

      3. *-commutative 74.6%

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

      4. associate-*r* 77.8%

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

      5. *-commutative 77.8%

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

      6. div-sub 86.0%

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

      7. associate-+l- 86.0%

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

   3. Simplified 84.5%

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

   4. Taylor expanded in b around inf 67.6%

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

      1. *-commutative 67.6%

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

   6. Simplified 67.6%

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

      1. frac-2neg 67.6%

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

      2. neg-mul-1 67.6%

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

      3. metadata-eval 67.6%

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

      4. distribute-rgt-neg-in 67.6%

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

      5. times-frac 70.3%

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

      6. metadata-eval 70.3%

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

   8. Applied egg-rr 70.3%

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

      1. associate-*l/ 70.4%

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

      2. associate-*r/ 70.4%

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

      3. neg-mul-1 70.4%

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

   10. Simplified 70.4%

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

       1. clear-num 69.2%

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

       2. frac-2neg 69.2%

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

       3. div-inv 69.2%

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

       4. metadata-eval 69.2%

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

       5. clear-num 69.1%

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

       6. associate-/l/ 67.5%

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

       7. clear-num 67.6%

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

       8. div-inv 67.6%

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

       9. associate-*r* 69.1%

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

       10. div-inv 69.1%

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

       11. frac-2neg 69.1%

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

   12. Applied egg-rr 69.1%

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

       1. associate-*r/ 69.1%

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

       2. metadata-eval 69.1%

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

       3. neg-mul-1 69.1%

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

       4. associate-/r* 69.1%

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

       5. metadata-eval 69.1%

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

       6. associate-/r* 70.4%

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

   14. Simplified 70.4%

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

   if -4.2e10 < b < -6.4999999999999996e-217

   1. Initial program 88.6%

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

      1. associate-+l- 88.6%

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

      2. div-sub 79.5%

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

      3. *-commutative 79.5%

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

      4. associate-*r* 75.2%

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

      5. *-commutative 75.2%

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

      6. div-sub 82.0%

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

      7. associate-+l- 82.0%

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

   3. Simplified 84.6%

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

   4. Taylor expanded in z around inf 64.7%

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

      1. associate-/l* 66.6%

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

      2. associate-/r/ 62.5%

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

   6. Applied egg-rr 62.5%

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

   if -6.4999999999999996e-217 < b < -1.3999999999999999e-260

   1. Initial program 78.0%

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

      1. associate-+l- 78.0%

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

      2. div-sub 47.3%

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

      3. *-commutative 47.3%

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

      4. associate-*r* 47.3%

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

      5. *-commutative 47.3%

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

      6. div-sub 78.0%

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

      7. associate-+l- 78.0%

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

   3. Simplified 78.0%

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

   4. Taylor expanded in x around inf 50.2%

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

      1. *-commutative 50.2%

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

      2. associate-*r/ 50.2%

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

      3. associate-*r* 50.2%

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

      4. *-commutative 50.2%

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

      5. associate-*r* 50.2%

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

      6. *-commutative 50.2%

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

      7. times-frac 57.3%

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

   6. Simplified 57.3%

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

   if -1.3999999999999999e-260 < b < 4.3000000000000002e-302

   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-+l- 81.2%

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

      2. div-sub 81.2%

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

      3. *-commutative 81.2%

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

      4. associate-*r* 81.2%

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

      5. *-commutative 81.2%

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

      6. div-sub 81.2%

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

      7. associate-+l- 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in z around inf 80.0%

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

      1. *-commutative 80.0%

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

      2. *-commutative 80.0%

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

      3. associate-/l* 80.0%

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

   6. Simplified 80.0%

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

   if 4.3000000000000002e-302 < b < 4.10000000000000021e-196

   1. Initial program 92.1%

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

      1. associate-+l- 92.1%

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

      2. div-sub 92.1%

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

      3. *-commutative 92.1%

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

      4. associate-*r* 92.1%

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

      5. *-commutative 92.1%

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

      6. div-sub 92.1%

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

      7. associate-+l- 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in x around inf 84.8%

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

   if 4.10000000000000021e-196 < b < 2.64999999999999989e46

   1. Initial program 81.9%

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

      1. associate-+l- 81.9%

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

      2. div-sub 68.3%

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

      3. *-commutative 68.3%

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

      4. associate-*r* 66.1%

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

      5. *-commutative 66.1%

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

      6. div-sub 79.8%

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

      7. associate-+l- 79.8%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in z around inf 48.6%

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

      1. *-commutative 48.6%

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

      2. associate-/l* 52.9%

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

   6. Simplified 52.9%

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

   if 2.64999999999999989e46 < b

   1. Initial program 71.0%

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

      1. associate-+l- 71.0%

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

      2. div-sub 64.7%

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

      3. *-commutative 64.7%

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

      4. associate-*r* 63.0%

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

      5. *-commutative 63.0%

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

      6. div-sub 69.4%

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

      7. associate-+l- 69.4%

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

   3. Simplified 71.1%

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

   4. Taylor expanded in b around inf 51.2%

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

      1. *-commutative 51.2%

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

   6. Simplified 51.2%

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

      1. frac-2neg 51.2%

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

      2. neg-mul-1 51.2%

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

      3. metadata-eval 51.2%

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

      4. distribute-rgt-neg-in 51.2%

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

      5. times-frac 64.2%

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

      6. metadata-eval 64.2%

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

   8. Applied egg-rr 64.2%

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

      1. associate-*l/ 64.2%

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

      2. associate-*r/ 64.2%

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

      3. neg-mul-1 64.2%

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

   10. Simplified 64.2%

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

       1. div-inv 64.2%

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

       2. frac-2neg 64.2%

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

       3. frac-times 51.2%

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

       4. remove-double-neg 51.2%

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

       5. remove-double-neg 51.2%

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

       6. times-frac 64.2%

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

       7. associate-*l/ 59.5%

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

       8. *-rgt-identity 59.5%

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

       9. *-commutative 59.5%

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

       10. times-frac 51.2%

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

       11. remove-double-neg 51.2%

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

       12. metadata-eval 51.2%

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

       13. metadata-eval 51.2%

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

       14. frac-2neg 51.2%

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

       15. div-inv 51.2%

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

       16. metadata-eval 51.2%

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

       17. metadata-eval 51.2%

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

       18. metadata-eval 51.2%

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

       19. *-commutative 51.2%

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

       20. metadata-eval 51.2%

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

       21. neg-mul-1 51.2%

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

       22. remove-double-neg 51.2%

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

   12. Applied egg-rr 51.2%

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

       1. *-commutative 51.2%

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

       2. associate-/l/ 51.1%

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

       3. un-div-inv 51.2%

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

       4. associate-/r* 64.2%

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

   14. Applied egg-rr 64.2%

       \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -42000000000:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-217}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-260}:\\ \;\;\;\;\frac{x}{c} \cdot \frac{9 \cdot y}{z}\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{-302}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-196}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{+46}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 7: 50.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -265000000:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-218}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-276}:\\ \;\;\;\;\frac{y \cdot \frac{x}{c}}{z \cdot 0.1111111111111111}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-299}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-198}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;b \leq 2.02 \cdot 10^{+46}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -265000000.0)
   (/ (/ 1.0 z) (/ c b))
   (if (<= b -4.2e-218)
     (* -4.0 (* t (/ a c)))
     (if (<= b -7.5e-276)
       (/ (* y (/ x c)) (* z 0.1111111111111111))
       (if (<= b 5.2e-299)
         (* -4.0 (/ t (/ c a)))
         (if (<= b 1.45e-198)
           (* 9.0 (/ (* x y) (* z c)))
           (if (<= b 2.02e+46) (* -4.0 (/ a (/ c t))) (/ (/ b c) z))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -265000000.0) {
		tmp = (1.0 / z) / (c / b);
	} else if (b <= -4.2e-218) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= -7.5e-276) {
		tmp = (y * (x / c)) / (z * 0.1111111111111111);
	} else if (b <= 5.2e-299) {
		tmp = -4.0 * (t / (c / a));
	} else if (b <= 1.45e-198) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (b <= 2.02e+46) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-265000000.0d0)) then
        tmp = (1.0d0 / z) / (c / b)
    else if (b <= (-4.2d-218)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (b <= (-7.5d-276)) then
        tmp = (y * (x / c)) / (z * 0.1111111111111111d0)
    else if (b <= 5.2d-299) then
        tmp = (-4.0d0) * (t / (c / a))
    else if (b <= 1.45d-198) then
        tmp = 9.0d0 * ((x * y) / (z * c))
    else if (b <= 2.02d+46) then
        tmp = (-4.0d0) * (a / (c / t))
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -265000000.0) {
		tmp = (1.0 / z) / (c / b);
	} else if (b <= -4.2e-218) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= -7.5e-276) {
		tmp = (y * (x / c)) / (z * 0.1111111111111111);
	} else if (b <= 5.2e-299) {
		tmp = -4.0 * (t / (c / a));
	} else if (b <= 1.45e-198) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (b <= 2.02e+46) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -265000000.0:
		tmp = (1.0 / z) / (c / b)
	elif b <= -4.2e-218:
		tmp = -4.0 * (t * (a / c))
	elif b <= -7.5e-276:
		tmp = (y * (x / c)) / (z * 0.1111111111111111)
	elif b <= 5.2e-299:
		tmp = -4.0 * (t / (c / a))
	elif b <= 1.45e-198:
		tmp = 9.0 * ((x * y) / (z * c))
	elif b <= 2.02e+46:
		tmp = -4.0 * (a / (c / t))
	else:
		tmp = (b / c) / z
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -265000000.0)
		tmp = Float64(Float64(1.0 / z) / Float64(c / b));
	elseif (b <= -4.2e-218)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (b <= -7.5e-276)
		tmp = Float64(Float64(y * Float64(x / c)) / Float64(z * 0.1111111111111111));
	elseif (b <= 5.2e-299)
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	elseif (b <= 1.45e-198)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)));
	elseif (b <= 2.02e+46)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -265000000.0)
		tmp = (1.0 / z) / (c / b);
	elseif (b <= -4.2e-218)
		tmp = -4.0 * (t * (a / c));
	elseif (b <= -7.5e-276)
		tmp = (y * (x / c)) / (z * 0.1111111111111111);
	elseif (b <= 5.2e-299)
		tmp = -4.0 * (t / (c / a));
	elseif (b <= 1.45e-198)
		tmp = 9.0 * ((x * y) / (z * c));
	elseif (b <= 2.02e+46)
		tmp = -4.0 * (a / (c / t));
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -265000000.0], N[(N[(1.0 / z), $MachinePrecision] / N[(c / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.2e-218], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.5e-276], N[(N[(y * N[(x / c), $MachinePrecision]), $MachinePrecision] / N[(z * 0.1111111111111111), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.2e-299], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.45e-198], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.02e+46], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -2.65e8

   1. Initial program 82.8%

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

      1. associate-+l- 82.8%

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

      2. div-sub 74.6%

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

      3. *-commutative 74.6%

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

      4. associate-*r* 77.8%

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

      5. *-commutative 77.8%

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

      6. div-sub 86.0%

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

      7. associate-+l- 86.0%

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

   3. Simplified 84.5%

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

   4. Taylor expanded in b around inf 67.6%

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

      1. *-commutative 67.6%

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

   6. Simplified 67.6%

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

      1. frac-2neg 67.6%

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

      2. neg-mul-1 67.6%

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

      3. metadata-eval 67.6%

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

      4. distribute-rgt-neg-in 67.6%

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

      5. times-frac 70.3%

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

      6. metadata-eval 70.3%

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

   8. Applied egg-rr 70.3%

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

      1. associate-*l/ 70.4%

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

      2. associate-*r/ 70.4%

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

      3. neg-mul-1 70.4%

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

   10. Simplified 70.4%

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

       1. clear-num 69.2%

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

       2. frac-2neg 69.2%

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

       3. div-inv 69.2%

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

       4. metadata-eval 69.2%

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

       5. clear-num 69.1%

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

       6. associate-/l/ 67.5%

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

       7. clear-num 67.6%

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

       8. div-inv 67.6%

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

       9. associate-*r* 69.1%

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

       10. div-inv 69.1%

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

       11. frac-2neg 69.1%

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

   12. Applied egg-rr 69.1%

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

       1. associate-*r/ 69.1%

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

       2. metadata-eval 69.1%

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

       3. neg-mul-1 69.1%

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

       4. associate-/r* 69.1%

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

       5. metadata-eval 69.1%

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

       6. associate-/r* 70.4%

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

   14. Simplified 70.4%

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

   if -2.65e8 < b < -4.19999999999999988e-218

   1. Initial program 88.6%

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

      1. associate-+l- 88.6%

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

      2. div-sub 79.5%

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

      3. *-commutative 79.5%

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

      4. associate-*r* 75.2%

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

      5. *-commutative 75.2%

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

      6. div-sub 82.0%

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

      7. associate-+l- 82.0%

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

   3. Simplified 84.6%

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

   4. Taylor expanded in z around inf 64.7%

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

      1. associate-/l* 66.6%

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

      2. associate-/r/ 62.5%

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

   6. Applied egg-rr 62.5%

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

   if -4.19999999999999988e-218 < b < -7.500000000000001e-276

   1. Initial program 74.7%

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

      1. associate-+l- 74.7%

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

      2. div-sub 48.0%

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

      3. *-commutative 48.0%

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

      4. associate-*r* 48.0%

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

      5. *-commutative 48.0%

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

      6. div-sub 74.7%

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

      7. associate-+l- 74.7%

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

   3. Simplified 74.8%

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

   4. Taylor expanded in x around inf 44.2%

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

      1. times-frac 50.3%

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

   6. Simplified 50.3%

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

      1. associate-*r* 50.3%

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

      2. clear-num 50.2%

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

      3. un-div-inv 50.3%

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

      4. frac-times 56.6%

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

      5. *-commutative 56.6%

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

   8. Applied egg-rr 56.6%

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

      1. associate-/r* 50.2%

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

      2. associate-/r/ 44.4%

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

      3. *-commutative 44.4%

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

      4. associate-/l* 44.3%

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

      5. div-inv 44.3%

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

      6. clear-num 44.3%

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

   10. Applied egg-rr 44.3%

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

       1. div-inv 44.3%

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

       2. associate-*l* 50.3%

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

       3. clear-num 50.3%

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

       4. un-div-inv 50.3%

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

       5. associate-*l/ 63.0%

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

       6. associate-*l/ 63.0%

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

       7. *-lft-identity 63.0%

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

       8. div-inv 62.9%

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

       9. metadata-eval 62.9%

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

   12. Applied egg-rr 62.9%

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

   if -7.500000000000001e-276 < b < 5.1999999999999998e-299

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. div-sub 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-*r* 100.0%

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

      5. *-commutative 100.0%

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

      6. div-sub 100.0%

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

      7. associate-+l- 100.0%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in z around inf 99.5%

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

      1. *-commutative 99.5%

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

      2. *-commutative 99.5%

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

      3. associate-/l* 99.5%

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

   6. Simplified 99.5%

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

   if 5.1999999999999998e-299 < b < 1.45e-198

   1. Initial program 92.1%

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

      1. associate-+l- 92.1%

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

      2. div-sub 92.1%

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

      3. *-commutative 92.1%

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

      4. associate-*r* 92.1%

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

      5. *-commutative 92.1%

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

      6. div-sub 92.1%

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

      7. associate-+l- 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in x around inf 84.8%

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

   if 1.45e-198 < b < 2.01999999999999994e46

   1. Initial program 81.9%

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

      1. associate-+l- 81.9%

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

      2. div-sub 68.3%

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

      3. *-commutative 68.3%

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

      4. associate-*r* 66.1%

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

      5. *-commutative 66.1%

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

      6. div-sub 79.8%

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

      7. associate-+l- 79.8%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in z around inf 48.6%

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

      1. *-commutative 48.6%

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

      2. associate-/l* 52.9%

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

   6. Simplified 52.9%

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

   if 2.01999999999999994e46 < b

   1. Initial program 71.0%

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

      1. associate-+l- 71.0%

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

      2. div-sub 64.7%

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

      3. *-commutative 64.7%

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

      4. associate-*r* 63.0%

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

      5. *-commutative 63.0%

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

      6. div-sub 69.4%

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

      7. associate-+l- 69.4%

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

   3. Simplified 71.1%

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

   4. Taylor expanded in b around inf 51.2%

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

      1. *-commutative 51.2%

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

   6. Simplified 51.2%

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

      1. frac-2neg 51.2%

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

      2. neg-mul-1 51.2%

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

      3. metadata-eval 51.2%

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

      4. distribute-rgt-neg-in 51.2%

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

      5. times-frac 64.2%

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

      6. metadata-eval 64.2%

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

   8. Applied egg-rr 64.2%

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

      1. associate-*l/ 64.2%

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

      2. associate-*r/ 64.2%

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

      3. neg-mul-1 64.2%

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

   10. Simplified 64.2%

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

       1. div-inv 64.2%

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

       2. frac-2neg 64.2%

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

       3. frac-times 51.2%

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

       4. remove-double-neg 51.2%

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

       5. remove-double-neg 51.2%

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

       6. times-frac 64.2%

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

       7. associate-*l/ 59.5%

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

       8. *-rgt-identity 59.5%

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

       9. *-commutative 59.5%

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

       10. times-frac 51.2%

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

       11. remove-double-neg 51.2%

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

       12. metadata-eval 51.2%

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

       13. metadata-eval 51.2%

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

       14. frac-2neg 51.2%

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

       15. div-inv 51.2%

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

       16. metadata-eval 51.2%

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

       17. metadata-eval 51.2%

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

       18. metadata-eval 51.2%

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

       19. *-commutative 51.2%

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

       20. metadata-eval 51.2%

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

       21. neg-mul-1 51.2%

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

       22. remove-double-neg 51.2%

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

   12. Applied egg-rr 51.2%

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

       1. *-commutative 51.2%

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

       2. associate-/l/ 51.1%

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

       3. un-div-inv 51.2%

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

       4. associate-/r* 64.2%

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

   14. Applied egg-rr 64.2%

       \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -265000000:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-218}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-276}:\\ \;\;\;\;\frac{y \cdot \frac{x}{c}}{z \cdot 0.1111111111111111}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-299}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-198}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;b \leq 2.02 \cdot 10^{+46}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 8: 74.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;b \leq -8200000000000:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+96}:\\ \;\;\;\;\frac{t_1 + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

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 (<= b -8200000000000.0)
     (/ (+ b (* 9.0 (* x y))) (* z c))
     (if (<= b 1.3e+96)
       (/ (+ t_1 (* 9.0 (/ (* x y) z))) c)
       (/ (+ t_1 (/ b z)) c)))))

C

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 (b <= -8200000000000.0) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (b <= 1.3e+96) {
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = (t_1 + (b / z)) / c;
	}
	return tmp;
}

Fortran

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 * t)
    if (b <= (-8200000000000.0d0)) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else if (b <= 1.3d+96) then
        tmp = (t_1 + (9.0d0 * ((x * y) / z))) / c
    else
        tmp = (t_1 + (b / z)) / c
    end if
    code = tmp
end function

Java

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 tmp;
	if (b <= -8200000000000.0) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (b <= 1.3e+96) {
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = (t_1 + (b / z)) / c;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a * t)
	tmp = 0
	if b <= -8200000000000.0:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	elif b <= 1.3e+96:
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c
	else:
		tmp = (t_1 + (b / z)) / c
	return tmp

Julia

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 (b <= -8200000000000.0)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	elseif (b <= 1.3e+96)
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	else
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (a * t);
	tmp = 0.0;
	if (b <= -8200000000000.0)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	elseif (b <= 1.3e+96)
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	else
		tmp = (t_1 + (b / z)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

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[b, -8200000000000.0], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.3e+96], N[(N[(t$95$1 + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.2e12

   1. Initial program 84.1%

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

      1. associate-+l- 84.1%

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

      2. div-sub 75.8%

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

      3. *-commutative 75.8%

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

      4. associate-*r* 79.1%

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

      5. *-commutative 79.1%

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

      6. div-sub 87.4%

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

      7. associate-+l- 87.4%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in x around inf 81.5%

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

   if -8.2e12 < b < 1.3e96

   1. Initial program 85.3%

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

      1. associate-+l- 85.3%

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

      2. div-sub 75.3%

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

      3. *-commutative 75.3%

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

      4. associate-*r* 73.3%

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

      5. *-commutative 73.3%

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

      6. div-sub 82.5%

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

      7. associate-+l- 82.5%

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

   3. Simplified 84.0%

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

   5. Applied egg-rr 86.3%

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

   6. Taylor expanded in x around 0 91.0%

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

   7. Taylor expanded in b around 0 81.8%

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

   if 1.3e96 < b

   1. Initial program 68.7%

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

      1. associate-+l- 68.7%

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

      2. div-sub 61.4%

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

      3. *-commutative 61.4%

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

      4. associate-*r* 59.5%

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

      5. *-commutative 59.5%

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

      6. div-sub 66.8%

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

      7. associate-+l- 66.8%

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

   3. Simplified 68.7%

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

   5. Applied egg-rr 77.5%

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

   6. Taylor expanded in x around 0 82.3%

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

   7. Taylor expanded in x around 0 82.4%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8200000000000:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+96}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 9: 50.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -10500000000:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-218}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-194}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+49}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -10500000000.0)
   (/ (/ 1.0 z) (/ c b))
   (if (<= b -3.6e-218)
     (* -4.0 (* t (/ a c)))
     (if (<= b 3.5e-194)
       (* 9.0 (* (/ y z) (/ x c)))
       (if (<= b 3e+49) (* -4.0 (/ a (/ c t))) (/ (/ b c) z))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -10500000000.0) {
		tmp = (1.0 / z) / (c / b);
	} else if (b <= -3.6e-218) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 3.5e-194) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (b <= 3e+49) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-10500000000.0d0)) then
        tmp = (1.0d0 / z) / (c / b)
    else if (b <= (-3.6d-218)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (b <= 3.5d-194) then
        tmp = 9.0d0 * ((y / z) * (x / c))
    else if (b <= 3d+49) then
        tmp = (-4.0d0) * (a / (c / t))
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -10500000000.0) {
		tmp = (1.0 / z) / (c / b);
	} else if (b <= -3.6e-218) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 3.5e-194) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (b <= 3e+49) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -10500000000.0:
		tmp = (1.0 / z) / (c / b)
	elif b <= -3.6e-218:
		tmp = -4.0 * (t * (a / c))
	elif b <= 3.5e-194:
		tmp = 9.0 * ((y / z) * (x / c))
	elif b <= 3e+49:
		tmp = -4.0 * (a / (c / t))
	else:
		tmp = (b / c) / z
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -10500000000.0)
		tmp = Float64(Float64(1.0 / z) / Float64(c / b));
	elseif (b <= -3.6e-218)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (b <= 3.5e-194)
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	elseif (b <= 3e+49)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -10500000000.0)
		tmp = (1.0 / z) / (c / b);
	elseif (b <= -3.6e-218)
		tmp = -4.0 * (t * (a / c));
	elseif (b <= 3.5e-194)
		tmp = 9.0 * ((y / z) * (x / c));
	elseif (b <= 3e+49)
		tmp = -4.0 * (a / (c / t));
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -10500000000.0], N[(N[(1.0 / z), $MachinePrecision] / N[(c / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.6e-218], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.5e-194], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e+49], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.05e10

   1. Initial program 82.8%

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

      1. associate-+l- 82.8%

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

      2. div-sub 74.6%

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

      3. *-commutative 74.6%

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

      4. associate-*r* 77.8%

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

      5. *-commutative 77.8%

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

      6. div-sub 86.0%

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

      7. associate-+l- 86.0%

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

   3. Simplified 84.5%

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

   4. Taylor expanded in b around inf 67.6%

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

      1. *-commutative 67.6%

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

   6. Simplified 67.6%

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

      1. frac-2neg 67.6%

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

      2. neg-mul-1 67.6%

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

      3. metadata-eval 67.6%

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

      4. distribute-rgt-neg-in 67.6%

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

      5. times-frac 70.3%

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

      6. metadata-eval 70.3%

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

   8. Applied egg-rr 70.3%

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

      1. associate-*l/ 70.4%

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

      2. associate-*r/ 70.4%

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

      3. neg-mul-1 70.4%

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

   10. Simplified 70.4%

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

       1. clear-num 69.2%

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

       2. frac-2neg 69.2%

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

       3. div-inv 69.2%

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

       4. metadata-eval 69.2%

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

       5. clear-num 69.1%

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

       6. associate-/l/ 67.5%

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

       7. clear-num 67.6%

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

       8. div-inv 67.6%

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

       9. associate-*r* 69.1%

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

       10. div-inv 69.1%

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

       11. frac-2neg 69.1%

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

   12. Applied egg-rr 69.1%

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

       1. associate-*r/ 69.1%

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

       2. metadata-eval 69.1%

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

       3. neg-mul-1 69.1%

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

       4. associate-/r* 69.1%

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

       5. metadata-eval 69.1%

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

       6. associate-/r* 70.4%

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

   14. Simplified 70.4%

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

   if -1.05e10 < b < -3.60000000000000011e-218

   1. Initial program 88.6%

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

      1. associate-+l- 88.6%

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

      2. div-sub 79.5%

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

      3. *-commutative 79.5%

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

      4. associate-*r* 75.2%

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

      5. *-commutative 75.2%

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

      6. div-sub 82.0%

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

      7. associate-+l- 82.0%

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

   3. Simplified 84.6%

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

   4. Taylor expanded in z around inf 64.7%

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

      1. associate-/l* 66.6%

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

      2. associate-/r/ 62.5%

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

   6. Applied egg-rr 62.5%

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

   if -3.60000000000000011e-218 < b < 3.5000000000000003e-194

   1. Initial program 86.7%

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

      1. associate-+l- 86.7%

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

      2. div-sub 77.6%

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

      3. *-commutative 77.6%

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

      4. associate-*r* 77.6%

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

      5. *-commutative 77.6%

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

      6. div-sub 86.7%

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

      7. associate-+l- 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in x around inf 67.6%

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

      1. times-frac 58.7%

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

   6. Simplified 58.7%

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

   if 3.5000000000000003e-194 < b < 3.0000000000000002e49

   1. Initial program 81.9%

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

      1. associate-+l- 81.9%

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

      2. div-sub 68.3%

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

      3. *-commutative 68.3%

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

      4. associate-*r* 66.1%

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

      5. *-commutative 66.1%

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

      6. div-sub 79.8%

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

      7. associate-+l- 79.8%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in z around inf 48.6%

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

      1. *-commutative 48.6%

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

      2. associate-/l* 52.9%

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

   6. Simplified 52.9%

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

   if 3.0000000000000002e49 < b

   1. Initial program 71.0%

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

      1. associate-+l- 71.0%

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

      2. div-sub 64.7%

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

      3. *-commutative 64.7%

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

      4. associate-*r* 63.0%

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

      5. *-commutative 63.0%

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

      6. div-sub 69.4%

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

      7. associate-+l- 69.4%

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

   3. Simplified 71.1%

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

   4. Taylor expanded in b around inf 51.2%

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

      1. *-commutative 51.2%

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

   6. Simplified 51.2%

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

      1. frac-2neg 51.2%

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

      2. neg-mul-1 51.2%

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

      3. metadata-eval 51.2%

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

      4. distribute-rgt-neg-in 51.2%

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

      5. times-frac 64.2%

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

      6. metadata-eval 64.2%

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

   8. Applied egg-rr 64.2%

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

      1. associate-*l/ 64.2%

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

      2. associate-*r/ 64.2%

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

      3. neg-mul-1 64.2%

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

   10. Simplified 64.2%

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

       1. div-inv 64.2%

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

       2. frac-2neg 64.2%

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

       3. frac-times 51.2%

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

       4. remove-double-neg 51.2%

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

       5. remove-double-neg 51.2%

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

       6. times-frac 64.2%

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

       7. associate-*l/ 59.5%

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

       8. *-rgt-identity 59.5%

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

       9. *-commutative 59.5%

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

       10. times-frac 51.2%

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

       11. remove-double-neg 51.2%

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

       12. metadata-eval 51.2%

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

       13. metadata-eval 51.2%

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

       14. frac-2neg 51.2%

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

       15. div-inv 51.2%

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

       16. metadata-eval 51.2%

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

       17. metadata-eval 51.2%

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

       18. metadata-eval 51.2%

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

       19. *-commutative 51.2%

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

       20. metadata-eval 51.2%

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

       21. neg-mul-1 51.2%

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

       22. remove-double-neg 51.2%

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

   12. Applied egg-rr 51.2%

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

       1. *-commutative 51.2%

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

       2. associate-/l/ 51.1%

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

       3. un-div-inv 51.2%

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

       4. associate-/r* 64.2%

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

   14. Applied egg-rr 64.2%

       \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -10500000000:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-218}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-194}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+49}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 10: 66.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00072:\\ \;\;\;\;\frac{9 \cdot y}{z \cdot \frac{c}{x}}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+195}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot \frac{y}{z}\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -0.00072)
   (/ (* 9.0 y) (* z (/ c x)))
   (if (<= y 2e+195)
     (/ (+ (* -4.0 (* a t)) (/ b z)) c)
     (/ (* x (* 9.0 (/ y z))) c))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -0.00072) {
		tmp = (9.0 * y) / (z * (c / x));
	} else if (y <= 2e+195) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (x * (9.0 * (y / z))) / c;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= (-0.00072d0)) then
        tmp = (9.0d0 * y) / (z * (c / x))
    else if (y <= 2d+195) then
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    else
        tmp = (x * (9.0d0 * (y / z))) / c
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -0.00072) {
		tmp = (9.0 * y) / (z * (c / x));
	} else if (y <= 2e+195) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (x * (9.0 * (y / z))) / c;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -0.00072:
		tmp = (9.0 * y) / (z * (c / x))
	elif y <= 2e+195:
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	else:
		tmp = (x * (9.0 * (y / z))) / c
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -0.00072)
		tmp = Float64(Float64(9.0 * y) / Float64(z * Float64(c / x)));
	elseif (y <= 2e+195)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(x * Float64(9.0 * Float64(y / z))) / c);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -0.00072)
		tmp = (9.0 * y) / (z * (c / x));
	elseif (y <= 2e+195)
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	else
		tmp = (x * (9.0 * (y / z))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -0.00072], N[(N[(9.0 * y), $MachinePrecision] / N[(z * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+195], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(x * N[(9.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.20000000000000045e-4

   1. Initial program 77.8%

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

      1. associate-+l- 77.8%

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

      2. div-sub 67.3%

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

      3. *-commutative 67.3%

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

      4. associate-*r* 68.9%

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

      5. *-commutative 68.9%

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

      6. div-sub 79.5%

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

      7. associate-+l- 79.5%

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

   3. Simplified 78.1%

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

   4. Taylor expanded in x around inf 52.4%

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

      1. times-frac 54.8%

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

   6. Simplified 54.8%

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

      1. associate-*r* 54.8%

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

      2. clear-num 54.8%

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

      3. un-div-inv 54.8%

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

      4. frac-times 59.0%

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

      5. *-commutative 59.0%

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

   8. Applied egg-rr 59.0%

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

   if -7.20000000000000045e-4 < y < 1.99999999999999995e195

   1. Initial program 82.2%

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

      1. associate-+l- 82.2%

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

      2. div-sub 73.8%

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

      3. *-commutative 73.8%

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

      4. associate-*r* 72.2%

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

      5. *-commutative 72.2%

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

      6. div-sub 80.0%

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

      7. associate-+l- 80.0%

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

   3. Simplified 81.7%

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

   5. Applied egg-rr 84.0%

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

   6. Taylor expanded in x around 0 89.2%

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

   7. Taylor expanded in x around 0 74.2%

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

   if 1.99999999999999995e195 < y

   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-+l- 84.8%

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

      2. div-sub 74.8%

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

      3. *-commutative 74.8%

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

      4. associate-*r* 74.8%

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

      5. *-commutative 74.8%

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

      6. div-sub 84.8%

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

      7. associate-+l- 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in x around inf 75.2%

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

      1. times-frac 65.7%

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

   6. Simplified 65.7%

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

      1. *-commutative 65.7%

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

      2. associate-*l* 65.8%

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

      3. associate-*l/ 70.6%

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

      4. *-commutative 70.6%

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

   8. Applied egg-rr 70.6%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00072:\\ \;\;\;\;\frac{9 \cdot y}{z \cdot \frac{c}{x}}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+195}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot \frac{y}{z}\right)}{c}\\ \end{array} \]

Alternative 11: 69.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+77}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq 10^{+95}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

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 -7.2e+77)
   (/ (+ (* -4.0 (* a t)) (/ b z)) c)
   (if (<= t 1e+95) (/ (+ b (* 9.0 (* x y))) (* z c)) (* -4.0 (* t (/ a c))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -7.2e+77) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else if (t <= 1e+95) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

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 <= (-7.2d+77)) then
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    else if (t <= 1d+95) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

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 <= -7.2e+77) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else if (t <= 1e+95) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -7.2e+77:
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	elif t <= 1e+95:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -7.2e+77)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	elseif (t <= 1e+95)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -7.2e+77)
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	elseif (t <= 1e+95)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

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, -7.2e+77], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, 1e+95], N[(N[(b + N[(9.0 * N[(x * 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 < -7.1999999999999996e77

   1. Initial program 67.9%

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

      1. associate-+l- 67.9%

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

      2. div-sub 55.6%

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

      3. *-commutative 55.6%

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

      4. associate-*r* 57.7%

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

      5. *-commutative 57.7%

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

      6. div-sub 70.0%

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

      7. associate-+l- 70.0%

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

   3. Simplified 66.5%

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

   5. Applied egg-rr 74.8%

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

   6. Taylor expanded in x around 0 86.6%

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

   7. Taylor expanded in x around 0 72.0%

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

   if -7.1999999999999996e77 < t < 1.00000000000000002e95

   1. Initial program 84.9%

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

      1. associate-+l- 84.9%

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

      2. div-sub 77.3%

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

      3. *-commutative 77.3%

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

      4. associate-*r* 74.5%

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

      5. *-commutative 74.5%

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

      6. div-sub 81.5%

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

      7. associate-+l- 81.5%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in x around inf 72.3%

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

   if 1.00000000000000002e95 < t

   1. Initial program 83.2%

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

      1. associate-+l- 83.2%

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

      2. div-sub 71.8%

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

      3. *-commutative 71.8%

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

      4. associate-*r* 77.4%

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

      5. *-commutative 77.4%

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

      6. div-sub 88.9%

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

      7. associate-+l- 88.9%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in z around inf 52.8%

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

      1. associate-/l* 63.4%

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

      2. associate-/r/ 63.3%

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

   6. Applied egg-rr 63.3%

      \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+77}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq 10^{+95}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 12: 51.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2400000000000 \lor \neg \left(b \leq 1.45 \cdot 10^{+48}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

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 (<= b -2400000000000.0) (not (<= b 1.45e+48)))
   (/ (/ b c) z)
   (* -4.0 (* t (/ a c)))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -2400000000000.0) || !(b <= 1.45e+48)) {
		tmp = (b / c) / z;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-2400000000000.0d0)) .or. (.not. (b <= 1.45d+48))) then
        tmp = (b / c) / z
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -2400000000000.0) || !(b <= 1.45e+48)) {
		tmp = (b / c) / z;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -2400000000000.0) or not (b <= 1.45e+48):
		tmp = (b / c) / z
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -2400000000000.0) || !(b <= 1.45e+48))
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -2400000000000.0) || ~((b <= 1.45e+48)))
		tmp = (b / c) / z;
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

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[b, -2400000000000.0], N[Not[LessEqual[b, 1.45e+48]], $MachinePrecision]], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.4e12 or 1.4499999999999999e48 < b

   1. Initial program 77.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 77.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. div-sub 70.1%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

      3. *-commutative 70.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b}{z \cdot c} \]

      4. associate-*r* 70.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b}{z \cdot c} \]

      5. *-commutative 70.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b}{z \cdot c} \]

      6. div-sub 78.2%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot a\right) \cdot t - b\right)}{z \cdot c}} \]

      7. associate-+l- 78.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 78.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 59.7%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 59.7%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 59.7%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   7. Step-by-step derivation

      1. frac-2neg 59.7%

         \[\leadsto \color{blue}{\frac{-b}{-z \cdot c}} \]

      2. neg-mul-1 59.7%

         \[\leadsto \frac{\color{blue}{-1 \cdot b}}{-z \cdot c} \]

      3. metadata-eval 59.7%

         \[\leadsto \frac{\color{blue}{\left(-1\right)} \cdot b}{-z \cdot c} \]

      4. distribute-rgt-neg-in 59.7%

         \[\leadsto \frac{\left(-1\right) \cdot b}{\color{blue}{z \cdot \left(-c\right)}} \]

      5. times-frac 67.7%

         \[\leadsto \color{blue}{\frac{-1}{z} \cdot \frac{b}{-c}} \]

      6. metadata-eval 67.7%

         \[\leadsto \frac{\color{blue}{-1}}{z} \cdot \frac{b}{-c} \]

   8. Applied egg-rr 67.7%

      \[\leadsto \color{blue}{\frac{-1}{z} \cdot \frac{b}{-c}} \]
   9. Step-by-step derivation

      1. associate-*l/ 67.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot \frac{b}{-c}}{z}} \]

      2. associate-*r/ 67.8%

         \[\leadsto \frac{\color{blue}{\frac{-1 \cdot b}{-c}}}{z} \]

      3. neg-mul-1 67.8%

         \[\leadsto \frac{\frac{\color{blue}{-b}}{-c}}{z} \]

   10. Simplified 67.8%

       \[\leadsto \color{blue}{\frac{\frac{-b}{-c}}{z}} \]
   11. Step-by-step derivation

       1. div-inv 67.7%

          \[\leadsto \color{blue}{\frac{-b}{-c} \cdot \frac{1}{z}} \]

       2. frac-2neg 67.7%

          \[\leadsto \color{blue}{\frac{-\left(-b\right)}{-\left(-c\right)}} \cdot \frac{1}{z} \]

       3. frac-times 59.7%

          \[\leadsto \color{blue}{\frac{\left(-\left(-b\right)\right) \cdot 1}{\left(-\left(-c\right)\right) \cdot z}} \]

       4. remove-double-neg 59.7%

          \[\leadsto \frac{\color{blue}{b} \cdot 1}{\left(-\left(-c\right)\right) \cdot z} \]

       5. remove-double-neg 59.7%

          \[\leadsto \frac{b \cdot 1}{\color{blue}{c} \cdot z} \]

       6. times-frac 67.7%

          \[\leadsto \color{blue}{\frac{b}{c} \cdot \frac{1}{z}} \]

       7. associate-*l/ 60.8%

          \[\leadsto \color{blue}{\frac{b \cdot \frac{1}{z}}{c}} \]

       8. *-rgt-identity 60.8%

          \[\leadsto \frac{b \cdot \frac{1}{z}}{\color{blue}{c \cdot 1}} \]

       9. *-commutative 60.8%

          \[\leadsto \frac{\color{blue}{\frac{1}{z} \cdot b}}{c \cdot 1} \]

       10. times-frac 59.7%

           \[\leadsto \color{blue}{\frac{\frac{1}{z}}{c} \cdot \frac{b}{1}} \]

       11. remove-double-neg 59.7%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \frac{\color{blue}{-\left(-b\right)}}{1} \]

       12. metadata-eval 59.7%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \frac{-\left(-b\right)}{\color{blue}{--1}} \]

       13. metadata-eval 59.7%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \frac{-\left(-b\right)}{-\color{blue}{\left(-1\right)}} \]

       14. frac-2neg 59.7%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \color{blue}{\frac{-b}{-1}} \]

       15. div-inv 59.7%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \color{blue}{\left(\left(-b\right) \cdot \frac{1}{-1}\right)} \]

       16. metadata-eval 59.7%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \left(\left(-b\right) \cdot \frac{1}{\color{blue}{-1}}\right) \]

       17. metadata-eval 59.7%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \left(\left(-b\right) \cdot \color{blue}{-1}\right) \]

       18. metadata-eval 59.7%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \left(\left(-b\right) \cdot \color{blue}{\left(-1\right)}\right) \]

       19. *-commutative 59.7%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \color{blue}{\left(\left(-1\right) \cdot \left(-b\right)\right)} \]

       20. metadata-eval 59.7%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \left(\color{blue}{-1} \cdot \left(-b\right)\right) \]

       21. neg-mul-1 59.7%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \color{blue}{\left(-\left(-b\right)\right)} \]

       22. remove-double-neg 59.7%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \color{blue}{b} \]

   12. Applied egg-rr 59.7%

       \[\leadsto \color{blue}{\frac{\frac{1}{z}}{c} \cdot b} \]
   13. Step-by-step derivation

       1. *-commutative 59.7%

          \[\leadsto \color{blue}{b \cdot \frac{\frac{1}{z}}{c}} \]

       2. associate-/l/ 59.7%

          \[\leadsto b \cdot \color{blue}{\frac{1}{c \cdot z}} \]

       3. un-div-inv 59.7%

          \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

       4. associate-/r* 67.8%

          \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   14. Applied egg-rr 67.8%

       \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   if -2.4e12 < b < 1.4499999999999999e48

   1. Initial program 85.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 85.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. div-sub 74.6%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

      3. *-commutative 74.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b}{z \cdot c} \]

      4. associate-*r* 72.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b}{z \cdot c} \]

      5. *-commutative 72.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b}{z \cdot c} \]

      6. div-sub 82.3%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot a\right) \cdot t - b\right)}{z \cdot c}} \]

      7. associate-+l- 82.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 83.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 47.2%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. associate-/l* 50.0%

         \[\leadsto -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

      2. associate-/r/ 46.4%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

   6. Applied egg-rr 46.4%

      \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2400000000000 \lor \neg \left(b \leq 1.45 \cdot 10^{+48}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 13: 51.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1200000000000 \lor \neg \left(b \leq 2.25 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \end{array} \]

FPCore

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 (<= b -1200000000000.0) (not (<= b 2.25e+46)))
   (/ (/ b c) z)
   (* -4.0 (/ t (/ c a)))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1200000000000.0) || !(b <= 2.25e+46)) {
		tmp = (b / c) / z;
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-1200000000000.0d0)) .or. (.not. (b <= 2.25d+46))) then
        tmp = (b / c) / z
    else
        tmp = (-4.0d0) * (t / (c / a))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1200000000000.0) || !(b <= 2.25e+46)) {
		tmp = (b / c) / z;
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -1200000000000.0) or not (b <= 2.25e+46):
		tmp = (b / c) / z
	else:
		tmp = -4.0 * (t / (c / a))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -1200000000000.0) || !(b <= 2.25e+46))
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -1200000000000.0) || ~((b <= 2.25e+46)))
		tmp = (b / c) / z;
	else
		tmp = -4.0 * (t / (c / a));
	end
	tmp_2 = tmp;
end

Wolfram

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[b, -1200000000000.0], N[Not[LessEqual[b, 2.25e+46]], $MachinePrecision]], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.2e12 or 2.25000000000000005e46 < b

   1. Initial program 77.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 77.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. div-sub 70.1%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

      3. *-commutative 70.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b}{z \cdot c} \]

      4. associate-*r* 70.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b}{z \cdot c} \]

      5. *-commutative 70.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b}{z \cdot c} \]

      6. div-sub 78.2%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot a\right) \cdot t - b\right)}{z \cdot c}} \]

      7. associate-+l- 78.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 78.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 59.7%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 59.7%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 59.7%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   7. Step-by-step derivation

      1. frac-2neg 59.7%

         \[\leadsto \color{blue}{\frac{-b}{-z \cdot c}} \]

      2. neg-mul-1 59.7%

         \[\leadsto \frac{\color{blue}{-1 \cdot b}}{-z \cdot c} \]

      3. metadata-eval 59.7%

         \[\leadsto \frac{\color{blue}{\left(-1\right)} \cdot b}{-z \cdot c} \]

      4. distribute-rgt-neg-in 59.7%

         \[\leadsto \frac{\left(-1\right) \cdot b}{\color{blue}{z \cdot \left(-c\right)}} \]

      5. times-frac 67.7%

         \[\leadsto \color{blue}{\frac{-1}{z} \cdot \frac{b}{-c}} \]

      6. metadata-eval 67.7%

         \[\leadsto \frac{\color{blue}{-1}}{z} \cdot \frac{b}{-c} \]

   8. Applied egg-rr 67.7%

      \[\leadsto \color{blue}{\frac{-1}{z} \cdot \frac{b}{-c}} \]
   9. Step-by-step derivation

      1. associate-*l/ 67.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot \frac{b}{-c}}{z}} \]

      2. associate-*r/ 67.8%

         \[\leadsto \frac{\color{blue}{\frac{-1 \cdot b}{-c}}}{z} \]

      3. neg-mul-1 67.8%

         \[\leadsto \frac{\frac{\color{blue}{-b}}{-c}}{z} \]

   10. Simplified 67.8%

       \[\leadsto \color{blue}{\frac{\frac{-b}{-c}}{z}} \]
   11. Step-by-step derivation

       1. div-inv 67.7%

          \[\leadsto \color{blue}{\frac{-b}{-c} \cdot \frac{1}{z}} \]

       2. frac-2neg 67.7%

          \[\leadsto \color{blue}{\frac{-\left(-b\right)}{-\left(-c\right)}} \cdot \frac{1}{z} \]

       3. frac-times 59.7%

          \[\leadsto \color{blue}{\frac{\left(-\left(-b\right)\right) \cdot 1}{\left(-\left(-c\right)\right) \cdot z}} \]

       4. remove-double-neg 59.7%

          \[\leadsto \frac{\color{blue}{b} \cdot 1}{\left(-\left(-c\right)\right) \cdot z} \]

       5. remove-double-neg 59.7%

          \[\leadsto \frac{b \cdot 1}{\color{blue}{c} \cdot z} \]

       6. times-frac 67.7%

          \[\leadsto \color{blue}{\frac{b}{c} \cdot \frac{1}{z}} \]

       7. associate-*l/ 60.8%

          \[\leadsto \color{blue}{\frac{b \cdot \frac{1}{z}}{c}} \]

       8. *-rgt-identity 60.8%

          \[\leadsto \frac{b \cdot \frac{1}{z}}{\color{blue}{c \cdot 1}} \]

       9. *-commutative 60.8%

          \[\leadsto \frac{\color{blue}{\frac{1}{z} \cdot b}}{c \cdot 1} \]

       10. times-frac 59.7%

           \[\leadsto \color{blue}{\frac{\frac{1}{z}}{c} \cdot \frac{b}{1}} \]

       11. remove-double-neg 59.7%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \frac{\color{blue}{-\left(-b\right)}}{1} \]

       12. metadata-eval 59.7%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \frac{-\left(-b\right)}{\color{blue}{--1}} \]

       13. metadata-eval 59.7%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \frac{-\left(-b\right)}{-\color{blue}{\left(-1\right)}} \]

       14. frac-2neg 59.7%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \color{blue}{\frac{-b}{-1}} \]

       15. div-inv 59.7%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \color{blue}{\left(\left(-b\right) \cdot \frac{1}{-1}\right)} \]

       16. metadata-eval 59.7%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \left(\left(-b\right) \cdot \frac{1}{\color{blue}{-1}}\right) \]

       17. metadata-eval 59.7%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \left(\left(-b\right) \cdot \color{blue}{-1}\right) \]

       18. metadata-eval 59.7%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \left(\left(-b\right) \cdot \color{blue}{\left(-1\right)}\right) \]

       19. *-commutative 59.7%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \color{blue}{\left(\left(-1\right) \cdot \left(-b\right)\right)} \]

       20. metadata-eval 59.7%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \left(\color{blue}{-1} \cdot \left(-b\right)\right) \]

       21. neg-mul-1 59.7%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \color{blue}{\left(-\left(-b\right)\right)} \]

       22. remove-double-neg 59.7%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \color{blue}{b} \]

   12. Applied egg-rr 59.7%

       \[\leadsto \color{blue}{\frac{\frac{1}{z}}{c} \cdot b} \]
   13. Step-by-step derivation

       1. *-commutative 59.7%

          \[\leadsto \color{blue}{b \cdot \frac{\frac{1}{z}}{c}} \]

       2. associate-/l/ 59.7%

          \[\leadsto b \cdot \color{blue}{\frac{1}{c \cdot z}} \]

       3. un-div-inv 59.7%

          \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

       4. associate-/r* 67.8%

          \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   14. Applied egg-rr 67.8%

       \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   if -1.2e12 < b < 2.25000000000000005e46

   1. Initial program 85.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 85.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. div-sub 74.6%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

      3. *-commutative 74.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b}{z \cdot c} \]

      4. associate-*r* 72.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b}{z \cdot c} \]

      5. *-commutative 72.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b}{z \cdot c} \]

      6. div-sub 82.3%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot a\right) \cdot t - b\right)}{z \cdot c}} \]

      7. associate-+l- 82.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 83.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 47.2%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. *-commutative 47.2%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. *-commutative 47.2%

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      3. associate-/l* 47.1%

         \[\leadsto \color{blue}{\frac{t}{\frac{c}{a}}} \cdot -4 \]

   6. Simplified 47.1%

      \[\leadsto \color{blue}{\frac{t}{\frac{c}{a}} \cdot -4} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1200000000000 \lor \neg \left(b \leq 2.25 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 14: 51.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -5200000000000:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{+47}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -5200000000000.0)
   (/ (/ 1.0 z) (/ c b))
   (if (<= b 4.1e+47) (* -4.0 (/ t (/ c a))) (/ (/ b c) z))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -5200000000000.0) {
		tmp = (1.0 / z) / (c / b);
	} else if (b <= 4.1e+47) {
		tmp = -4.0 * (t / (c / a));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-5200000000000.0d0)) then
        tmp = (1.0d0 / z) / (c / b)
    else if (b <= 4.1d+47) then
        tmp = (-4.0d0) * (t / (c / a))
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -5200000000000.0) {
		tmp = (1.0 / z) / (c / b);
	} else if (b <= 4.1e+47) {
		tmp = -4.0 * (t / (c / a));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -5200000000000.0:
		tmp = (1.0 / z) / (c / b)
	elif b <= 4.1e+47:
		tmp = -4.0 * (t / (c / a))
	else:
		tmp = (b / c) / z
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -5200000000000.0)
		tmp = Float64(Float64(1.0 / z) / Float64(c / b));
	elseif (b <= 4.1e+47)
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -5200000000000.0)
		tmp = (1.0 / z) / (c / b);
	elseif (b <= 4.1e+47)
		tmp = -4.0 * (t / (c / a));
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -5200000000000.0], N[(N[(1.0 / z), $MachinePrecision] / N[(c / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.1e+47], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.2e12

   1. Initial program 84.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 84.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. div-sub 75.8%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

      3. *-commutative 75.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b}{z \cdot c} \]

      4. associate-*r* 79.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b}{z \cdot c} \]

      5. *-commutative 79.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b}{z \cdot c} \]

      6. div-sub 87.4%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot a\right) \cdot t - b\right)}{z \cdot c}} \]

      7. associate-+l- 87.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 85.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 68.6%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 68.6%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 68.6%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   7. Step-by-step derivation

      1. frac-2neg 68.6%

         \[\leadsto \color{blue}{\frac{-b}{-z \cdot c}} \]

      2. neg-mul-1 68.6%

         \[\leadsto \frac{\color{blue}{-1 \cdot b}}{-z \cdot c} \]

      3. metadata-eval 68.6%

         \[\leadsto \frac{\color{blue}{\left(-1\right)} \cdot b}{-z \cdot c} \]

      4. distribute-rgt-neg-in 68.6%

         \[\leadsto \frac{\left(-1\right) \cdot b}{\color{blue}{z \cdot \left(-c\right)}} \]

      5. times-frac 71.4%

         \[\leadsto \color{blue}{\frac{-1}{z} \cdot \frac{b}{-c}} \]

      6. metadata-eval 71.4%

         \[\leadsto \frac{\color{blue}{-1}}{z} \cdot \frac{b}{-c} \]

   8. Applied egg-rr 71.4%

      \[\leadsto \color{blue}{\frac{-1}{z} \cdot \frac{b}{-c}} \]
   9. Step-by-step derivation

      1. associate-*l/ 71.5%

         \[\leadsto \color{blue}{\frac{-1 \cdot \frac{b}{-c}}{z}} \]

      2. associate-*r/ 71.5%

         \[\leadsto \frac{\color{blue}{\frac{-1 \cdot b}{-c}}}{z} \]

      3. neg-mul-1 71.5%

         \[\leadsto \frac{\frac{\color{blue}{-b}}{-c}}{z} \]

   10. Simplified 71.5%

       \[\leadsto \color{blue}{\frac{\frac{-b}{-c}}{z}} \]
   11. Step-by-step derivation

       1. clear-num 70.2%

          \[\leadsto \color{blue}{\frac{1}{\frac{z}{\frac{-b}{-c}}}} \]

       2. frac-2neg 70.2%

          \[\leadsto \color{blue}{\frac{-1}{-\frac{z}{\frac{-b}{-c}}}} \]

       3. div-inv 70.2%

          \[\leadsto \color{blue}{\left(-1\right) \cdot \frac{1}{-\frac{z}{\frac{-b}{-c}}}} \]

       4. metadata-eval 70.2%

          \[\leadsto \color{blue}{-1} \cdot \frac{1}{-\frac{z}{\frac{-b}{-c}}} \]

       5. clear-num 70.2%

          \[\leadsto -1 \cdot \frac{1}{-\color{blue}{\frac{1}{\frac{\frac{-b}{-c}}{z}}}} \]

       6. associate-/l/ 68.6%

          \[\leadsto -1 \cdot \frac{1}{-\frac{1}{\color{blue}{\frac{-b}{z \cdot \left(-c\right)}}}} \]

       7. clear-num 68.6%

          \[\leadsto -1 \cdot \frac{1}{-\color{blue}{\frac{z \cdot \left(-c\right)}{-b}}} \]

       8. div-inv 68.6%

          \[\leadsto -1 \cdot \frac{1}{-\color{blue}{\left(z \cdot \left(-c\right)\right) \cdot \frac{1}{-b}}} \]

       9. associate-*r* 70.2%

          \[\leadsto -1 \cdot \frac{1}{-\color{blue}{z \cdot \left(\left(-c\right) \cdot \frac{1}{-b}\right)}} \]

       10. div-inv 70.2%

           \[\leadsto -1 \cdot \frac{1}{-z \cdot \color{blue}{\frac{-c}{-b}}} \]

       11. frac-2neg 70.2%

           \[\leadsto -1 \cdot \frac{1}{-z \cdot \color{blue}{\frac{c}{b}}} \]

   12. Applied egg-rr 70.2%

       \[\leadsto \color{blue}{-1 \cdot \frac{1}{-z \cdot \frac{c}{b}}} \]
   13. Step-by-step derivation

       1. associate-*r/ 70.2%

          \[\leadsto \color{blue}{\frac{-1 \cdot 1}{-z \cdot \frac{c}{b}}} \]

       2. metadata-eval 70.2%

          \[\leadsto \frac{\color{blue}{-1}}{-z \cdot \frac{c}{b}} \]

       3. neg-mul-1 70.2%

          \[\leadsto \frac{-1}{\color{blue}{-1 \cdot \left(z \cdot \frac{c}{b}\right)}} \]

       4. associate-/r* 70.2%

          \[\leadsto \color{blue}{\frac{\frac{-1}{-1}}{z \cdot \frac{c}{b}}} \]

       5. metadata-eval 70.2%

          \[\leadsto \frac{\color{blue}{1}}{z \cdot \frac{c}{b}} \]

       6. associate-/r* 71.5%

          \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{b}}} \]

   14. Simplified 71.5%

       \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{b}}} \]

   if -5.2e12 < b < 4.1000000000000001e47

   1. Initial program 85.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 85.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. div-sub 74.6%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

      3. *-commutative 74.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b}{z \cdot c} \]

      4. associate-*r* 72.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b}{z \cdot c} \]

      5. *-commutative 72.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b}{z \cdot c} \]

      6. div-sub 82.3%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot a\right) \cdot t - b\right)}{z \cdot c}} \]

      7. associate-+l- 82.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 83.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 47.2%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. *-commutative 47.2%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. *-commutative 47.2%

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      3. associate-/l* 47.1%

         \[\leadsto \color{blue}{\frac{t}{\frac{c}{a}}} \cdot -4 \]

   6. Simplified 47.1%

      \[\leadsto \color{blue}{\frac{t}{\frac{c}{a}} \cdot -4} \]

   if 4.1000000000000001e47 < b

   1. Initial program 71.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 71.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. div-sub 64.7%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

      3. *-commutative 64.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b}{z \cdot c} \]

      4. associate-*r* 63.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b}{z \cdot c} \]

      5. *-commutative 63.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b}{z \cdot c} \]

      6. div-sub 69.4%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot a\right) \cdot t - b\right)}{z \cdot c}} \]

      7. associate-+l- 69.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 71.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 51.2%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 51.2%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 51.2%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   7. Step-by-step derivation

      1. frac-2neg 51.2%

         \[\leadsto \color{blue}{\frac{-b}{-z \cdot c}} \]

      2. neg-mul-1 51.2%

         \[\leadsto \frac{\color{blue}{-1 \cdot b}}{-z \cdot c} \]

      3. metadata-eval 51.2%

         \[\leadsto \frac{\color{blue}{\left(-1\right)} \cdot b}{-z \cdot c} \]

      4. distribute-rgt-neg-in 51.2%

         \[\leadsto \frac{\left(-1\right) \cdot b}{\color{blue}{z \cdot \left(-c\right)}} \]

      5. times-frac 64.2%

         \[\leadsto \color{blue}{\frac{-1}{z} \cdot \frac{b}{-c}} \]

      6. metadata-eval 64.2%

         \[\leadsto \frac{\color{blue}{-1}}{z} \cdot \frac{b}{-c} \]

   8. Applied egg-rr 64.2%

      \[\leadsto \color{blue}{\frac{-1}{z} \cdot \frac{b}{-c}} \]
   9. Step-by-step derivation

      1. associate-*l/ 64.2%

         \[\leadsto \color{blue}{\frac{-1 \cdot \frac{b}{-c}}{z}} \]

      2. associate-*r/ 64.2%

         \[\leadsto \frac{\color{blue}{\frac{-1 \cdot b}{-c}}}{z} \]

      3. neg-mul-1 64.2%

         \[\leadsto \frac{\frac{\color{blue}{-b}}{-c}}{z} \]

   10. Simplified 64.2%

       \[\leadsto \color{blue}{\frac{\frac{-b}{-c}}{z}} \]
   11. Step-by-step derivation

       1. div-inv 64.2%

          \[\leadsto \color{blue}{\frac{-b}{-c} \cdot \frac{1}{z}} \]

       2. frac-2neg 64.2%

          \[\leadsto \color{blue}{\frac{-\left(-b\right)}{-\left(-c\right)}} \cdot \frac{1}{z} \]

       3. frac-times 51.2%

          \[\leadsto \color{blue}{\frac{\left(-\left(-b\right)\right) \cdot 1}{\left(-\left(-c\right)\right) \cdot z}} \]

       4. remove-double-neg 51.2%

          \[\leadsto \frac{\color{blue}{b} \cdot 1}{\left(-\left(-c\right)\right) \cdot z} \]

       5. remove-double-neg 51.2%

          \[\leadsto \frac{b \cdot 1}{\color{blue}{c} \cdot z} \]

       6. times-frac 64.2%

          \[\leadsto \color{blue}{\frac{b}{c} \cdot \frac{1}{z}} \]

       7. associate-*l/ 59.5%

          \[\leadsto \color{blue}{\frac{b \cdot \frac{1}{z}}{c}} \]

       8. *-rgt-identity 59.5%

          \[\leadsto \frac{b \cdot \frac{1}{z}}{\color{blue}{c \cdot 1}} \]

       9. *-commutative 59.5%

          \[\leadsto \frac{\color{blue}{\frac{1}{z} \cdot b}}{c \cdot 1} \]

       10. times-frac 51.2%

           \[\leadsto \color{blue}{\frac{\frac{1}{z}}{c} \cdot \frac{b}{1}} \]

       11. remove-double-neg 51.2%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \frac{\color{blue}{-\left(-b\right)}}{1} \]

       12. metadata-eval 51.2%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \frac{-\left(-b\right)}{\color{blue}{--1}} \]

       13. metadata-eval 51.2%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \frac{-\left(-b\right)}{-\color{blue}{\left(-1\right)}} \]

       14. frac-2neg 51.2%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \color{blue}{\frac{-b}{-1}} \]

       15. div-inv 51.2%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \color{blue}{\left(\left(-b\right) \cdot \frac{1}{-1}\right)} \]

       16. metadata-eval 51.2%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \left(\left(-b\right) \cdot \frac{1}{\color{blue}{-1}}\right) \]

       17. metadata-eval 51.2%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \left(\left(-b\right) \cdot \color{blue}{-1}\right) \]

       18. metadata-eval 51.2%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \left(\left(-b\right) \cdot \color{blue}{\left(-1\right)}\right) \]

       19. *-commutative 51.2%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \color{blue}{\left(\left(-1\right) \cdot \left(-b\right)\right)} \]

       20. metadata-eval 51.2%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \left(\color{blue}{-1} \cdot \left(-b\right)\right) \]

       21. neg-mul-1 51.2%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \color{blue}{\left(-\left(-b\right)\right)} \]

       22. remove-double-neg 51.2%

           \[\leadsto \frac{\frac{1}{z}}{c} \cdot \color{blue}{b} \]

   12. Applied egg-rr 51.2%

       \[\leadsto \color{blue}{\frac{\frac{1}{z}}{c} \cdot b} \]
   13. Step-by-step derivation

       1. *-commutative 51.2%

          \[\leadsto \color{blue}{b \cdot \frac{\frac{1}{z}}{c}} \]

       2. associate-/l/ 51.1%

          \[\leadsto b \cdot \color{blue}{\frac{1}{c \cdot z}} \]

       3. un-div-inv 51.2%

          \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

       4. associate-/r* 64.2%

          \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   14. Applied egg-rr 64.2%

       \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5200000000000:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{+47}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 15: 35.0% accurate, 3.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

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(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Fortran

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 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

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	return b / (z * c)

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(z * c))
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (z * c);
end

Wolfram

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 81.4%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 81.4%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. div-sub 72.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

   3. *-commutative 72.4%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b}{z \cdot c} \]

   4. associate-*r* 71.7%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b}{z \cdot c} \]

   5. *-commutative 71.7%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b}{z \cdot c} \]

   6. div-sub 80.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot a\right) \cdot t - b\right)}{z \cdot c}} \]

   7. associate-+l- 80.3%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

3. Simplified 81.1%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

4. Taylor expanded in b around inf 38.0%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
5. Step-by-step derivation

   1. *-commutative 38.0%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

6. Simplified 38.0%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

7. Final simplification 38.0%

   \[\leadsto \frac{b}{z \cdot c} \]

Alternative 16: 34.7% accurate, 3.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \frac{\frac{b}{c}}{z} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ (/ b c) z))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return (b / c) / z;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (b / c) / z
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (b / c) / z;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	return (b / c) / z

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	return Float64(Float64(b / c) / z)
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = (b / c) / z;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]

Derivation

1. Initial program 81.4%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 81.4%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. div-sub 72.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

   3. *-commutative 72.4%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b}{z \cdot c} \]

   4. associate-*r* 71.7%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b}{z \cdot c} \]

   5. *-commutative 71.7%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b}{z \cdot c} \]

   6. div-sub 80.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot a\right) \cdot t - b\right)}{z \cdot c}} \]

   7. associate-+l- 80.3%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

3. Simplified 81.1%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

4. Taylor expanded in b around inf 38.0%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
5. Step-by-step derivation

   1. *-commutative 38.0%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

6. Simplified 38.0%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
7. Step-by-step derivation

   1. frac-2neg 38.0%

      \[\leadsto \color{blue}{\frac{-b}{-z \cdot c}} \]

   2. neg-mul-1 38.0%

      \[\leadsto \frac{\color{blue}{-1 \cdot b}}{-z \cdot c} \]

   3. metadata-eval 38.0%

      \[\leadsto \frac{\color{blue}{\left(-1\right)} \cdot b}{-z \cdot c} \]

   4. distribute-rgt-neg-in 38.0%

      \[\leadsto \frac{\left(-1\right) \cdot b}{\color{blue}{z \cdot \left(-c\right)}} \]

   5. times-frac 40.4%

      \[\leadsto \color{blue}{\frac{-1}{z} \cdot \frac{b}{-c}} \]

   6. metadata-eval 40.4%

      \[\leadsto \frac{\color{blue}{-1}}{z} \cdot \frac{b}{-c} \]

8. Applied egg-rr 40.4%

   \[\leadsto \color{blue}{\frac{-1}{z} \cdot \frac{b}{-c}} \]
9. Step-by-step derivation

   1. associate-*l/ 40.5%

      \[\leadsto \color{blue}{\frac{-1 \cdot \frac{b}{-c}}{z}} \]

   2. associate-*r/ 40.5%

      \[\leadsto \frac{\color{blue}{\frac{-1 \cdot b}{-c}}}{z} \]

   3. neg-mul-1 40.5%

      \[\leadsto \frac{\frac{\color{blue}{-b}}{-c}}{z} \]

10. Simplified 40.5%

    \[\leadsto \color{blue}{\frac{\frac{-b}{-c}}{z}} \]
11. Step-by-step derivation

    1. div-inv 40.4%

       \[\leadsto \color{blue}{\frac{-b}{-c} \cdot \frac{1}{z}} \]

    2. frac-2neg 40.4%

       \[\leadsto \color{blue}{\frac{-\left(-b\right)}{-\left(-c\right)}} \cdot \frac{1}{z} \]

    3. frac-times 38.0%

       \[\leadsto \color{blue}{\frac{\left(-\left(-b\right)\right) \cdot 1}{\left(-\left(-c\right)\right) \cdot z}} \]

    4. remove-double-neg 38.0%

       \[\leadsto \frac{\color{blue}{b} \cdot 1}{\left(-\left(-c\right)\right) \cdot z} \]

    5. remove-double-neg 38.0%

       \[\leadsto \frac{b \cdot 1}{\color{blue}{c} \cdot z} \]

    6. times-frac 40.4%

       \[\leadsto \color{blue}{\frac{b}{c} \cdot \frac{1}{z}} \]

    7. associate-*l/ 38.1%

       \[\leadsto \color{blue}{\frac{b \cdot \frac{1}{z}}{c}} \]

    8. *-rgt-identity 38.1%

       \[\leadsto \frac{b \cdot \frac{1}{z}}{\color{blue}{c \cdot 1}} \]

    9. *-commutative 38.1%

       \[\leadsto \frac{\color{blue}{\frac{1}{z} \cdot b}}{c \cdot 1} \]

    10. times-frac 38.0%

        \[\leadsto \color{blue}{\frac{\frac{1}{z}}{c} \cdot \frac{b}{1}} \]

    11. remove-double-neg 38.0%

        \[\leadsto \frac{\frac{1}{z}}{c} \cdot \frac{\color{blue}{-\left(-b\right)}}{1} \]

    12. metadata-eval 38.0%

        \[\leadsto \frac{\frac{1}{z}}{c} \cdot \frac{-\left(-b\right)}{\color{blue}{--1}} \]

    13. metadata-eval 38.0%

        \[\leadsto \frac{\frac{1}{z}}{c} \cdot \frac{-\left(-b\right)}{-\color{blue}{\left(-1\right)}} \]

    14. frac-2neg 38.0%

        \[\leadsto \frac{\frac{1}{z}}{c} \cdot \color{blue}{\frac{-b}{-1}} \]

    15. div-inv 38.0%

        \[\leadsto \frac{\frac{1}{z}}{c} \cdot \color{blue}{\left(\left(-b\right) \cdot \frac{1}{-1}\right)} \]

    16. metadata-eval 38.0%

        \[\leadsto \frac{\frac{1}{z}}{c} \cdot \left(\left(-b\right) \cdot \frac{1}{\color{blue}{-1}}\right) \]

    17. metadata-eval 38.0%

        \[\leadsto \frac{\frac{1}{z}}{c} \cdot \left(\left(-b\right) \cdot \color{blue}{-1}\right) \]

    18. metadata-eval 38.0%

        \[\leadsto \frac{\frac{1}{z}}{c} \cdot \left(\left(-b\right) \cdot \color{blue}{\left(-1\right)}\right) \]

    19. *-commutative 38.0%

        \[\leadsto \frac{\frac{1}{z}}{c} \cdot \color{blue}{\left(\left(-1\right) \cdot \left(-b\right)\right)} \]

    20. metadata-eval 38.0%

        \[\leadsto \frac{\frac{1}{z}}{c} \cdot \left(\color{blue}{-1} \cdot \left(-b\right)\right) \]

    21. neg-mul-1 38.0%

        \[\leadsto \frac{\frac{1}{z}}{c} \cdot \color{blue}{\left(-\left(-b\right)\right)} \]

    22. remove-double-neg 38.0%

        \[\leadsto \frac{\frac{1}{z}}{c} \cdot \color{blue}{b} \]

12. Applied egg-rr 38.0%

    \[\leadsto \color{blue}{\frac{\frac{1}{z}}{c} \cdot b} \]
13. Step-by-step derivation

    1. *-commutative 38.0%

       \[\leadsto \color{blue}{b \cdot \frac{\frac{1}{z}}{c}} \]

    2. associate-/l/ 38.0%

       \[\leadsto b \cdot \color{blue}{\frac{1}{c \cdot z}} \]

    3. un-div-inv 38.0%

       \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

    4. associate-/r* 40.5%

       \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

14. Applied egg-rr 40.5%

    \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

15. Final simplification 40.5%

    \[\leadsto \frac{\frac{b}{c}}{z} \]

Developer target: 80.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t_4}{z \cdot c}\\ t_6 := \frac{\left(t_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 < 0:\\ \;\;\;\;\frac{\frac{t_4}{z}}{c}\\ \mathbf{elif}\;t_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t_1\right) - t_2\\ \mathbf{elif}\;t_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t_1\right) - t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2023297 
(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)))